Finite Group Databasebeta

← #33102724

Subgroups — #33102724

Order 18688.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989119C211yesmaximal, characteristic
2C2×#17988716C211yesmaximal, characteristic, complemented
3C2×#17988715C211yesmaximal, characteristic, complemented
4#22610730C211yesmaximal, characteristic, complemented
5#22610727C211yesmaximal, characteristic, complemented
6#22610727C211yesmaximal, characteristic, complemented
7#22610723C211yesmaximal, characteristic, complemented
8#22610723C211yesmaximal, characteristic, complemented
9#22609913C211yesmaximal, characteristic, complemented
10#22609913C211yesmaximal, characteristic, complemented
11#22609908C211yesmaximal, characteristic, complemented
12#22609699C211yesmaximal, characteristic, complemented
13#22609699C211yesmaximal, characteristic, complemented
14#22609694C211yesmaximal, characteristic, complemented
15C73×#1955C211yesmaximal, characteristic, complemented
16#17989119—24no—
17#17989119—24no—
18C2×#14556584C411yescharacteristic
19C2×#14556584C411yescharacteristic
20C2×#14556582C411yescharacteristic
21C2×#14556578C411yescharacteristic
22C2×#14556573C411yescharacteristic
23C2×#14556573C411yescharacteristic
24C2×#14556571C411yescharacteristic
25C2×#14556562C411yescharacteristic
26C2×C4×Dic146C2211yescharacteristic
27C2×C4×C22⋊D73C2211yescharacteristic
28C2×C4×C22⋊D73C2211yescharacteristic
29C2×#14556550C2211yescharacteristic
30C2×#14556550C2211yescharacteristic
31C2×C42×D73C2211yescharacteristic
32#17988716—24no—
33#17988715—24no—
34C2×C4⋊#10596831C2211yescharacteristic
35C2×#14556520C2211yescharacteristic
36C2×#14556520C2211yescharacteristic
37C2×#14556520C2211yescharacteristic
38C2×#14556520C2211yescharacteristic
39C2×C22⋊#10596831C2211yescharacteristic
40C2×C22⋊#10596831C2211yescharacteristic
41C2×C22⋊#10596831C2211yescharacteristic
42C2×C22⋊#10596831C2211yescharacteristic
43C2×#14556503C2211yescharacteristic
44C2×#14556503C2211yescharacteristic
45C2×#14556503C2211yescharacteristic
46C2×#14556503C2211yescharacteristic
47C2×#14556502C2211yescharacteristic
48C2×#14556501C2211yescharacteristic
49C2×#14556501C2211yescharacteristic
50C2×C8×Dic73C2211yescharacteristic
51C2×C8×Dic73C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56C2×C4×D4×C73C2211yescharacteristic
57C2×C4⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59C2×C22⋊C8×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61C2×C22⋊C8×C73C2211yescharacteristic
62C2×#97×C73C2211yescharacteristic
63C22×Dic146C2×C411yescharacteristic
64C22×C22⋊D73C2×C411yescharacteristic
65C22×C22⋊D73C2×C411yescharacteristic
66C22×C4×D73C2×C411yescharacteristic
67C22×C4×D73C2×C411yescharacteristic
68C22×C4×D73C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73#14556584—24no—
74#14556584—24no—
75#14556582—24no—
76#14556578—24no—
77#14556573—24no—
78#14556573—24no—
79#14556571—24no—
80#14556562—24no—
81C4×Dic146D414yes—
82C4×Dic146D414yes—
83C4×C22⋊D73—22no—
84C4×C22⋊D73—22no—
85C4×C22⋊D73—22no—
86C4×C22⋊D73—22no—
87#14556550—22no—
88#14556550—22no—
89#14556550—22no—
90#14556550—22no—
91C2×C4⋊Dic73C2×C411yescharacteristic
92C2×C4⋊Dic73C2×C411yescharacteristic
93C2×C4⋊Dic73C2×C411yescharacteristic
94C2×C4⋊Dic73C2×C411yescharacteristic
95C2×C4⋊Dic73C2×C411yescharacteristic
96C2×#11924007C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×C22⋊Dic73C2×C411yescharacteristic
101C2×C22⋊Dic73C2×C411yescharacteristic
102C2×C22⋊Dic73C2×C411yescharacteristic
103C2×C22⋊Dic73C2×C411yescharacteristic
104C2×C22⋊Dic73C2×C411yescharacteristic
105C2×C22⋊Dic73C2×C411yescharacteristic
106C2×#11924005C2×C411yescharacteristic
107C2×#11924005C2×C411yescharacteristic
108C2×C4×Dic73C2×C411yescharacteristic
109C2×C4×Dic73C2×C411yescharacteristic
110C2×C4×Dic73C2311yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C42×D73—22no—
114C42×D73—22no—
115C4⋊#10596831—22no—
116#14556520—22no—
117#14556520—22no—
118#14556520—22no—
119#14556520—22no—
120C22⋊#10596831—22no—
121C22⋊#10596831—22no—
122C22⋊#10596831—41no—
123C22⋊#10596831—41no—
124#14556503—22no—
125#14556503—22no—
126#14556503—41no—
127#14556503—41no—
128#14556502—22no—
129#14556501—22no—
130#14556501—22no—
131C8×Dic73—22no—
132C8×Dic73—22no—
133C22×D4×C73C2×C411yescharacteristic
134C23×C4×C73C2311yescharacteristic
135C23×C4×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139C22×C8×C73C2311yescharacteristic
140C4×D4×C73—22no—
141C4×D4×C73—22no—
142C2×C4⋊C4×C73C2×C411yescharacteristic
143C2×C22⋊C4×C73C2×C411yescharacteristic
144C2×C22⋊C4×C73C2×C411yescharacteristic
145C2×C42×C73C2311yescharacteristic
146C4⋊C8×C73—22no—
147C22⋊C8×C73—22no—
148C22⋊C8×C73—22no—
149C22⋊C8×C73—41no—
150C22⋊C8×C73—41no—
151#97×C73—22no—
152C23×D73C22×C411yescharacteristic
153C2×Dic146—41no—
154C2×Dic146—41no—
155C2×Dic146C22⋊C414yes—
156C2×C22⋊D73—22no—
157C2×C22⋊D73—22no—
158C2×C22⋊D73—22no—
159C2×C22⋊D73—22no—
160C2×C22⋊D73—41no—
161C2×C22⋊D73—41no—
162C22×Dic73C22×C411yescharacteristic
163C22×Dic73C22×C411yescharacteristic
164C22×Dic73C22×C411yescharacteristic
165C22×Dic73C22×C411yescharacteristic
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C2×C4×D73—22no—
170C2×C4×D73—22no—
171C2×C4×D73—22no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—21no—
177C2×C4×D73—21no—
178C2×C4×D73—41no—
179C2×C4×D73—41no—
180C2×C4×D73—41no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186C2×#10596831—21no—
187C2×#10596831—21no—
188C2×#10596831—21no—
189C2×#10596831—21no—
190C2×#10596831—21no—
191C2×#10596831—21no—
192C2×#10596831#4112yes—
193C4⋊Dic73—22no—
194C4⋊Dic73—22no—
195C4⋊Dic73—22no—
196C4⋊Dic73—22no—
197C4⋊Dic73C22⋊C414yes—
198#11924007—22no—
199#11924007—22no—
200#11924007C22⋊C414yes—
201#11924007C22⋊C414yes—
202C22⋊Dic73—22no—
203C22⋊Dic73—22no—
204C22⋊Dic73—22no—
205C22⋊Dic73—22no—
206C22⋊Dic73—22no—
207C22⋊Dic73—22no—
208#11924005—22no—
209#11924005—22no—
210C4×Dic73—22no—
211C4×Dic73—22no—
212C4×Dic73—21no—
213C4×Dic73—21no—
214C4×Dic73C2×D412yes—
215C4×Dic73C2×D412yes—
216C4×Dic73C2×D412yes—
217C4×Dic73C2×D412yes—
218C24×C73C22×C411yescharacteristic
219C24×C73C22×C411yescharacteristic
220C2×D4×C73—22no—
221C2×D4×C73—41no—
222C2×D4×C73—41no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73C22×C411yescharacteristic
236C22×C4×C73C22×C411yescharacteristic
237C22×C4×C73C22×C411yescharacteristic
238C22×C4×C73C22×C411yescharacteristic
239C22×C4×C73C2411yescharacteristic
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73#4112yes—
252C4⋊C4×C73—22no—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C42×C73C2×D412yes—
256C42×C73C2×D412yes—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—21no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73C23×C411yescharacteristic
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277C22×D73—21no—
278C22×D73#13112yes—
279D4×C73—44no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—21no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—41no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—41no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73C2×C22⋊C412yes—
299C2×C4×C73C2×C22⋊C412yes—
300C2×C4×C73C22×D411yescharacteristic
301C2×C4×C73C22×D411yescharacteristic
302C2×C4×C73C2×#4111yescharacteristic
303C2×C4×C73C2×#4111yescharacteristic
304C2×C4×C73H(5,𝔽2)11yescharacteristic
305C2×C4×C732−1+411yescharacteristic
306C22⋊D73—44no—
307C22⋊D73—44no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
311C2×Dic73—21no—
312C2×Dic73—21no—
313C2×Dic73—21no—
314C2×Dic73—21no—
315C2×Dic73—21no—
316C2×Dic73—21no—
317C2×Dic73—21no—
318C2×Dic73—21no—
319C2×Dic73—21no—
320C2×Dic73—21no—
321C2×Dic73—21no—
322C2×Dic73—21no—
323C2×Dic73—21no—
324C2×Dic73—21no—
325C2×Dic73C2×C22⋊C412yes—
326C2×Dic73C2×C22⋊C412yes—
327C2×Dic73C2×C22⋊C412yes—
328C2×Dic73C2×C22⋊C412yes—
329C4×D73—44no—
330C4×D73—44no—
331C4×D73—41no—
332C4×D73—41no—
333C4×D73—41no—
334C4×D73—41no—
335Dic146—44no—
336C8×C73—22no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340#10596831—22no—
341#10596831—41no—
342#10596831—41no—
343#10596831—41no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73C22×C22⋊C411yescharacteristic
359C22×C73C4×#4111yescharacteristic
360C22×C73#52011yescharacteristic
361C22×C73C2×#13111yescharacteristic
362C22×C73#56811yescharacteristic
363C22×C73#56811yescharacteristic
364C22×C73#56811yescharacteristic
365C2×D73—22no—
366C2×D73—22no—
367C2×D73—22no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C4×C73—22no—
373C4×C73—22no—
374C4×C73—41no—
375C4×C73—41no—
376C4×C73#54811yescharacteristic
377C4×C73#54811yescharacteristic
378C4×C73#55011yescharacteristic
379C4×C73#55011yescharacteristic
380Dic73—22no—
381Dic73—22no—
382Dic73—22no—
383Dic73—22no—
384Dic73—41no—
385Dic73—41no—
386Dic73—41no—
387#22533—731nomaximal, Sylow
388C2×C73—81no—
389C2×C73—81no—
390C2×C73#234111yescharacteristic
391C2×C73#287911yescharacteristic
392C2×C73#288011yescharacteristic
393C2×C73#296711yescharacteristic
394C2×C73#296811yescharacteristic
395C2×C73#299211yescharacteristic
396C2×C73#299511yescharacteristic
397D73—42no—
398C2×#529—731no—
399C2×#446—731no—
400C2×#446—731no—
401#1955—731no—
402#1955—731no—
403#1955—731no—
404#1955D7311yescharacteristic, complemented
405#1954—731no—
406#1954—731no—
407#1798—731no—
408#1798—731no—
409#1797—731no—
410#1750—731no—
411#1750—731no—
412#1749—731no—
413C73#2253311yescharacteristic, complemented, Sylow
414#529—1464no—
415#529—1464no—
416C2×#126—731no—
417C2×#126—731no—
418C2×#125—731no—
419C2×#124—731no—
420C2×#123—731no—
421C2×#123—731no—
422C2×C22⋊Q8—731no—
423C2×#121—731no—
424C2×C4×Q8—731no—
425C2×C4×D4—731no—
426C2×C4×D4—731no—
427C2×C4×D4C2×D7311yescharacteristic
428C2×#117—731no—
429C2×#117—731no—
430C22×C42—731no—
431#446—1464no—
432#446—1464no—
433C2×C4⋊C8—731no—
434C2×C4⋊C8—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8—731no—
437C2×C4⋊C8—731no—
438C2×C4⋊C8C2×D7311yescharacteristic
439C2×C22⋊C8—731no—
440C2×C22⋊C8—731no—
441C2×C22⋊C8—731no—
442C2×C22⋊C8—731no—
443C2×C22⋊C8—731no—
444C2×C22⋊C8—731no—
445C2×C22⋊C8—731no—
446C2×C22⋊C8—731no—
447C2×C22⋊C8C2×D7311yescharacteristic
448C2×C22⋊C8C2×D7311yescharacteristic
449C2×C22⋊C8C2×D7311yescharacteristic
450C2×C22⋊C8C2×D7311yescharacteristic
451C2×#97—731no—
452C2×#97—731no—
453C2×#97—731no—
454C2×#97C2×D7311yescharacteristic
455C2×C4×C8—731no—
456C2×C4×C8—731no—
457#336—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461C22×Q8—731no—
462C22×D4—731no—
463C22×D4—731no—
464C22×D4C4×D7311yescharacteristic
465C23×C4—731no—
466C23×C4—731no—
467C23×C4—731no—
468C23×C4C22×D7311yescharacteristic
469C23×C4C22×D7311yescharacteristic
470C22×C8—731no—
471C22×C8—731no—
472C22×C8—731no—
473C22×C8—731no—
474C22×C8C22×D7311yescharacteristic
475C22×C8C22×D7311yescharacteristic
476C22×C8C22×D7311yescharacteristic
477C22×C8C22×D7311yescharacteristic
478#126—1464no—
479#126—1464no—
480#125—1464no—
481#124—1464no—
482#123—1464no—
483#123—1464no—
484C22⋊Q8—1464no—
485#121—1464no—
486C4×Q8—734no—
487C4×Q8—734no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—1462no—
491C4×D4—1462no—
492C4×D4—1462no—
493C4×D4—1462no—
494#117—1462no—
495#117—1462no—
496#117—1462no—
497#117—1462no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4—731no—
501C2×C4⋊C4—731no—
502C2×C4⋊C4—731no—
503C2×C4⋊C4—731no—
504C2×C4⋊C4—731no—
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C4⋊C4C4×D7311yescharacteristic
508C2×C22⋊C4—731no—
509C2×C22⋊C4—731no—
510C2×C22⋊C4—731no—
511C2×C22⋊C4—731no—
512C2×C22⋊C4—731no—
513C2×C22⋊C4—731no—
514C2×C22⋊C4—731no—
515C2×C22⋊C4—731no—
516C2×C22⋊C4C4×D7311yescharacteristic
517C2×C22⋊C4C4×D7311yescharacteristic
518C2×C42—731no—
519C2×C42—731no—
520C2×C42—731no—
521C2×C42—731no—
522C2×C42—731no—
523C2×C42—1462no—
524C2×C42—1462no—
525C2×C42C22×D7311yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—1462no—
528C4⋊C8—1462no—
529C4⋊C8—1462no—
530C4⋊C8—1462no—
531C4⋊C8—1462no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—41no—
535C22⋊C8—41no—
536C22⋊C8—2921no—
537C22⋊C8—2921no—
538C22⋊C8—2921no—
539C22⋊C8—2921no—
540C22⋊C8—1462no—
541C22⋊C8—1462no—
542C22⋊C8—1462no—
543C22⋊C8—1462no—
544#97—22no—
545#97—1462no—
546#97—1462no—
547#97—1462no—
548C4×C8—1462no—
549C4×C8—1462no—
550C24—731no—
551C24C2×C4×D7311yescharacteristic
552C24C2×C4×D7311yescharacteristic
553C2×Q8—2921no—
554C2×Q8—2921no—
555C2×Q8—734no—
556C2×D4—22no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—2921no—
560C2×D4—2921no—
561C2×D4—1462no—
562C2×D4—1462no—
563C2×D4—1462no—
564C2×D4—1462no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—2921no—
578C22×C4—2921no—
579C22×C4—2921no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—731no—
583C22×C4—731no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—1462no—
588C22×C4—1462no—
589C22×C4—1462no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4C2×C4×D7311yescharacteristic
597C22×C4C2×C4×D7311yescharacteristic
598C22×C4C2×C4×D7311yescharacteristic
599C22×C4C2×C4×D7311yescharacteristic
600C22×C4C23×D7311yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—732no—
613C2×C8—1461no—
614C2×C8—1461no—
615C2×C8—1461no—
616C2×C8—1461no—
617C2×C8—1461no—
618C2×C8—1461no—
619C2×C8—1461no—
620C2×C8—1461no—
621C2×C8—1461no—
622C2×C8—1461no—
623C2×C8—1461no—
624C2×C8#1192402712yes—
625C4⋊C4—22no—
626C4⋊C4—734no—
627C4⋊C4—734no—
628C4⋊C4—734no—
629C4⋊C4—1462no—
630C4⋊C4—1462no—
631C4⋊C4—1462no—
632C4⋊C4—1462no—
633C4⋊C4—1462no—
634C4⋊C4—1462no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—1462no—
638C22⋊C4—1462no—
639C22⋊C4—1462no—
640C22⋊C4—1462no—
641C22⋊C4—1462no—
642C22⋊C4—1462no—
643C22⋊C4—1462no—
644C22⋊C4—1462no—
645C42—732no—
646C42—732no—
647C42—732no—
648C42—732no—
649C42—1462no—
650C42—1462no—
651C42—1461no—
652C42—1461no—
653C42D4×D7312yes—
654C42D4×D7312yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—732no—
670C23—1461no—
671C23—1461no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23C22×C4×D7311yescharacteristic
677Q8—2924no—
678D4—44no—
679D4—2924no—
680D4—2924no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—2924no—
700C2×C4—2924no—
701C2×C4—2921no—
702C2×C4—2921no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—732no—
706C2×C4—732no—
707C2×C4—732no—
708C2×C4—732no—
709C2×C4—1461no—
710C2×C4—1461no—
711C2×C4—1461no—
712C2×C4—1461no—
713C2×C4—1461no—
714C2×C4—1461no—
715C2×C4—1461no—
716C2×C4—1461no—
717C2×C4—1461no—
718C2×C4—1461no—
719C2×C4—1461no—
720C2×C4—1461no—
721C2×C4—1461no—
722C2×C4—1461no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4C22⋊C4×D7312yes—
727C2×C4C22⋊C4×D7312yes—
728C2×C4C2×D4×D7311yescharacteristic
729C2×C4C2×D4×D7311yescharacteristic
730C2×C4#41×D7311yescharacteristic
731C2×C4C2×#1192402711yescharacteristic
732C2×C4#1455663611yescharacteristic
733C2×C4#1455663811yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—2921no—
739C8—2921no—
740C8—2921no—
741C8—1462no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—2921no—
757C22—2921no—
758C22—2921no—
759C22—2921no—
760C22—1462no—
761C22—1462no—
762C22—1462no—
763C22C2×C22⋊C4×D7311yescharacteristic
764C22C4×#1192402711yescharacteristic
765C22#1798906611yescharacteristic
766C22#131×D7311yescharacteristic
767C22#1798935211yescharacteristic
768C22#1798935311yescharacteristic
769C22#1798935311yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—2921no—
775C4—2921no—
776C4—2921no—
777C4—1462no—
778C4—1462no—
779C4—1462no—
780C4—1462no—
781C4#1798924311yescharacteristic
782C4#1798924511yescharacteristic
783C4#1798925511yescharacteristic
784C4#1798925711yescharacteristic
785C2—81no—
786C2—81no—
787C2—2922no—
788C2#2261277011yescharacteristic
789C2#2261837411yescharacteristic
790C2#2261837911yescharacteristic
791C2#2261891311yescharacteristic
792C2#2261892211yescharacteristic
793C2#2261906611yescharacteristic
794C2#2261909711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1955C2
prime radicalC2×#14556562C4
cosocleC22×C4×C73C24
hypercenter#1955D73
hypocenterC73#22533
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1955

Complements

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

NH ≅ G/Ntype
2. C2×#17988716C2semidirect
3. C2×#17988715C2semidirect
4. #22610730C2semidirect
5. #22610727C2semidirect
6. #22610727C2semidirect
7. #22610723C2semidirect
8. #22610723C2semidirect
9. #22609913C2semidirect
10. #22609913C2semidirect
11. #22609908C2semidirect
12. #22609699C2semidirect
13. #22609699C2semidirect
14. #22609694C2semidirect
15. C73×#1955C2semidirect
404. #1955D73semidirect
413. C73#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#179891192
C2×#179887162
C2×#179887152
#226107302
#226107272
#226107232
#226099132
#226099082
#226096992
#226096942
C73×#19552
#2253373