Finite Group Databasebeta

← #33102041

Subgroups — #33102041

Order 18688.

1202 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989115C211yesmaximal, characteristic
2C2×#17988661C211yesmaximal, characteristic, complemented
3C2×#17988650C211yesmaximal, characteristic, complemented
4#22610869C211yesmaximal, characteristic, complemented
5#22610865C211yesmaximal, characteristic, complemented
6#22610226C211yesmaximal, characteristic, complemented
7#22610222C211yesmaximal, characteristic, complemented
8#22610222C211yesmaximal, characteristic, complemented
9#22610221C211yesmaximal, characteristic, complemented
10#22609998C211yesmaximal, characteristic, complemented
11#22609914C211yesmaximal, characteristic, complemented
12#22609696C211yesmaximal, characteristic, complemented
13#22609628C211yesmaximal, characteristic, complemented
14#336×D73C211yesmaximal, characteristic, complemented
15C73×#1818C211yesmaximal, characteristic, complemented
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19C22×C8×D73C2211yescharacteristic
20#17989115—24no—
21#17989115—24no—
22C2×#14556586C411yescharacteristic
23C2×#14556584C411yescharacteristic
24C2×#14556581C411yescharacteristic
25C2×#14556577C411yescharacteristic
26C2×#14556576C411yescharacteristic
27C2×#14556573C411yescharacteristic
28C2×#14556569C411yescharacteristic
29C2×#14556564C411yescharacteristic
30C2×C4×Dic146C2211yescharacteristic
31C2×C4×D292C2211yescharacteristic
32C2×C4×C22⋊D73C2211yescharacteristic
33C2×C4×C22⋊D73C2211yescharacteristic
34C2×#14556548C2211yescharacteristic
35C2×C42×D73C2211yescharacteristic
36#17988661—24no—
37#17988650—24no—
38C2×#14556520C2211yescharacteristic
39C2×#14556520C2211yescharacteristic
40C2×#14556503C2211yescharacteristic
41C2×#14556503C2211yescharacteristic
42C2×#14556503C2211yescharacteristic
43C2×#14556503C2211yescharacteristic
44C2×#14556503C2211yescharacteristic
45C2×#14556503C2211yescharacteristic
46C2×#14556501C2211yescharacteristic
47C2×C8×Dic73C2211yescharacteristic
48#17988342C2211yescharacteristic
49#17988342C2211yescharacteristic
50#17988342C2211yescharacteristic
51#17988342C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55#17988341C2211yescharacteristic
56C2×#117×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C22⋊C8×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61#336×C73C2211yescharacteristic
62#336×C73C2211yescharacteristic
63C22×Dic146C2×C411yescharacteristic
64C22×D292C2×C411yescharacteristic
65C22×C22⋊D73C2×C411yescharacteristic
66C22×C22⋊D73C2×C411yescharacteristic
67C22×C4×D73C2×C411yescharacteristic
68C22×C4×D73C2×C411yescharacteristic
69C22×C4×D73C2311yescharacteristic
70C22×C4×D73C2311yescharacteristic
71C2×#11924012—22no—
72C2×#11924012—22no—
73C2×#11924012—41no—
74C22×#10596831—22no—
75C22×#10596831—22no—
76C22×#10596831—41no—
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C22×#10596831C2311yescharacteristic
81C2×C8×D73—22no—
82C2×C8×D73—22no—
83C2×C8×D73—22no—
84C2×C8×D73—22no—
85C2×C8×D73—41no—
86C2×C8×D73—41no—
87#14556586—24no—
88#14556584—24no—
89#14556581—24no—
90#14556577—24no—
91#14556576—24no—
92#14556573—24no—
93#14556569—24no—
94#14556564—24no—
95C4×Dic146—22no—
96C4×Dic146—22no—
97C4×D292—22no—
98C4×D292—22no—
99C4×C22⋊D73—22no—
100C4×C22⋊D73—22no—
101C4×C22⋊D73D414yes—
102C4×C22⋊D73D414yes—
103#14556548—22no—
104#14556548—22no—
105C2×C4⋊Dic73C2×C411yescharacteristic
106C2×C4⋊Dic73C2×C411yescharacteristic
107C2×#11924007C2×C411yescharacteristic
108C2×#11924007C2×C411yescharacteristic
109C2×#11924007C2×C411yescharacteristic
110C2×#11924007C2×C411yescharacteristic
111C2×#11924007C2×C411yescharacteristic
112C2×#11924007C2×C411yescharacteristic
113C2×C22⋊Dic73C2×C411yescharacteristic
114C2×C22⋊Dic73C2×C411yescharacteristic
115C2×#11924005C2×C411yescharacteristic
116C2×#11924005C2×C411yescharacteristic
117C2×#11924005C2×C411yescharacteristic
118C2×#11924005C2×C411yescharacteristic
119C2×#11924005C2×C411yescharacteristic
120C2×#11924005C2×C411yescharacteristic
121C2×C4×Dic73C2×C411yescharacteristic
122C2×C4×Dic73C2×C411yescharacteristic
123C2×C4×Dic73C2311yescharacteristic
124C2×C4×Dic73C2311yescharacteristic
125C42×D73—22no—
126C42×D73—22no—
127#14556520—22no—
128#14556520—22no—
129#14556503—22no—
130#14556503—22no—
131#14556503—22no—
132#14556503—22no—
133#14556503—41no—
134#14556503—41no—
135#14556501—22no—
136C8×Dic73—22no—
137C23×C4×C73C2311yescharacteristic
138C22×C8×C73C2311yescharacteristic
139C22×C8×C73C2311yescharacteristic
140C22×C8×C73C2311yescharacteristic
141C22×C8×C73C2311yescharacteristic
142#117×C73—22no—
143#117×C73—22no—
144C2×C4⋊C4×C73C2×C411yescharacteristic
145C2×C4⋊C4×C73C2×C411yescharacteristic
146C2×C22⋊C4×C73C2×C411yescharacteristic
147C2×C22⋊C4×C73C2×C411yescharacteristic
148C2×C42×C73C2311yescharacteristic
149C2×C42×C73C2311yescharacteristic
150C22⋊C8×C73—22no—
151C22⋊C8×C73—22no—
152C23×D73C22×C411yescharacteristic
153C23×D73C22×C411yescharacteristic
154C2×Dic146—22no—
155C2×Dic146—22no—
156C2×Dic146—41no—
157C2×D292—22no—
158C2×D292—22no—
159C2×D292—22no—
160C2×C22⋊D73—22no—
161C2×C22⋊D73—22no—
162C2×C22⋊D73—22no—
163C2×C22⋊D73—22no—
164C2×C22⋊D73—41no—
165C2×C22⋊D73C22⋊C414yes—
166C22×Dic73C22×C411yescharacteristic
167C22×Dic73C22×C411yescharacteristic
168C22×Dic73C22×C411yescharacteristic
169C22×Dic73C22×C411yescharacteristic
170C22×Dic73C22×C411yescharacteristic
171C22×Dic73C22×C411yescharacteristic
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—21no—
176C2×C4×D73—22no—
177C2×C4×D73—22no—
178C2×C4×D73—22no—
179C2×C4×D73—22no—
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—22no—
187C2×C4×D73—41no—
188C2×C4×D73C2×D412yes—
189C2×C4×D73C2×D412yes—
190#11924012—44no—
191C2×#10596831—21no—
192C2×#10596831—21no—
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—44no—
202C2×#10596831#4112yes—
203C2×#10596831#4112yes—
204C8×D73—44no—
205C8×D73—44no—
206C4⋊Dic73—22no—
207C4⋊Dic73—22no—
208#11924007—22no—
209#11924007—22no—
210#11924007—22no—
211#11924007—22no—
212#11924007—22no—
213#11924007C22⋊C414yes—
214C22⋊Dic73—22no—
215C22⋊Dic73C22⋊C414yes—
216#11924005—22no—
217#11924005—22no—
218#11924005—22no—
219#11924005—22no—
220#11924005—22no—
221#11924005C22⋊C414yes—
222C4×Dic73—21no—
223C4×Dic73—21no—
224C4×Dic73—22no—
225C4×Dic73—22no—
226C4×Dic73C2×D412yes—
227C4×Dic73C2×D412yes—
228C24×C73C22×C411yescharacteristic
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C22×C411yescharacteristic
236C22×C4×C73C22×C411yescharacteristic
237C22×C4×C73C22×C411yescharacteristic
238C22×C4×C73C2×D412yes—
239C22×C4×C73C2×D412yes—
240C22×C4×C73C2411yescharacteristic
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—21no—
252C2×C8×C73—21no—
253C4⋊C4×C73—22no—
254C4⋊C4×C73—22no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—22no—
257C42×C73—21no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—21no—
261C23×C73—21no—
262C23×C73—21no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—21no—
267C23×C73C2×C22⋊C412yes—
268C23×C73C23×C411yescharacteristic
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—21no—
279C22×D73—21no—
280C22×D73C2×C22⋊C412yes—
281C22×D73#13112yes—
282C22×D73#13112yes—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—22no—
286C2×C4×C73—22no—
287C2×C4×C73—22no—
288C2×C4×C73—22no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73C2×C22⋊C412yes—
302C2×C4×C73C22×D411yescharacteristic
303C2×C4×C73C22×D411yescharacteristic
304C2×C4×C73C2×#4111yescharacteristic
305C2×C4×C73C2×#4111yescharacteristic
306C2×C4×C73H(5,𝔽2)11yescharacteristic
307C2×C4×C732−1+411yescharacteristic
308C22⋊D73—28no—
309C22⋊D73—44no—
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×Dic73C2×C22⋊C412yes—
325C2×Dic73C2×C22⋊C412yes—
326C2×Dic73C2×C22⋊C412yes—
327C2×Dic73#13112yes—
328D292—44no—
329C4×D73—22no—
330C4×D73—22no—
331C4×D73—22no—
332C4×D73—22no—
333C4×D73—44no—
334C4×D73—44no—
335C4×D73—41no—
336C4×D73—41no—
337C4×D73—41no—
338C4×D73—41no—
339Dic146—44no—
340C8×C73—41no—
341C8×C73—41no—
342C8×C73—41no—
343C8×C73—41no—
344#10596831—22no—
345#10596831—22no—
346#10596831—41no—
347#10596831—41no—
348C22×C73—22no—
349C22×C73—22no—
350C22×C73—22no—
351C22×C73—41no—
352C22×C73—41no—
353C22×C73—41no—
354C22×C73—41no—
355C22×C73C22×C22⋊C411yescharacteristic
356C22×C73C4×#4111yescharacteristic
357C22×C73#52011yescharacteristic
358C22×C73C2×#13111yescharacteristic
359C22×C73C2×#13111yescharacteristic
360C22×C73C2×#13111yescharacteristic
361C22×C73#56811yescharacteristic
362C2×D73—22no—
363C2×D73—22no—
364C2×D73—22no—
365C2×D73—22no—
366C2×D73—22no—
367C2×D73—22no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C2×D73—41no—
373C2×D73—41no—
374C2×D73—41no—
375C2×D73#40814yes—
376C4×C73—22no—
377C4×C73—41no—
378C4×C73—41no—
379C4×C73—41no—
380C4×C73—41no—
381C4×C73#54611yescharacteristic
382C4×C73#54611yescharacteristic
383C4×C73#54711yescharacteristic
384C4×C73#54711yescharacteristic
385Dic73—22no—
386Dic73—22no—
387Dic73—22no—
388Dic73—22no—
389Dic73—41no—
390Dic73—41no—
391#22470—731nomaximal, Sylow
392C2×C73—42no—
393C2×C73#233911yescharacteristic
394C2×C73C2×#40811yescharacteristic
395C2×C73#288011yescharacteristic
396C2×C73#296611yescharacteristic
397C2×C73#296811yescharacteristic
398C2×C73#299211yescharacteristic
399C2×C73#299411yescharacteristic
400D73—24no—
401D73—81no—
402C2×#529—731no—
403C2×#435—731no—
404C2×C8×D4—731no—
405#1985—731no—
406#1984—731no—
407#1870—731no—
408#1869—731no—
409#1869—731no—
410#1869—731no—
411#1818D7311yescharacteristic, complemented
412#1817—731no—
413#1798—731no—
414#1750—731no—
415#1729—731no—
416C2×#336—731no—
417C73#2247011yescharacteristic, complemented, Sylow
418C22×M16—731no—
419C23×C8—731no—
420C23×C8—731no—
421C23×C8—731no—
422#529—1464no—
423#529—1464no—
424C2×#126—731no—
425C2×#126—731no—
426C2×#125—731no—
427C2×#124—731no—
428C2×#123—731no—
429C2×#123—731no—
430C2×C22⋊Q8—731no—
431C2×#121—731no—
432C2×C4×Q8—731no—
433C2×C4×D4—731no—
434C2×C4×D4—731no—
435C2×C4×D4—731no—
436C2×#117—731no—
437C2×#117C2×D7311yescharacteristic
438C22×C42—731no—
439#435—1464no—
440C8×D4—1464no—
441C2×C4⋊C8—731no—
442C2×C4⋊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⋊C8C2×D7311yescharacteristic
450C2×C22⋊C8C2×D7311yescharacteristic
451C2×#97—731no—
452C2×C4×C8—731no—
453#336—731no—
454#336—731no—
455#336—731no—
456#336—731no—
457#336—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461#336C2×D7311yescharacteristic
462#336C2×D7311yescharacteristic
463#336C2×D7311yescharacteristic
464#336C2×D7311yescharacteristic
465C22×Q8—731no—
466C22×D4—731no—
467C22×D4—731no—
468C22×D4—731no—
469C23×C4—731no—
470C23×C4—731no—
471C23×C4—731no—
472C23×C4—731no—
473C23×C4C22×D7311yescharacteristic
474C2×M16—2921no—
475C2×M16—1462no—
476C2×M16—1462no—
477C22×C8—2921no—
478C22×C8—2921no—
479C22×C8—2921no—
480C22×C8—731no—
481C22×C8—731no—
482C22×C8—731no—
483C22×C8—731no—
484C22×C8—1462no—
485C22×C8—1462no—
486C22×C8—1462no—
487C22×C8—1462no—
488C22×C8—1462no—
489C22×C8—1462no—
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492C22×C8C22×D7311yescharacteristic
493C22×C8C22×D7311yescharacteristic
494#126—1464no—
495#126—1464no—
496#125—1464no—
497#124—1464no—
498#123—1464no—
499#123—1464no—
500C22⋊Q8—1464no—
501#121—1464no—
502C4×Q8—1462no—
503C4×Q8—1462no—
504C4×D4—734no—
505C4×D4—734no—
506C4×D4—1462no—
507C4×D4—1462no—
508C4×D4—1462no—
509C4×D4—1462no—
510#117—22no—
511#117—22no—
512#117—1462no—
513#117—1462no—
514C2×C4⋊C4—731no—
515C2×C4⋊C4—731no—
516C2×C4⋊C4—731no—
517C2×C4⋊C4—731no—
518C2×C4⋊C4—731no—
519C2×C4⋊C4—731no—
520C2×C4⋊C4—731no—
521C2×C4⋊C4—731no—
522C2×C4⋊C4C4×D7311yescharacteristic
523C2×C4⋊C4C4×D7311yescharacteristic
524C2×C22⋊C4—731no—
525C2×C22⋊C4—731no—
526C2×C22⋊C4—731no—
527C2×C22⋊C4—731no—
528C2×C22⋊C4—731no—
529C2×C22⋊C4—731no—
530C2×C22⋊C4—731no—
531C2×C22⋊C4—731no—
532C2×C22⋊C4C4×D7311yescharacteristic
533C2×C22⋊C4C4×D7311yescharacteristic
534C2×C42—731no—
535C2×C42—731no—
536C2×C42—731no—
537C2×C42—731no—
538C2×C42—1462no—
539C2×C42—1462no—
540C2×C42C22×D7311yescharacteristic
541C2×C42C22×D7311yescharacteristic
542C4⋊C8—1462no—
543C4⋊C8—1462no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—2921no—
547C22⋊C8—2921no—
548C22⋊C8—1462no—
549C22⋊C8—1462no—
550C22⋊C8—1462no—
551C22⋊C8—1462no—
552#97—1462no—
553C4×C8—1462no—
554C24—731no—
555C24—731no—
556C24C2×C4×D7311yescharacteristic
557C2×Q8—2921no—
558C2×Q8—1462no—
559C2×Q8—1462no—
560C2×D4—2921no—
561C2×D4—734no—
562C2×D4—1462no—
563C2×D4—1462no—
564C2×D4—1462no—
565C2×D4—1462no—
566C2×D4—1462no—
567C2×D4—1462no—
568C2×D4—1462no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—2921no—
574C22×C4—731no—
575C22×C4—731no—
576C22×C4—731no—
577C22×C4—731no—
578C22×C4—732no—
579C22×C4—732no—
580C22×C4—731no—
581C22×C4—731no—
582C22×C4—1462no—
583C22×C4—1462no—
584C22×C4—1462no—
585C22×C4—1462no—
586C22×C4—1462no—
587C22×C4—1461no—
588C22×C4—1461no—
589C22×C4—1461no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4C2×C4×D7311yescharacteristic
598C22×C4C2×C4×D7311yescharacteristic
599C22×C4C2×C4×D7311yescharacteristic
600C22×C4C2×C4×D7311yescharacteristic
601C22×C4C2×C4×D7311yescharacteristic
602C22×C4D4×D7312yes—
603C22×C4D4×D7312yes—
604C22×C4C23×D7311yescharacteristic
605M16—2924no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—2924no—
619C2×C8—2924no—
620C2×C8—2924no—
621C2×C8—732no—
622C2×C8—732no—
623C2×C8—1461no—
624C2×C8—1461no—
625C2×C8—1461no—
626C2×C8—1461no—
627C2×C8—1461no—
628C2×C8—1461no—
629C2×C8—1461no—
630C2×C8—1461no—
631C2×C8—1461no—
632C2×C8—1461no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—734no—
636C4⋊C4—1462no—
637C4⋊C4—1462no—
638C4⋊C4—1462no—
639C4⋊C4—1462no—
640C4⋊C4—1462no—
641C4⋊C4—1462no—
642C4⋊C4—1462no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—734no—
646C22⋊C4—734no—
647C22⋊C4—1462no—
648C22⋊C4—1462no—
649C22⋊C4—1462no—
650C22⋊C4—1462no—
651C22⋊C4—1462no—
652C22⋊C4—1462no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—732no—
658C42—732no—
659C42—1462no—
660C42—1462no—
661C42—1461no—
662C42—1461no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—732no—
670C23—732no—
671C23—732no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23—1461no—
680C23—1461no—
681C23—1461no—
682C23—1461no—
683C23C22⋊C4×D7312yes—
684C23C22×C4×D7311yescharacteristic
685Q8—2924no—
686D4—2924no—
687D4—2924no—
688D4—1468no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—2924no—
708C2×C4—2924no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—732no—
714C2×C4—732no—
715C2×C4—732no—
716C2×C4—732no—
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×C4—1461no—
727C2×C4—1461no—
728C2×C4—1461no—
729C2×C4—1461no—
730C2×C4—1461no—
731C2×C4—1462no—
732C2×C4—1462no—
733C2×C4—1462no—
734C2×C4—1462no—
735C2×C4C22⋊C4×D7312yes—
736C2×C4C2×D4×D7311yescharacteristic
737C2×C4C2×D4×D7311yescharacteristic
738C2×C4#41×D7311yescharacteristic
739C2×C4#41×D7311yescharacteristic
740C2×C4#1455663711yescharacteristic
741C2×C4#1455663811yescharacteristic
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—2921no—
747C8—2921no—
748C8—1462no—
749C8—1462no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—2921no—
758C22—2921no—
759C22—2921no—
760C22—2921no—
761C22—2921no—
762C22—2921no—
763C22—2921no—
764C22—734no—
765C22—1462no—
766C22—1462no—
767C22—1462no—
768C22—1462no—
769C22—1462no—
770C22—1462no—
771C22C2×C22⋊C4×D7311yescharacteristic
772C22#1798905511yescharacteristic
773C22#1798906711yescharacteristic
774C22#131×D7311yescharacteristic
775C22#131×D7311yescharacteristic
776C22#131×D7311yescharacteristic
777C22#1798935211yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—2921no—
784C4—2921no—
785C4—1462no—
786C4—1462no—
787C4—1462no—
788C4—1462no—
789C4#1798922911yescharacteristic
790C4#1798922911yescharacteristic
791C4#1798923511yescharacteristic
792C4#1798923511yescharacteristic
793C2—42no—
794C2—5841no—
795C2—1464no—
796C2#2261275511yescharacteristic
797C2#408×D7311yescharacteristic
798C2#2261837911yescharacteristic
799C2#2261890411yescharacteristic
800C2#2261892311yescharacteristic
801C2#2261906511yescharacteristic
802C2#2261908511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1818C2
prime radicalC2×#14556564C4
cosocleC22×C4×C73C24
hypercenter#1818D73
hypocenterC73#22470
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. C2×#17988661C2semidirect
3. C2×#17988650C2semidirect
4. #22610869C2semidirect
5. #22610865C2semidirect
6. #22610226C2semidirect
7. #22610222C2semidirect
8. #22610222C2semidirect
9. #22610221C2semidirect
10. #22609998C2semidirect
11. #22609914C2semidirect
12. #22609696C2semidirect
13. #22609628C2semidirect
14. #336×D73C2semidirect
15. C73×#1818C2semidirect
411. #1818D73semidirect
417. C73#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#179891152
C2×#179886612
C2×#179886502
#226108692
#226108652
#226102262
#226102222
#226102212
#226099982
#226099142
#226096962
#226096282
#336×D732
C73×#18182
#2247073