Finite Group Databasebeta

← #33102721

Subgroups — #33102721

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×#17989124C211yesmaximal, characteristic
2C2×#17988718C211yesmaximal, characteristic, complemented
3#22610729C211yesmaximal, characteristic, complemented
4#22610729C211yesmaximal, characteristic, complemented
5#22610728C211yesmaximal, characteristic, complemented
6#22610728C211yesmaximal, characteristic, complemented
7#22610725C211yesmaximal, characteristic, complemented
8#22610724C211yesmaximal, characteristic, complemented
9#22609912C211yesmaximal, characteristic, complemented
10#22609912C211yesmaximal, characteristic, complemented
11#22609908C211yesmaximal, characteristic, complemented
12#22609700C211yesmaximal, characteristic, complemented
13#22609698C211yesmaximal, characteristic, complemented
14#22609694C211yesmaximal, characteristic, complemented
15C2×#446×C73C211yesmaximal, characteristic, complemented
16#17989124—24no—
17#17989124—24no—
18C2×#14556586C411yescharacteristic
19C2×#14556586C411yescharacteristic
20C2×#14556582C411yescharacteristic
21C2×#14556580C411yescharacteristic
22C2×#14556576C411yescharacteristic
23C2×#14556576C411yescharacteristic
24C2×#14556567C411yescharacteristic
25C2×#14556566C411yescharacteristic
26C2×C4×D292C2211yescharacteristic
27C2×C4×D292C2211yescharacteristic
28C2×C4×D292C2211yescharacteristic
29C2×#14556548C2211yescharacteristic
30C2×#14556548C2211yescharacteristic
31C2×C42×D73C2211yescharacteristic
32#17988718—24no—
33C2×C4⋊#10596831C2211yescharacteristic
34C2×C4⋊#10596831C2211yescharacteristic
35C2×C4⋊#10596831C2211yescharacteristic
36C2×#14556503C2211yescharacteristic
37C2×#14556503C2211yescharacteristic
38C2×#14556503C2211yescharacteristic
39C2×#14556503C2211yescharacteristic
40C2×#14556503C2211yescharacteristic
41C2×#14556503C2211yescharacteristic
42C2×#14556503C2211yescharacteristic
43C2×#14556503C2211yescharacteristic
44C2×#14556503C2211yescharacteristic
45C2×#14556503C2211yescharacteristic
46C2×#14556503C2211yescharacteristic
47C2×#14556503C2211yescharacteristic
48C2×#14556502C2211yescharacteristic
49C2×#14556502C2211yescharacteristic
50C2×C4×#10596831C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55C2×C4×Q8×C73C2211yescharacteristic
56#446×C73—24no—
57C2×C4⋊C8×C73C2211yescharacteristic
58C2×C4⋊C8×C73C2211yescharacteristic
59C2×C4⋊C8×C73C2211yescharacteristic
60C2×#97×C73C2211yescharacteristic
61C2×#97×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63C22×D292C2×C411yescharacteristic
64C22×D292C2×C411yescharacteristic
65C22×D292C2×C411yescharacteristic
66C22×C4×D73C2×C411yescharacteristic
67C22×C4×D73C2×C411yescharacteristic
68C22×C4×D73C2311yescharacteristic
69C22×C4×D73C2311yescharacteristic
70C22×C4×D73C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75#14556586—24no—
76#14556586—24no—
77#14556582—24no—
78#14556580—24no—
79#14556576—24no—
80#14556576—24no—
81#14556567—24no—
82#14556566—24no—
83C4×D292—22no—
84C4×D292—22no—
85C4×D292—22no—
86C4×D292—22no—
87C4×D292—22no—
88C4×D292—22no—
89#14556548—22no—
90#14556548—22no—
91#14556548—22no—
92#14556548—22no—
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×#11924005C2×C411yescharacteristic
101C2×#11924005C2×C411yescharacteristic
102C2×#11924005C2×C411yescharacteristic
103C2×#11924005C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×#11924005C2×C411yescharacteristic
106C2×#11924005C2×C411yescharacteristic
107C2×#11924005C2×C411yescharacteristic
108C2×#11924005C2×C411yescharacteristic
109C2×#11924005C2×C411yescharacteristic
110C2×C4×Dic73C2×C411yescharacteristic
111C2×C4×Dic73C2×C411yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C42×D73—22no—
114C42×D73—22no—
115C4⋊#10596831—22no—
116C4⋊#10596831—22no—
117C4⋊#10596831—22no—
118#14556503—22no—
119#14556503—22no—
120#14556503—22no—
121#14556503—22no—
122#14556503—22no—
123#14556503—22no—
124#14556503—41no—
125#14556503—41no—
126#14556503—41no—
127#14556503—41no—
128#14556503—41no—
129#14556503—41no—
130#14556502—22no—
131#14556502—22no—
132C4×#10596831—22no—
133C22×Q8×C73C2×C411yescharacteristic
134C22×C8×C73C2311yescharacteristic
135C22×C8×C73C2311yescharacteristic
136C22×C8×C73C2311yescharacteristic
137C22×C8×C73C2311yescharacteristic
138C4×Q8×C73D414yes—
139C4×Q8×C73D414yes—
140C2×C4⋊C4×C73C2×C411yescharacteristic
141C2×C4⋊C4×C73C2×C411yescharacteristic
142C2×C4⋊C4×C73C2×C411yescharacteristic
143C2×C42×C73C2311yescharacteristic
144C2×C42×C73C2311yescharacteristic
145C2×C42×C73C2311yescharacteristic
146C4⋊C8×C73—22no—
147C4⋊C8×C73—22no—
148C4⋊C8×C73—22no—
149#97×C73—22no—
150#97×C73—22no—
151C4×C8×C73—22no—
152C23×D73C22×C411yescharacteristic
153C23×D73C22×C411yescharacteristic
154C23×D73C22×C411yescharacteristic
155C2×D292—22no—
156C2×D292—22no—
157C2×D292—22no—
158C2×D292—22no—
159C2×D292—22no—
160C2×D292—41no—
161C2×D292—41no—
162C2×D292—41no—
163C2×D292—41no—
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—21no—
179C2×C4×D73—21no—
180C2×C4×D73—21no—
181C2×C4×D73—21no—
182C2×C4×D73—21no—
183C2×C4×D73—21no—
184C2×C4×D73—21no—
185C2×C4×D73—21no—
186C2×C4×D73—21no—
187C2×C4×D73—21no—
188C2×C4×D73—21no—
189C2×C4×D73—21no—
190C2×C4×D73—41no—
191C2×C4×D73—41no—
192C2×C4×D73—41no—
193C2×#10596831—21no—
194C2×#10596831—21no—
195C2×#10596831—21no—
196C2×#10596831—21no—
197C2×#10596831—21no—
198C2×#10596831—21no—
199C2×#10596831—21no—
200C2×#10596831—21no—
201C2×#10596831—21no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204C2×#10596831#4112yes—
205C4⋊Dic73—22no—
206C4⋊Dic73—22no—
207C4⋊Dic73—22no—
208#11924007—22no—
209#11924007—22no—
210#11924007—22no—
211#11924007—22no—
212#11924005—22no—
213#11924005—22no—
214#11924005—22no—
215#11924005—22no—
216#11924005—22no—
217#11924005—22no—
218#11924005—22no—
219#11924005—22no—
220#11924005—22no—
221#11924005—22no—
222C4×Dic73—22no—
223C4×Dic73—22no—
224C4×Dic73—21no—
225C4×Dic73—21no—
226C2×Q8×C73—41no—
227C2×Q8×C73—41no—
228C2×Q8×C73C22⋊C414yes—
229C22×C4×C73C22×C411yescharacteristic
230C22×C4×C73C22×C411yescharacteristic
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C2411yescharacteristic
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
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#4112yes—
248C4⋊C4×C73C22⋊C414yes—
249C4⋊C4×C73C22⋊C414yes—
250C4⋊C4×C73C22⋊C414yes—
251C42×C73C2×D412yes—
252C42×C73C2×D412yes—
253C42×C73C2×D412yes—
254C42×C73C2×D412yes—
255C42×C73C2×D412yes—
256C42×C73C2×D412yes—
257C23×C73C23×C411yescharacteristic
258C22×D73—21no—
259C22×D73—21no—
260C22×D73—21no—
261C22×D73—21no—
262C22×D73—21no—
263C22×D73—21no—
264C22×D73—21no—
265C22×D73—21no—
266C22×D73—21no—
267C22×D73—21no—
268C22×D73—21no—
269C22×D73—21no—
270C22×D73—21no—
271C22×D73—21no—
272C22×D73—21no—
273C22×D73—21no—
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—21no—
277C22×D73—21no—
278C22×D73#13112yes—
279Q8×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—21no—
291C2×C4×C73—21no—
292C2×C4×C73C2×C22⋊C412yes—
293C2×C4×C73C2×C22⋊C412yes—
294C2×C4×C73C2×C22⋊C412yes—
295C2×C4×C73C2×C22⋊C412yes—
296C2×C4×C73C2×C22⋊C412yes—
297C2×C4×C73C2×C22⋊C412yes—
298C2×C4×C73C22×D411yescharacteristic
299C2×C4×C73C22×D411yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C732−1+411yescharacteristic
304C2×Dic73—21no—
305C2×Dic73—21no—
306C2×Dic73—21no—
307C2×Dic73—21no—
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—
319D292—44no—
320D292—44no—
321D292—44no—
322C4×D73—44no—
323C4×D73—44no—
324C4×D73—41no—
325C4×D73—41no—
326C4×D73—41no—
327C4×D73—41no—
328C4×D73—41no—
329C4×D73—41no—
330C4×D73—41no—
331C4×D73—41no—
332C4×D73—41no—
333C4×D73—41no—
334C4×D73—41no—
335C4×D73—41no—
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×C73C22×C22⋊C411yescharacteristic
345C22×C73C4×#4111yescharacteristic
346C22×C73#52011yescharacteristic
347C22×C73C2×#13111yescharacteristic
348C22×C73#56811yescharacteristic
349C22×C73#56811yescharacteristic
350C22×C73#56811yescharacteristic
351C2×D73—22no—
352C2×D73—22no—
353C2×D73—22no—
354C2×D73—41no—
355C2×D73—41no—
356C2×D73—41no—
357C2×D73—41no—
358C2×D73—41no—
359C2×D73—41no—
360C2×D73—41no—
361C2×D73—41no—
362C2×D73—41no—
363C2×D73—41no—
364C2×D73—41no—
365C2×D73—41no—
366C2×D73—41no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C4×C73—22no—
373C4×C73—22no—
374C4×C73—22no—
375C4×C73—22no—
376C4×C73—22no—
377C4×C73—22no—
378C4×C73#54811yescharacteristic
379C4×C73#54811yescharacteristic
380C4×C73#55011yescharacteristic
381C4×C73#55011yescharacteristic
382Dic73—41no—
383Dic73—41no—
384Dic73—41no—
385Dic73—41no—
386Dic73—41no—
387#22533—731nomaximal, Sylow
388C2×C73#234111yescharacteristic
389C2×C73#287911yescharacteristic
390C2×C73#288011yescharacteristic
391C2×C73#296711yescharacteristic
392C2×C73#296811yescharacteristic
393C2×C73#299211yescharacteristic
394C2×C73#299511yescharacteristic
395D73—42no—
396D73—81no—
397D73—81no—
398C2×#529—731no—
399C2×#446—731no—
400C2×#446D7311yescharacteristic, complemented
401#1955—731no—
402#1955—731no—
403#1955—731no—
404#1955—731no—
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×Q8C2×D7311yescharacteristic
425C2×C4×D4—731no—
426C2×C4×D4—731no—
427C2×C4×D4—731no—
428C2×#117—731no—
429C2×#117—731no—
430C22×C42—731no—
431#446—24no—
432#446—1464no—
433C2×C4⋊C8—731no—
434C2×C4⋊C8—731no—
435C2×C4⋊C8—731no—
436C2×C4⋊C8C2×D7311yescharacteristic
437C2×C4⋊C8C2×D7311yescharacteristic
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⋊C8—731no—
448C2×C22⋊C8—731no—
449C2×C22⋊C8—731no—
450C2×C22⋊C8—731no—
451C2×#97—731no—
452C2×#97—731no—
453C2×#97C2×D7311yescharacteristic
454C2×#97C2×D7311yescharacteristic
455C2×C4×C8—731no—
456C2×C4×C8C2×D7311yescharacteristic
457#336—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461C22×Q8C4×D7311yescharacteristic
462C22×D4—731no—
463C22×D4—731no—
464C22×D4—731no—
465C23×C4—731no—
466C23×C4—731no—
467C23×C4—731no—
468C23×C4—731no—
469C23×C4—731no—
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×Q8D29214yes—
487C4×Q8C22⋊D7314yes—
488C4×D4—1462no—
489C4×D4—1462no—
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⋊C4C4×D7311yescharacteristic
506C2×C4⋊C4C4×D7311yescharacteristic
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⋊C4—731no—
517C2×C22⋊C4—731no—
518C2×C42—731no—
519C2×C42—731no—
520C2×C42—731no—
521C2×C42—1462no—
522C2×C42—1462no—
523C2×C42C22×D7311yescharacteristic
524C2×C42C22×D7311yescharacteristic
525C2×C42C22×D7311yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—1462no—
530C4⋊C8—1462no—
531C4⋊C8—1462no—
532C22⋊C8—2921no—
533C22⋊C8—2921no—
534C22⋊C8—2921no—
535C22⋊C8—2921no—
536C22⋊C8—2921no—
537C22⋊C8—2921no—
538C22⋊C8—1462no—
539C22⋊C8—1462no—
540C22⋊C8—1462no—
541C22⋊C8—1462no—
542C22⋊C8—1462no—
543C22⋊C8—1462no—
544#97—22no—
545#97—22no—
546#97—1462no—
547#97—1462no—
548C4×C8—22no—
549C4×C8—1462no—
550C24—731no—
551C24—731no—
552C24—731no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8#1192400514yes—
556C2×D4—2921no—
557C2×D4—2921no—
558C2×D4—2921no—
559C2×D4—2921no—
560C2×D4—1462no—
561C2×D4—1462no—
562C2×D4—1462no—
563C2×D4—1462no—
564C2×D4—1462no—
565C22×C4—2921no—
566C22×C4—2921no—
567C22×C4—2921no—
568C22×C4—731no—
569C22×C4—731no—
570C22×C4—731no—
571C22×C4—731no—
572C22×C4—731no—
573C22×C4—1462no—
574C22×C4—1462no—
575C22×C4—1462no—
576C22×C4—1461no—
577C22×C4—1461no—
578C22×C4—1461no—
579C22×C4—1461no—
580C22×C4—1461no—
581C22×C4—1461no—
582C22×C4—1461no—
583C22×C4—1461no—
584C22×C4—1461no—
585C22×C4—1461no—
586C22×C4—1461no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4C2×C4×D7311yescharacteristic
595C22×C4C2×C4×D7311yescharacteristic
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#1192402912yes—
625C4⋊C4—1462no—
626C4⋊C4—1462no—
627C4⋊C4—1462no—
628C4⋊C4—1462no—
629C4⋊C4—1462no—
630C4⋊C4—1462no—
631C4⋊C4—1462no—
632C4⋊C4#1192400514yes—
633C4⋊C4#1192400514yes—
634C4⋊C4#1192400514yes—
635C22⋊C4—1462no—
636C22⋊C4—1462no—
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—1462no—
646C42—1462no—
647C42—1461no—
648C42—1461no—
649C42C2×C22⋊D7312yes—
650C42C2×C22⋊D7312yes—
651C42C2×C22⋊D7312yes—
652C42C2×D29212yes—
653C42C2×D29212yes—
654C42C2×D29212yes—
655C23—732no—
656C23—1461no—
657C23—1461no—
658C23—1461no—
659C23—1461no—
660C23—1461no—
661C23—1461no—
662C23—1461no—
663C23—1461no—
664C23—1461no—
665C23—1461no—
666C23—1461no—
667C23—1461no—
668C23—1461no—
669C23—1461no—
670C23—1461no—
671C23—1461no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23C22×C4×D7311yescharacteristic
677Q8—44no—
678D4—2924no—
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—21no—
692C2×C4—21no—
693C2×C4—2924no—
694C2×C4—2924no—
695C2×C4—2921no—
696C2×C4—2921no—
697C2×C4—2921no—
698C2×C4—2921no—
699C2×C4—2921no—
700C2×C4—2921no—
701C2×C4—2921no—
702C2×C4—2921no—
703C2×C4—2921no—
704C2×C4—2921no—
705C2×C4—2921no—
706C2×C4—2921no—
707C2×C4—1461no—
708C2×C4—1461no—
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×C4C2×#1192400512yes—
723C2×C4C2×#1192400512yes—
724C2×C4C2×#1192400512yes—
725C2×C4C2×#1192400512yes—
726C2×C4C2×#1192400512yes—
727C2×C4C2×#1192400512yes—
728C2×C4C22×C22⋊D7311yescharacteristic
729C2×C4C22×D29211yescharacteristic
730C2×C4#41×D7311yescharacteristic
731C2×C4C2×#1192402911yescharacteristic
732C2×C4#1455663711yescharacteristic
733C2×C4#1455663911yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—2921no—
739C8—2921no—
740C8—2921no—
741C8—1462no—
742C22—2921no—
743C22—2921no—
744C22—2921no—
745C22—2921no—
746C22—2921no—
747C22—2921no—
748C22—2921no—
749C22—2921no—
750C22—2921no—
751C22—2921no—
752C22—2921no—
753C22—2921no—
754C22—2921no—
755C22—2921no—
756C22—2921no—
757C22—2921no—
758C22—2921no—
759C22—2921no—
760C22—1462no—
761C22—1462no—
762C22—1462no—
763C22C22×#1192400511yescharacteristic
764C22C4×#1192402911yescharacteristic
765C22#1798906911yescharacteristic
766C22#131×D7311yescharacteristic
767C22#1798935211yescharacteristic
768C22#1798935311yescharacteristic
769C22#1798935311yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—2921no—
777C4—2921no—
778C4—2921no—
779C4—2921no—
780C4—2921no—
781C4#1798924811yescharacteristic
782C4#1798924911yescharacteristic
783C4#1798925611yescharacteristic
784C4#1798925911yescharacteristic
785C2—2922no—
786C2—5841no—
787C2—5841no—
788C2#2261276911yescharacteristic
789C2#2261837511yescharacteristic
790C2#2261837811yescharacteristic
791C2#2261891511yescharacteristic
792C2#2261892411yescharacteristic
793C2#2261906911yescharacteristic
794C2#2261910011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#446×C73C2
prime radicalC2×#14556566C4
cosocleC22×C4×C73C24
hypercenterC2×#446D73
hypocenterC73#22533
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#17988718C2semidirect
3. #22610729C2semidirect
4. #22610729C2semidirect
5. #22610728C2semidirect
6. #22610728C2semidirect
7. #22610725C2semidirect
8. #22610724C2semidirect
9. #22609912C2semidirect
10. #22609912C2semidirect
11. #22609908C2semidirect
12. #22609700C2semidirect
13. #22609698C2semidirect
14. #22609694C2semidirect
15. C2×#446×C73C2semidirect
400. C2×#446D73semidirect
413. C73#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#179891242
C2×#179887182
#226107292
#226107282
#226107252
#226107242
#226099122
#226099082
#226097002
#226096982
#226096942
C2×#446×C732
#2253373