Finite Group Databasebeta

← #33112250

Subgroups — #33112250

Order 18688.

802 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22613169C211yesmaximal, characteristic
2#22610727C211yesmaximal, characteristic, complemented
3#22610723C211yesmaximal, characteristic, complemented
4#22610541C211yesmaximal, characteristic, complemented
5#22610540C211yesmaximal, characteristic, complemented
6#22610494C211yesmaximal, characteristic, complemented
7#22610489C211yesmaximal, characteristic, complemented
8#22610224C211yesmaximal, characteristic, complemented
9#22610223C211yesmaximal, characteristic, complemented
10#22610221C211yesmaximal, characteristic, complemented
11#22610109C211yesmaximal, characteristic, complemented
12#22610108C211yesmaximal, characteristic, complemented
13#22610001C211yesmaximal, characteristic, complemented
14#22609914C211yesmaximal, characteristic, complemented
15C73×#1869C211yesmaximal, characteristic, complemented
16C23×#10596831C2211yescharacteristic
17C2×C4×C22⋊D73C2211yescharacteristic
18C2×C4×C22⋊D73C2211yescharacteristic
19C2×#14556548C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×#14556520C2211yescharacteristic
23C2×#14556520C2211yescharacteristic
24C2×C22⋊#10596831C2211yescharacteristic
25C2×C22⋊#10596831C2211yescharacteristic
26C2×C22⋊#10596831C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556501C2211yescharacteristic
32C2×C8×Dic73C2211yescharacteristic
33#17988518C411yescharacteristic
34#17988513C411yescharacteristic
35#17988510C411yescharacteristic
36#17988510C411yescharacteristic
37#17988503C411yescharacteristic
38#17988503C411yescharacteristic
39#17988501C411yescharacteristic
40#17988495C411yescharacteristic
41C4×C4⋊Dic73C2211yescharacteristic
42C4×C22⋊Dic73C2211yescharacteristic
43C4×C22⋊Dic73C2211yescharacteristic
44#17988342C2211yescharacteristic
45#17988342C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C23×C8×C73C2211yescharacteristic
53C2×C4×D4×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C22⋊C8×C73C2211yescharacteristic
56C2×C22⋊C8×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×C22⋊D73C2×C411yescharacteristic
60C22×C22⋊D73C2×C411yescharacteristic
61C22×C4×D73C2311yescharacteristic
62C22×#10596831—41no—
63C22×#10596831—41no—
64C22×#10596831—41no—
65C22×#10596831C2311yescharacteristic
66C22×#10596831C2311yescharacteristic
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C4×C22⋊D73—41no—
70C4×C22⋊D73—41no—
71C4×C22⋊D73—41no—
72C4×C22⋊D73—41no—
73#14556548—41no—
74#14556548—41no—
75C2×C4⋊Dic73C2×C411yescharacteristic
76C2×C4⋊Dic73C2×C411yescharacteristic
77C2×#11924007C2×C411yescharacteristic
78C2×#11924007C2×C411yescharacteristic
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×C22⋊Dic73C2×C411yescharacteristic
83C2×C22⋊Dic73C2×C411yescharacteristic
84C2×C22⋊Dic73C2×C411yescharacteristic
85C2×C22⋊Dic73C2×C411yescharacteristic
86C2×C22⋊Dic73C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×#11924005C2×C411yescharacteristic
90C2×#11924005C2×C411yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C2×C4×Dic73C2311yescharacteristic
94#14556520—41no—
95#14556520—41no—
96#14556520—41no—
97#14556520—41no—
98C22⋊#10596831—41no—
99C22⋊#10596831—41no—
100C22⋊#10596831—41no—
101#14556503—41no—
102#14556503—41no—
103#14556503—41no—
104#14556503—41no—
105#14556501—41no—
106C8×Dic73—41no—
107#14556498C2×C411yescharacteristic
108#14556498C2×C411yescharacteristic
109#14556498C2×C411yescharacteristic
110#14556498C2×C411yescharacteristic
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113C22×D4×C73C2×C411yescharacteristic
114C23×C4×C73C2311yescharacteristic
115C23×C4×C73C2311yescharacteristic
116C22×C8×C73—41no—
117C22×C8×C73—41no—
118C22×C8×C73—41no—
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C22×C8×C73C2311yescharacteristic
123C4×D4×C73—41no—
124C4×D4×C73—41no—
125C2×C4⋊C4×C73C2×C411yescharacteristic
126C2×C22⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128C2×C42×C73C2311yescharacteristic
129C22⋊C8×C73—41no—
130C22⋊C8×C73—41no—
131C22⋊C8×C73—41no—
132C23×D73C22×C411yescharacteristic
133C2×C22⋊D73—22no—
134C2×C22⋊D73—22no—
135C2×C22⋊D73—22no—
136C2×C22⋊D73—41no—
137C2×C22⋊D73—41no—
138C2×C22⋊D73—41no—
139C22×Dic73C22×C411yescharacteristic
140C22×Dic73C22×C411yescharacteristic
141C22×Dic73C22×C411yescharacteristic
142C22×Dic73C22×C411yescharacteristic
143C22×Dic73C22×C411yescharacteristic
144C22×Dic73C22×C411yescharacteristic
145C22×Dic73C22×C411yescharacteristic
146C2×C4×D73—21no—
147C2×C4×D73—21no—
148C2×C4×D73—21no—
149C2×C4×D73—21no—
150C2×C4×D73—21no—
151C2×C4×D73—21no—
152C2×#10596831—21no—
153C2×#10596831—21no—
154C2×#10596831—21no—
155C2×#10596831—21no—
156C2×#10596831—21no—
157C2×#10596831—21no—
158C2×#10596831—21no—
159C2×#10596831—21no—
160C2×#10596831—21no—
161C2×#10596831—21no—
162C2×#10596831—21no—
163C2×#10596831—21no—
164C2×#10596831—44no—
165C4⋊Dic73—22no—
166C4⋊Dic73—41no—
167#11924007—41no—
168#11924007—41no—
169#11924007—41no—
170#11924007—41no—
171C22⋊Dic73—22no—
172C22⋊Dic73—22no—
173C22⋊Dic73—22no—
174C22⋊Dic73—41no—
175C22⋊Dic73—41no—
176C22⋊Dic73—41no—
177#11924005—41no—
178#11924005—41no—
179#11924005—41no—
180#11924005—41no—
181C4×Dic73—21no—
182C4×Dic73—21no—
183C4×Dic73—21no—
184C4×Dic73—21no—
185C4×Dic73—21no—
186C4×Dic73—21no—
187C24×C73C22×C411yescharacteristic
188C24×C73C22×C411yescharacteristic
189C2×D4×C73—22no—
190C2×D4×C73—22no—
191C2×D4×C73—41no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73C22×C411yescharacteristic
205C22×C4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207C22×C4×C73C22×C411yescharacteristic
208C22×C4×C73C2411yescharacteristic
209C2×C8×C73—21no—
210C2×C8×C73—21no—
211C2×C8×C73—21no—
212C2×C8×C73—21no—
213C2×C8×C73—21no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—44no—
222C4⋊C4×C73—41no—
223C22⋊C4×C73—41no—
224C22⋊C4×C73—41no—
225C42×C73—21no—
226C42×C73—21no—
227C23×C73—21no—
228C23×C73—21no—
229C23×C73—21no—
230C23×C73—21no—
231C23×C73—21no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73#13112yes—
240C23×C73#13112yes—
241C23×C73C23×C411yescharacteristic
242C22×D73—21no—
243C22×D73—21no—
244C22×D73—21no—
245C22×D73—21no—
246C22×D73—21no—
247C22×D73—21no—
248C22×D73—21no—
249D4×C73—44no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73H(5,𝔽2)11yescharacteristic
271C2×C4×C73H(5,𝔽2)11yescharacteristic
272C2×C4×C73H(5,𝔽2)11yescharacteristic
273C2×C4×C73H(5,𝔽2)11yescharacteristic
274C2×C4×C73H(5,𝔽2)11yescharacteristic
275C2×C4×C732−1+411yescharacteristic
276C22⋊D73—44no—
277C22⋊D73—44no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73—21no—
281C2×Dic73—21no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73#13112yes—
299C4×D73—41no—
300C4×D73—41no—
301C4×D73—41no—
302C4×D73—41no—
303C8×C73—41no—
304C8×C73—41no—
305C8×C73—41no—
306C8×C73—41no—
307#10596831—41no—
308#10596831—41no—
309#10596831—41no—
310#10596831—41no—
311C22×C73—22no—
312C22×C73—22no—
313C22×C73—22no—
314C22×C73—22no—
315C22×C73—22no—
316C22×C73—22no—
317C22×C73—41no—
318C22×C73—41no—
319C22×C73—41no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73#51811yescharacteristic
326C22×C73#51811yescharacteristic
327C22×C73#52011yescharacteristic
328C22×C73C2×#13111yescharacteristic
329C22×C73C2×#13111yescharacteristic
330C22×C73C2×#13111yescharacteristic
331C22×C73#56811yescharacteristic
332C2×D73—41no—
333C2×D73—41no—
334C2×D73—41no—
335C2×D73—41no—
336C2×D73—41no—
337C2×D73—41no—
338C2×D73—41no—
339C4×C73—41no—
340C4×C73—41no—
341C4×C73—41no—
342C4×C73—41no—
343C4×C73#56011yescharacteristic
344C4×C73#56011yescharacteristic
345C4×C73#56211yescharacteristic
346C4×C73#56211yescharacteristic
347Dic73—22no—
348Dic73—41no—
349Dic73—41no—
350Dic73—41no—
351Dic73—41no—
352Dic73—41no—
353Dic73—41no—
354#23330—731nomaximal, Sylow
355C2×C73—42no—
356C2×C73—42no—
357C2×C73#237711yescharacteristic
358C2×C73#297611yescharacteristic
359C2×C73#297711yescharacteristic
360C2×C73#297711yescharacteristic
361C2×C73#298111yescharacteristic
362C2×C73#299211yescharacteristic
363C2×C73#299411yescharacteristic
364D73—81no—
365#2392—731no—
366#1955—731no—
367#1954—731no—
368#1924—731no—
369#1923—731no—
370#1917—731no—
371#1916—731no—
372#1869—731no—
373#1869—731no—
374#1869—731no—
375#1869D7311yescharacteristic, complemented
376#1850—731no—
377#1850—731no—
378#1818—731no—
379#1798—731no—
380C73#2333011yescharacteristic, complemented, Sylow
381C23×C8—731no—
382C23×C8C2×D7311yescharacteristic
383C2×C4×D4—731no—
384C2×C4×D4—731no—
385C2×C4×D4C2×D7311yescharacteristic
386C2×#117—731no—
387C2×C4⋊C8—731no—
388C2×C4⋊C8—731no—
389C2×C4⋊C8—731no—
390C2×C4⋊C8—731no—
391C2×C22⋊C8—731no—
392C2×C22⋊C8—731no—
393C2×C22⋊C8—731no—
394C2×C22⋊C8—731no—
395C2×C22⋊C8—731no—
396C2×C22⋊C8—731no—
397C2×C22⋊C8—731no—
398C2×C22⋊C8C2×D7311yescharacteristic
399C2×C22⋊C8C2×D7311yescharacteristic
400C2×C22⋊C8C2×D7311yescharacteristic
401C2×#97—731no—
402C2×C4×C8—731no—
403#398—731no—
404#397—731no—
405#396—731no—
406#396—731no—
407#394—731no—
408#394—731no—
409#394—731no—
410#392—731no—
411C4×C4⋊C4—731no—
412C4×C22⋊C4—731no—
413C4×C22⋊C4—731no—
414#336—731no—
415#336—731no—
416#336—731no—
417#336—731no—
418#336—731no—
419#336—731no—
420#336—731no—
421#336—731no—
422#336C2×D7311yescharacteristic
423#336C2×D7311yescharacteristic
424C22×D4—731no—
425C22×D4—731no—
426C22×D4C4×D7311yescharacteristic
427C23×C4—731no—
428C23×C4C22×D7311yescharacteristic
429C23×C4C22×D7311yescharacteristic
430C22×C8—41no—
431C22×C8—41no—
432C22×C8—41no—
433C22×C8—2921no—
434C22×C8—2921no—
435C22×C8—2921no—
436C22×C8—731no—
437C22×C8—731no—
438C22×C8—731no—
439C22×C8—731no—
440C22×C8C22×D7311yescharacteristic
441C22×C8C22×D7311yescharacteristic
442C22×C8C22×D7311yescharacteristic
443C22×C8C22×D7311yescharacteristic
444C4×D4—41no—
445C4×D4—41no—
446C4×D4—2921no—
447C4×D4—2921no—
448C4×D4—2921no—
449C4×D4—2921no—
450#117—2921no—
451#117—2921no—
452C2×C4⋊C4—731no—
453C2×C4⋊C4—731no—
454C2×C4⋊C4—731no—
455C2×C4⋊C4—731no—
456C2×C4⋊C4—731no—
457C2×C4⋊C4—731no—
458C2×C4⋊C4C4×D7311yescharacteristic
459C2×C22⋊C4—731no—
460C2×C22⋊C4—731no—
461C2×C22⋊C4—731no—
462C2×C22⋊C4—731no—
463C2×C22⋊C4—731no—
464C2×C22⋊C4—731no—
465C2×C22⋊C4—731no—
466C2×C22⋊C4—731no—
467C2×C22⋊C4—731no—
468C2×C22⋊C4—731no—
469C2×C22⋊C4C4×D7311yescharacteristic
470C2×C22⋊C4C4×D7311yescharacteristic
471C2×C42—731no—
472C2×C42—731no—
473C2×C42—731no—
474C2×C42C22×D7311yescharacteristic
475C4⋊C8—2921no—
476C4⋊C8—2921no—
477C4⋊C8—2921no—
478C4⋊C8—2921no—
479C22⋊C8—41no—
480C22⋊C8—41no—
481C22⋊C8—41no—
482C22⋊C8—2921no—
483C22⋊C8—2921no—
484C22⋊C8—2921no—
485C22⋊C8—2921no—
486C22⋊C8—2921no—
487C22⋊C8—2921no—
488C22⋊C8—2921no—
489#97—2921no—
490C4×C8—2921no—
491#95—731no—
492#95—731no—
493#95—731no—
494#95—731no—
495#95—731no—
496#95—731no—
497C24—731no—
498C24C2×C4×D7311yescharacteristic
499C24C2×C4×D7311yescharacteristic
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—41no—
503C2×D4—2921no—
504C2×D4—2921no—
505C2×D4—2921no—
506C2×D4—1462no—
507C2×D4—1462no—
508C2×D4—1462no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—731no—
522C22×C4—731no—
523C22×C4—731no—
524C22×C4—731no—
525C22×C4—731no—
526C22×C4—731no—
527C22×C4—731no—
528C22×C4—1461no—
529C22×C4—1461no—
530C22×C4—1461no—
531C22×C4—1461no—
532C22×C4—1461no—
533C22×C4—1461no—
534C22×C4C2×C4×D7311yescharacteristic
535C22×C4C2×C4×D7311yescharacteristic
536C22×C4C2×C4×D7311yescharacteristic
537C22×C4C2×C4×D7311yescharacteristic
538C22×C4C23×D7311yescharacteristic
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—44no—
552C2×C8—2924no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C2×C8—1461no—
557C2×C8—1461no—
558C2×C8—1461no—
559C2×C8—1461no—
560C2×C8—1461no—
561C2×C8—1461no—
562C2×C8—1461no—
563C2×C8—1461no—
564C2×C8—1461no—
565C4⋊C4—41no—
566C4⋊C4—2921no—
567C4⋊C4—2921no—
568C4⋊C4—2921no—
569C4⋊C4—2921no—
570C4⋊C4—2921no—
571C4⋊C4—1462no—
572C22⋊C4—41no—
573C22⋊C4—41no—
574C22⋊C4—2921no—
575C22⋊C4—2921no—
576C22⋊C4—2921no—
577C22⋊C4—2921no—
578C22⋊C4—2921no—
579C22⋊C4—2921no—
580C22⋊C4—2921no—
581C22⋊C4—1462no—
582C22⋊C4—1462no—
583C22⋊C4—1462no—
584C42—21no—
585C42—21no—
586C42—1461no—
587C42—1461no—
588C42—1461no—
589C42—1461no—
590C42—1461no—
591C42—1461no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23—21no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—1461no—
605C23—1461no—
606C23—1461no—
607C23—1461no—
608C23—1461no—
609C23—1461no—
610C23—1461no—
611C23#1455659712yes—
612C23#1455659912yes—
613C23C22×C4×D7311yescharacteristic
614D4—44no—
615D4—2924no—
616D4—2924no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—2921no—
638C2×C4—2921no—
639C2×C4—2921no—
640C2×C4—2921no—
641C2×C4—732no—
642C2×C4—1461no—
643C2×C4—1461no—
644C2×C4—1461no—
645C2×C4—1461no—
646C2×C4—1461no—
647C2×C4—1461no—
648C2×C4—1461no—
649C2×C4—1461no—
650C2×C4—1461no—
651C2×C4—1461no—
652C2×C4—1461no—
653C2×C4—1461no—
654C2×C4—1461no—
655C2×C4—1461no—
656C2×C4—1461no—
657C2×C4—1461no—
658C2×C4—1461no—
659C2×C4—1461no—
660C2×C4—1461no—
661C2×C4—1461no—
662C2×C4#1455663611yescharacteristic
663C2×C4#1455663611yescharacteristic
664C2×C4#1455663611yescharacteristic
665C2×C4#1455663611yescharacteristic
666C2×C4#1455663711yescharacteristic
667C2×C4#1455663811yescharacteristic
668C8—41no—
669C8—41no—
670C8—41no—
671C8—41no—
672C8—2921no—
673C8—2921no—
674C8—2921no—
675C8—2921no—
676C22—22no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—2921no—
691C22—2921no—
692C22—2921no—
693C22—2921no—
694C22—2921no—
695C22—2921no—
696C22—2921no—
697C22#1798905911yescharacteristic
698C22#1798906011yescharacteristic
699C22#1798906611yescharacteristic
700C22#131×D7311yescharacteristic
701C22C2×#1455659711yescharacteristic
702C22C2×#1455659911yescharacteristic
703C22#1798935211yescharacteristic
704C4—41no—
705C4—41no—
706C4—41no—
707C4—41no—
708C4—2921no—
709C4—2921no—
710C4—2921no—
711C4—2921no—
712C4—2921no—
713C4—2921no—
714C4—1462no—
715C4#1798932511yescharacteristic
716C4#1798932611yescharacteristic
717C4#1798933211yescharacteristic
718C4#1798933411yescharacteristic
719C2—42no—
720C2—42no—
721C2—5841no—
722C2#2261308311yescharacteristic
723C2#2261898011yescharacteristic
724C2#2261898411yescharacteristic
725C2#2261898511yescharacteristic
726C2#2261900411yescharacteristic
727C2#2261906411yescharacteristic
728C2#2261908411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1869C2
prime radical#17988495C4
cosocleC22×C4×C73C24
hypercenter#1869D73
hypocenterC73#23330
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. #22610727C2semidirect
3. #22610723C2semidirect
4. #22610541C2semidirect
5. #22610540C2semidirect
6. #22610494C2semidirect
7. #22610489C2semidirect
8. #22610224C2semidirect
9. #22610223C2semidirect
10. #22610221C2semidirect
11. #22610109C2semidirect
12. #22610108C2semidirect
13. #22610001C2semidirect
14. #22609914C2semidirect
15. C73×#1869C2semidirect
375. #1869D73semidirect
380. C73#23330semidirect

Maximal subgroups

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

subgroupindex
#226131692
#226107272
#226107232
#226105412
#226105402
#226104942
#226104892
#226102242
#226102232
#226102212
#226101092
#226101082
#226100012
#226099142
C73×#18692
#2333073