Finite Group Databasebeta

← #33112041

Subgroups — #33112041

Order 18688.

918 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613146C211yesmaximal, characteristic
2#22610727C211yesmaximal, characteristic, complemented
3#22610723C211yesmaximal, characteristic, complemented
4#22610543C211yesmaximal, characteristic, complemented
5#22610541C211yesmaximal, characteristic, complemented
6#22610537C211yesmaximal, characteristic, complemented
7#22610537C211yesmaximal, characteristic, complemented
8#22610536C211yesmaximal, characteristic, complemented
9#22610534C211yesmaximal, characteristic, complemented
10#22610224C211yesmaximal, characteristic, complemented
11#22610221C211yesmaximal, characteristic, complemented
12#22610221C211yesmaximal, characteristic, complemented
13#22609842C211yesmaximal, characteristic, complemented
14#22609842C211yesmaximal, characteristic, complemented
15C73×#1954C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×C4×C22⋊D73C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×C22⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556503C2211yescharacteristic
33C2×#14556501C2211yescharacteristic
34C2×C8×Dic73C2211yescharacteristic
35#17988507C411yescharacteristic
36#17988504C411yescharacteristic
37#17988502C411yescharacteristic
38#17988502C411yescharacteristic
39#17988499C411yescharacteristic
40#17988496C411yescharacteristic
41#17988495C411yescharacteristic
42#17988495C411yescharacteristic
43C4×#11924005C2211yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4×D4×C73C2211yescharacteristic
53C2×C4⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57C2×C22⋊C8×C73C2211yescharacteristic
58C2×C4×C8×C73C2211yescharacteristic
59C2×#11924028—41no—
60C2×#11924028—41no—
61C2×#11924028—41no—
62C2×#11924028—41no—
63C2×#11924028—41no—
64C2×#11924028—41no—
65C22×Dic146C2×C411yescharacteristic
66C22×D292C2×C411yescharacteristic
67C22×C22⋊D73C2×C411yescharacteristic
68C22×C22⋊D73C2×C411yescharacteristic
69C22×C22⋊D73C2×C411yescharacteristic
70C22×C22⋊D73C2×C411yescharacteristic
71C22×C4×D73C2311yescharacteristic
72C22×C4×D73C2311yescharacteristic
73C22×#10596831—41no—
74C22×#10596831—41no—
75C22×#10596831—41no—
76C22×#10596831C2311yescharacteristic
77C22×#10596831C2311yescharacteristic
78C22×#10596831C2311yescharacteristic
79C22×#10596831C2311yescharacteristic
80C4×C22⋊D73—41no—
81C4×C22⋊D73—41no—
82C4×C22⋊D73—41no—
83C4×C22⋊D73—41no—
84C2×#11924007C2×C411yescharacteristic
85C2×#11924007C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×C22⋊Dic73C2×C411yescharacteristic
88C2×C22⋊Dic73C2×C411yescharacteristic
89C2×C22⋊Dic73C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×#11924005C2×C411yescharacteristic
92C2×#11924005C2×C411yescharacteristic
93C2×#11924005C2×C411yescharacteristic
94C2×#11924005C2×C411yescharacteristic
95C2×#11924005C2×C411yescharacteristic
96C2×C4×Dic73C2311yescharacteristic
97C2×C4×Dic73C2311yescharacteristic
98#14556520—41no—
99#14556520—41no—
100C22⋊#10596831—41no—
101C22⋊#10596831—41no—
102C22⋊#10596831—41no—
103#14556503—41no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556503—41no—
109#14556503—41no—
110#14556503—41no—
111#14556501—41no—
112C8×Dic73—41no—
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117#14556498C2×C411yescharacteristic
118#14556498C2×C411yescharacteristic
119C22×D4×C73C2×C411yescharacteristic
120C23×C4×C73C2311yescharacteristic
121C23×C4×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125C22×C8×C73C2311yescharacteristic
126C4×D4×C73—41no—
127C4×D4×C73—41no—
128C2×C4⋊C4×C73C2×C411yescharacteristic
129C2×C22⋊C4×C73C2×C411yescharacteristic
130C2×C22⋊C4×C73C2×C411yescharacteristic
131C2×C42×C73C2311yescharacteristic
132C4⋊C8×C73—41no—
133C22⋊C8×C73—41no—
134C22⋊C8×C73—41no—
135C22⋊C8×C73—41no—
136C22⋊C8×C73—41no—
137C4×C8×C73—41no—
138C23×D73C22×C411yescharacteristic
139C23×D73C22×C411yescharacteristic
140#11924028—44no—
141#11924028—44no—
142#11924028—44no—
143#11924028—44no—
144C2×Dic146—41no—
145C2×Dic146—41no—
146C2×Dic146—41no—
147C2×D292—41no—
148C2×D292—41no—
149C2×D292—41no—
150C2×C22⋊D73—22no—
151C2×C22⋊D73—22no—
152C2×C22⋊D73—22no—
153C2×C22⋊D73—41no—
154C2×C22⋊D73—41no—
155C2×C22⋊D73—41no—
156C2×C22⋊D73—41no—
157C2×C22⋊D73—41no—
158C2×C22⋊D73—41no—
159C2×C22⋊D73—41no—
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
168C2×C4×D73—21no—
169C2×C4×D73—21no—
170C2×C4×D73—21no—
171C2×C4×D73—21no—
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×#10596831—21no—
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—44no—
193#11924007—41no—
194#11924007—41no—
195C22⋊Dic73—22no—
196C22⋊Dic73—41no—
197C22⋊Dic73—41no—
198C22⋊Dic73—41no—
199#11924005—22no—
200#11924005—22no—
201#11924005—22no—
202#11924005—41no—
203#11924005—41no—
204#11924005—41no—
205C4×Dic73—21no—
206C4×Dic73—21no—
207C4×Dic73—21no—
208C4×Dic73—21no—
209C24×C73C22×C411yescharacteristic
210C24×C73C22×C411yescharacteristic
211C2×D4×C73—22no—
212C2×D4×C73—22no—
213C2×D4×C73—41no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73C22×C411yescharacteristic
227C22×C4×C73C22×C411yescharacteristic
228C22×C4×C73C22×C411yescharacteristic
229C22×C4×C73C22×C411yescharacteristic
230C22×C4×C73C2411yescharacteristic
231C2×C8×C73—21no—
232C2×C8×C73—21no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
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—
243C4⋊C4×C73—41no—
244C22⋊C4×C73—41no—
245C22⋊C4×C73—41no—
246C42×C73—21no—
247C42×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73—21no—
253C23×C73—21no—
254C23×C73—21no—
255C23×C73—21no—
256C23×C73—21no—
257C23×C73—21no—
258C23×C73—21no—
259C23×C73—21no—
260C23×C73—21no—
261C23×C73#13112yes—
262C23×C73C23×C411yescharacteristic
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—
277D4×C73—44no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
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—41no—
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#13112yes—
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×C4×C73H(5,𝔽2)11yescharacteristic
301C2×C4×C73H(5,𝔽2)11yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C22⋊D73—44no—
305C22⋊D73—44no—
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×Dic73#13112yes—
326D292—44no—
327C4×D73—41no—
328C4×D73—41no—
329C4×D73—41no—
330C4×D73—41no—
331C4×D73—41no—
332C4×D73—41no—
333C4×D73—41no—
334C4×D73—41no—
335Dic146—44no—
336C8×C73—41no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340#10596831—41no—
341#10596831—41no—
342#10596831—41no—
343#10596831—41no—
344C22×C73—22no—
345C22×C73—22no—
346C22×C73—22no—
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×C73#51811yescharacteristic
359C22×C73#51811yescharacteristic
360C22×C73#51811yescharacteristic
361C22×C73C2×#13111yescharacteristic
362C22×C73C2×#13111yescharacteristic
363C22×C73C2×#13111yescharacteristic
364C22×C73#56811yescharacteristic
365C2×D73—41no—
366C2×D73—41no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—41no—
370C2×D73—41no—
371C2×D73—41no—
372C2×D73—41no—
373C2×D73—41no—
374C2×D73—41no—
375C2×D73—41no—
376C2×D73—41no—
377C2×D73—41no—
378C2×D73—41no—
379C4×C73—22no—
380C4×C73—41no—
381C4×C73—41no—
382C4×C73—41no—
383C4×C73#56011yescharacteristic
384C4×C73#56011yescharacteristic
385C4×C73#56011yescharacteristic
386C4×C73H(3,𝔽4)11yescharacteristic
387Dic73—22no—
388Dic73—41no—
389Dic73—41no—
390Dic73—41no—
391Dic73—41no—
392Dic73—41no—
393#23310—731nomaximal, Sylow
394C2×C73—42no—
395C2×C73—81no—
396C2×C73#237511yescharacteristic
397C2×C73#297611yescharacteristic
398C2×C73#297711yescharacteristic
399C2×C73#297711yescharacteristic
400C2×C73#297911yescharacteristic
401C2×C73#298111yescharacteristic
402C2×C73#298111yescharacteristic
403D73—81no—
404D73—81no—
405#2388—731no—
406#1955—731no—
407#1954—731no—
408#1954D7311yescharacteristic, complemented
409#1924—731no—
410#1924—731no—
411#1923—731no—
412#1923—731no—
413#1923—731no—
414#1923—731no—
415#1869—731no—
416#1869—731no—
417#1869—731no—
418#1780—731no—
419#1780—731no—
420C73#2331011yescharacteristic, complemented, Sylow
421C22×#41—731no—
422C23×C8—731no—
423C2×C4×D4—731no—
424C2×C4×D4—731no—
425C2×C4×D4C2×D7311yescharacteristic
426C2×C4⋊C8—731no—
427C2×C4⋊C8—731no—
428C2×C4⋊C8C2×D7311yescharacteristic
429C2×C22⋊C8—731no—
430C2×C22⋊C8—731no—
431C2×C22⋊C8—731no—
432C2×C22⋊C8—731no—
433C2×C22⋊C8—731no—
434C2×C22⋊C8—731no—
435C2×C22⋊C8—731no—
436C2×C22⋊C8—731no—
437C2×C22⋊C8—731no—
438C2×C22⋊C8—731no—
439C2×C22⋊C8—731no—
440C2×C22⋊C8C2×D7311yescharacteristic
441C2×C22⋊C8C2×D7311yescharacteristic
442C2×C22⋊C8C2×D7311yescharacteristic
443C2×C22⋊C8C2×D7311yescharacteristic
444C2×#97—731no—
445C2×C4×C8—731no—
446C2×C4×C8C2×D7311yescharacteristic
447#395—731no—
448#394—731no—
449#394—731no—
450#394—731no—
451#393—731no—
452#392—731no—
453#392—731no—
454#392—731no—
455C4×C22⋊C4—731no—
456C4×C22⋊C4—731no—
457C4×C22⋊C4—731no—
458#336—731no—
459#336—731no—
460#336—731no—
461#336—731no—
462#336—731no—
463#336—731no—
464C2×#41—2921no—
465C2×#41—2921no—
466C2×#41—2921no—
467C2×#41—2921no—
468C2×#41—2921no—
469C2×#41—2921no—
470C22×Q8—731no—
471C22×D4—731no—
472C22×D4—731no—
473C22×D4—731no—
474C22×D4—731no—
475C22×D4—731no—
476C22×D4C4×D7311yescharacteristic
477C23×C4—731no—
478C23×C4—731no—
479C23×C4C22×D7311yescharacteristic
480C23×C4C22×D7311yescharacteristic
481C22×C8—2921no—
482C22×C8—2921no—
483C22×C8—2921no—
484C22×C8—731no—
485C22×C8—731no—
486C22×C8—731no—
487C22×C8—731no—
488C22×C8C22×D7311yescharacteristic
489C22×C8C22×D7311yescharacteristic
490C22×C8C22×D7311yescharacteristic
491C22×C8C22×D7311yescharacteristic
492C4×D4—41no—
493C4×D4—41no—
494C4×D4—2921no—
495C4×D4—2921no—
496C4×D4—2921no—
497C4×D4—2921no—
498C2×C4⋊C4—731no—
499C2×C4⋊C4—731no—
500C2×C4⋊C4C4×D7311yescharacteristic
501C2×C22⋊C4—731no—
502C2×C22⋊C4—731no—
503C2×C22⋊C4—731no—
504C2×C22⋊C4—731no—
505C2×C22⋊C4—731no—
506C2×C22⋊C4—731no—
507C2×C22⋊C4—731no—
508C2×C22⋊C4—731no—
509C2×C22⋊C4—731no—
510C2×C22⋊C4—731no—
511C2×C22⋊C4C4×D7311yescharacteristic
512C2×C22⋊C4C4×D7311yescharacteristic
513C2×C42—731no—
514C2×C42—731no—
515C2×C42C22×D7311yescharacteristic
516C4⋊C8—41no—
517C4⋊C8—2921no—
518C4⋊C8—2921no—
519C22⋊C8—41no—
520C22⋊C8—41no—
521C22⋊C8—41no—
522C22⋊C8—41no—
523C22⋊C8—2921no—
524C22⋊C8—2921no—
525C22⋊C8—2921no—
526C22⋊C8—2921no—
527C22⋊C8—2921no—
528C22⋊C8—2921no—
529C22⋊C8—2921no—
530C22⋊C8—2921no—
531C22⋊C8—2921no—
532C22⋊C8—2921no—
533C22⋊C8—2921no—
534#97—2921no—
535C4×C8—41no—
536C4×C8—2921no—
537#95—731no—
538#95—731no—
539#95—731no—
540#95—731no—
541#95—731no—
542#95—731no—
543C24—731no—
544C24—731no—
545C24C2×C4×D7311yescharacteristic
546C24C2×C4×D7311yescharacteristic
547#41—2924no—
548#41—2924no—
549#41—2924no—
550#41—2924no—
551C2×Q8—2921no—
552C2×Q8—2921no—
553C2×Q8—2921no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—41no—
557C2×D4—2921no—
558C2×D4—2921no—
559C2×D4—2921no—
560C2×D4—2921no—
561C2×D4—2921no—
562C2×D4—2921no—
563C2×D4—2921no—
564C2×D4—2921no—
565C2×D4—2921no—
566C2×D4—2921no—
567C2×D4—2921no—
568C2×D4—2921no—
569C2×D4—1462no—
570C2×D4—1462no—
571C2×D4—1462no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—731no—
585C22×C4—731no—
586C22×C4—731no—
587C22×C4—731no—
588C22×C4—731no—
589C22×C4—731no—
590C22×C4—1461no—
591C22×C4—1461no—
592C22×C4—1461no—
593C22×C4—1461no—
594C22×C4—1461no—
595C22×C4—1461no—
596C22×C4—1461no—
597C22×C4—1461no—
598C22×C4—1461no—
599C22×C4—1461no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4C2×C4×D7311yescharacteristic
603C22×C4C2×C4×D7311yescharacteristic
604C22×C4C2×C4×D7311yescharacteristic
605C22×C4C2×C4×D7311yescharacteristic
606C22×C4C23×D7311yescharacteristic
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—21no—
619C2×C8—2924no—
620C2×C8—1461no—
621C2×C8—1461no—
622C2×C8—1461no—
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—
632C4⋊C4—41no—
633C4⋊C4—2921no—
634C4⋊C4—2921no—
635C22⋊C4—41no—
636C22⋊C4—41no—
637C22⋊C4—2921no—
638C22⋊C4—2921no—
639C22⋊C4—2921no—
640C22⋊C4—2921no—
641C22⋊C4—2921no—
642C22⋊C4—2921no—
643C22⋊C4—1462no—
644C22⋊C4—1462no—
645C22⋊C4—1462no—
646C22⋊C4—1462no—
647C42—21no—
648C42—21no—
649C42—1461no—
650C42—1461no—
651C42—1461no—
652C42—1461no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—1461no—
667C23—1461no—
668C23—1461no—
669C23—1461no—
670C23—1461no—
671C23—1461no—
672C23—1461no—
673C23—1461no—
674C23—1461no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23—1461no—
679C23—1461no—
680C23#1455659712yes—
681C23C22×C4×D7311yescharacteristic
682Q8—2924no—
683D4—44no—
684D4—2924no—
685D4—2924no—
686D4—2924no—
687D4—2924no—
688D4—2924no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—2921no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—2921no—
713C2×C4—2921no—
714C2×C4—2921no—
715C2×C4—2921no—
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—1461no—
732C2×C4—1461no—
733C2×C4—1461no—
734C2×C4#1455659912yes—
735C2×C4#1455663611yescharacteristic
736C2×C4#1455663611yescharacteristic
737C2×C4#1455663611yescharacteristic
738C2×C4#1455663611yescharacteristic
739C2×C4#1455663711yescharacteristic
740C2×C4#1455663711yescharacteristic
741C8—41no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—2921no—
746C8—2921no—
747C8—2921no—
748C8—2921no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—2921no—
764C22—2921no—
765C22—2921no—
766C22—2921no—
767C22—2921no—
768C22—2921no—
769C22—2921no—
770C22—2921no—
771C22—2921no—
772C22—2921no—
773C22—2921no—
774C22—2921no—
775C22—2921no—
776C22—2921no—
777C22#1798905911yescharacteristic
778C22#1798905911yescharacteristic
779C22#1798906011yescharacteristic
780C22#131×D7311yescharacteristic
781C22C2×#1455659711yescharacteristic
782C22C2×#1455659911yescharacteristic
783C22#1798935211yescharacteristic
784C4—22no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—2921no—
789C4—2921no—
790C4—2921no—
791C4—2921no—
792C4—2921no—
793C4—1462no—
794C4#1798932411yescharacteristic
795C4#1798932511yescharacteristic
796C4#1798932511yescharacteristic
797C4#1798932911yescharacteristic
798C2—42no—
799C2—81no—
800C2—5841no—
801C2—5841no—
802C2#2261306811yescharacteristic
803C2#2261897311yescharacteristic
804C2#2261898411yescharacteristic
805C2#2261898511yescharacteristic
806C2#2261899611yescharacteristic
807C2#2261900411yescharacteristic
808C2#2261900811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1954C2
prime radical#22613146C2
cosocleC22×C4×C73C24
hypercenter#1954D73
hypocenterC73#23310
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. #22610727C2semidirect
3. #22610723C2semidirect
4. #22610543C2semidirect
5. #22610541C2semidirect
6. #22610537C2semidirect
7. #22610537C2semidirect
8. #22610536C2semidirect
9. #22610534C2semidirect
10. #22610224C2semidirect
11. #22610221C2semidirect
12. #22610221C2semidirect
13. #22609842C2semidirect
14. #22609842C2semidirect
15. C73×#1954C2semidirect
408. #1954D73semidirect
420. C73#23310semidirect

Maximal subgroups

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

subgroupindex
#226131462
#226107272
#226107232
#226105432
#226105412
#226105372
#226105362
#226105342
#226102242
#226102212
#226098422
C73×#19542
#2331073