Finite Group Databasebeta

← #33256164

Subgroups — #33256164

Order 18688.

2804 conjugacy classes of subgroups.

The subgroup lattice has 1708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989117C211yesmaximal, characteristic, complemented
2C2×#17989098C211yesmaximal, characteristic, complemented
3#22615079C211yesmaximal, characteristic, complemented
4#22615064C211yesmaximal, characteristic, complemented
5#22615049C211yesmaximal, characteristic, complemented
6#22615034C211yesmaximal, characteristic, complemented
7#22615021C211yesmaximal, characteristic, complemented
8#22615003C211yesmaximal, characteristic, complemented
9#22614995C211yesmaximal, characteristic, complemented
10#22614980C211yesmaximal, characteristic, complemented
11#22614944C211yesmaximal, characteristic, complemented
12#22614895C211yesmaximal, characteristic, complemented
13#22614859C211yesmaximal, characteristic, complemented
14#22614824C211yesmaximal, characteristic, complemented
15#22614255C211yesmaximal, characteristic, complemented
16#22614054C211yesmaximal, characteristic, complemented
17#22613480C211yesmaximal, characteristic, complemented
18#22613463C211yesmaximal, characteristic, complemented
19#22613205C211yesmaximal, characteristic, complemented
20#22613192C211yesmaximal, characteristic, complemented
21#22613173C211yesmaximal, characteristic, complemented
22#22613146C211yesmaximal, characteristic, complemented
23C4×#14556577C211yesmaximal, characteristic, complemented
24C4×#14556575C211yesmaximal, characteristic, complemented
25C4×#14556563C211yesmaximal, characteristic, complemented
26C4×#14556562C211yesmaximal, characteristic, complemented
27#22612417C211yesmaximal, characteristic, complemented
28#22612396C211yesmaximal, characteristic, complemented
29C4×#14556551C211yesmaximal, characteristic, complemented
30C2×C4×C22⋊Dic73C211yesmaximal, characteristic, complemented
31C4×#120×C73C211yesmaximal, characteristic, complemented
32C22×#11924028C2211yescharacteristic
33#17989117—28no—
34C2×#14556586C2211yescharacteristic, complemented
35C2×#14556584C2211yescharacteristic, complemented
36C2×#14556581C2211yescharacteristic, complemented
37C2×#14556577C2211yescharacteristic
38C2×#14556577C2211yescharacteristic, complemented
39#17989098—28no—
40C2×#14556575C2211yescharacteristic
41C2×#14556575C2211yescharacteristic
42C2×#14556574C2211yescharacteristic
43C2×#14556574C2211yescharacteristic
44C2×#14556572C2211yescharacteristic
45C2×#14556570C2211yescharacteristic
46C2×#14556570C2211yescharacteristic
47C2×#14556568C2211yescharacteristic
48C2×#14556565C2211yescharacteristic
49C2×#14556565C2211yescharacteristic
50C2×#14556563C2211yescharacteristic
51C2×#14556563C2211yescharacteristic
52C2×#14556562C2211yescharacteristic
53C2×#14556560C2211yescharacteristic
54C2×#14556560C2211yescharacteristic
55C2×C4×Dic146C2211yescharacteristic, complemented
56C2×C4×C22⋊D73C2211yescharacteristic
57C2×C4×C22⋊D73C2211yescharacteristic
58C2×C4×C22⋊D73C2211yescharacteristic
59C2×C4×C22⋊D73C2211yescharacteristic
60C2×C4×C22⋊D73C2211yescharacteristic, complemented
61C2×C4×C22⋊D73C2211yescharacteristic, complemented
62C2×#14556551C2211yescharacteristic
63C2×#14556551C2211yescharacteristic
64C2×#14556550C2211yescharacteristic
65C2×#14556550C2211yescharacteristic, complemented
66C2×#14556548C2211yescharacteristic, complemented
67C22×C22⋊Dic73C2211yescharacteristic
68C22×C22⋊Dic73C2211yescharacteristic
69C22×C4×Dic73C2211yescharacteristic
70C22×C4×Dic73C2211yescharacteristic
71C2×C42×D73C2211yescharacteristic, complemented
72#17988529C2211yescharacteristic, complemented
73#17988528C2211yescharacteristic, complemented
74#17988523C2211yescharacteristic
75#17988523C2211yescharacteristic
76#17988521C2211yescharacteristic, complemented
77#17988521C2211yescharacteristic, complemented
78#17988520C2211yescharacteristic, complemented
79#17988519C2211yescharacteristic, complemented
80#17988516C2211yescharacteristic, complemented
81#17988515C2211yescharacteristic
82#17988515C2211yescharacteristic, complemented
83#17988514C2211yescharacteristic, complemented
84#17988510C2211yescharacteristic
85#17988510C2211yescharacteristic
86#17988510C2211yescharacteristic
87#17988509C2211yescharacteristic, complemented
88#17988508C2211yescharacteristic, complemented
89#17988507C2211yescharacteristic, complemented
90#17988504C2211yescharacteristic, complemented
91#17988503C2211yescharacteristic
92#17988503C2211yescharacteristic
93#17988502C2211yescharacteristic
94#17988502C2211yescharacteristic
95#17988502C2211yescharacteristic
96#17988502C2211yescharacteristic, complemented
97#17988501C2211yescharacteristic
98#17988499C2211yescharacteristic
99#17988499C2211yescharacteristic, complemented
100#17988496C2211yescharacteristic, complemented
101#17988495C2211yescharacteristic
102#17988495C2211yescharacteristic
103#17988495C2211yescharacteristic
104#17988491C2211yescharacteristic, complemented
105#17988491C2211yescharacteristic, complemented
106#17988491C2211yescharacteristic, complemented
107#17988490C2211yescharacteristic
108#17988490C2211yescharacteristic
109#17988490C2211yescharacteristic
110#17988487C2211yescharacteristic
111#17988487C2211yescharacteristic
112#17988487C2211yescharacteristic
113#17988487C2211yescharacteristic, complemented
114#17988486C2211yescharacteristic, complemented
115#17988486C2211yescharacteristic, complemented
116#17988483C2211yescharacteristic, complemented
117#17988482C2211yescharacteristic, complemented
118#17988481C2211yescharacteristic, complemented
119#17988480C2211yescharacteristic
120#17988480C2211yescharacteristic
121#17988480C2211yescharacteristic
122#17988480C2211yescharacteristic, complemented
123#17988480C2211yescharacteristic, complemented
124#17988479C2211yescharacteristic, complemented
125#17988479C2211yescharacteristic, complemented
126#17988479C2211yescharacteristic, complemented
127#17988477C2211yescharacteristic, complemented
128#17988476C2211yescharacteristic, complemented
129#17988475C2211yescharacteristic
130#17988475C2211yescharacteristic
131#17988475C2211yescharacteristic, complemented
132#17988472C2211yescharacteristic, complemented
133#17988472C2211yescharacteristic, complemented
134#17988467C2211yescharacteristic
135#17988465C2211yescharacteristic, complemented
136#17988465C2211yescharacteristic, complemented
137#17988464C2211yescharacteristic
138#17988464C2211yescharacteristic
139#17988463C2211yescharacteristic
140#17988463C2211yescharacteristic
141#17988463C2211yescharacteristic
142#17988463C2211yescharacteristic, complemented
143#17988462C2211yescharacteristic
144#17988451C2211yescharacteristic, complemented
145#17988448C2211yescharacteristic
146#17988445C2211yescharacteristic
147#17988444C2211yescharacteristic, complemented
148C4×#11924007C2211yescharacteristic, complemented
149C4×#11924007C2211yescharacteristic, complemented
150C4×C4⋊Dic73C2211yescharacteristic, complemented
151C4×C4⋊Dic73C2211yescharacteristic, complemented
152#17988438C2211yescharacteristic, complemented
153#17988438C2211yescharacteristic, complemented
154C22⋊C4×Dic73C2211yescharacteristic
155C22⋊C4×Dic73C2211yescharacteristic
156C4×#11924005C2211yescharacteristic, complemented
157C4×#11924005C2211yescharacteristic, complemented
158C4×#11924005C2211yescharacteristic, complemented
159C4×#11924005C2211yescharacteristic, complemented
160C4×C22⋊Dic73C2211yescharacteristic
161C4×C22⋊Dic73C2211yescharacteristic
162C4×C22⋊Dic73C2211yescharacteristic
163C4×C22⋊Dic73C2211yescharacteristic
164C4×C22⋊Dic73C2211yescharacteristic
165C4×C22⋊Dic73C2211yescharacteristic
166C4×C22⋊Dic73C2211yescharacteristic
167C4×C22⋊Dic73C2211yescharacteristic
168C4×C22⋊Dic73C2211yescharacteristic, complemented
169#17988434C2211yescharacteristic, complemented
170#17988434C2211yescharacteristic, complemented
171C2×#14556498C2211yescharacteristic
172C2×#14556498C2211yescharacteristic
173C42×Dic73C2211yescharacteristic, complemented
174C24×C4×C73C2211yescharacteristic
175C2×#120×C73C2211yescharacteristic
176C2×C4×D4×C73C2211yescharacteristic
177C2×C4×D4×C73C2211yescharacteristic
178C2×C4×D4×C73C2211yescharacteristic
179#386×C73C2211yescharacteristic
180#386×C73C2211yescharacteristic
181#386×C73C2211yescharacteristic
182#385×C73C2211yescharacteristic
183#385×C73C2211yescharacteristic
184#385×C73C2211yescharacteristic
185#379×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic
187C4×C22⋊C4×C73C2211yescharacteristic
188C4×C22⋊C4×C73C2211yescharacteristic
189C2×#11924028—24no—
190C2×#11924028—24no—
191C2×#11924028—42no—
192C22×Dic146C2311yescharacteristic
193C22×Dic146C2311yescharacteristic
194C22×D292C2311yescharacteristic
195C22×C22⋊D73C2311yescharacteristic
196C22×C22⋊D73C2311yescharacteristic
197C22×C22⋊D73C2311yescharacteristic
198C22×C22⋊D73C2311yescharacteristic
199C22×C22⋊D73C2311yescharacteristic
200C22×C22⋊D73C2311yescharacteristic
201C22×C22⋊D73C2311yescharacteristic
202C22×C22⋊D73C2311yescharacteristic
203C23×Dic73C2311yescharacteristic
204C23×Dic73C2311yescharacteristic
205C23×Dic73C2311yescharacteristic
206C23×Dic73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210C22×C4×D73C2311yescharacteristic
211#14556586—24no—
212#14556584—24no—
213#14556581—24no—
214#14556577—24no—
215#14556577—24no—
216#14556575—24no—
217#14556575—24no—
218#14556574—24no—
219#14556574—24no—
220#14556572—24no—
221#14556570—24no—
222#14556570—24no—
223#14556568—24no—
224#14556565—24no—
225#14556565—24no—
226#14556563—24no—
227#14556563—24no—
228#14556562—24no—
229#14556560—24no—
230#14556560—24no—
231C4×Dic146—24no—
232C4×C22⋊D73—24no—
233C4×C22⋊D73—24no—
234C4×C22⋊D73—24no—
235C4×C22⋊D73—24no—
236C4×C22⋊D73—42no—
237C4×C22⋊D73D418yescomplemented
238#14556551—24no—
239#14556551—24no—
240#14556550—24no—
241#14556550—24no—
242#14556548—24no—
243C2×C4⋊Dic73C2311yescharacteristic
244C2×C4⋊Dic73C2311yescharacteristic
245C2×C4⋊Dic73C2311yescharacteristic
246C2×C4⋊Dic73C2311yescharacteristic
247C2×C4⋊Dic73C2311yescharacteristic
248C2×C4⋊Dic73C2311yescharacteristic
249C2×C4⋊Dic73C2311yescharacteristic
250C2×C4⋊Dic73C2311yescharacteristic
251C2×C4⋊Dic73C2311yescharacteristic
252C2×#11924007C2311yescharacteristic
253C2×#11924007C2311yescharacteristic
254C2×#11924007C2311yescharacteristic
255C2×#11924007C2311yescharacteristic
256C2×#11924007C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×#11924007C2311yescharacteristic
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C2×#11924007C2311yescharacteristic
266C2×C22⋊Dic73—24no—
267C2×C22⋊Dic73—24no—
268C2×C22⋊Dic73C2311yescharacteristic
269C2×C22⋊Dic73C2311yescharacteristic
270C2×C22⋊Dic73C2311yescharacteristic
271C2×C22⋊Dic73C2311yescharacteristic
272C2×C22⋊Dic73C2311yescharacteristic
273C2×C22⋊Dic73C2311yescharacteristic
274C2×C22⋊Dic73C2311yescharacteristic
275C2×C22⋊Dic73C2311yescharacteristic
276C2×C22⋊Dic73C2311yescharacteristic
277C2×C22⋊Dic73C2311yescharacteristic
278C2×C22⋊Dic73C2311yescharacteristic
279C2×C22⋊Dic73C2311yescharacteristic
280C2×C22⋊Dic73C2311yescharacteristic
281C2×C22⋊Dic73C2311yescharacteristic
282C2×C22⋊Dic73C2311yescharacteristic
283C2×C22⋊Dic73C2311yescharacteristic
284C2×C22⋊Dic73C2311yescharacteristic
285C2×C22⋊Dic73C2311yescharacteristic
286C2×C22⋊Dic73C2311yescharacteristic
287C2×C22⋊Dic73C2311yescharacteristic
288C2×#11924005C2311yescharacteristic
289C2×#11924005C2311yescharacteristic
290C2×#11924005C2311yescharacteristic
291C2×#11924005C2311yescharacteristic
292C2×#11924005C2311yescharacteristic
293C2×#11924005C2311yescharacteristic
294C2×#11924005C2311yescharacteristic
295C2×#11924005C2311yescharacteristic
296C2×#11924005C2311yescharacteristic
297C2×#11924005C2311yescharacteristic
298C2×#11924005C2311yescharacteristic
299C2×#11924005C2311yescharacteristic
300C2×#11924005C2311yescharacteristic
301C2×#11924005C2311yescharacteristic
302C2×#11924005C2311yescharacteristic
303C2×#11924005C2311yescharacteristic
304C2×C4×Dic73—24no—
305C2×C4×Dic73—42no—
306C2×C4×Dic73C2311yescharacteristic
307C2×C4×Dic73C2311yescharacteristic
308C2×C4×Dic73C2311yescharacteristic
309C2×C4×Dic73C2311yescharacteristic
310C2×C4×Dic73C2311yescharacteristic
311C2×C4×Dic73C2311yescharacteristic
312C2×C4×Dic73C2311yescharacteristic
313C2×C4×Dic73C2311yescharacteristic
314C2×C4×Dic73C2311yescharacteristic
315C2×C4×Dic73C2311yescharacteristic
316C2×C4×Dic73C2311yescharacteristic
317C2×C4×Dic73C2311yescharacteristic
318C2×C4×Dic73C2311yescharacteristic
319C2×C4×Dic73C2311yescharacteristic
320C2×C4×Dic73C2311yescharacteristic
321C2×C4×Dic73C2311yescharacteristic
322C42×D73—42no—
323#14556498C2311yescharacteristic
324#14556498C2311yescharacteristic
325#14556498C2311yescharacteristic
326#14556498C2311yescharacteristic
327#14556498C2311yescharacteristic
328#14556498C2311yescharacteristic
329#14556498C2311yescharacteristic
330#14556498C2311yescharacteristic
331#14556498C2311yescharacteristic
332#14556498C2311yescharacteristic
333#14556498C2311yescharacteristic
334#14556498C2311yescharacteristic
335#14556498C2311yescharacteristic
336#14556498C2311yescharacteristic
337#14556498C2311yescharacteristic
338#14556498C2311yescharacteristic
339#14556498C2311yescharacteristic
340#14556498C2311yescharacteristic
341#14556498C2311yescharacteristic
342#14556498C2311yescharacteristic
343#14556498C2311yescharacteristic
344#14556498C2311yescharacteristic
345#14556498C2311yescharacteristic
346#14556498C2311yescharacteristic
347#14556498C2311yescharacteristic
348#14556498C2311yescharacteristic
349C25×C73C2311yescharacteristic
350C22×D4×C73C2311yescharacteristic
351C22×D4×C73C2311yescharacteristic
352C22×D4×C73C2311yescharacteristic
353C23×C4×C73—24no—
354C23×C4×C73—24no—
355C23×C4×C73—42no—
356C23×C4×C73C2311yescharacteristic
357C23×C4×C73C2311yescharacteristic
358C23×C4×C73C2311yescharacteristic
359C23×C4×C73C2311yescharacteristic
360C23×C4×C73C2311yescharacteristic
361C23×C4×C73C2311yescharacteristic
362C23×C4×C73C2311yescharacteristic
363#120×C73—24no—
364C4×D4×C73—24no—
365C4×D4×C73—24no—
366C4×D4×C73—42no—
367C2×C4⋊C4×C73C2311yescharacteristic
368C2×C4⋊C4×C73C2311yescharacteristic
369C2×C4⋊C4×C73C2311yescharacteristic
370C2×C22⋊C4×C73C2311yescharacteristic
371C2×C22⋊C4×C73C2311yescharacteristic
372C2×C22⋊C4×C73C2311yescharacteristic
373C2×C22⋊C4×C73C2311yescharacteristic
374C2×C22⋊C4×C73C2311yescharacteristic
375C2×C22⋊C4×C73C2311yescharacteristic
376C2×C22⋊C4×C73C2311yescharacteristic
377C2×C22⋊C4×C73C2311yescharacteristic
378C2×C22⋊C4×C73C2311yescharacteristic
379C2×C22⋊C4×C73C2311yescharacteristic
380C2×C22⋊C4×C73C2311yescharacteristic
381C2×C22⋊C4×C73C2311yescharacteristic
382C2×C42×C73C2311yescharacteristic
383C2×C42×C73C2311yescharacteristic
384C2×C42×C73C2311yescharacteristic
385#95×C73C2311yescharacteristic
386#95×C73C2311yescharacteristic
387#95×C73C2311yescharacteristic
388#95×C73C2311yescharacteristic
389#95×C73C2311yescharacteristic
390#95×C73C2311yescharacteristic
391C23×D73C2411yescharacteristic
392C23×D73C2411yescharacteristic
393#11924028—416no—
394C2×Dic146—22no—
395C2×Dic146—22no—
396C2×Dic146—22no—
397C2×Dic146—22no—
398C2×Dic146—41no—
399C2×Dic146—41no—
400C2×D292—22no—
401C2×D292—22no—
402C2×D292—41no—
403C2×C22⋊D73—22no—
404C2×C22⋊D73—22no—
405C2×C22⋊D73—22no—
406C2×C22⋊D73—22no—
407C2×C22⋊D73—22no—
408C2×C22⋊D73—22no—
409C2×C22⋊D73—22no—
410C2×C22⋊D73—22no—
411C2×C22⋊D73—22no—
412C2×C22⋊D73—22no—
413C2×C22⋊D73—22no—
414C2×C22⋊D73—22no—
415C2×C22⋊D73—22no—
416C2×C22⋊D73—22no—
417C2×C22⋊D73—22no—
418C2×C22⋊D73—22no—
419C2×C22⋊D73—41no—
420C2×C22⋊D73—41no—
421C2×C22⋊D73—41no—
422C2×C22⋊D73—41no—
423C2×C22⋊D73—41no—
424C2×C22⋊D73—41no—
425C2×C22⋊D73—41no—
426C2×C22⋊D73C2×D414yes—
427C22×Dic73—22no—
428C22×Dic73—22no—
429C22×Dic73—22no—
430C22×Dic73—22no—
431C22×Dic73—22no—
432C22×Dic73—22no—
433C22×Dic73—22no—
434C22×Dic73—41no—
435C22×Dic73—41no—
436C22×Dic73—41no—
437C22×Dic73—41no—
438C22×Dic73#4114yescomplemented
439C22×Dic73C2411yescharacteristic
440C22×Dic73C2411yescharacteristic
441C22×Dic73C2411yescharacteristic
442C22×Dic73C2411yescharacteristic
443C22×Dic73C2411yescharacteristic
444C22×Dic73C2411yescharacteristic
445C22×Dic73C2411yescharacteristic
446C22×Dic73C2411yescharacteristic
447C22×Dic73C2411yescharacteristic
448C22×Dic73C2411yescharacteristic
449C22×Dic73C2411yescharacteristic
450C22×Dic73C2411yescharacteristic
451C22×Dic73C2411yescharacteristic
452C22×Dic73C2411yescharacteristic
453C2×C4×D73—22no—
454C2×C4×D73—22no—
455C2×C4×D73—22no—
456C2×C4×D73—22no—
457C2×C4×D73—22no—
458C2×C4×D73—22no—
459C2×C4×D73—22no—
460C2×C4×D73—22no—
461C2×C4×D73—41no—
462C2×C4×D73—41no—
463C2×C4×D73—41no—
464C2×C4×D73C2×D414yes—
465C4⋊Dic73—22no—
466C4⋊Dic73—22no—
467C4⋊Dic73—22no—
468C4⋊Dic73—22no—
469C4⋊Dic73—22no—
470C4⋊Dic73—22no—
471C4⋊Dic73—22no—
472C4⋊Dic73—22no—
473C4⋊Dic73—41no—
474#11924007—22no—
475#11924007—22no—
476#11924007—22no—
477#11924007—22no—
478#11924007—22no—
479#11924007—22no—
480#11924007—22no—
481#11924007—22no—
482#11924007—22no—
483#11924007—22no—
484#11924007—22no—
485#11924007—41no—
486#11924007—41no—
487#11924007C2×D414yes—
488C22⋊Dic73—22no—
489C22⋊Dic73—22no—
490C22⋊Dic73—22no—
491C22⋊Dic73—22no—
492C22⋊Dic73—22no—
493C22⋊Dic73—22no—
494C22⋊Dic73—22no—
495C22⋊Dic73—22no—
496C22⋊Dic73—22no—
497C22⋊Dic73—22no—
498C22⋊Dic73—22no—
499C22⋊Dic73—22no—
500C22⋊Dic73—22no—
501C22⋊Dic73—22no—
502C22⋊Dic73—22no—
503C22⋊Dic73—22no—
504C22⋊Dic73—22no—
505C22⋊Dic73—41no—
506C22⋊Dic73C2×D414yes—
507C22⋊Dic73#4114yescomplemented
508#11924005—22no—
509#11924005—22no—
510#11924005—22no—
511#11924005—22no—
512#11924005—22no—
513#11924005—22no—
514#11924005—22no—
515#11924005—22no—
516#11924005—22no—
517#11924005—22no—
518#11924005—22no—
519#11924005—22no—
520#11924005—22no—
521#11924005—41no—
522#11924005—41no—
523#11924005C2×D414yes—
524C4×Dic73—22no—
525C4×Dic73—22no—
526C4×Dic73—22no—
527C4×Dic73—22no—
528C4×Dic73—22no—
529C4×Dic73—22no—
530C4×Dic73—22no—
531C4×Dic73—22no—
532C4×Dic73—22no—
533C4×Dic73—22no—
534C4×Dic73—41no—
535C4×Dic73—41no—
536C4×Dic73—41no—
537C4×Dic73—41no—
538C4×Dic73—41no—
539C4×Dic73C2×D414yes—
540C24×C73—22no—
541C24×C73—22no—
542C24×C73—22no—
543C24×C73—22no—
544C24×C73—22no—
545C24×C73—41no—
546C24×C73—41no—
547C24×C73C2411yescharacteristic
548C24×C73C2411yescharacteristic
549C24×C73C2411yescharacteristic
550C24×C73C2411yescharacteristic
551C2×D4×C73—22no—
552C2×D4×C73—22no—
553C2×D4×C73—22no—
554C2×D4×C73—22no—
555C2×D4×C73—22no—
556C2×D4×C73—22no—
557C2×D4×C73—22no—
558C2×D4×C73—41no—
559C2×D4×C73—41no—
560C22×C4×C73—22no—
561C22×C4×C73—22no—
562C22×C4×C73—22no—
563C22×C4×C73—22no—
564C22×C4×C73—22no—
565C22×C4×C73—22no—
566C22×C4×C73—22no—
567C22×C4×C73—22no—
568C22×C4×C73—22no—
569C22×C4×C73—22no—
570C22×C4×C73—22no—
571C22×C4×C73—22no—
572C22×C4×C73—22no—
573C22×C4×C73—22no—
574C22×C4×C73—22no—
575C22×C4×C73—22no—
576C22×C4×C73—41no—
577C22×C4×C73—41no—
578C22×C4×C73—41no—
579C22×C4×C73—416no—
580C22×C4×C73C2×D414yes—
581C22×C4×C73#4114yes—
582C22×C4×C73C2411yescharacteristic
583C22×C4×C73C2411yescharacteristic
584C22×C4×C73C2411yescharacteristic
585C22×C4×C73C2411yescharacteristic
586C22×C4×C73C2411yescharacteristic
587C22×C4×C73C2411yescharacteristic
588C22×C4×C73C2411yescharacteristic
589C22×C4×C73C2411yescharacteristic
590C22×C4×C73C2411yescharacteristic
591C22×C4×C73C2411yescharacteristic
592C22×C4×C73C2411yescharacteristic
593C4⋊C4×C73—22no—
594C4⋊C4×C73—22no—
595C4⋊C4×C73—41no—
596C22⋊C4×C73—22no—
597C22⋊C4×C73—22no—
598C22⋊C4×C73—22no—
599C22⋊C4×C73—22no—
600C22⋊C4×C73—22no—
601C22⋊C4×C73—22no—
602C22⋊C4×C73—22no—
603C22⋊C4×C73—22no—
604C22⋊C4×C73—41no—
605C22⋊C4×C73—41no—
606C22⋊C4×C73—41no—
607C22⋊C4×C73#4114yescomplemented
608C42×C73—22no—
609C42×C73—22no—
610C42×C73—22no—
611C23×C73—21no—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—28no—
616C23×C73—21no—
617C23×C73—21no—
618C23×C73—21no—
619C23×C73—21no—
620C23×C73—21no—
621C23×C73—21no—
622C23×C73—21no—
623C23×C73—21no—
624C23×C73—21no—
625C23×C73—21no—
626C23×C73—21no—
627C23×C73—21no—
628C23×C73—21no—
629C23×C73—21no—
630C23×C73—21no—
631C23×C73—21no—
632C23×C73—21no—
633C23×C73—21no—
634C23×C73—21no—
635C23×C73—44no—
636C23×C73—44no—
637C23×C73—44no—
638C23×C73—44no—
639C23×C73—44no—
640C23×C73—44no—
641C23×C73C22×D412yes—
642C23×C73C2×#4112yes—
643C23×C73C2×#4112yes—
644C23×C73C2×#4112yes—
645C23×C73C2×#4112yes—
646C23×C73C2511yescharacteristic
647C22×D73—21no—
648C22×D73—21no—
649C22×D73—21no—
650C22×D73—21no—
651C22×D73—21no—
652C22×D73—21no—
653C22×D73—21no—
654C22×D73—21no—
655C22×D73—21no—
656C22×D73—21no—
657C22×D73—21no—
658C22×D73—21no—
659C22×D73—21no—
660C22×D73C22×D412yes—
661D4×C73—44no—
662D4×C73—44no—
663D4×C73—44no—
664C2×C4×C73—21no—
665C2×C4×C73—21no—
666C2×C4×C73—21no—
667C2×C4×C73—21no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—28no—
673C2×C4×C73—28no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—21no—
687C2×C4×C73—21no—
688C2×C4×C73—21no—
689C2×C4×C73—21no—
690C2×C4×C73—21no—
691C2×C4×C73—21no—
692C2×C4×C73—44no—
693C2×C4×C73—44no—
694C2×C4×C73—44no—
695C2×C4×C73—44no—
696C2×C4×C73—44no—
697C2×C4×C73C22×D412yes—
698C2×C4×C73C22×D412yes—
699C2×C4×C73C2×#4112yes—
700C2×C4×C73C2×#4112yes—
701C2×C4×C73C2×#4112yes—
702C2×C4×C73C2×#4112yes—
703C2×C4×C73H(5,𝔽2)12yes—
704C22⋊D73—28no—
705C22⋊D73—44no—
706C22⋊D73—44no—
707C22⋊D73—44no—
708C22⋊D73—44no—
709C22⋊D73—44no—
710C22⋊D73—44no—
711C22⋊D73—44no—
712C2×Dic73—21no—
713C2×Dic73—21no—
714C2×Dic73—21no—
715C2×Dic73—21no—
716C2×Dic73—21no—
717C2×Dic73—21no—
718C2×Dic73—21no—
719C2×Dic73—21no—
720C2×Dic73—21no—
721C2×Dic73—21no—
722C2×Dic73—21no—
723C2×Dic73—21no—
724C2×Dic73—21no—
725C2×Dic73—21no—
726C2×Dic73—21no—
727C2×Dic73—21no—
728C2×Dic73—21no—
729C2×Dic73—21no—
730C2×Dic73—21no—
731C2×Dic73—21no—
732C2×Dic73—21no—
733C2×Dic73—21no—
734C2×Dic73—21no—
735C2×Dic73—21no—
736C2×Dic73—21no—
737C2×Dic73—21no—
738C2×Dic73—21no—
739C2×Dic73—21no—
740C2×Dic73—21no—
741C2×Dic73—21no—
742C2×Dic73—21no—
743C2×Dic73—21no—
744C2×Dic73—21no—
745C2×Dic73—21no—
746C2×Dic73—21no—
747C2×Dic73—44no—
748C2×Dic73—44no—
749C2×Dic73—44no—
750C2×Dic73—44no—
751C2×Dic73C22×D412yes—
752C2×Dic73C22×D412yes—
753C2×Dic73C22×D412yes—
754C2×Dic73C2×#4112yes—
755C2×Dic73C2×#4112yes—
756C2×Dic73C2×#4112yes—
757C2×Dic73C2×#4112yes—
758D292—44no—
759C4×D73—28no—
760C4×D73—44no—
761C4×D73—44no—
762C4×D73—44no—
763Dic146—44no—
764Dic146—44no—
765C22×C73—22no—
766C22×C73—22no—
767C22×C73—22no—
768C22×C73—22no—
769C22×C73—22no—
770C22×C73—22no—
771C22×C73—22no—
772C22×C73—22no—
773C22×C73—22no—
774C22×C73—22no—
775C22×C73—22no—
776C22×C73—22no—
777C22×C73—416no—
778C22×C73—41no—
779C22×C73—41no—
780C22×C73—41no—
781C22×C73—41no—
782C22×C73—41no—
783C22×C73—41no—
784C22×C73—41no—
785C22×C73—41no—
786C22×C73—41no—
787C22×C73—41no—
788C22×C73—41no—
789C22×C73—41no—
790C22×C73—41no—
791C22×C73—41no—
792C22×C73—41no—
793C22×C73#53214yes—
794C22×C73C23×D411yescharacteristic
795C22×C73C22×#4111yescharacteristic
796C22×C73C22×#4111yescharacteristic
797C22×C73C22×#4111yescharacteristic
798C22×C73C22×#4111yescharacteristic
799C22×C73C2×H(5,𝔽2)11yescharacteristic
800C22×C73#58511yescharacteristic
801C2×D73—22no—
802C2×D73—22no—
803C2×D73—22no—
804C2×D73—41no—
805C2×D73—41no—
806C2×D73—41no—
807C2×D73—41no—
808C2×D73—41no—
809C2×D73—41no—
810C2×D73—41no—
811C2×D73—41no—
812C2×D73—41no—
813C2×D73—41no—
814C2×D73—41no—
815C4×C73—22no—
816C4×C73—22no—
817C4×C73—22no—
818C4×C73—22no—
819C4×C73—41no—
820C4×C73—41no—
821C4×C73—41no—
822C4×C73—41no—
823C4×C73—41no—
824C4×C73—41no—
825C4×C73#54614yes—
826Dic73—22no—
827Dic73—22no—
828Dic73—22no—
829Dic73—22no—
830Dic73—22no—
831Dic73—22no—
832Dic73—22no—
833Dic73—41no—
834Dic73—41no—
835Dic73—41no—
836Dic73—41no—
837Dic73—41no—
838Dic73—41no—
839Dic73—41no—
840#34829—731nomaximal, Sylow
841C2×C73—24no—
842C2×C73—42no—
843C2×C73—42no—
844C2×C73—81no—
845C2×C73C2×#53211yescharacteristic
846C2×C73#344411yescharacteristic
847C2×C73#345911yescharacteristic
848C2×C73C2×#54611yescharacteristic
849C2×C73D4×#4111yescharacteristic
850C2×C73#347511yescharacteristic
851C2×C73#348111yescharacteristic
852D73—42no—
853D73—81no—
854C2×#529—731no—
855C2×#525—731no—
856#2560—731no—
857#2559—731no—
858#2558—731no—
859#2557—731no—
860#2556—731no—
861#2555—731no—
862#2554—731no—
863#2553—731no—
864#2549—731no—
865#2543—731no—
866#2539—731no—
867#2534—731no—
868#2488—731no—
869#2472—731no—
870#2425—731no—
871#2424—731no—
872#2396—731no—
873#2395—731no—
874#2392—731no—
875#2388—731no—
876C4×#124—731no—
877C4×#123—731no—
878C4×#121—731no—
879C4×#121—731no—
880C4×#120D7311yescharacteristic, complemented
881#2297—731no—
882#2293—731no—
883C42×D4—731no—
884C2×C4×C22⋊C4—731no—
885C73#3482911yescharacteristic, complemented, Sylow
886C22×#41—731no—
887C24×C4C2×D7311yescharacteristic
888#529—1468no—
889C2×#126—731no—
890C2×#126—731no—
891C2×#125—731no—
892C2×#124—731no—
893C2×#124—731no—
894#525—1468no—
895C2×#123—731no—
896C2×#123—731no—
897C2×#123—731no—
898C2×#123—731no—
899C2×#123—731no—
900C2×C22⋊Q8—731no—
901C2×C22⋊Q8—731no—
902C2×C22⋊Q8—731no—
903C2×#121—731no—
904C2×#121—731no—
905C2×#121—731no—
906C2×#121—731no—
907C2×#121—731no—
908C2×#120—731no—
909C2×#120—731no—
910C2×#120C2×D7311yescharacteristic
911C2×C4×Q8—731no—
912C2×C4×D4—731no—
913C2×C4×D4—731no—
914C2×C4×D4—731no—
915C2×C4×D4—731no—
916C2×C4×D4—731no—
917C2×C4×D4—731no—
918C2×C4×D4—731no—
919C2×C4×D4—731no—
920C2×C4×D4C2×D7311yescharacteristic
921C2×C4×D4C2×D7311yescharacteristic
922C2×C4×D4C2×D7311yescharacteristic
923C2×#117—731no—
924C2×#117—731no—
925C2×#117—731no—
926C22×C22⋊C4—731no—
927C22×C22⋊C4—731no—
928C22×C42—731no—
929C22×C42—731no—
930C22×C42—731no—
931#400—731no—
932#400—731no—
933#399—731no—
934#399—731no—
935#398—731no—
936#398—731no—
937#398—731no—
938#398—731no—
939#397—731no—
940#397—731no—
941#397—731no—
942#397—731no—
943#396—731no—
944#396—731no—
945#396—731no—
946#396—731no—
947#395—731no—
948#395—731no—
949#394—731no—
950#394—731no—
951#394—731no—
952#394—731no—
953#394—731no—
954#394—731no—
955#394—731no—
956#394—731no—
957#393—731no—
958#393—731no—
959#392—731no—
960#392—731no—
961#392—731no—
962#392—731no—
963#391—731no—
964#391—731no—
965#391—731no—
966#390—731no—
967#390—731no—
968#390—731no—
969#390—731no—
970#390—731no—
971#390—731no—
972#390—731no—
973#389—731no—
974#389—731no—
975#389—731no—
976#389—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#388—731no—
982#388—731no—
983#388—731no—
984#388—731no—
985#388—731no—
986#388—731no—
987#388—731no—
988#388—731no—
989#388—731no—
990#388—731no—
991#387—731no—
992#387—731no—
993#386—731no—
994#386—731no—
995#386—731no—
996#386—731no—
997#386—731no—
998#386—731no—
999#386—731no—
1000#386—731no—
1001#386—731no—
1002#386C2×D7311yescharacteristic
1003#386C2×D7311yescharacteristic
1004#386C2×D7311yescharacteristic
1005#385—731no—
1006#385C2×D7311yescharacteristic
1007#385C2×D7311yescharacteristic
1008#385C2×D7311yescharacteristic
1009#382—731no—
1010#381—731no—
1011#380—731no—
1012#380—731no—
1013#379C2×D7311yescharacteristic
1014C4×C4⋊C4—731no—
1015C4×C4⋊C4—731no—
1016C4×C4⋊C4—731no—
1017C4×C4⋊C4—731no—
1018C4×C4⋊C4—731no—
1019C4×C4⋊C4—731no—
1020C4×C22⋊C4—731no—
1021C4×C22⋊C4—731no—
1022C4×C22⋊C4—731no—
1023C4×C22⋊C4—731no—
1024C4×C22⋊C4—731no—
1025C4×C22⋊C4—731no—
1026C4×C22⋊C4—731no—
1027C4×C22⋊C4—731no—
1028C4×C22⋊C4—731no—
1029C4×C22⋊C4—731no—
1030C4×C22⋊C4—731no—
1031C4×C22⋊C4—731no—
1032C4×C22⋊C4—731no—
1033C4×C22⋊C4—731no—
1034C4×C22⋊C4—731no—
1035C4×C22⋊C4—731no—
1036C4×C22⋊C4—731no—
1037C4×C22⋊C4C2×D7311yescharacteristic
1038C4×C22⋊C4C2×D7311yescharacteristic
1039C4×C22⋊C4C2×D7311yescharacteristic
1040C2×#95—731no—
1041C2×#95—731no—
1042C43—731no—
1043C25C22×D7311yescharacteristic
1044C2×#41—2922no—
1045C2×#41—1464no—
1046C2×#41—1464no—
1047C22×Q8—731no—
1048C22×Q8—731no—
1049C22×D4—731no—
1050C22×D4—731no—
1051C22×D4—731no—
1052C22×D4—731no—
1053C22×D4—731no—
1054C22×D4—731no—
1055C22×D4—731no—
1056C22×D4—731no—
1057C22×D4—731no—
1058C22×D4C22×D7311yescharacteristic
1059C22×D4C22×D7311yescharacteristic
1060C22×D4C22×D7311yescharacteristic
1061C23×C4—24no—
1062C23×C4—24no—
1063C23×C4—42no—
1064C23×C4—731no—
1065C23×C4—731no—
1066C23×C4—731no—
1067C23×C4—731no—
1068C23×C4—731no—
1069C23×C4—731no—
1070C23×C4—731no—
1071C23×C4—731no—
1072C23×C4C22×D7311yescharacteristic
1073C23×C4C22×D7311yescharacteristic
1074C23×C4C22×D7311yescharacteristic
1075C23×C4C22×D7311yescharacteristic
1076C23×C4C22×D7311yescharacteristic
1077C23×C4C22×D7311yescharacteristic
1078C23×C4C22×D7311yescharacteristic
1079#126—1464no—
1080#126—1464no—
1081#125—1464no—
1082#124—1464no—
1083#124—1464no—
1084#123—1464no—
1085#123—1464no—
1086#123—1464no—
1087#123—1464no—
1088#123—1464no—
1089C22⋊Q8—1464no—
1090C22⋊Q8—1464no—
1091C22⋊Q8—1464no—
1092#121—1464no—
1093#121—1464no—
1094#121—1464no—
1095#121—1464no—
1096#121—1464no—
1097#120—24no—
1098#120—1464no—
1099#120—1464no—
1100C4×Q8—1464no—
1101C4×D4—24no—
1102C4×D4—24no—
1103C4×D4—42no—
1104C4×D4—2922no—
1105C4×D4—738no—
1106C4×D4—1464no—
1107C4×D4—1464no—
1108C4×D4—1464no—
1109C4×D4—1464no—
1110C4×D4—1464no—
1111C4×D4—1464no—
1112#117—1464no—
1113#117—1464no—
1114#117—1464no—
1115C2×C4⋊C4—731no—
1116C2×C4⋊C4—731no—
1117C2×C4⋊C4—731no—
1118C2×C4⋊C4—731no—
1119C2×C4⋊C4—731no—
1120C2×C4⋊C4—731no—
1121C2×C4⋊C4—731no—
1122C2×C4⋊C4—731no—
1123C2×C4⋊C4—731no—
1124C2×C4⋊C4—731no—
1125C2×C4⋊C4—731no—
1126C2×C4⋊C4—731no—
1127C2×C4⋊C4—731no—
1128C2×C4⋊C4—731no—
1129C2×C4⋊C4—731no—
1130C2×C4⋊C4—731no—
1131C2×C4⋊C4—731no—
1132C2×C4⋊C4—731no—
1133C2×C4⋊C4—731no—
1134C2×C4⋊C4—731no—
1135C2×C4⋊C4—731no—
1136C2×C4⋊C4—731no—
1137C2×C4⋊C4—731no—
1138C2×C4⋊C4C22×D7311yescharacteristic
1139C2×C4⋊C4C22×D7311yescharacteristic
1140C2×C4⋊C4C22×D7311yescharacteristic
1141C2×C22⋊C4—731no—
1142C2×C22⋊C4—731no—
1143C2×C22⋊C4—731no—
1144C2×C22⋊C4—731no—
1145C2×C22⋊C4—731no—
1146C2×C22⋊C4—731no—
1147C2×C22⋊C4—731no—
1148C2×C22⋊C4—731no—
1149C2×C22⋊C4—731no—
1150C2×C22⋊C4—731no—
1151C2×C22⋊C4—731no—
1152C2×C22⋊C4—731no—
1153C2×C22⋊C4—731no—
1154C2×C22⋊C4—731no—
1155C2×C22⋊C4—731no—
1156C2×C22⋊C4—731no—
1157C2×C22⋊C4—731no—
1158C2×C22⋊C4—731no—
1159C2×C22⋊C4—731no—
1160C2×C22⋊C4—731no—
1161C2×C22⋊C4—731no—
1162C2×C22⋊C4—731no—
1163C2×C22⋊C4—731no—
1164C2×C22⋊C4—731no—
1165C2×C22⋊C4—731no—
1166C2×C22⋊C4—731no—
1167C2×C22⋊C4—731no—
1168C2×C22⋊C4—731no—
1169C2×C22⋊C4—731no—
1170C2×C22⋊C4—731no—
1171C2×C22⋊C4—731no—
1172C2×C22⋊C4—731no—
1173C2×C22⋊C4—731no—
1174C2×C22⋊C4—731no—
1175C2×C22⋊C4—731no—
1176C2×C22⋊C4—731no—
1177C2×C22⋊C4—1464no—
1178C2×C22⋊C4—1464no—
1179C2×C22⋊C4C22×D7311yescharacteristic
1180C2×C22⋊C4C22×D7311yescharacteristic
1181C2×C22⋊C4C22×D7311yescharacteristic
1182C2×C22⋊C4C22×D7311yescharacteristic
1183C2×C22⋊C4C22×D7311yescharacteristic
1184C2×C22⋊C4C22×D7311yescharacteristic
1185C2×C22⋊C4C22×D7311yescharacteristic
1186C2×C22⋊C4C22×D7311yescharacteristic
1187C2×C22⋊C4C22×D7311yescharacteristic
1188C2×C22⋊C4C22×D7311yescharacteristic
1189C2×C22⋊C4C22×D7311yescharacteristic
1190C2×C22⋊C4C22×D7311yescharacteristic
1191C2×C42—2922no—
1192C2×C42—2922no—
1193C2×C42—731no—
1194C2×C42—731no—
1195C2×C42—731no—
1196C2×C42—731no—
1197C2×C42—731no—
1198C2×C42—731no—
1199C2×C42—731no—
1200C2×C42—731no—
1201C2×C42—731no—
1202C2×C42—731no—
1203C2×C42—731no—
1204C2×C42—731no—
1205C2×C42—731no—
1206C2×C42—731no—
1207C2×C42—731no—
1208C2×C42—731no—
1209C2×C42—1464no—
1210C2×C42C22×D7311yescharacteristic
1211C2×C42C22×D7311yescharacteristic
1212C2×C42C22×D7311yescharacteristic
1213#95—731no—
1214#95—731no—
1215#95—731no—
1216#95—731no—
1217#95—731no—
1218#95—731no—
1219#95—731no—
1220#95—731no—
1221#95—731no—
1222#95—731no—
1223#95—731no—
1224#95—731no—
1225#95—731no—
1226#95—731no—
1227#95—731no—
1228#95—731no—
1229#95—731no—
1230#95—731no—
1231#95—731no—
1232#95—731no—
1233#95—731no—
1234#95—731no—
1235#95—731no—
1236#95—731no—
1237#95—731no—
1238#95—731no—
1239#95C22×D7311yescharacteristic
1240#95C22×D7311yescharacteristic
1241#95C22×D7311yescharacteristic
1242#95C22×D7311yescharacteristic
1243#95C22×D7311yescharacteristic
1244#95C22×D7311yescharacteristic
1245C24—22no—
1246C24—22no—
1247C24—22no—
1248C24—22no—
1249C24—22no—
1250C24—41no—
1251C24—41no—
1252C24—731no—
1253C24—731no—
1254C24C23×D7311yescharacteristic
1255C24C23×D7311yescharacteristic
1256C24C23×D7311yescharacteristic
1257C24C23×D7311yescharacteristic
1258#41—29216no—
1259C2×Q8—2921no—
1260C2×Q8—2921no—
1261C2×Q8—1462no—
1262C2×Q8—1462no—
1263C2×Q8—1462no—
1264C2×Q8—1462no—
1265C2×D4—22no—
1266C2×D4—22no—
1267C2×D4—22no—
1268C2×D4—22no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—41no—
1273C2×D4—41no—
1274C2×D4—2921no—
1275C2×D4—2921no—
1276C2×D4—2921no—
1277C2×D4—2921no—
1278C2×D4—2921no—
1279C2×D4—2921no—
1280C2×D4—2921no—
1281C2×D4—2921no—
1282C2×D4—734no—
1283C2×D4—1462no—
1284C2×D4—1462no—
1285C2×D4—1462no—
1286C2×D4—1462no—
1287C2×D4—1462no—
1288C2×D4—1462no—
1289C2×D4—1462no—
1290C2×D4—1462no—
1291C2×D4—1462no—
1292C2×D4—1462no—
1293C2×D4—1462no—
1294C2×D4—1462no—
1295C2×D4—1462no—
1296C2×D4—1462no—
1297C2×D4—1462no—
1298C2×D4—1462no—
1299C2×D4—1462no—
1300C2×D4—1462no—
1301C22×C4—22no—
1302C22×C4—22no—
1303C22×C4—22no—
1304C22×C4—22no—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—22no—
1312C22×C4—22no—
1313C22×C4—22no—
1314C22×C4—22no—
1315C22×C4—22no—
1316C22×C4—22no—
1317C22×C4—41no—
1318C22×C4—41no—
1319C22×C4—41no—
1320C22×C4—416no—
1321C22×C4—2921no—
1322C22×C4—2921no—
1323C22×C4—2921no—
1324C22×C4—2921no—
1325C22×C4—2921no—
1326C22×C4—2921no—
1327C22×C4—2921no—
1328C22×C4—734no—
1329C22×C4—731no—
1330C22×C4—731no—
1331C22×C4—731no—
1332C22×C4—731no—
1333C22×C4—731no—
1334C22×C4—731no—
1335C22×C4—731no—
1336C22×C4—734no—
1337C22×C4—731no—
1338C22×C4—731no—
1339C22×C4—731no—
1340C22×C4—731no—
1341C22×C4—731no—
1342C22×C4—731no—
1343C22×C4—731no—
1344C22×C4—1462no—
1345C22×C4—1462no—
1346C22×C4—1462no—
1347C22×C4—1462no—
1348C22×C4—1462no—
1349C22×C4—1462no—
1350C22×C4—1462no—
1351C22×C4—1462no—
1352C22×C4—1462no—
1353C22×C4—1462no—
1354C22×C4—1462no—
1355C22×C4—1462no—
1356C22×C4—1462no—
1357C22×C4—1462no—
1358C22×C4—1462no—
1359C22×C4D4×D7314yes—
1360C22×C4#1192402714yes—
1361C22×C4C23×D7311yescharacteristic
1362C22×C4C23×D7311yescharacteristic
1363C22×C4C23×D7311yescharacteristic
1364C22×C4C23×D7311yescharacteristic
1365C22×C4C23×D7311yescharacteristic
1366C22×C4C23×D7311yescharacteristic
1367C22×C4C23×D7311yescharacteristic
1368C22×C4C23×D7311yescharacteristic
1369C22×C4C23×D7311yescharacteristic
1370C22×C4C23×D7311yescharacteristic
1371C22×C4C23×D7311yescharacteristic
1372C4⋊C4—22no—
1373C4⋊C4—22no—
1374C4⋊C4—41no—
1375C4⋊C4—2921no—
1376C4⋊C4—2921no—
1377C4⋊C4—2921no—
1378C4⋊C4—734no—
1379C4⋊C4—1462no—
1380C4⋊C4—1462no—
1381C4⋊C4—1462no—
1382C4⋊C4—1462no—
1383C4⋊C4—1462no—
1384C4⋊C4—1462no—
1385C4⋊C4—1462no—
1386C4⋊C4—1462no—
1387C4⋊C4—1462no—
1388C4⋊C4—1462no—
1389C4⋊C4—1462no—
1390C4⋊C4—1462no—
1391C4⋊C4—1462no—
1392C4⋊C4—1462no—
1393C4⋊C4—1462no—
1394C4⋊C4—1462no—
1395C4⋊C4—1462no—
1396C4⋊C4—1462no—
1397C4⋊C4—1462no—
1398C22⋊C4—22no—
1399C22⋊C4—22no—
1400C22⋊C4—22no—
1401C22⋊C4—22no—
1402C22⋊C4—22no—
1403C22⋊C4—22no—
1404C22⋊C4—22no—
1405C22⋊C4—22no—
1406C22⋊C4—41no—
1407C22⋊C4—41no—
1408C22⋊C4—41no—
1409C22⋊C4—2921no—
1410C22⋊C4—2921no—
1411C22⋊C4—2921no—
1412C22⋊C4—734no—
1413C22⋊C4—734no—
1414C22⋊C4—734no—
1415C22⋊C4—1462no—
1416C22⋊C4—1462no—
1417C22⋊C4—1462no—
1418C22⋊C4—1462no—
1419C22⋊C4—1462no—
1420C22⋊C4—1462no—
1421C22⋊C4—1462no—
1422C22⋊C4—1462no—
1423C22⋊C4—1462no—
1424C22⋊C4—1462no—
1425C22⋊C4—1462no—
1426C22⋊C4—1462no—
1427C22⋊C4—1462no—
1428C22⋊C4—1462no—
1429C22⋊C4—1462no—
1430C22⋊C4—1462no—
1431C22⋊C4—1462no—
1432C22⋊C4—1462no—
1433C22⋊C4—1462no—
1434C22⋊C4—1462no—
1435C22⋊C4—1462no—
1436C22⋊C4—1462no—
1437C22⋊C4—1462no—
1438C22⋊C4—1462no—
1439C22⋊C4—1462no—
1440C22⋊C4—1462no—
1441C22⋊C4—1462no—
1442C22⋊C4—1462no—
1443C22⋊C4—1462no—
1444C22⋊C4—1462no—
1445C22⋊C4#1192402814yescomplemented
1446C42—22no—
1447C42—22no—
1448C42—22no—
1449C42—2921no—
1450C42—2921no—
1451C42—2921no—
1452C42—2921no—
1453C42—2921no—
1454C42—734no—
1455C42—1462no—
1456C42—1462no—
1457C42—1462no—
1458C42—1462no—
1459C42—1462no—
1460C42—1462no—
1461C42—1462no—
1462C42—1462no—
1463C42—1462no—
1464C42—1462no—
1465C23—21no—
1466C23—21no—
1467C23—21no—
1468C23—21no—
1469C23—28no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—21no—
1474C23—21no—
1475C23—21no—
1476C23—21no—
1477C23—21no—
1478C23—21no—
1479C23—21no—
1480C23—21no—
1481C23—21no—
1482C23—21no—
1483C23—21no—
1484C23—21no—
1485C23—21no—
1486C23—21no—
1487C23—21no—
1488C23—21no—
1489C23—44no—
1490C23—44no—
1491C23—44no—
1492C23—44no—
1493C23—44no—
1494C23—44no—
1495C23—732no—
1496C23—1461no—
1497C23—1461no—
1498C23—1461no—
1499C23—1461no—
1500C23—1461no—
1501C23—1461no—
1502C23—1461no—
1503C23—1461no—
1504C23—1461no—
1505C23—1461no—
1506C23—1461no—
1507C23—1461no—
1508C23—1461no—
1509C23C2×D4×D7312yes—
1510C23#41×D7312yes—
1511C23#41×D7312yes—
1512C23C2×#1192402712yes—
1513C23C2×#1192402812yes—
1514C23C24×D7311yescharacteristic
1515Q8—2924no—
1516Q8—2924no—
1517D4—44no—
1518D4—44no—
1519D4—44no—
1520D4—2924no—
1521D4—2924no—
1522D4—2924no—
1523D4—2924no—
1524D4—2924no—
1525D4—2924no—
1526D4—2924no—
1527D4—2924no—
1528D4—1468no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—28no—
1538C2×C4—28no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—21no—
1550C2×C4—21no—
1551C2×C4—21no—
1552C2×C4—21no—
1553C2×C4—21no—
1554C2×C4—21no—
1555C2×C4—21no—
1556C2×C4—21no—
1557C2×C4—44no—
1558C2×C4—44no—
1559C2×C4—44no—
1560C2×C4—44no—
1561C2×C4—44no—
1562C2×C4—2924no—
1563C2×C4—2924no—
1564C2×C4—2924no—
1565C2×C4—2924no—
1566C2×C4—2924no—
1567C2×C4—2924no—
1568C2×C4—2924no—
1569C2×C4—732no—
1570C2×C4—732no—
1571C2×C4—732no—
1572C2×C4—732no—
1573C2×C4—732no—
1574C2×C4—732no—
1575C2×C4—732no—
1576C2×C4—1461no—
1577C2×C4—1461no—
1578C2×C4—1461no—
1579C2×C4—1461no—
1580C2×C4—1461no—
1581C2×C4—1461no—
1582C2×C4—1461no—
1583C2×C4—1461no—
1584C2×C4—1461no—
1585C2×C4—1461no—
1586C2×C4—1461no—
1587C2×C4—1461no—
1588C2×C4—1461no—
1589C2×C4—1461no—
1590C2×C4—1461no—
1591C2×C4—1461no—
1592C2×C4—1461no—
1593C2×C4—1461no—
1594C2×C4—1461no—
1595C2×C4—1461no—
1596C2×C4—1461no—
1597C2×C4—1461no—
1598C2×C4—1461no—
1599C2×C4—1461no—
1600C2×C4—1461no—
1601C2×C4—1461no—
1602C2×C4—1461no—
1603C2×C4—1461no—
1604C2×C4—1461no—
1605C2×C4—1461no—
1606C2×C4—1461no—
1607C2×C4—1461no—
1608C2×C4—1461no—
1609C2×C4—1461no—
1610C2×C4—1461no—
1611C2×C4—1468no—
1612C2×C4C2×D4×D7312yes—
1613C2×C4C2×D4×D7312yes—
1614C2×C4C2×#1192402712yes—
1615C2×C4C2×#1192402712yes—
1616C2×C4C2×#1192402812yes—
1617C2×C4C2×#1192402812yes—
1618C2×C4#1455663612yes—
1619C22—22no—
1620C22—22no—
1621C22—22no—
1622C22—22no—
1623C22—22no—
1624C22—22no—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—416no—
1632C22—41no—
1633C22—41no—
1634C22—41no—
1635C22—41no—
1636C22—41no—
1637C22—41no—
1638C22—41no—
1639C22—41no—
1640C22—41no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—2921no—
1648C22—2921no—
1649C22—2921no—
1650C22—2921no—
1651C22—2921no—
1652C22—2921no—
1653C22—2921no—
1654C22—2921no—
1655C22—2921no—
1656C22—2921no—
1657C22—2921no—
1658C22—1462no—
1659C22—1462no—
1660C22—1462no—
1661C22#1798913414yes—
1662C22C22×D4×D7311yescharacteristic
1663C22C2×#41×D7311yescharacteristic
1664C22C2×#41×D7311yescharacteristic
1665C22C22×#1192402711yescharacteristic
1666C22C22×#1192402811yescharacteristic
1667C22C2×#1455663611yescharacteristic
1668C22#1798942311yescharacteristic
1669C4—22no—
1670C4—22no—
1671C4—22no—
1672C4—22no—
1673C4—41no—
1674C4—41no—
1675C4—41no—
1676C4—41no—
1677C4—41no—
1678C4—41no—
1679C4—2921no—
1680C4—2921no—
1681C4—2921no—
1682C4—2921no—
1683C4—2921no—
1684C4—2921no—
1685C4—2921no—
1686C4—1462no—
1687C4—1462no—
1688C4—1462no—
1689C4—1462no—
1690C4—1462no—
1691C4—1462no—
1692C4—1462no—
1693C4#1798922414yes—
1694C2—24no—
1695C2—42no—
1696C2—42no—
1697C2—81no—
1698C2—2922no—
1699C2—5841no—
1700C2C2×#1798913411yescharacteristic
1701C2#2262322311yescharacteristic
1702C2#2262333811yescharacteristic
1703C2C2×#1798922411yescharacteristic
1704C2#2262341411yescharacteristic
1705C2#2262348911yescharacteristic
1706C2#2262353511yescharacteristic
subgroupG/H
centerC22×C4C23×D73
commutator, socle, cosocleC23×C73C25
FrattiniC23C24×D73
FittingC4×#120×C73C2
hypercenterC4×#120D73
hypocenterC73#34829
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#17989117C2semidirect
2. C2×#17989098C2semidirect
3. #22615079C2semidirect
4. #22615064C2semidirect
5. #22615049C2semidirect
6. #22615034C2semidirect
7. #22615021C2semidirect
8. #22615003C2semidirect
9. #22614995C2semidirect
10. #22614980C2semidirect
11. #22614944C2semidirect
12. #22614895C2semidirect
13. #22614859C2semidirect
14. #22614824C2semidirect
15. #22614255C2semidirect
16. #22614054C2semidirect
17. #22613480C2semidirect
18. #22613463C2semidirect
19. #22613205C2semidirect
20. #22613192C2semidirect
21. #22613173C2semidirect
22. #22613146C2semidirect
23. C4×#14556577C2semidirect
24. C4×#14556575C2semidirect
25. C4×#14556563C2semidirect
26. C4×#14556562C2semidirect
27. #22612417C2semidirect
28. #22612396C2semidirect
29. C4×#14556551C2semidirect
30. C2×C4×C22⋊Dic73C2semidirect
31. C4×#120×C73C2semidirect
34. C2×#14556586C22semidirect
35. C2×#14556584C22semidirect
36. C2×#14556581C22semidirect
38. C2×#14556577C22semidirect
55. C2×C4×Dic146C22semidirect
60. C2×C4×C22⋊D73C22semidirect
61. C2×C4×C22⋊D73C22semidirect
65. C2×#14556550C22semidirect
66. C2×#14556548C22semidirect
71. C2×C42×D73C22semidirect
72. #17988529C22semidirect
73. #17988528C22semidirect
76. #17988521C22semidirect
77. #17988521C22semidirect
78. #17988520C22semidirect
79. #17988519C22semidirect
80. #17988516C22semidirect
82. #17988515C22semidirect
83. #17988514C22semidirect
87. #17988509C22semidirect
88. #17988508C22semidirect
89. #17988507C22semidirect
90. #17988504C22semidirect
96. #17988502C22semidirect
99. #17988499C22semidirect
100. #17988496C22semidirect
104. #17988491C22semidirect
105. #17988491C22semidirect
106. #17988491C22semidirect
113. #17988487C22semidirect
114. #17988486C22semidirect
115. #17988486C22semidirect
116. #17988483C22semidirect
117. #17988482C22semidirect
118. #17988481C22semidirect
122. #17988480C22semidirect
123. #17988480C22semidirect
124. #17988479C22semidirect
125. #17988479C22semidirect
126. #17988479C22semidirect
127. #17988477C22semidirect
128. #17988476C22semidirect
131. #17988475C22semidirect
132. #17988472C22semidirect
133. #17988472C22semidirect
135. #17988465C22semidirect
136. #17988465C22semidirect
142. #17988463C22semidirect
144. #17988451C22semidirect
147. #17988444C22semidirect
148. C4×#11924007C22semidirect
149. C4×#11924007C22semidirect
150. C4×C4⋊Dic73C22semidirect
151. C4×C4⋊Dic73C22semidirect
152. #17988438C22semidirect
153. #17988438C22semidirect
156. C4×#11924005C22semidirect
157. C4×#11924005C22semidirect
158. C4×#11924005C22semidirect
159. C4×#11924005C22semidirect
168. C4×C22⋊Dic73C22semidirect
169. #17988434C22semidirect
170. #17988434C22semidirect
173. C42×Dic73C22semidirect
237. C4×C22⋊D73D4semidirect
438. C22×Dic73#41semidirect
507. C22⋊Dic73#41semidirect
607. C22⋊C4×C73#41semidirect
880. C4×#120D73semidirect
885. C73#34829semidirect
1445. C22⋊C4#11924028semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#179891172
C2×#179890982
#226150792
#226150642
#226150492
#226150342
#226150212
#226150032
#226149952
#226149802
#226149442
#226148952
#226148592
#226148242
#226142552
#226140542
#226134802
#226134632
#226132052
#226131922
#226131732
#226131462
C4×#145565772
C4×#145565752
C4×#145565632
C4×#145565622
#226124172
#226123962
C4×#145565512
C2×C4×C22⋊Dic732
C4×#120×C732
#3482973