Finite Group Databasebeta

← #33254644

Subgroups — #33254644

Order 18688.

2938 conjugacy classes of subgroups.

The subgroup lattice has 1714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989093C211yesmaximal, characteristic, complemented
2C2×C4×#11924027C211yesmaximal, characteristic, complemented
3#22614125C211yesmaximal, characteristic, complemented
4#22614110C211yesmaximal, characteristic, complemented
5#22614035C211yesmaximal, characteristic, complemented
6#22614020C211yesmaximal, characteristic, complemented
7#22613949C211yesmaximal, characteristic, complemented
8#22613934C211yesmaximal, characteristic, complemented
9#22613850C211yesmaximal, characteristic, complemented
10#22613835C211yesmaximal, characteristic, complemented
11#22613757C211yesmaximal, characteristic, complemented
12#22613675C211yesmaximal, characteristic, complemented
13#22613613C211yesmaximal, characteristic, complemented
14#22613539C211yesmaximal, characteristic, complemented
15#22613467C211yesmaximal, characteristic, complemented
16#22613318C211yesmaximal, characteristic, complemented
17#22613247C211yesmaximal, characteristic, complemented
18#22613216C211yesmaximal, characteristic, complemented
19#22613200C211yesmaximal, characteristic, complemented
20#22613174C211yesmaximal, characteristic, complemented
21#22613145C211yesmaximal, characteristic, complemented
22#123×Dic73C211yesmaximal, characteristic, complemented
23#22612450C211yesmaximal, characteristic, complemented
24#22612443C211yesmaximal, characteristic, complemented
25#22612437C211yesmaximal, characteristic, complemented
26#22612430C211yesmaximal, characteristic, complemented
27#22612416C211yesmaximal, characteristic, complemented
28#22612373C211yesmaximal, characteristic, complemented
29#22612371C211yesmaximal, characteristic, complemented
30C2×C22⋊C4×Dic73C211yesmaximal, characteristic, complemented
31C73×#2418C211yesmaximal, characteristic, complemented
32C22×#11924027C2211yescharacteristic
33C22×#11924027C2211yescharacteristic
34C24×Dic73C2211yescharacteristic
35#17989093—28no—
36C2×#14556575C2211yescharacteristic
37C2×#14556575C2211yescharacteristic
38C2×#14556572C2211yescharacteristic
39C2×#14556568C2211yescharacteristic
40C2×#14556568C2211yescharacteristic
41C2×#14556565C2211yescharacteristic
42C2×#14556564C2211yescharacteristic
43C2×#14556563C2211yescharacteristic
44C2×#14556563C2211yescharacteristic
45C2×#14556560C2211yescharacteristic
46C2×#14556560C2211yescharacteristic
47C4×#11924027—28no—
48C2×C4×Dic146C2211yescharacteristic, complemented
49C2×#14556556C2211yescharacteristic, complemented
50C2×D4×Dic73C2211yescharacteristic
51C2×D4×Dic73C2211yescharacteristic
52C2×#14556553C2211yescharacteristic, complemented
53C2×C4×C22⋊D73C2211yescharacteristic
54C2×C4×C22⋊D73C2211yescharacteristic, complemented
55C2×#14556551C2211yescharacteristic
56C2×#14556551C2211yescharacteristic
57C2×#14556551C2211yescharacteristic
58C2×#14556551C2211yescharacteristic
59C2×#14556551C2211yescharacteristic
60C2×#14556551C2211yescharacteristic, complemented
61C2×#14556549C2211yescharacteristic, complemented
62C2×#14556547C2211yescharacteristic
63C2×#14556547C2211yescharacteristic
64C2×#14556547C2211yescharacteristic, complemented
65C2×#14556547C2211yescharacteristic, complemented
66C22×C22⋊Dic73C2211yescharacteristic
67C22×C4×Dic73C2211yescharacteristic
68C22×C4×Dic73C2211yescharacteristic
69C22×C4×Dic73C2211yescharacteristic, complemented
70C2×C42×D73C2211yescharacteristic, complemented
71#17988528C2211yescharacteristic, complemented
72#17988528C2211yescharacteristic, complemented
73#17988525C2211yescharacteristic, complemented
74#17988521C2211yescharacteristic, complemented
75#17988518C2211yescharacteristic, complemented
76#17988518C2211yescharacteristic, complemented
77#17988515C2211yescharacteristic, complemented
78#17988513C2211yescharacteristic, complemented
79#17988510C2211yescharacteristic
80#17988510C2211yescharacteristic
81#17988510C2211yescharacteristic
82#17988509C2211yescharacteristic, complemented
83#17988508C2211yescharacteristic, complemented
84#17988507C2211yescharacteristic, complemented
85#17988503C2211yescharacteristic, complemented
86#17988502C2211yescharacteristic
87#17988502C2211yescharacteristic
88#17988502C2211yescharacteristic
89#17988502C2211yescharacteristic
90#17988502C2211yescharacteristic, complemented
91#17988500C2211yescharacteristic, complemented
92#17988500C2211yescharacteristic, complemented
93#17988499C2211yescharacteristic
94#17988499C2211yescharacteristic
95#17988496C2211yescharacteristic
96#17988496C2211yescharacteristic, complemented
97#17988495C2211yescharacteristic
98#17988495C2211yescharacteristic
99#17988491C2211yescharacteristic, complemented
100#17988491C2211yescharacteristic, complemented
101#17988488C2211yescharacteristic, complemented
102#17988487C2211yescharacteristic
103#17988487C2211yescharacteristic
104#17988487C2211yescharacteristic
105#17988483C2211yescharacteristic, complemented
106#17988482C2211yescharacteristic, complemented
107#17988481C2211yescharacteristic, complemented
108#17988480C2211yescharacteristic
109#17988480C2211yescharacteristic
110#17988480C2211yescharacteristic
111#17988478C2211yescharacteristic, complemented
112#17988477C2211yescharacteristic, complemented
113#17988477C2211yescharacteristic, complemented
114#17988476C2211yescharacteristic, complemented
115#17988476C2211yescharacteristic, complemented
116#17988475C2211yescharacteristic, complemented
117#17988473C2211yescharacteristic, complemented
118#17988473C2211yescharacteristic, complemented
119#17988472C2211yescharacteristic, complemented
120#17988471C2211yescharacteristic, complemented
121#17988470C2211yescharacteristic, complemented
122#17988470C2211yescharacteristic, complemented
123#17988470C2211yescharacteristic, complemented
124#17988469C2211yescharacteristic, complemented
125#17988467C2211yescharacteristic
126#17988467C2211yescharacteristic
127#17988467C2211yescharacteristic
128#17988466C2211yescharacteristic
129#17988466C2211yescharacteristic, complemented
130#17988465C2211yescharacteristic, complemented
131#17988464C2211yescharacteristic
132#17988464C2211yescharacteristic
133#17988464C2211yescharacteristic
134#17988464C2211yescharacteristic
135#17988464C2211yescharacteristic
136#17988464C2211yescharacteristic, complemented
137#17988463C2211yescharacteristic
138#17988463C2211yescharacteristic
139#17988463C2211yescharacteristic
140#17988462C2211yescharacteristic, complemented
141#17988461C2211yescharacteristic, complemented
142#17988460C2211yescharacteristic
143#17988459C2211yescharacteristic
144#17988459C2211yescharacteristic
145#17988459C2211yescharacteristic
146#17988459C2211yescharacteristic
147#17988458C2211yescharacteristic, complemented
148#17988450C2211yescharacteristic, complemented
149#17988448C2211yescharacteristic
150#17988446C2211yescharacteristic, complemented
151C4⋊C4×Dic73C2211yescharacteristic, complemented
152C4⋊C4×Dic73C2211yescharacteristic, complemented
153C4⋊C4×Dic73C2211yescharacteristic, complemented
154#17988438C2211yescharacteristic, complemented
155C22⋊C4×Dic73C2211yescharacteristic
156C22⋊C4×Dic73C2211yescharacteristic
157C22⋊C4×Dic73C2211yescharacteristic
158C22⋊C4×Dic73C2211yescharacteristic
159C22⋊C4×Dic73C2211yescharacteristic
160C22⋊C4×Dic73C2211yescharacteristic
161C22⋊C4×Dic73C2211yescharacteristic
162C22⋊C4×Dic73C2211yescharacteristic
163C22⋊C4×Dic73C2211yescharacteristic
164C22⋊C4×Dic73C2211yescharacteristic
165C22⋊C4×Dic73C2211yescharacteristic
166C22⋊C4×Dic73C2211yescharacteristic, complemented
167#17988434C2211yescharacteristic, complemented
168#17988434C2211yescharacteristic, complemented
169#17988434C2211yescharacteristic, complemented
170#17988434C2211yescharacteristic, complemented
171#17988432C2211yescharacteristic, complemented
172C2×#14556498C2211yescharacteristic
173C2×#14556498C2211yescharacteristic
174C2×#123×C73C2211yescharacteristic
175C2×#120×C73C2211yescharacteristic
176C2×C4×D4×C73C2211yescharacteristic
177C22×C22⋊C4×C73C2211yescharacteristic
178#399×C73C2211yescharacteristic
179#397×C73C2211yescharacteristic
180#394×C73C2211yescharacteristic
181#394×C73C2211yescharacteristic
182#388×C73C2211yescharacteristic
183#388×C73C2211yescharacteristic
184#386×C73C2211yescharacteristic
185#386×C73C2211yescharacteristic
186#385×C73C2211yescharacteristic
187#380×C73C2211yescharacteristic
188#379×C73C2211yescharacteristic
189C2×#11924027—24no—
190C2×#11924027—24no—
191C2×#11924027—24no—
192C2×#11924027—24no—
193C2×#11924027—24no—
194C2×#11924027—42no—
195C22×Dic146C2311yescharacteristic
196C22×Dic146C2311yescharacteristic
197C22×D292C2311yescharacteristic
198C22×C22⋊D73C2311yescharacteristic
199C22×C22⋊D73C2311yescharacteristic
200C22×C22⋊D73C2311yescharacteristic
201C22×C22⋊D73C2311yescharacteristic
202C22×C22⋊D73C2311yescharacteristic
203C22×C22⋊D73C2311yescharacteristic
204C22×C22⋊D73C2311yescharacteristic
205C22×C22⋊D73C2311yescharacteristic
206C23×Dic73—24no—
207C23×Dic73—24no—
208C23×Dic73—42no—
209C23×Dic73C2311yescharacteristic
210C23×Dic73C2311yescharacteristic
211C23×Dic73C2311yescharacteristic
212C23×Dic73C2311yescharacteristic
213C23×Dic73C2311yescharacteristic
214C23×Dic73C2311yescharacteristic
215C23×Dic73C2311yescharacteristic
216C23×Dic73C2311yescharacteristic
217C23×Dic73C2311yescharacteristic
218C23×Dic73C2311yescharacteristic
219C22×C4×D73C2311yescharacteristic
220C22×C4×D73C2311yescharacteristic
221C22×C4×D73C2311yescharacteristic
222C22×C4×D73C2311yescharacteristic
223#14556575—24no—
224#14556575—24no—
225#14556572—24no—
226#14556568—24no—
227#14556568—24no—
228#14556565—24no—
229#14556564—24no—
230#14556563—24no—
231#14556563—24no—
232#14556560—24no—
233#14556560—24no—
234C4×Dic146—24no—
235#14556556—24no—
236D4×Dic73—24no—
237D4×Dic73D418yescomplemented
238#14556553—42no—
239C4×C22⋊D73—24no—
240C4×C22⋊D73—24no—
241#14556551—24no—
242#14556551—24no—
243#14556551—24no—
244#14556551—24no—
245#14556551—24no—
246#14556551—42no—
247#14556549—24no—
248#14556547—24no—
249#14556547—24no—
250#14556547—24no—
251#14556547—42no—
252C2×C4⋊Dic73C2311yescharacteristic
253C2×C4⋊Dic73C2311yescharacteristic
254C2×C4⋊Dic73C2311yescharacteristic
255C2×C4⋊Dic73C2311yescharacteristic
256C2×C4⋊Dic73C2311yescharacteristic
257C2×#11924007C2311yescharacteristic
258C2×#11924007C2311yescharacteristic
259C2×#11924007C2311yescharacteristic
260C2×#11924007C2311yescharacteristic
261C2×#11924007C2311yescharacteristic
262C2×#11924007C2311yescharacteristic
263C2×#11924007C2311yescharacteristic
264C2×#11924007C2311yescharacteristic
265C2×#11924007C2311yescharacteristic
266C2×#11924007C2311yescharacteristic
267C2×#11924007C2311yescharacteristic
268C2×#11924007C2311yescharacteristic
269C2×#11924007C2311yescharacteristic
270C2×#11924007C2311yescharacteristic
271C2×C22⋊Dic73—24no—
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×#11924005C2311yescharacteristic
287C2×#11924005C2311yescharacteristic
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×C4×Dic73—24no—
303C2×C4×Dic73—24no—
304C2×C4×Dic73—42no—
305C2×C4×Dic73C2311yescharacteristic
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
321C42×D73—24no—
322#14556498C2311yescharacteristic
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
349#14556498C2311yescharacteristic
350#14556498C2311yescharacteristic
351#14556498C2311yescharacteristic
352C25×C73C2311yescharacteristic
353C22×D4×C73C2311yescharacteristic
354C22×D4×C73C2311yescharacteristic
355C22×D4×C73C2311yescharacteristic
356C23×C4×C73C2311yescharacteristic
357C23×C4×C73C2311yescharacteristic
358C23×C4×C73C2311yescharacteristic
359#123×C73—24no—
360#120×C73—24no—
361C4×D4×C73—24no—
362C2×C4⋊C4×C73C2311yescharacteristic
363C2×C4⋊C4×C73C2311yescharacteristic
364C2×C4⋊C4×C73C2311yescharacteristic
365C2×C4⋊C4×C73C2311yescharacteristic
366C2×C4⋊C4×C73C2311yescharacteristic
367C2×C22⋊C4×C73—24no—
368C2×C22⋊C4×C73C2311yescharacteristic
369C2×C22⋊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×C22⋊C4×C73C2311yescharacteristic
383C2×C22⋊C4×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#11924027—232no—
394#11924027—416no—
395C2×Dic146—22no—
396C2×Dic146—22no—
397C2×Dic146—22no—
398C2×Dic146—22no—
399C2×Dic146—22no—
400C2×Dic146—41no—
401C2×D292—22no—
402C2×D292—22no—
403C2×D292—41no—
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—22no—
420C2×C22⋊D73—22no—
421C2×C22⋊D73—22no—
422C2×C22⋊D73—41no—
423C2×C22⋊D73—41no—
424C2×C22⋊D73—41no—
425C2×C22⋊D73—41no—
426C2×C22⋊D73—41no—
427C2×C22⋊D73#4114yescomplemented
428C22×Dic73—22no—
429C22×Dic73—22no—
430C22×Dic73—22no—
431C22×Dic73—22no—
432C22×Dic73—22no—
433C22×Dic73—22no—
434C22×Dic73—22no—
435C22×Dic73—22no—
436C22×Dic73—22no—
437C22×Dic73—22no—
438C22×Dic73—22no—
439C22×Dic73—22no—
440C22×Dic73—22no—
441C22×Dic73—22no—
442C22×Dic73—22no—
443C22×Dic73—22no—
444C22×Dic73—22no—
445C22×Dic73—22no—
446C22×Dic73—22no—
447C22×Dic73—22no—
448C22×Dic73—22no—
449C22×Dic73—41no—
450C22×Dic73—41no—
451C22×Dic73—41no—
452C22×Dic73—41no—
453C22×Dic73—41no—
454C22×Dic73—416no—
455C22×Dic73C2×D414yes—
456C22×Dic73C2×D414yes—
457C22×Dic73#4114yescomplemented
458C22×Dic73#4114yescomplemented
459C22×Dic73C2411yescharacteristic
460C22×Dic73C2411yescharacteristic
461C22×Dic73C2411yescharacteristic
462C22×Dic73C2411yescharacteristic
463C22×Dic73C2411yescharacteristic
464C22×Dic73C2411yescharacteristic
465C22×Dic73C2411yescharacteristic
466C22×Dic73C2411yescharacteristic
467C22×Dic73C2411yescharacteristic
468C22×Dic73C2411yescharacteristic
469C22×Dic73C2411yescharacteristic
470C22×Dic73C2411yescharacteristic
471C22×Dic73C2411yescharacteristic
472C22×Dic73C2411yescharacteristic
473C2×C4×D73—22no—
474C2×C4×D73—22no—
475C2×C4×D73—22no—
476C2×C4×D73—22no—
477C2×C4×D73—22no—
478C2×C4×D73—22no—
479C2×C4×D73—22no—
480C2×C4×D73—22no—
481C2×C4×D73—22no—
482C2×C4×D73—22no—
483C2×C4×D73—22no—
484C2×C4×D73—41no—
485C4⋊Dic73—22no—
486C4⋊Dic73—22no—
487C4⋊Dic73—22no—
488C4⋊Dic73—22no—
489C4⋊Dic73C2×D414yes—
490#11924007—22no—
491#11924007—22no—
492#11924007—22no—
493#11924007—22no—
494#11924007—22no—
495#11924007—22no—
496#11924007—22no—
497#11924007—22no—
498#11924007—22no—
499#11924007—22no—
500#11924007—41no—
501#11924007—41no—
502#11924007—41no—
503#11924007—41no—
504C22⋊Dic73—22no—
505C22⋊Dic73—22no—
506C22⋊Dic73—22no—
507C22⋊Dic73—22no—
508C22⋊Dic73—22no—
509C22⋊Dic73—22no—
510C22⋊Dic73—22no—
511C22⋊Dic73—22no—
512C22⋊Dic73—22no—
513C22⋊Dic73—22no—
514C22⋊Dic73—41no—
515C22⋊Dic73—41no—
516C22⋊Dic73C2×D414yes—
517C22⋊Dic73C2×D414yes—
518#11924005—22no—
519#11924005—22no—
520#11924005—22no—
521#11924005—22no—
522#11924005—22no—
523#11924005—22no—
524#11924005—22no—
525#11924005—22no—
526#11924005—22no—
527#11924005—22no—
528#11924005—41no—
529#11924005—41no—
530#11924005—41no—
531#11924005—41no—
532#11924005—41no—
533#11924005—41no—
534C4×Dic73—22no—
535C4×Dic73—22no—
536C4×Dic73—22no—
537C4×Dic73—22no—
538C4×Dic73—22no—
539C4×Dic73—22no—
540C4×Dic73—22no—
541C4×Dic73—22no—
542C4×Dic73—22no—
543C4×Dic73—22no—
544C4×Dic73—22no—
545C4×Dic73—22no—
546C4×Dic73—22no—
547C4×Dic73—41no—
548C4×Dic73—41no—
549C4×Dic73C2×D414yes—
550C24×C73—22no—
551C24×C73—22no—
552C24×C73—22no—
553C24×C73—22no—
554C24×C73—22no—
555C24×C73—41no—
556C24×C73—41no—
557C24×C73C2411yescharacteristic
558C24×C73C2411yescharacteristic
559C24×C73C2411yescharacteristic
560C24×C73C2411yescharacteristic
561C2×D4×C73—22no—
562C2×D4×C73—22no—
563C2×D4×C73—22no—
564C2×D4×C73—22no—
565C2×D4×C73—22no—
566C2×D4×C73—22no—
567C2×D4×C73—41no—
568C2×D4×C73—41no—
569C2×D4×C73C2×D414yes—
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×C73C2411yescharacteristic
580C22×C4×C73C2411yescharacteristic
581C22×C4×C73C2411yescharacteristic
582C22×C4×C73C2411yescharacteristic
583C22×C4×C73C2411yescharacteristic
584C22×C4×C73C2411yescharacteristic
585C22×C4×C73C2411yescharacteristic
586C22×C4×C73C2411yescharacteristic
587C22×C4×C73C2411yescharacteristic
588C22×C4×C73C2411yescharacteristic
589C22×C4×C73C2411yescharacteristic
590C4⋊C4×C73—22no—
591C4⋊C4×C73—22no—
592C4⋊C4×C73—22no—
593C4⋊C4×C73—41no—
594C4⋊C4×C73—41no—
595C22⋊C4×C73—22no—
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—22no—
605C22⋊C4×C73—22no—
606C22⋊C4×C73—22no—
607C22⋊C4×C73—41no—
608C22⋊C4×C73—41no—
609C22⋊C4×C73—41no—
610C22⋊C4×C73#4114yescomplemented
611C42×C73—22no—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—21no—
616C23×C73—28no—
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×C73C22×D412yes—
643C23×C73C2×#4112yes—
644C23×C73C2×#4112yes—
645C23×C73C2×#4112yes—
646C23×C73C2×#4112yes—
647C23×C73C2511yescharacteristic
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×D73—21no—
661C22×D73C2×#4112yes—
662D4×C73—28no—
663D4×C73—44no—
664D4×C73—44no—
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—21no—
673C2×C4×C73—21no—
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—21no—
693C2×C4×C73—21no—
694C2×C4×C73—21no—
695C2×C4×C73—44no—
696C2×C4×C73—44no—
697C2×C4×C73—44no—
698C2×C4×C73C22×D412yes—
699C2×C4×C73C2×#4112yes—
700C2×C4×C73C2×#4112yes—
701C22⋊D73—28no—
702C22⋊D73—28no—
703C22⋊D73—44no—
704C22⋊D73—44no—
705C22⋊D73—44no—
706C22⋊D73—44no—
707C22⋊D73—44no—
708C22⋊D73—44no—
709C2×Dic73—28no—
710C2×Dic73—28no—
711C2×Dic73—21no—
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—28no—
726C2×Dic73—28no—
727C2×Dic73—28no—
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—44no—
747C2×Dic73—44no—
748C2×Dic73—44no—
749C2×Dic73—44no—
750C2×Dic73—44no—
751C2×Dic73C22×D412yes—
752C2×Dic73C22×D412yes—
753C2×Dic73C22×D412yes—
754C2×Dic73C22×D412yes—
755C2×Dic73C2×#4112yes—
756C2×Dic73C2×#4112yes—
757C2×Dic73C2×#4112yes—
758C2×Dic73C2×#4112yes—
759C2×Dic73C2×#4112yes—
760C2×Dic73H(5,𝔽2)12yes—
761D292—44no—
762C4×D73—28no—
763C4×D73—44no—
764C4×D73—44no—
765C4×D73—44no—
766Dic146—28no—
767Dic146—44no—
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—22no—
778C22×C73—22no—
779C22×C73—22no—
780C22×C73—22no—
781C22×C73—22no—
782C22×C73—22no—
783C22×C73—416no—
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—41no—
794C22×C73—41no—
795C22×C73—41no—
796C22×C73#52514yes—
797C22×C73C23×D411yescharacteristic
798C22×C73C22×#4111yescharacteristic
799C22×C73C22×#4111yescharacteristic
800C22×C73C22×#4111yescharacteristic
801C22×C73C22×#4111yescharacteristic
802C22×C73C2×H(5,𝔽2)11yescharacteristic
803C22×C73#58511yescharacteristic
804C2×D73—22no—
805C2×D73—22no—
806C2×D73—22no—
807C2×D73—41no—
808C2×D73—41no—
809C2×D73—41no—
810C2×D73—41no—
811C2×D73—41no—
812C2×D73—41no—
813C2×D73—41no—
814C2×D73—41no—
815C2×D73—41no—
816C2×D73—41no—
817C2×D73—41no—
818C4×C73—22no—
819C4×C73—22no—
820C4×C73—22no—
821C4×C73—41no—
822C4×C73—41no—
823C4×C73—41no—
824C4×C73—41no—
825C4×C73—41no—
826C4×C73—41no—
827C4×C73—41no—
828C4×C73—41no—
829Dic73—22no—
830Dic73—22no—
831Dic73—22no—
832Dic73—22no—
833Dic73—22no—
834Dic73—22no—
835Dic73—22no—
836Dic73—41no—
837Dic73—41no—
838Dic73—41no—
839Dic73—41no—
840Dic73—41no—
841Dic73—41no—
842Dic73#54614yes—
843#34732—731nomaximal, Sylow
844C2×C73—24no—
845C2×C73—42no—
846C2×C73—42no—
847C2×C73—42no—
848C2×C73C2×#52511yescharacteristic
849C2×C73#344411yescharacteristic
850C2×C73#346011yescharacteristic
851C2×C73C2×#54611yescharacteristic
852C2×C73D4×#4111yescharacteristic
853C2×C73#347511yescharacteristic
854C2×C73#348111yescharacteristic
855D73—42no—
856D73—81no—
857C2×#525—731no—
858C2×C4×#41—731no—
859#2477—731no—
860#2476—731no—
861#2471—731no—
862#2470—731no—
863#2465—731no—
864#2464—731no—
865#2458—731no—
866#2457—731no—
867#2450—731no—
868#2444—731no—
869#2438—731no—
870#2430—731no—
871#2424—731no—
872#2418D7311yescharacteristic, complemented
873#2411—731no—
874#2404—731no—
875#2398—731no—
876#2396—731no—
877#2392—731no—
878#2388—731no—
879C4×#123—731no—
880C4×#123—731no—
881C4×#121—731no—
882C4×#121—731no—
883C4×#120—731no—
884#2297—731no—
885#2290—731no—
886#2290—731no—
887C2×C4×C22⋊C4—731no—
888C73#3473211yescharacteristic, complemented, Sylow
889C22×#41—731no—
890C22×#41—731no—
891C24×C4—731no—
892#525—1468no—
893C2×#123—731no—
894C2×#123—731no—
895C2×#123—731no—
896C2×#123C2×D7311yescharacteristic
897C2×C22⋊Q8—731no—
898C2×C22⋊Q8—731no—
899C2×#121—731no—
900C2×#121—731no—
901C2×#121—731no—
902C2×#121—731no—
903C2×#120—731no—
904C2×#120—731no—
905C2×#120C2×D7311yescharacteristic
906C4×#41—1468no—
907C2×C4×Q8—731no—
908C2×C4×Q8—731no—
909C2×C4×D4—731no—
910C2×C4×D4—731no—
911C2×C4×D4—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×#117—731no—
922C2×#117—731no—
923C2×#117—731no—
924C2×#117—731no—
925C2×#117—731no—
926C22×C22⋊C4—731no—
927C22×C22⋊C4C2×D7311yescharacteristic
928C22×C42—731no—
929C22×C42—731no—
930C22×C42—731no—
931C22×C42—731no—
932#400—731no—
933#400—731no—
934#400—731no—
935#399C2×D7311yescharacteristic
936#398—731no—
937#398—731no—
938#398—731no—
939#397—731no—
940#397—731no—
941#397C2×D7311yescharacteristic
942#396—731no—
943#396—731no—
944#396—731no—
945#396—731no—
946#395—731no—
947#395—731no—
948#394—731no—
949#394—731no—
950#394—731no—
951#394—731no—
952#394—731no—
953#394—731no—
954#394C2×D7311yescharacteristic
955#394C2×D7311yescharacteristic
956#393—731no—
957#393—731no—
958#393—731no—
959#393—731no—
960#392—731no—
961#392—731no—
962#392—731no—
963#392—731no—
964#391—731no—
965#391—731no—
966#390—731no—
967#390—731no—
968#390—731no—
969#390—731no—
970#389—731no—
971#389—731no—
972#388—731no—
973#388—731no—
974#388—731no—
975#388—731no—
976#388—731no—
977#388—731no—
978#388—731no—
979#388—731no—
980#388—731no—
981#388—731no—
982#388C2×D7311yescharacteristic
983#388C2×D7311yescharacteristic
984#387—731no—
985#387—731no—
986#387—731no—
987#387—731no—
988#387—731no—
989#387—731no—
990#387—731no—
991#387—731no—
992#386—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#386—731no—
1003#386—731no—
1004#386—731no—
1005#386—731no—
1006#386—731no—
1007#386C2×D7311yescharacteristic
1008#386C2×D7311yescharacteristic
1009#385—731no—
1010#385—731no—
1011#385—731no—
1012#385—731no—
1013#385—731no—
1014#385—731no—
1015#385—731no—
1016#385—731no—
1017#385C2×D7311yescharacteristic
1018#381—731no—
1019#381—731no—
1020#380—731no—
1021#380C2×D7311yescharacteristic
1022#379C2×D7311yescharacteristic
1023C4×C4⋊C4—731no—
1024C4×C4⋊C4—731no—
1025C4×C4⋊C4—731no—
1026C4×C4⋊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⋊C4—731no—
1038C4×C22⋊C4—731no—
1039C4×C22⋊C4—731no—
1040C4×C22⋊C4—731no—
1041C4×C22⋊C4—731no—
1042C4×C22⋊C4—731no—
1043#376—731no—
1044C2×#95—731no—
1045C2×#95—731no—
1046C25C22×D7311yescharacteristic
1047C2×#41—2922no—
1048C2×#41—1464no—
1049C2×#41—1464no—
1050C2×#41—1464no—
1051C2×#41—1464no—
1052C2×#41—1464no—
1053C22×Q8—731no—
1054C22×Q8—731no—
1055C22×D4—731no—
1056C22×D4—731no—
1057C22×D4—731no—
1058C22×D4—731no—
1059C22×D4—731no—
1060C22×D4—731no—
1061C22×D4—731no—
1062C22×D4—731no—
1063C22×D4—731no—
1064C22×D4C22×D7311yescharacteristic
1065C22×D4C22×D7311yescharacteristic
1066C22×D4C22×D7311yescharacteristic
1067C23×C4—2922no—
1068C23×C4—731no—
1069C23×C4—731no—
1070C23×C4—731no—
1071C23×C4—731no—
1072C23×C4—731no—
1073C23×C4—731no—
1074C23×C4—731no—
1075C23×C4—731no—
1076C23×C4—731no—
1077C23×C4—731no—
1078C23×C4—731no—
1079C23×C4—731no—
1080C23×C4—731no—
1081C23×C4—731no—
1082C23×C4—1464no—
1083C23×C4—1464no—
1084C23×C4C22×D7311yescharacteristic
1085C23×C4C22×D7311yescharacteristic
1086C23×C4C22×D7311yescharacteristic
1087#123—24no—
1088#123—1464no—
1089#123—1464no—
1090#123—1464no—
1091C22⋊Q8—1464no—
1092C22⋊Q8—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×Q8—1464no—
1102C4×D4—24no—
1103C4×D4—2922no—
1104C4×D4—2922no—
1105C4×D4—738no—
1106C4×D4—1464no—
1107C4×D4—1464no—
1108C4×D4—1464no—
1109C4×D4—1464no—
1110C4×D4—1464no—
1111C4×D4—1464no—
1112C4×D4—1464no—
1113C4×D4—1464no—
1114#117—2922no—
1115#117—1464no—
1116#117—1464no—
1117#117—1464no—
1118#117—1464no—
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×C4⋊C4C22×D7311yescharacteristic
1142C2×C4⋊C4C22×D7311yescharacteristic
1143C2×C22⋊C4—24no—
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—1464no—
1175C2×C22⋊C4C22×D7311yescharacteristic
1176C2×C22⋊C4C22×D7311yescharacteristic
1177C2×C22⋊C4C22×D7311yescharacteristic
1178C2×C22⋊C4C22×D7311yescharacteristic
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—731no—
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—1464no—
1209C2×C42—1464no—
1210C2×C42—1464no—
1211C2×C42C22×D7311yescharacteristic
1212#95—731no—
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#95—731no—
1240#95—731no—
1241#95—731no—
1242#95C22×D7311yescharacteristic
1243#95C22×D7311yescharacteristic
1244#95C22×D7311yescharacteristic
1245#95C22×D7311yescharacteristic
1246#95C22×D7311yescharacteristic
1247#95C22×D7311yescharacteristic
1248C24—22no—
1249C24—22no—
1250C24—22no—
1251C24—22no—
1252C24—22no—
1253C24—41no—
1254C24—41no—
1255C24—731no—
1256C24—731no—
1257C24C23×D7311yescharacteristic
1258C24C23×D7311yescharacteristic
1259C24C23×D7311yescharacteristic
1260C24C23×D7311yescharacteristic
1261#41—29216no—
1262#41—14632no—
1263C2×Q8—2921no—
1264C2×Q8—1462no—
1265C2×Q8—1462no—
1266C2×Q8—1462no—
1267C2×Q8—1462no—
1268C2×Q8—1462no—
1269C2×D4—22no—
1270C2×D4—22no—
1271C2×D4—22no—
1272C2×D4—22no—
1273C2×D4—22no—
1274C2×D4—22no—
1275C2×D4—41no—
1276C2×D4—41no—
1277C2×D4—2921no—
1278C2×D4—2921no—
1279C2×D4—2921no—
1280C2×D4—2921no—
1281C2×D4—2921no—
1282C2×D4—2921no—
1283C2×D4—734no—
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—
1301C2×D4—1462no—
1302C2×D4—1462no—
1303C2×D4—1462no—
1304C2×D4D4×D7314yes—
1305C22×C4—22no—
1306C22×C4—22no—
1307C22×C4—22no—
1308C22×C4—22no—
1309C22×C4—22no—
1310C22×C4—22no—
1311C22×C4—41no—
1312C22×C4—41no—
1313C22×C4—41no—
1314C22×C4—2921no—
1315C22×C4—2921no—
1316C22×C4—2921no—
1317C22×C4—2921no—
1318C22×C4—2921no—
1319C22×C4—2921no—
1320C22×C4—29216no—
1321C22×C4—731no—
1322C22×C4—734no—
1323C22×C4—734no—
1324C22×C4—734no—
1325C22×C4—734no—
1326C22×C4—731no—
1327C22×C4—731no—
1328C22×C4—731no—
1329C22×C4—731no—
1330C22×C4—731no—
1331C22×C4—731no—
1332C22×C4—731no—
1333C22×C4—731no—
1334C22×C4—731no—
1335C22×C4—731no—
1336C22×C4—731no—
1337C22×C4—731no—
1338C22×C4—731no—
1339C22×C4—1462no—
1340C22×C4—1462no—
1341C22×C4—1462no—
1342C22×C4—1462no—
1343C22×C4—1462no—
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×C4—1462no—
1360C22×C4—1462no—
1361C22×C4—1462no—
1362C22×C4—1462no—
1363C22×C4—1462no—
1364C22×C4—1462no—
1365C22×C4—1462no—
1366C22×C4—1462no—
1367C22×C4—1462no—
1368C22×C4—1462no—
1369C22×C4—1462no—
1370C22×C4—1462no—
1371C22×C4C23×D7311yescharacteristic
1372C22×C4C23×D7311yescharacteristic
1373C22×C4C23×D7311yescharacteristic
1374C22×C4C23×D7311yescharacteristic
1375C22×C4C23×D7311yescharacteristic
1376C22×C4C23×D7311yescharacteristic
1377C22×C4C23×D7311yescharacteristic
1378C22×C4C23×D7311yescharacteristic
1379C22×C4C23×D7311yescharacteristic
1380C22×C4C23×D7311yescharacteristic
1381C22×C4C23×D7311yescharacteristic
1382C4⋊C4—22no—
1383C4⋊C4—22no—
1384C4⋊C4—22no—
1385C4⋊C4—41no—
1386C4⋊C4—41no—
1387C4⋊C4—2921no—
1388C4⋊C4—2921no—
1389C4⋊C4—2921no—
1390C4⋊C4—2921no—
1391C4⋊C4—734no—
1392C4⋊C4—1462no—
1393C4⋊C4—1462no—
1394C4⋊C4—1462no—
1395C4⋊C4—1462no—
1396C4⋊C4—1462no—
1397C4⋊C4—1462no—
1398C4⋊C4—1462no—
1399C4⋊C4—1462no—
1400C4⋊C4—1462no—
1401C4⋊C4—1462no—
1402C4⋊C4—1462no—
1403C4⋊C4—1462no—
1404C4⋊C4—1462no—
1405C4⋊C4—1462no—
1406C22⋊C4—22no—
1407C22⋊C4—22no—
1408C22⋊C4—22no—
1409C22⋊C4—22no—
1410C22⋊C4—22no—
1411C22⋊C4—22no—
1412C22⋊C4—22no—
1413C22⋊C4—22no—
1414C22⋊C4—22no—
1415C22⋊C4—22no—
1416C22⋊C4—22no—
1417C22⋊C4—22no—
1418C22⋊C4—41no—
1419C22⋊C4—41no—
1420C22⋊C4—41no—
1421C22⋊C4—2921no—
1422C22⋊C4—2921no—
1423C22⋊C4—2921no—
1424C22⋊C4—2921no—
1425C22⋊C4—2921no—
1426C22⋊C4—2921no—
1427C22⋊C4—2921no—
1428C22⋊C4—2921no—
1429C22⋊C4—734no—
1430C22⋊C4—734no—
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—1462no—
1446C22⋊C4—1462no—
1447C22⋊C4—1462no—
1448C22⋊C4—1462no—
1449C22⋊C4—1462no—
1450C22⋊C4—1462no—
1451C22⋊C4#1192402714yescomplemented
1452C42—22no—
1453C42—2921no—
1454C42—2921no—
1455C42—734no—
1456C42—1462no—
1457C42—1462no—
1458C42—1462no—
1459C42—1462no—
1460C42—1462no—
1461C42—1462no—
1462C42—1462no—
1463C42—1462no—
1464C42—1462no—
1465C42—1462no—
1466C42—1462no—
1467C42—1462no—
1468C42—1462no—
1469C23—21no—
1470C23—21no—
1471C23—21no—
1472C23—21no—
1473C23—28no—
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—21no—
1490C23—21no—
1491C23—21no—
1492C23—44no—
1493C23—44no—
1494C23—44no—
1495C23—44no—
1496C23—44no—
1497C23—44no—
1498C23—732no—
1499C23—1461no—
1500C23—1461no—
1501C23—1461no—
1502C23—1461no—
1503C23—1461no—
1504C23—1461no—
1505C23—1461no—
1506C23—1461no—
1507C23—1461no—
1508C23—1461no—
1509C23—1461no—
1510C23—1461no—
1511C23—1461no—
1512C23C2×D4×D7312yes—
1513C23C2×D4×D7312yes—
1514C23#41×D7312yes—
1515C23#41×D7312yes—
1516C23#41×D7312yes—
1517C23C2×#1192402712yes—
1518C23C24×D7311yescharacteristic
1519Q8—2924no—
1520Q8—1468no—
1521D4—28no—
1522D4—44no—
1523D4—44no—
1524D4—2924no—
1525D4—2924no—
1526D4—2924no—
1527D4—2924no—
1528D4—2924no—
1529D4—2924no—
1530D4—2924no—
1531D4—1468no—
1532D4—1468no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
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—21no—
1558C2×C4—21no—
1559C2×C4—21no—
1560C2×C4—21no—
1561C2×C4—21no—
1562C2×C4—21no—
1563C2×C4—44no—
1564C2×C4—44no—
1565C2×C4—44no—
1566C2×C4—2924no—
1567C2×C4—2924no—
1568C2×C4—2924no—
1569C2×C4—2924no—
1570C2×C4—2924no—
1571C2×C4—2924no—
1572C2×C4—2924no—
1573C2×C4—2924no—
1574C2×C4—732no—
1575C2×C4—732no—
1576C2×C4—732no—
1577C2×C4—732no—
1578C2×C4—732no—
1579C2×C4—732no—
1580C2×C4—732no—
1581C2×C4—732no—
1582C2×C4—732no—
1583C2×C4—732no—
1584C2×C4—1468no—
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—1468no—
1604C2×C4—1468no—
1605C2×C4—1468no—
1606C2×C4—1468no—
1607C2×C4—1461no—
1608C2×C4—1461no—
1609C2×C4—1461no—
1610C2×C4—1461no—
1611C2×C4—1461no—
1612C2×C4—1461no—
1613C2×C4—1461no—
1614C2×C4—1461no—
1615C2×C4—1461no—
1616C2×C4—1461no—
1617C2×C4—1461no—
1618C2×C4—1461no—
1619C2×C4—1461no—
1620C2×C4—1461no—
1621C2×C4—1468no—
1622C2×C4C2×D4×D7312yes—
1623C2×C4C2×#1192402712yes—
1624C2×C4C2×#1192402712yes—
1625C22—22no—
1626C22—22no—
1627C22—22no—
1628C22—22no—
1629C22—22no—
1630C22—22no—
1631C22—22no—
1632C22—22no—
1633C22—22no—
1634C22—22no—
1635C22—22no—
1636C22—22no—
1637C22—22no—
1638C22—22no—
1639C22—22no—
1640C22—416no—
1641C22—41no—
1642C22—41no—
1643C22—41no—
1644C22—41no—
1645C22—41no—
1646C22—41no—
1647C22—41no—
1648C22—41no—
1649C22—41no—
1650C22—41no—
1651C22—41no—
1652C22—41no—
1653C22—2921no—
1654C22—2921no—
1655C22—2921no—
1656C22—2921no—
1657C22—2921no—
1658C22—2921no—
1659C22—2921no—
1660C22—2921no—
1661C22—2921no—
1662C22—2921no—
1663C22—2921no—
1664C22—1462no—
1665C22—1462no—
1666C22—1462no—
1667C22#1798909514yes—
1668C22C22×D4×D7311yescharacteristic
1669C22C2×#41×D7311yescharacteristic
1670C22C2×#41×D7311yescharacteristic
1671C22C2×#41×D7311yescharacteristic
1672C22C22×#1192402711yescharacteristic
1673C22H(5,𝔽2)×D7311yescharacteristic
1674C22#1798942211yescharacteristic
1675C4—22no—
1676C4—22no—
1677C4—22no—
1678C4—41no—
1679C4—41no—
1680C4—41no—
1681C4—41no—
1682C4—41no—
1683C4—41no—
1684C4—41no—
1685C4—41no—
1686C4—2921no—
1687C4—2921no—
1688C4—2921no—
1689C4—2921no—
1690C4—2921no—
1691C4—2921no—
1692C4—734no—
1693C4—1462no—
1694C4—1462no—
1695C4—1462no—
1696C4—1462no—
1697C4—1462no—
1698C4—1462no—
1699C4—1462no—
1700C2—24no—
1701C2—42no—
1702C2—42no—
1703C2—42no—
1704C2—2922no—
1705C2—5841no—
1706C2C2×#1798909511yescharacteristic
1707C2#2262322311yescharacteristic
1708C2#2262335011yescharacteristic
1709C2#546×D7311yescharacteristic
1710C2D4×#1192402711yescharacteristic
1711C2#2262348611yescharacteristic
1712C2#2262353611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutator, socle, cosocleC23×C73C25
FittingC73×#2418C2
hypercenter#2418D73
hypocenterC73#34732
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2418

Complements

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

NH ≅ G/Ntype
1. C2×#17989093C2semidirect
2. C2×C4×#11924027C2semidirect
3. #22614125C2semidirect
4. #22614110C2semidirect
5. #22614035C2semidirect
6. #22614020C2semidirect
7. #22613949C2semidirect
8. #22613934C2semidirect
9. #22613850C2semidirect
10. #22613835C2semidirect
11. #22613757C2semidirect
12. #22613675C2semidirect
13. #22613613C2semidirect
14. #22613539C2semidirect
15. #22613467C2semidirect
16. #22613318C2semidirect
17. #22613247C2semidirect
18. #22613216C2semidirect
19. #22613200C2semidirect
20. #22613174C2semidirect
21. #22613145C2semidirect
22. #123×Dic73C2semidirect
23. #22612450C2semidirect
24. #22612443C2semidirect
25. #22612437C2semidirect
26. #22612430C2semidirect
27. #22612416C2semidirect
28. #22612373C2semidirect
29. #22612371C2semidirect
30. C2×C22⋊C4×Dic73C2semidirect
31. C73×#2418C2semidirect
48. C2×C4×Dic146C22semidirect
49. C2×#14556556C22semidirect
52. C2×#14556553C22semidirect
54. C2×C4×C22⋊D73C22semidirect
60. C2×#14556551C22semidirect
61. C2×#14556549C22semidirect
64. C2×#14556547C22semidirect
65. C2×#14556547C22semidirect
69. C22×C4×Dic73C22semidirect
70. C2×C42×D73C22semidirect
71. #17988528C22semidirect
72. #17988528C22semidirect
73. #17988525C22semidirect
74. #17988521C22semidirect
75. #17988518C22semidirect
76. #17988518C22semidirect
77. #17988515C22semidirect
78. #17988513C22semidirect
82. #17988509C22semidirect
83. #17988508C22semidirect
84. #17988507C22semidirect
85. #17988503C22semidirect
90. #17988502C22semidirect
91. #17988500C22semidirect
92. #17988500C22semidirect
96. #17988496C22semidirect
99. #17988491C22semidirect
100. #17988491C22semidirect
101. #17988488C22semidirect
105. #17988483C22semidirect
106. #17988482C22semidirect
107. #17988481C22semidirect
111. #17988478C22semidirect
112. #17988477C22semidirect
113. #17988477C22semidirect
114. #17988476C22semidirect
115. #17988476C22semidirect
116. #17988475C22semidirect
117. #17988473C22semidirect
118. #17988473C22semidirect
119. #17988472C22semidirect
120. #17988471C22semidirect
121. #17988470C22semidirect
122. #17988470C22semidirect
123. #17988470C22semidirect
124. #17988469C22semidirect
129. #17988466C22semidirect
130. #17988465C22semidirect
136. #17988464C22semidirect
140. #17988462C22semidirect
141. #17988461C22semidirect
147. #17988458C22semidirect
148. #17988450C22semidirect
150. #17988446C22semidirect
151. C4⋊C4×Dic73C22semidirect
152. C4⋊C4×Dic73C22semidirect
153. C4⋊C4×Dic73C22semidirect
154. #17988438C22semidirect
166. C22⋊C4×Dic73C22semidirect
167. #17988434C22semidirect
168. #17988434C22semidirect
169. #17988434C22semidirect
170. #17988434C22semidirect
171. #17988432C22semidirect
237. D4×Dic73D4semidirect
427. C2×C22⋊D73#41semidirect
457. C22×Dic73#41semidirect
458. C22×Dic73#41semidirect
610. C22⋊C4×C73#41semidirect
872. #2418D73semidirect
888. C73#34732semidirect
1451. C22⋊C4#11924027semidirect

Maximal subgroups

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

subgroupindex
C2×#179890932
C2×C4×#119240272
#226141252
#226141102
#226140352
#226140202
#226139492
#226139342
#226138502
#226138352
#226137572
#226136752
#226136132
#226135392
#226134672
#226133182
#226132472
#226132162
#226132002
#226131742
#226131452
#123×Dic732
#226124502
#226124432
#226124372
#226124302
#226124162
#226123732
#226123712
C2×C22⋊C4×Dic732
C73×#24182
#3473273