Finite Group Databasebeta

← #33245060

Subgroups — #33245060

Order 18688.

2650 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989169C211yesmaximal, characteristic
2#22612740C211yesmaximal, characteristic, complemented
3#22612739C211yesmaximal, characteristic, complemented
4#22612722C211yesmaximal, characteristic, complemented
5#22612721C211yesmaximal, characteristic, complemented
6#22612709C211yesmaximal, characteristic, complemented
7#22612708C211yesmaximal, characteristic, complemented
8#22612690C211yesmaximal, characteristic, complemented
9#22612658C211yesmaximal, characteristic, complemented
10#22612633C211yesmaximal, characteristic, complemented
11#22612590C211yesmaximal, characteristic, complemented
12#22612587C211yesmaximal, characteristic, complemented
13#22612561C211yesmaximal, characteristic, complemented
14#22612560C211yesmaximal, characteristic, complemented
15#22612525C211yesmaximal, characteristic, complemented
16#22612485C211yesmaximal, characteristic, complemented
17#22612481C211yesmaximal, characteristic, complemented
18#22612478C211yesmaximal, characteristic, complemented
19#22612472C211yesmaximal, characteristic, complemented
20#22612465C211yesmaximal, characteristic, complemented
21#22612456C211yesmaximal, characteristic, complemented
22#22612448C211yesmaximal, characteristic, complemented
23#22612447C211yesmaximal, characteristic, complemented
24#121×Dic73C211yesmaximal, characteristic, complemented
25#22612441C211yesmaximal, characteristic, complemented
26#22612436C211yesmaximal, characteristic, complemented
27#22612436C211yesmaximal, characteristic, complemented
28C4×#14556551C211yesmaximal, characteristic, complemented
29C4×#14556551C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D73C211yesmaximal, characteristic, complemented
31C73×#2333C211yesmaximal, characteristic, complemented
32C23×C4×D73C2211yescharacteristic
33#17989169C4116yescomplemented
34C2×#14556586C2211yescharacteristic
35C2×#14556584C2211yescharacteristic
36C2×#14556578C2211yescharacteristic
37C2×#14556577C2211yescharacteristic
38C2×#14556574C2211yescharacteristic
39C2×#14556572C2211yescharacteristic
40C2×#14556569C2211yescharacteristic
41C2×#14556563C2211yescharacteristic
42C2×#14556562C2211yescharacteristic
43C2×#14556559C2211yescharacteristic
44C2×#14556559C2211yescharacteristic
45C2×#14556556C2211yescharacteristic, complemented
46C2×D4×Dic73C2211yescharacteristic
47C2×D4×Dic73C2211yescharacteristic
48C2×D4×Dic73C2211yescharacteristic, complemented
49C2×C4×C22⋊D73C2211yescharacteristic
50C2×C4×C22⋊D73C2211yescharacteristic
51C2×#14556551C2211yescharacteristic
52C2×#14556551C2211yescharacteristic
53C2×#14556551C2211yescharacteristic
54C2×#14556551C2211yescharacteristic
55C2×#14556551C2211yescharacteristic
56C2×#14556551C2211yescharacteristic
57C2×C22⋊C4×D73C2211yescharacteristic
58C2×C22⋊C4×D73C2211yescharacteristic
59C22×C4×Dic73C2211yescharacteristic, complemented
60C22×C4×Dic73C2211yescharacteristic, complemented
61C2×C42×D73C2211yescharacteristic
62C2×C42×D73C2211yescharacteristic
63#17988493C2211yescharacteristic, complemented
64#17988491C2211yescharacteristic, complemented
65#17988491C2211yescharacteristic, complemented
66#17988490C2211yescharacteristic
67#17988487C2211yescharacteristic
68#17988487C2211yescharacteristic
69#17988486C2211yescharacteristic, complemented
70#17988485C2211yescharacteristic, complemented
71#17988484C2211yescharacteristic, complemented
72#17988484C2211yescharacteristic, complemented
73#17988481C2211yescharacteristic
74#17988481C2211yescharacteristic
75#17988481C2211yescharacteristic
76#17988481C2211yescharacteristic, complemented
77#17988481C2211yescharacteristic, complemented
78#17988481C2211yescharacteristic, complemented
79#17988480C2211yescharacteristic
80#17988480C2211yescharacteristic, complemented
81#17988479C2211yescharacteristic
82#17988479C2211yescharacteristic
83#17988478C2211yescharacteristic
84#17988478C2211yescharacteristic
85#17988477C2211yescharacteristic
86#17988477C2211yescharacteristic
87#17988476C2211yescharacteristic
88#17988476C2211yescharacteristic
89#17988475C2211yescharacteristic
90#17988475C2211yescharacteristic
91#17988475C2211yescharacteristic
92#17988475C2211yescharacteristic, complemented
93#17988475C2211yescharacteristic, complemented
94#17988475C2211yescharacteristic, complemented
95#17988474C2211yescharacteristic, complemented
96#17988474C2211yescharacteristic, complemented
97#17988474C2211yescharacteristic, complemented
98#17988472C2211yescharacteristic, complemented
99#17988471C2211yescharacteristic, complemented
100#17988471C2211yescharacteristic, complemented
101#17988470C2211yescharacteristic, complemented
102#17988469C2211yescharacteristic, complemented
103#17988469C2211yescharacteristic, complemented
104#17988468C2211yescharacteristic, complemented
105#17988467C2211yescharacteristic
106#17988467C2211yescharacteristic, complemented
107#17988466C2211yescharacteristic
108#17988464C2211yescharacteristic
109#17988463C2211yescharacteristic
110#17988463C2211yescharacteristic
111#17988463C2211yescharacteristic
112#17988463C2211yescharacteristic
113#17988463C2211yescharacteristic
114#17988463C2211yescharacteristic
115#17988461C2211yescharacteristic
116#17988461C2211yescharacteristic
117#17988461C2211yescharacteristic
118#17988461C2211yescharacteristic
119#17988461C2211yescharacteristic
120#17988460C2211yescharacteristic
121#17988460C2211yescharacteristic
122#17988460C2211yescharacteristic, complemented
123#17988459C2211yescharacteristic, complemented
124#17988458C2211yescharacteristic
125#17988454C2211yescharacteristic, complemented
126#17988454C2211yescharacteristic, complemented
127#17988452C2211yescharacteristic, complemented
128#17988451C2211yescharacteristic, complemented
129#17988448C2211yescharacteristic, complemented
130#17988447C2211yescharacteristic, complemented
131#17988446C2211yescharacteristic
132#17988445C2211yescharacteristic, complemented
133#17988444C2211yescharacteristic
134#17988442C2211yescharacteristic
135#17988442C2211yescharacteristic
136C4⋊C4×Dic73C2211yescharacteristic, complemented
137C4⋊C4×Dic73C2211yescharacteristic, complemented
138C4×#11924007C2211yescharacteristic, complemented
139C4×#11924007C2211yescharacteristic, complemented
140#17988438C2211yescharacteristic, complemented
141#17988438C2211yescharacteristic, complemented
142#17988438C2211yescharacteristic, complemented
143#17988438C2211yescharacteristic, complemented
144#17988438C2211yescharacteristic, complemented
145#17988438C2211yescharacteristic, complemented
146C22⋊C4×Dic73C2211yescharacteristic
147C22⋊C4×Dic73C2211yescharacteristic
148C22⋊C4×Dic73C2211yescharacteristic
149C22⋊C4×Dic73C2211yescharacteristic
150C22⋊C4×Dic73C2211yescharacteristic, complemented
151C22⋊C4×Dic73C2211yescharacteristic, complemented
152C22⋊C4×Dic73C2211yescharacteristic, complemented
153C22⋊C4×Dic73C2211yescharacteristic, complemented
154C22⋊C4×Dic73C2211yescharacteristic, complemented
155C22⋊C4×Dic73C2211yescharacteristic, complemented
156C4×#11924005C2211yescharacteristic
157C4×#11924005C2211yescharacteristic
158C4×#11924005C2211yescharacteristic
159C4×#11924005C2211yescharacteristic
160C4×C22⋊Dic73C2211yescharacteristic
161#17988434C2211yescharacteristic
162#17988434C2211yescharacteristic
163#17988434C2211yescharacteristic
164#17988434C2211yescharacteristic
165#17988434C2211yescharacteristic
166#17988434C2211yescharacteristic
167#17988434C2211yescharacteristic
168#17988434C2211yescharacteristic
169#95×D73C2211yescharacteristic
170#95×D73C2211yescharacteristic
171C42×Dic73C2211yescharacteristic, complemented
172C42×Dic73C2211yescharacteristic, complemented
173C2×#121×C73C2211yescharacteristic
174#390×C73C2211yescharacteristic
175#390×C73C2211yescharacteristic, complemented
176#388×C73C2211yescharacteristic
177#388×C73C2211yescharacteristic, complemented
178#387×C73C2211yescharacteristic, complemented
179#387×C73C2211yescharacteristic, complemented
180#386×C73C2211yescharacteristic
181#386×C73C2211yescharacteristic
182#386×C73C2211yescharacteristic
183#386×C73C2211yescharacteristic, complemented
184#381×C73C2211yescharacteristic, complemented
185C4×C22⋊C4×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic, complemented
187C4×C22⋊C4×C73C2211yescharacteristic, complemented
188C24×D73C2311yescharacteristic
189C22×Dic146C2311yescharacteristic
190C22×C22⋊D73C2311yescharacteristic
191C22×C22⋊D73C2311yescharacteristic
192C22×C22⋊D73C2311yescharacteristic
193C22×C22⋊D73C2311yescharacteristic
194C23×Dic73C2311yescharacteristic
195C23×Dic73C2311yescharacteristic
196C23×Dic73C2311yescharacteristic
197C23×Dic73C2311yescharacteristic
198C23×Dic73C2311yescharacteristic
199C22×C4×D73—24no—
200C22×C4×D73—42no—
201C22×C4×D73—42no—
202C22×C4×D73C2311yescharacteristic
203C22×C4×D73C2311yescharacteristic
204C22×C4×D73C2311yescharacteristic
205C22×C4×D73C2311yescharacteristic
206C22×C4×D73C2311yescharacteristic
207C22×C4×D73C2311yescharacteristic
208C22×C4×D73C2311yescharacteristic
209C22×C4×D73C2311yescharacteristic
210#14556586C2×C418yescomplemented
211#14556584C2×C418yescomplemented
212#14556578C2×C418yescomplemented
213#14556577C2×C418yescomplemented
214#14556574C2×C418yescomplemented
215#14556572C2×C418yescomplemented
216#14556569C2×C418yescomplemented
217#14556563C2×C418yescomplemented
218#14556562C2×C418yescomplemented
219#14556559C2×C418yescomplemented
220#14556559C2×C418yescomplemented
221#14556556—42no—
222D4×Dic73—42no—
223D4×Dic73—42no—
224D4×Dic73—42no—
225C4×C22⋊D73—24no—
226C4×C22⋊D73C2×C418yescomplemented
227#14556551—24no—
228#14556551—24no—
229#14556551—24no—
230#14556551—42no—
231#14556551—42no—
232#14556551C2×C418yescomplemented
233C2×C4⋊Dic73C2311yescharacteristic
234C2×C4⋊Dic73C2311yescharacteristic
235C2×C4⋊Dic73C2311yescharacteristic
236C2×C4⋊Dic73C2311yescharacteristic
237C2×C4⋊Dic73C2311yescharacteristic
238C2×#11924007C2311yescharacteristic
239C2×#11924007C2311yescharacteristic
240C2×#11924007C2311yescharacteristic
241C2×#11924007C2311yescharacteristic
242C2×#11924007C2311yescharacteristic
243C2×#11924007C2311yescharacteristic
244C2×#11924007C2311yescharacteristic
245C2×#11924007C2311yescharacteristic
246C2×#11924007C2311yescharacteristic
247C2×#11924007C2311yescharacteristic
248C2×#11924007C2311yescharacteristic
249C2×#11924007C2311yescharacteristic
250C2×#11924007C2311yescharacteristic
251C2×#11924007C2311yescharacteristic
252C2×C22⋊Dic73C2311yescharacteristic
253C2×C22⋊Dic73C2311yescharacteristic
254C2×C22⋊Dic73C2311yescharacteristic
255C2×C22⋊Dic73C2311yescharacteristic
256C2×C22⋊Dic73C2311yescharacteristic
257C2×C22⋊Dic73C2311yescharacteristic
258C2×C22⋊Dic73C2311yescharacteristic
259C2×C22⋊Dic73C2311yescharacteristic
260C2×C22⋊Dic73C2311yescharacteristic
261C2×C22⋊Dic73C2311yescharacteristic
262C2×C22⋊Dic73C2311yescharacteristic
263C2×C22⋊Dic73C2311yescharacteristic
264C2×C22⋊Dic73C2311yescharacteristic
265C2×C22⋊Dic73C2311yescharacteristic
266C2×#11924005C2311yescharacteristic
267C2×#11924005C2311yescharacteristic
268C2×#11924005C2311yescharacteristic
269C2×#11924005C2311yescharacteristic
270C2×#11924005C2311yescharacteristic
271C2×#11924005C2311yescharacteristic
272C2×#11924005C2311yescharacteristic
273C2×#11924005C2311yescharacteristic
274C2×#11924005C2311yescharacteristic
275C2×#11924005C2311yescharacteristic
276C2×#11924005C2311yescharacteristic
277C2×#11924005C2311yescharacteristic
278C2×#11924005C2311yescharacteristic
279C2×#11924005C2311yescharacteristic
280C2×#11924005C2311yescharacteristic
281C2×#11924005C2311yescharacteristic
282C22⋊C4×D73—24no—
283C22⋊C4×D73C2×C418yescomplemented
284C2×C4×Dic73—42no—
285C2×C4×Dic73—42no—
286C2×C4×Dic73C2311yescharacteristic
287C2×C4×Dic73C2311yescharacteristic
288C2×C4×Dic73C2311yescharacteristic
289C2×C4×Dic73C2311yescharacteristic
290C2×C4×Dic73C2311yescharacteristic
291C2×C4×Dic73C2311yescharacteristic
292C2×C4×Dic73C2311yescharacteristic
293C2×C4×Dic73C2311yescharacteristic
294C2×C4×Dic73C2311yescharacteristic
295C2×C4×Dic73C2311yescharacteristic
296C2×C4×Dic73C2311yescharacteristic
297C2×C4×Dic73C2311yescharacteristic
298C2×C4×Dic73C2311yescharacteristic
299C2×C4×Dic73C2311yescharacteristic
300C2×C4×Dic73C2311yescharacteristic
301C2×C4×Dic73C2311yescharacteristic
302C2×C4×Dic73C2311yescharacteristic
303C2×C4×Dic73C2311yescharacteristic
304C2×C4×Dic73C2311yescharacteristic
305C2×C4×Dic73C2311yescharacteristic
306C2×C4×Dic73C2311yescharacteristic
307C2×C4×Dic73C2311yescharacteristic
308C42×D73—42no—
309C42×D73—42no—
310#14556498C2311yescharacteristic
311#14556498C2311yescharacteristic
312#14556498C2311yescharacteristic
313#14556498C2311yescharacteristic
314#14556498C2311yescharacteristic
315#14556498C2311yescharacteristic
316#14556498C2311yescharacteristic
317#14556498C2311yescharacteristic
318#14556498C2311yescharacteristic
319#14556498C2311yescharacteristic
320#14556498C2311yescharacteristic
321#14556498C2311yescharacteristic
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
340C22×D4×C73C2311yescharacteristic
341C22×D4×C73C2311yescharacteristic
342C22×D4×C73C2311yescharacteristic
343C23×C4×C73C2311yescharacteristic
344C23×C4×C73C2311yescharacteristic
345C23×C4×C73C2311yescharacteristic
346#121×C73C2×C418yescomplemented
347C2×C4⋊C4×C73C2311yescharacteristic
348C2×C4⋊C4×C73C2311yescharacteristic
349C2×C4⋊C4×C73C2311yescharacteristic
350C2×C22⋊C4×C73C2311yescharacteristic
351C2×C22⋊C4×C73C2311yescharacteristic
352C2×C22⋊C4×C73C2311yescharacteristic
353C2×C22⋊C4×C73C2311yescharacteristic
354C2×C22⋊C4×C73C2311yescharacteristic
355C2×C22⋊C4×C73C2311yescharacteristic
356C2×C22⋊C4×C73C2311yescharacteristic
357C2×C22⋊C4×C73C2311yescharacteristic
358C2×C22⋊C4×C73C2311yescharacteristic
359C2×C22⋊C4×C73C2311yescharacteristic
360C2×C22⋊C4×C73C2311yescharacteristic
361C2×C22⋊C4×C73C2311yescharacteristic
362C2×C42×C73C2311yescharacteristic
363C2×C42×C73C2311yescharacteristic
364C2×C42×C73C2311yescharacteristic
365C2×C42×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376C23×D73—22no—
377C23×D73—22no—
378C23×D73—41no—
379C23×D73—41no—
380C23×D73—41no—
381C23×D73—41no—
382C23×D73C22×C414yes—
383C23×D73C2411yescharacteristic
384C23×D73C2411yescharacteristic
385C2×Dic146—41no—
386C2×Dic146—41no—
387C2×Dic146C22×C414yescomplemented
388C2×C22⋊D73—22no—
389C2×C22⋊D73—22no—
390C2×C22⋊D73—22no—
391C2×C22⋊D73—22no—
392C2×C22⋊D73—41no—
393C2×C22⋊D73—41no—
394C2×C22⋊D73—41no—
395C2×C22⋊D73—41no—
396C2×C22⋊D73C22×C414yes—
397C2×C22⋊D73C22×C414yes—
398C2×C22⋊D73C22×C414yes—
399C2×C22⋊D73C22×C414yes—
400C22×Dic73—22no—
401C22×Dic73—22no—
402C22×Dic73—22no—
403C22×Dic73—22no—
404C22×Dic73—22no—
405C22×Dic73—22no—
406C22×Dic73—22no—
407C22×Dic73—22no—
408C22×Dic73—22no—
409C22×Dic73—22no—
410C22×Dic73—41no—
411C22×Dic73—41no—
412C22×Dic73—41no—
413C22×Dic73—41no—
414C22×Dic73C22×C414yescomplemented
415C22×Dic73C2411yescharacteristic
416C22×Dic73C2411yescharacteristic
417C22×Dic73C2411yescharacteristic
418C22×Dic73C2411yescharacteristic
419C22×Dic73C2411yescharacteristic
420C22×Dic73C2411yescharacteristic
421C22×Dic73C2411yescharacteristic
422C22×Dic73C2411yescharacteristic
423C22×Dic73C2411yescharacteristic
424C22×Dic73C2411yescharacteristic
425C22×Dic73C2411yescharacteristic
426C22×Dic73C2411yescharacteristic
427C22×Dic73C2411yescharacteristic
428C22×Dic73C2411yescharacteristic
429C2×C4×D73—22no—
430C2×C4×D73—22no—
431C2×C4×D73—22no—
432C2×C4×D73—22no—
433C2×C4×D73—22no—
434C2×C4×D73—22no—
435C2×C4×D73—22no—
436C2×C4×D73—22no—
437C2×C4×D73—416no—
438C2×C4×D73—41no—
439C2×C4×D73—41no—
440C2×C4×D73—41no—
441C2×C4×D73—41no—
442C2×C4×D73—41no—
443C2×C4×D73—41no—
444C2×C4×D73—41no—
445C2×C4×D73—41no—
446C2×C4×D73—41no—
447C2×C4×D73—41no—
448C2×C4×D73—41no—
449C2×C4×D73—41no—
450C2×C4×D73C22×C414yes—
451C2×C4×D73C22×C414yes—
452C2×C4×D73#4114yes—
453C2×C4×D73#4114yes—
454C4⋊Dic73—41no—
455C4⋊Dic73—41no—
456C4⋊Dic73—41no—
457C4⋊Dic73—41no—
458C4⋊Dic73C22×C414yescomplemented
459#11924007—22no—
460#11924007—22no—
461#11924007—22no—
462#11924007—22no—
463#11924007—41no—
464#11924007—41no—
465#11924007—41no—
466#11924007—41no—
467#11924007—41no—
468#11924007—41no—
469#11924007C22×C414yescomplemented
470#11924007C22×C414yescomplemented
471#11924007C22×C414yescomplemented
472#11924007C22×C414yescomplemented
473C22⋊Dic73—22no—
474C22⋊Dic73—22no—
475C22⋊Dic73—41no—
476C22⋊Dic73—41no—
477C22⋊Dic73—41no—
478C22⋊Dic73—41no—
479C22⋊Dic73—41no—
480C22⋊Dic73—41no—
481C22⋊Dic73C22×C414yes—
482C22⋊Dic73C22×C414yes—
483C22⋊Dic73C22×C414yes—
484C22⋊Dic73C22×C414yescomplemented
485C22⋊Dic73C22×C414yescomplemented
486C22⋊Dic73C22×C414yescomplemented
487#11924005—22no—
488#11924005—22no—
489#11924005—22no—
490#11924005—22no—
491#11924005—22no—
492#11924005—22no—
493#11924005—41no—
494#11924005—41no—
495#11924005—41no—
496#11924005—41no—
497#11924005C22×C414yes—
498#11924005C22×C414yes—
499#11924005C22×C414yes—
500#11924005C22×C414yes—
501#11924005C22×C414yes—
502#11924005C22×C414yes—
503C4×Dic73—22no—
504C4×Dic73—22no—
505C4×Dic73—22no—
506C4×Dic73—22no—
507C4×Dic73—22no—
508C4×Dic73—22no—
509C4×Dic73—22no—
510C4×Dic73—22no—
511C4×Dic73—22no—
512C4×Dic73—22no—
513C4×Dic73—22no—
514C4×Dic73—22no—
515C4×Dic73—41no—
516C4×Dic73—41no—
517C4×Dic73—41no—
518C4×Dic73—41no—
519C4×Dic73—41no—
520C4×Dic73—41no—
521C4×Dic73—41no—
522C4×Dic73—41no—
523C4×Dic73C22×C414yescomplemented
524C4×Dic73C22×C414yescomplemented
525C24×C73C2411yescharacteristic
526C24×C73C2411yescharacteristic
527C24×C73C2411yescharacteristic
528C2×D4×C73—41no—
529C2×D4×C73—41no—
530C2×D4×C73—41no—
531C2×D4×C73—41no—
532C2×D4×C73—41no—
533C2×D4×C73—41no—
534C2×D4×C73C22×C414yes—
535C2×D4×C73C22×C414yes—
536C2×D4×C73C22×C414yescomplemented
537C22×C4×C73—22no—
538C22×C4×C73—22no—
539C22×C4×C73—41no—
540C22×C4×C73—41no—
541C22×C4×C73—41no—
542C22×C4×C73—41no—
543C22×C4×C73—41no—
544C22×C4×C73—41no—
545C22×C4×C73C22×C414yescomplemented
546C22×C4×C73C2411yescharacteristic
547C22×C4×C73C2411yescharacteristic
548C22×C4×C73C2411yescharacteristic
549C22×C4×C73C2411yescharacteristic
550C22×C4×C73C2411yescharacteristic
551C22×C4×C73C2411yescharacteristic
552C22×C4×C73C2411yescharacteristic
553C22×C4×C73C2411yescharacteristic
554C22×C4×C73C2411yescharacteristic
555C22×C4×C73C2411yescharacteristic
556C22×C4×C73C2411yescharacteristic
557C22×C4×C73C2411yescharacteristic
558C4⋊C4×C73—41no—
559C4⋊C4×C73—41no—
560C4⋊C4×C73C22×C414yescomplemented
561C22⋊C4×C73—22no—
562C22⋊C4×C73—22no—
563C22⋊C4×C73—22no—
564C22⋊C4×C73—22no—
565C22⋊C4×C73—41no—
566C22⋊C4×C73—41no—
567C22⋊C4×C73—41no—
568C22⋊C4×C73—41no—
569C22⋊C4×C73—41no—
570C22⋊C4×C73—41no—
571C22⋊C4×C73C22×C414yes—
572C22⋊C4×C73C22×C414yescomplemented
573C42×C73—41no—
574C42×C73—41no—
575C42×C73—41no—
576C42×C73—41no—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73—21no—
595C23×C73C23×C412yes—
596C23×C73C23×C412yes—
597C23×C73C23×C412yes—
598C23×C73C2511yescharacteristic
599C22×D73—21no—
600C22×D73—21no—
601C22×D73—21no—
602C22×D73—21no—
603C22×D73—21no—
604C22×D73—21no—
605C22×D73—21no—
606C22×D73—21no—
607C22×D73—21no—
608C22×D73—21no—
609C22×D73—28no—
610C22×D73—44no—
611C22×D73—44no—
612C22×D73—44no—
613C22×D73—44no—
614C22×D73—44no—
615C22×D73—44no—
616C22×D73C23×C412yes—
617C22×D73C23×C412yes—
618C22×D73C2×#4112yes—
619C22×D73C2×#4112yes—
620D4×C73—44no—
621D4×C73—44no—
622D4×C73—44no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—44no—
654C2×C4×C73—44no—
655C2×C4×C73—44no—
656C2×C4×C73C23×C412yes—
657C2×C4×C73C23×C412yes—
658C2×C4×C73C23×C412yes—
659C2×C4×C73C23×C412yes—
660C2×C4×C73C2×#4112yes—
661C2×C4×C73C2×#4112yes—
662C22⋊D73—28no—
663C22⋊D73—28no—
664C22⋊D73—44no—
665C22⋊D73—44no—
666C2×Dic73—21no—
667C2×Dic73—21no—
668C2×Dic73—21no—
669C2×Dic73—21no—
670C2×Dic73—21no—
671C2×Dic73—21no—
672C2×Dic73—21no—
673C2×Dic73—21no—
674C2×Dic73—21no—
675C2×Dic73—21no—
676C2×Dic73—21no—
677C2×Dic73—21no—
678C2×Dic73—21no—
679C2×Dic73—21no—
680C2×Dic73—21no—
681C2×Dic73—21no—
682C2×Dic73—21no—
683C2×Dic73—21no—
684C2×Dic73—21no—
685C2×Dic73—21no—
686C2×Dic73—21no—
687C2×Dic73—21no—
688C2×Dic73—21no—
689C2×Dic73—21no—
690C2×Dic73—21no—
691C2×Dic73—21no—
692C2×Dic73—21no—
693C2×Dic73—21no—
694C2×Dic73—21no—
695C2×Dic73—21no—
696C2×Dic73—21no—
697C2×Dic73—21no—
698C2×Dic73—44no—
699C2×Dic73—44no—
700C2×Dic73—44no—
701C2×Dic73—44no—
702C2×Dic73—44no—
703C2×Dic73C23×C412yes—
704C2×Dic73C23×C412yes—
705C2×Dic73C23×C412yes—
706C2×Dic73C23×C412yes—
707C2×Dic73C23×C412yes—
708C2×Dic73C23×C412yes—
709C2×Dic73C2×#4112yes—
710C2×Dic73C2×#4112yes—
711C2×Dic73H(5,𝔽2)12yes—
712C2×Dic73H(5,𝔽2)12yes—
713C4×D73—28no—
714C4×D73—44no—
715C4×D73—44no—
716C4×D73—44no—
717C4×D73—44no—
718C4×D73—44no—
719C4×D73—44no—
720C4×D73—44no—
721Dic146—44no—
722C22×C73—22no—
723C22×C73—22no—
724C22×C73—22no—
725C22×C73—22no—
726C22×C73—22no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—22no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73—41no—
735C22×C73—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73—41no—
740C22×C73—41no—
741C22×C73—41no—
742C22×C73—41no—
743C22×C73C24×C411yescharacteristic
744C22×C73C22×#4111yescharacteristic
745C22×C73C22×#4111yescharacteristic
746C22×C73C2×H(5,𝔽2)11yescharacteristic
747C22×C73C2×H(5,𝔽2)11yescharacteristic
748C22×C73#58511yescharacteristic
749C22×C73#58511yescharacteristic
750C2×D73—22no—
751C2×D73—22no—
752C2×D73—22no—
753C2×D73—22no—
754C2×D73—22no—
755C2×D73—22no—
756C2×D73—22no—
757C2×D73—22no—
758C2×D73—22no—
759C2×D73—416no—
760C2×D73—41no—
761C2×D73—41no—
762C2×D73—41no—
763C2×D73—41no—
764C2×D73C4×#4114yes—
765C4×C73—22no—
766C4×C73—22no—
767C4×C73—22no—
768C4×C73—22no—
769C4×C73—22no—
770C4×C73—22no—
771C4×C73—41no—
772C4×C73—41no—
773C4×C73—41no—
774C4×C73—41no—
775C4×C73—41no—
776C4×C73—41no—
777Dic73—22no—
778Dic73—22no—
779Dic73—22no—
780Dic73—22no—
781Dic73—22no—
782Dic73—22no—
783Dic73—22no—
784Dic73—41no—
785Dic73—41no—
786Dic73—41no—
787Dic73—41no—
788Dic73—41no—
789Dic73—41no—
790Dic73#53814yescomplemented
791C4×#538—731nomaximal, Sylow
792C2×C73—42no—
793C2×C73—42no—
794C2×C73—42no—
795C2×C73C2×C4×#4111yescharacteristic
796C2×C73C4×H(5,𝔽2)11yescharacteristic
797C2×C73C4×H(5,𝔽2)11yescharacteristic
798C2×C73C2×#53811yescharacteristic
799C2×C73#345511yescharacteristic
800C2×C73#345911yescharacteristic
801C2×C73#346011yescharacteristic
802D73—24no—
803D73—42no—
804C2×#538—731no—
805#2337—731no—
806#2337—731no—
807#2335—731no—
808#2335—731no—
809#2334—731no—
810#2334—731no—
811#2333—731no—
812#2333D7311yescharacteristic, complemented
813#2329—731no—
814#2325—731no—
815#2321—731no—
816#2321—731no—
817#2318—731no—
818#2318—731no—
819#2312—731no—
820C4×#126—731no—
821C4×#126—731no—
822C4×#124—731no—
823C4×#124—731no—
824C4×C22⋊Q8—731no—
825C4×#123—731no—
826C4×#123—731no—
827C4×#121—731no—
828C4×#121—731no—
829C4×#121—731no—
830C4×#120—731no—
831C4×#120—731no—
832C42×D4—731no—
833C42×D4—731no—
834C2×C4×C22⋊C4—731no—
835C73C4×#53811yescharacteristic, complemented, Sylow
836C24×C4—731no—
837#538—7316no—
838C2×#126—731no—
839C2×#126—731no—
840C2×#124—731no—
841C2×#124—731no—
842C2×#123—731no—
843C2×#123—731no—
844C2×C22⋊Q8—731no—
845C2×#121—731no—
846C2×#121—731no—
847C2×#121C2×D7311yescharacteristic
848C2×#120—731no—
849C2×#120—731no—
850C2×C4×Q8—731no—
851C2×C4×D4—731no—
852C2×C4×D4—731no—
853C2×C4×D4—731no—
854C2×C4×D4—731no—
855C2×C4×D4—731no—
856C2×C4×D4—731no—
857C2×C4×D4—731no—
858C2×C4×D4—731no—
859C2×C4×D4—731no—
860C2×C4×D4—731no—
861C2×C4×D4—731no—
862C22×C22⋊C4—731no—
863C22×C22⋊C4—731no—
864C22×C42—731no—
865C22×C42—731no—
866C22×C42—731no—
867C22×C42—731no—
868#391—731no—
869#391—731no—
870#391—731no—
871#390—731no—
872#390—731no—
873#390—731no—
874#390C2×D7311yescharacteristic
875#390C2×D7311yescharacteristic, complemented
876#389—731no—
877#389—731no—
878#389—731no—
879#389—731no—
880#388—731no—
881#388—731no—
882#388—731no—
883#388—731no—
884#388—731no—
885#388—731no—
886#388—731no—
887#388—731no—
888#388—731no—
889#388—731no—
890#388—731no—
891#388—731no—
892#388—731no—
893#388—731no—
894#388—731no—
895#388—731no—
896#388—731no—
897#388—731no—
898#388—731no—
899#388—731no—
900#388—731no—
901#388—731no—
902#388C2×D7311yescharacteristic
903#388C2×D7311yescharacteristic, complemented
904#387—731no—
905#387—731no—
906#387—731no—
907#387—731no—
908#387—731no—
909#387—731no—
910#387—731no—
911#387—731no—
912#387—731no—
913#387—731no—
914#387C2×D7311yescharacteristic, complemented
915#387C2×D7311yescharacteristic, complemented
916#386—731no—
917#386—731no—
918#386—731no—
919#386—731no—
920#386—731no—
921#386—731no—
922#386—731no—
923#386—731no—
924#386—731no—
925#386—731no—
926#386C2×D7311yescharacteristic
927#386C2×D7311yescharacteristic
928#386C2×D7311yescharacteristic
929#386C2×D7311yescharacteristic, complemented
930#385—731no—
931#385—731no—
932#385—731no—
933#385—731no—
934#385—731no—
935#385—731no—
936#385—731no—
937#385—731no—
938#385—731no—
939#385—731no—
940#383—731no—
941#383—731no—
942#382—731no—
943#382—731no—
944#381—731no—
945#381C2×D7311yescharacteristic, complemented
946#380—731no—
947#380—731no—
948#380—731no—
949#380—731no—
950#379—731no—
951#379—731no—
952C4×C4⋊C4—731no—
953C4×C4⋊C4—731no—
954C4×C4⋊C4—731no—
955C4×C4⋊C4—731no—
956C4×C4⋊C4—731no—
957C4×C4⋊C4—731no—
958C4×C4⋊C4—731no—
959C4×C4⋊C4—731no—
960C4×C4⋊C4—731no—
961C4×C4⋊C4—731no—
962C4×C22⋊C4—731no—
963C4×C22⋊C4—731no—
964C4×C22⋊C4—731no—
965C4×C22⋊C4—731no—
966C4×C22⋊C4—731no—
967C4×C22⋊C4—731no—
968C4×C22⋊C4—731no—
969C4×C22⋊C4—731no—
970C4×C22⋊C4—731no—
971C4×C22⋊C4—731no—
972C4×C22⋊C4—731no—
973C4×C22⋊C4—731no—
974C4×C22⋊C4—731no—
975C4×C22⋊C4—731no—
976C4×C22⋊C4—731no—
977C4×C22⋊C4—731no—
978C4×C22⋊C4—731no—
979C4×C22⋊C4—731no—
980C4×C22⋊C4—731no—
981C4×C22⋊C4—731no—
982C4×C22⋊C4—731no—
983C4×C22⋊C4—731no—
984C4×C22⋊C4—731no—
985C4×C22⋊C4C2×D7311yescharacteristic
986C4×C22⋊C4C2×D7311yescharacteristic, complemented
987C4×C22⋊C4C2×D7311yescharacteristic, complemented
988C2×#95—731no—
989C2×#95—731no—
990C43—731no—
991C43—731no—
992C25—731no—
993C22×Q8—731no—
994C22×D4—731no—
995C22×D4—731no—
996C22×D4—731no—
997C22×D4—731no—
998C22×D4C22×D7311yescharacteristic
999C22×D4C22×D7311yescharacteristic
1000C22×D4C22×D7311yescharacteristic
1001C23×C4—2922no—
1002C23×C4—2922no—
1003C23×C4—731no—
1004C23×C4—731no—
1005C23×C4—731no—
1006C23×C4—731no—
1007C23×C4—731no—
1008C23×C4—731no—
1009C23×C4—731no—
1010C23×C4—731no—
1011C23×C4—731no—
1012C23×C4—731no—
1013C23×C4—731no—
1014C23×C4—731no—
1015C23×C4—731no—
1016C23×C4—1464no—
1017C23×C4C22×D7311yescharacteristic
1018C23×C4C22×D7311yescharacteristic
1019C23×C4C22×D7311yescharacteristic
1020#126—738no—
1021#126—738no—
1022#124—738no—
1023#124—738no—
1024#123—738no—
1025#123—738no—
1026C22⋊Q8—738no—
1027#121—738no—
1028#121—738no—
1029#121C4×D7318yescomplemented
1030#120—738no—
1031#120—738no—
1032C4×Q8—2922no—
1033C4×D4—2922no—
1034C4×D4—2922no—
1035C4×D4—2922no—
1036C4×D4—2922no—
1037C4×D4—2922no—
1038C4×D4—738no—
1039C4×D4—738no—
1040C4×D4—1464no—
1041C4×D4—1464no—
1042C4×D4—1464no—
1043C4×D4—1464no—
1044C2×C4⋊C4—731no—
1045C2×C4⋊C4—731no—
1046C2×C4⋊C4—731no—
1047C2×C4⋊C4—731no—
1048C2×C4⋊C4—731no—
1049C2×C4⋊C4—731no—
1050C2×C4⋊C4—731no—
1051C2×C4⋊C4—731no—
1052C2×C4⋊C4—731no—
1053C2×C4⋊C4—731no—
1054C2×C4⋊C4—731no—
1055C2×C4⋊C4—731no—
1056C2×C4⋊C4—731no—
1057C2×C4⋊C4—731no—
1058C2×C4⋊C4—731no—
1059C2×C4⋊C4—731no—
1060C2×C4⋊C4—731no—
1061C2×C4⋊C4—731no—
1062C2×C4⋊C4—731no—
1063C2×C4⋊C4C22×D7311yescharacteristic
1064C2×C4⋊C4C22×D7311yescharacteristic
1065C2×C4⋊C4C22×D7311yescharacteristic
1066C2×C22⋊C4—731no—
1067C2×C22⋊C4—731no—
1068C2×C22⋊C4—731no—
1069C2×C22⋊C4—731no—
1070C2×C22⋊C4—731no—
1071C2×C22⋊C4—731no—
1072C2×C22⋊C4—731no—
1073C2×C22⋊C4—731no—
1074C2×C22⋊C4—731no—
1075C2×C22⋊C4—731no—
1076C2×C22⋊C4—731no—
1077C2×C22⋊C4—731no—
1078C2×C22⋊C4—731no—
1079C2×C22⋊C4—731no—
1080C2×C22⋊C4—731no—
1081C2×C22⋊C4—731no—
1082C2×C22⋊C4—731no—
1083C2×C22⋊C4—731no—
1084C2×C22⋊C4—731no—
1085C2×C22⋊C4—731no—
1086C2×C22⋊C4—731no—
1087C2×C22⋊C4—731no—
1088C2×C22⋊C4—738no—
1089C2×C22⋊C4—731no—
1090C2×C22⋊C4—731no—
1091C2×C22⋊C4—731no—
1092C2×C22⋊C4—731no—
1093C2×C22⋊C4—731no—
1094C2×C22⋊C4—731no—
1095C2×C22⋊C4—731no—
1096C2×C22⋊C4—731no—
1097C2×C22⋊C4—1464no—
1098C2×C22⋊C4C22×D7311yescharacteristic
1099C2×C22⋊C4C22×D7311yescharacteristic
1100C2×C22⋊C4C22×D7311yescharacteristic
1101C2×C22⋊C4C22×D7311yescharacteristic
1102C2×C22⋊C4C22×D7311yescharacteristic
1103C2×C22⋊C4C22×D7311yescharacteristic
1104C2×C22⋊C4C22×D7311yescharacteristic
1105C2×C22⋊C4C22×D7311yescharacteristic
1106C2×C22⋊C4C22×D7311yescharacteristic
1107C2×C22⋊C4C22×D7311yescharacteristic
1108C2×C22⋊C4C22×D7311yescharacteristic
1109C2×C22⋊C4C22×D7311yescharacteristic
1110C2×C42—2922no—
1111C2×C42—2922no—
1112C2×C42—2922no—
1113C2×C42—2922no—
1114C2×C42—731no—
1115C2×C42—731no—
1116C2×C42—731no—
1117C2×C42—731no—
1118C2×C42—731no—
1119C2×C42—731no—
1120C2×C42—731no—
1121C2×C42—731no—
1122C2×C42—731no—
1123C2×C42—731no—
1124C2×C42—731no—
1125C2×C42—731no—
1126C2×C42—731no—
1127C2×C42—731no—
1128C2×C42—731no—
1129C2×C42—731no—
1130C2×C42—731no—
1131C2×C42—731no—
1132C2×C42—731no—
1133C2×C42—731no—
1134C2×C42—731no—
1135C2×C42—731no—
1136C2×C42C22×D7311yescharacteristic
1137C2×C42C22×D7311yescharacteristic
1138C2×C42C22×D7311yescharacteristic
1139C2×C42C22×D7311yescharacteristic
1140#95—731no—
1141#95—731no—
1142#95—731no—
1143#95—731no—
1144#95—731no—
1145#95—731no—
1146#95—731no—
1147#95—731no—
1148#95—731no—
1149#95—731no—
1150#95—731no—
1151#95—731no—
1152#95—731no—
1153#95—731no—
1154#95—731no—
1155#95—731no—
1156#95—731no—
1157#95—731no—
1158#95—731no—
1159#95—731no—
1160#95—731no—
1161#95—731no—
1162#95—731no—
1163#95—731no—
1164#95—731no—
1165#95—731no—
1166#95—731no—
1167#95—731no—
1168#95—731no—
1169#95—731no—
1170#95C22×D7311yescharacteristic
1171#95C22×D7311yescharacteristic
1172#95C22×D7311yescharacteristic
1173#95C22×D7311yescharacteristic
1174#95C22×D7311yescharacteristic
1175#95C22×D7311yescharacteristic
1176#95C22×D7311yescharacteristic
1177#95C22×D7311yescharacteristic
1178#95C22×D7311yescharacteristic
1179#95C22×D7311yescharacteristic
1180C24—2921no—
1181C24—2921no—
1182C24—2921no—
1183C24—2921no—
1184C24—734no—
1185C24—731no—
1186C24—731no—
1187C24—1462no—
1188C24—1462no—
1189C24C23×D7311yescharacteristic
1190C24C23×D7311yescharacteristic
1191C24C23×D7311yescharacteristic
1192C2×Q8—2921no—
1193C2×Q8—2921no—
1194C2×Q8—734no—
1195C2×D4—41no—
1196C2×D4—41no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—41no—
1200C2×D4—41no—
1201C2×D4—2921no—
1202C2×D4—2921no—
1203C2×D4—2921no—
1204C2×D4—2921no—
1205C2×D4—734no—
1206C2×D4—734no—
1207C2×D4—734no—
1208C2×D4—734no—
1209C2×D4—1462no—
1210C2×D4—1462no—
1211C2×D4—1462no—
1212C2×D4—1462no—
1213C2×D4C2×C4×D7314yes—
1214C2×D4C2×C4×D7314yes—
1215C2×D4C2×C4×D7314yescomplemented
1216C22×C4—22no—
1217C22×C4—22no—
1218C22×C4—41no—
1219C22×C4—41no—
1220C22×C4—41no—
1221C22×C4—41no—
1222C22×C4—41no—
1223C22×C4—41no—
1224C22×C4—2921no—
1225C22×C4—2921no—
1226C22×C4—2921no—
1227C22×C4—2921no—
1228C22×C4—2921no—
1229C22×C4—2921no—
1230C22×C4—2921no—
1231C22×C4—2921no—
1232C22×C4—2921no—
1233C22×C4—2921no—
1234C22×C4—2921no—
1235C22×C4—2921no—
1236C22×C4—29216no—
1237C22×C4—2921no—
1238C22×C4—2921no—
1239C22×C4—2921no—
1240C22×C4—2921no—
1241C22×C4—734no—
1242C22×C4—734no—
1243C22×C4—734no—
1244C22×C4—734no—
1245C22×C4—731no—
1246C22×C4—731no—
1247C22×C4—731no—
1248C22×C4—731no—
1249C22×C4—731no—
1250C22×C4—731no—
1251C22×C4—731no—
1252C22×C4—731no—
1253C22×C4—734no—
1254C22×C4—731no—
1255C22×C4—731no—
1256C22×C4—731no—
1257C22×C4—731no—
1258C22×C4—731no—
1259C22×C4—731no—
1260C22×C4—1462no—
1261C22×C4—1462no—
1262C22×C4—1462no—
1263C22×C4—1462no—
1264C22×C4—1462no—
1265C22×C4—1462no—
1266C22×C4—1462no—
1267C22×C4—1462no—
1268C22×C4—1462no—
1269C22×C4—1462no—
1270C22×C4—1462no—
1271C22×C4—1462no—
1272C22×C4—1462no—
1273C22×C4—1462no—
1274C22×C4—1462no—
1275C22×C4—1462no—
1276C22×C4—1462no—
1277C22×C4—1462no—
1278C22×C4C2×C4×D7314yescomplemented
1279C22×C4C23×D7311yescharacteristic
1280C22×C4C23×D7311yescharacteristic
1281C22×C4C23×D7311yescharacteristic
1282C22×C4C23×D7311yescharacteristic
1283C22×C4C23×D7311yescharacteristic
1284C22×C4C23×D7311yescharacteristic
1285C22×C4C23×D7311yescharacteristic
1286C22×C4C23×D7311yescharacteristic
1287C22×C4C23×D7311yescharacteristic
1288C22×C4C23×D7311yescharacteristic
1289C22×C4C23×D7311yescharacteristic
1290C22×C4C23×D7311yescharacteristic
1291C4⋊C4—41no—
1292C4⋊C4—41no—
1293C4⋊C4—2921no—
1294C4⋊C4—2921no—
1295C4⋊C4—2921no—
1296C4⋊C4—2921no—
1297C4⋊C4—2921no—
1298C4⋊C4—2921no—
1299C4⋊C4—2921no—
1300C4⋊C4—2921no—
1301C4⋊C4—2921no—
1302C4⋊C4—2921no—
1303C4⋊C4—734no—
1304C4⋊C4—734no—
1305C4⋊C4—734no—
1306C4⋊C4—734no—
1307C4⋊C4—734no—
1308C4⋊C4—1462no—
1309C4⋊C4—1462no—
1310C4⋊C4—1462no—
1311C4⋊C4—1462no—
1312C4⋊C4C2×C4×D7314yescomplemented
1313C22⋊C4—22no—
1314C22⋊C4—22no—
1315C22⋊C4—22no—
1316C22⋊C4—22no—
1317C22⋊C4—41no—
1318C22⋊C4—41no—
1319C22⋊C4—41no—
1320C22⋊C4—41no—
1321C22⋊C4—41no—
1322C22⋊C4—41no—
1323C22⋊C4—2921no—
1324C22⋊C4—2921no—
1325C22⋊C4—2921no—
1326C22⋊C4—2921no—
1327C22⋊C4—2921no—
1328C22⋊C4—2921no—
1329C22⋊C4—2921no—
1330C22⋊C4—2921no—
1331C22⋊C4—2921no—
1332C22⋊C4—2921no—
1333C22⋊C4—734no—
1334C22⋊C4—734no—
1335C22⋊C4—734no—
1336C22⋊C4—734no—
1337C22⋊C4—734no—
1338C22⋊C4—734no—
1339C22⋊C4—734no—
1340C22⋊C4—734no—
1341C22⋊C4—734no—
1342C22⋊C4—734no—
1343C22⋊C4—734no—
1344C22⋊C4—734no—
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⋊C4C2×C4×D7314yes—
1354C22⋊C4C2×C4×D7314yescomplemented
1355C42—41no—
1356C42—41no—
1357C42—41no—
1358C42—41no—
1359C42—2921no—
1360C42—2921no—
1361C42—2921no—
1362C42—2921no—
1363C42—2921no—
1364C42—2921no—
1365C42—2921no—
1366C42—2921no—
1367C42—734no—
1368C42—734no—
1369C42—1462no—
1370C42—1462no—
1371C42—1462no—
1372C42—1462no—
1373C42—1462no—
1374C42—1462no—
1375C42—1462no—
1376C42—1462no—
1377C42—1462no—
1378C42—1462no—
1379C42—1462no—
1380C42—1462no—
1381C23—21no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—2924no—
1400C23—2924no—
1401C23—2924no—
1402C23—2924no—
1403C23—2924no—
1404C23—2924no—
1405C23—732no—
1406C23—732no—
1407C23—732no—
1408C23—732no—
1409C23—1468no—
1410C23—1461no—
1411C23—1461no—
1412C23—1461no—
1413C23—1461no—
1414C23—1461no—
1415C23—1461no—
1416C23—1461no—
1417C23—1461no—
1418C23—1461no—
1419C23—1461no—
1420C23C22×C4×D7312yes—
1421C23C22×C4×D7312yes—
1422C23C22×C4×D7312yes—
1423C23C24×D7311yescharacteristic
1424Q8—2924no—
1425D4—44no—
1426D4—44no—
1427D4—44no—
1428D4—2924no—
1429D4—2924no—
1430D4—1468no—
1431D4—1468no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—44no—
1463C2×C4—44no—
1464C2×C4—44no—
1465C2×C4—2924no—
1466C2×C4—2924no—
1467C2×C4—2924no—
1468C2×C4—2924no—
1469C2×C4—2924no—
1470C2×C4—2924no—
1471C2×C4—2924no—
1472C2×C4—2924no—
1473C2×C4—2924no—
1474C2×C4—2924no—
1475C2×C4—2924no—
1476C2×C4—2924no—
1477C2×C4—732no—
1478C2×C4—732no—
1479C2×C4—732no—
1480C2×C4—732no—
1481C2×C4—732no—
1482C2×C4—732no—
1483C2×C4—732no—
1484C2×C4—732no—
1485C2×C4—732no—
1486C2×C4—732no—
1487C2×C4—1468no—
1488C2×C4—1461no—
1489C2×C4—1461no—
1490C2×C4—1461no—
1491C2×C4—1461no—
1492C2×C4—1461no—
1493C2×C4—1461no—
1494C2×C4—1461no—
1495C2×C4—1461no—
1496C2×C4—1461no—
1497C2×C4—1461no—
1498C2×C4—1461no—
1499C2×C4—1461no—
1500C2×C4—1461no—
1501C2×C4—1461no—
1502C2×C4—1461no—
1503C2×C4—1461no—
1504C2×C4—1461no—
1505C2×C4—1461no—
1506C2×C4—1461no—
1507C2×C4—1461no—
1508C2×C4—1461no—
1509C2×C4—1461no—
1510C2×C4—1461no—
1511C2×C4—1461no—
1512C2×C4—1461no—
1513C2×C4—1461no—
1514C2×C4—1461no—
1515C2×C4—1461no—
1516C2×C4—1461no—
1517C2×C4—1461no—
1518C2×C4—1461no—
1519C2×C4—1461no—
1520C2×C4C22×C4×D7312yes—
1521C2×C4C22×C4×D7312yes—
1522C2×C4C22×C4×D7312yes—
1523C2×C4C22×C4×D7312yes—
1524C2×C4#41×D7312yes—
1525C2×C4#41×D7312yes—
1526C22—22no—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—22no—
1535C22—41no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—29216no—
1548C22—2921no—
1549C22—2921no—
1550C22—2921no—
1551C22—2921no—
1552C22—734no—
1553C22—1462no—
1554C22—1462no—
1555C22—1462no—
1556C22—1462no—
1557C22—1462no—
1558C22—1462no—
1559C22—1462no—
1560C22—1462no—
1561C22—1462no—
1562C22C23×C4×D7311yescharacteristic
1563C22C2×#41×D7311yescharacteristic
1564C22C2×#41×D7311yescharacteristic
1565C22H(5,𝔽2)×D7311yescharacteristic
1566C22H(5,𝔽2)×D7311yescharacteristic
1567C22#1798942211yescharacteristic
1568C22#1798942211yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—22no—
1574C4—22no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—2921no—
1582C4—2921no—
1583C4—2921no—
1584C4—2921no—
1585C4—2921no—
1586C4—2921no—
1587C4—734no—
1588C4—1462no—
1589C4—1462no—
1590C4—1462no—
1591C4—1462no—
1592C4—1462no—
1593C4—1462no—
1594C4—1462no—
1595C2—42no—
1596C2—42no—
1597C2—42no—
1598C2—2922no—
1599C2—1464no—
1600C2C4×#41×D7311yescharacteristic
1601C2#2262313511yescharacteristic
1602C2#2262313511yescharacteristic
1603C2#538×D7311yescharacteristic
1604C2#2262331511yescharacteristic
1605C2#2262334211yescharacteristic
1606C2#2262334611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D73
commutatorC22×C73C24×C4
FittingC73×#2333C2
socle, cosocleC23×C73C25
prime radicalC2×#17989169C2
hypercenter#2333D73
hypocenterC73C4×#538
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #2333

Complements

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

NH ≅ G/Ntype
2. #22612740C2semidirect
3. #22612739C2semidirect
4. #22612722C2semidirect
5. #22612721C2semidirect
6. #22612709C2semidirect
7. #22612708C2semidirect
8. #22612690C2semidirect
9. #22612658C2semidirect
10. #22612633C2semidirect
11. #22612590C2semidirect
12. #22612587C2semidirect
13. #22612561C2semidirect
14. #22612560C2semidirect
15. #22612525C2semidirect
16. #22612485C2semidirect
17. #22612481C2semidirect
18. #22612478C2semidirect
19. #22612472C2semidirect
20. #22612465C2semidirect
21. #22612456C2semidirect
22. #22612448C2semidirect
23. #22612447C2semidirect
24. #121×Dic73C2semidirect
25. #22612441C2semidirect
26. #22612436C2semidirect
27. #22612436C2semidirect
28. C4×#14556551C2semidirect
29. C4×#14556551C2semidirect
30. C4×C22⋊C4×D73C2semidirect
31. C73×#2333C2semidirect
33. #17989169C4semidirect
45. C2×#14556556C22semidirect
48. C2×D4×Dic73C22semidirect
59. C22×C4×Dic73C22semidirect
60. C22×C4×Dic73C22semidirect
63. #17988493C22semidirect
64. #17988491C22semidirect
65. #17988491C22semidirect
69. #17988486C22semidirect
70. #17988485C22semidirect
71. #17988484C22semidirect
72. #17988484C22semidirect
76. #17988481C22semidirect
77. #17988481C22semidirect
78. #17988481C22semidirect
80. #17988480C22semidirect
92. #17988475C22semidirect
93. #17988475C22semidirect
94. #17988475C22semidirect
95. #17988474C22semidirect
96. #17988474C22semidirect
97. #17988474C22semidirect
98. #17988472C22semidirect
99. #17988471C22semidirect
100. #17988471C22semidirect
101. #17988470C22semidirect
102. #17988469C22semidirect
103. #17988469C22semidirect
104. #17988468C22semidirect
106. #17988467C22semidirect
122. #17988460C22semidirect
123. #17988459C22semidirect
125. #17988454C22semidirect
126. #17988454C22semidirect
127. #17988452C22semidirect
128. #17988451C22semidirect
129. #17988448C22semidirect
130. #17988447C22semidirect
132. #17988445C22semidirect
136. C4⋊C4×Dic73C22semidirect
137. C4⋊C4×Dic73C22semidirect
138. C4×#11924007C22semidirect
139. C4×#11924007C22semidirect
140. #17988438C22semidirect
141. #17988438C22semidirect
142. #17988438C22semidirect
143. #17988438C22semidirect
144. #17988438C22semidirect
145. #17988438C22semidirect
150. C22⋊C4×Dic73C22semidirect
151. C22⋊C4×Dic73C22semidirect
152. C22⋊C4×Dic73C22semidirect
153. C22⋊C4×Dic73C22semidirect
154. C22⋊C4×Dic73C22semidirect
155. C22⋊C4×Dic73C22semidirect
171. C42×Dic73C22semidirect
172. C42×Dic73C22semidirect
175. #390×C73C22semidirect
177. #388×C73C22semidirect
178. #387×C73C22semidirect
179. #387×C73C22semidirect
183. #386×C73C22semidirect
184. #381×C73C22semidirect
186. C4×C22⋊C4×C73C22semidirect
187. C4×C22⋊C4×C73C22semidirect
210. #14556586C2×C4semidirect
211. #14556584C2×C4semidirect
212. #14556578C2×C4semidirect
213. #14556577C2×C4semidirect
214. #14556574C2×C4semidirect
215. #14556572C2×C4semidirect
216. #14556569C2×C4semidirect
217. #14556563C2×C4semidirect
218. #14556562C2×C4semidirect
219. #14556559C2×C4semidirect
220. #14556559C2×C4semidirect
226. C4×C22⋊D73C2×C4semidirect
232. #14556551C2×C4semidirect
283. C22⋊C4×D73C2×C4semidirect
346. #121×C73C2×C4semidirect
387. C2×Dic146C22×C4semidirect
414. C22×Dic73C22×C4semidirect
458. C4⋊Dic73C22×C4semidirect
469. #11924007C22×C4semidirect
470. #11924007C22×C4semidirect
471. #11924007C22×C4semidirect
472. #11924007C22×C4semidirect
484. C22⋊Dic73C22×C4semidirect
485. C22⋊Dic73C22×C4semidirect
486. C22⋊Dic73C22×C4semidirect
523. C4×Dic73C22×C4semidirect
524. C4×Dic73C22×C4semidirect
536. C2×D4×C73C22×C4semidirect
545. C22×C4×C73C22×C4semidirect
560. C4⋊C4×C73C22×C4semidirect
572. C22⋊C4×C73C22×C4semidirect
790. Dic73#538semidirect
812. #2333D73semidirect
835. C73C4×#538semidirect
875. #390C2×D73semidirect
903. #388C2×D73semidirect
914. #387C2×D73semidirect
915. #387C2×D73semidirect
929. #386C2×D73semidirect
945. #381C2×D73semidirect
986. C4×C22⋊C4C2×D73semidirect
987. C4×C22⋊C4C2×D73semidirect
1029. #121C4×D73semidirect
1215. C2×D4C2×C4×D73semidirect
1278. C22×C4C2×C4×D73semidirect
1312. C4⋊C4C2×C4×D73semidirect
1354. C22⋊C4C2×C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×#179891692
#226127402
#226127392
#226127222
#226127212
#226127092
#226127082
#226126902
#226126582
#226126332
#226125902
#226125872
#226125612
#226125602
#226125252
#226124852
#226124812
#226124782
#226124722
#226124652
#226124562
#226124482
#226124472
#121×Dic732
#226124412
#226124362
C4×#145565512
C4×C22⋊C4×D732
C73×#23332
C4×#53873