Finite Group Databasebeta

← #34029435

Subgroups — #34029435

Order 18688.

888 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626054C211yesmaximal, characteristic, complemented
2#22626053C211yesmaximal, characteristic, complemented
3#22626003C211yesmaximal, characteristic, complemented
4#22626000C211yesmaximal, characteristic, complemented
5#22625986C211yesmaximal, characteristic, complemented
6#22625985C211yesmaximal, characteristic, complemented
7#22625907C211yesmaximal, characteristic, complemented
8#22625906C211yesmaximal, characteristic, complemented
9#22625906C211yesmaximal, characteristic, complemented
10#22625905C211yesmaximal, characteristic, complemented
11#22625876C211yesmaximal, characteristic, complemented
12#22625874C211yesmaximal, characteristic, complemented
13#22625823C211yesmaximal, characteristic, complemented
14#22625786C211yesmaximal, characteristic, complemented
15#22612443C211yesmaximal, characteristic
16C22×#11924036C2211yescharacteristic
17C23×#10596833C2211yescharacteristic
18C2×#14556658C2211yescharacteristic
19C2×C4⋊#10596833C2211yescharacteristic
20C2×C4⋊#10596833C2211yescharacteristic
21C2×C4⋊#10596833C2211yescharacteristic
22C2×#14556648C2211yescharacteristic
23C2×#14556648C2211yescharacteristic
24C2×#14556648C2211yescharacteristic
25C2×#14556648C2211yescharacteristic
26C2×#14556648C2211yescharacteristic
27C2×#14556648C2211yescharacteristic
28C2×#14556648C2211yescharacteristic
29C2×C22⋊#10596833C2211yescharacteristic
30C2×C22⋊#10596833C2211yescharacteristic
31C2×C22⋊#10596833C2211yescharacteristic
32C2×C4×#10596833C2211yescharacteristic
33C2×C4×#10596833C2211yescharacteristic
34#17989453C2211yescharacteristic
35#17989453C2211yescharacteristic
36#17989453C2211yescharacteristic
37#17989453C2211yescharacteristic
38#17989453C2211yescharacteristic
39#17989453C2211yescharacteristic
40#17989453C2211yescharacteristic
41#17989453C2211yescharacteristic
42#17989453C2211yescharacteristic
43#17989453C2211yescharacteristic
44C2×#14556564C411yescharacteristic
45C2×#14556553C2211yescharacteristic
46C2×#14556551C2211yescharacteristic
47C2×#14556551C2211yescharacteristic
48C2×C42×D73C2211yescharacteristic
49#17988487C411yescharacteristic
50#17988482C411yescharacteristic
51#17988478C411yescharacteristic
52#17988465C411yescharacteristic
53#17988463C411yescharacteristic
54#17988446C411yescharacteristic
55#17988438C2211yescharacteristic
56C22⋊C4×Dic73C2211yescharacteristic
57#17988434C2211yescharacteristic
58#388×C73C411yescharacteristic
59C2×#11924036—41no—
60C2×#11924036—41no—
61C2×#11924036—41no—
62C22×#10596833—41no—
63C22×#10596833—41no—
64C22×#10596833—41no—
65C22×#10596833C2311yescharacteristic
66C22×#10596833C2311yescharacteristic
67C22×#10596833C2311yescharacteristic
68C22×#10596833C2311yescharacteristic
69C22×#10596833C2311yescharacteristic
70C22×#10596833C2311yescharacteristic
71C22×#10596833C2311yescharacteristic
72C22×#10596833C2311yescharacteristic
73#14556658—41no—
74C4⋊#10596833—41no—
75C4⋊#10596833—41no—
76C4⋊#10596833—41no—
77#14556648—41no—
78#14556648—41no—
79#14556648—41no—
80#14556648—41no—
81#14556648—41no—
82#14556648—41no—
83#14556648—41no—
84C22⋊#10596833—41no—
85C22⋊#10596833—41no—
86C22⋊#10596833—41no—
87C4×#10596833—41no—
88C4×#10596833—41no—
89C22×D292C2×C411yescharacteristic
90C22×C22⋊D73C2×C411yescharacteristic
91C22×C22⋊D73C2×C411yescharacteristic
92C23×Dic73C2311yescharacteristic
93C22×C4×D73C2×C411yescharacteristic
94C22×C4×D73C2×C411yescharacteristic
95C22×C4×D73C2311yescharacteristic
96C22×C4×D73C2311yescharacteristic
97#14556564C818yescomplemented
98#14556553—41no—
99#14556553—41no—
100#14556551—41no—
101#14556551—41no—
102#14556551—41no—
103#14556551—41no—
104C2×#11924007C2×C411yescharacteristic
105C2×#11924007C2×C411yescharacteristic
106C2×#11924007C2×C411yescharacteristic
107C2×#11924007C2×C411yescharacteristic
108C2×C22⋊Dic73C2×C411yescharacteristic
109C2×#11924005C2×C411yescharacteristic
110C2×#11924005C2×C411yescharacteristic
111C2×#11924005C2×C411yescharacteristic
112C2×#11924005C2×C411yescharacteristic
113C2×#11924005C2×C411yescharacteristic
114C2×#11924005C2×C411yescharacteristic
115C2×C4×Dic73C2×C411yescharacteristic
116C2×C4×Dic73C2311yescharacteristic
117C2×C4×Dic73C2311yescharacteristic
118C2×C4×Dic73C2311yescharacteristic
119C2×C4×Dic73C2311yescharacteristic
120C42×D73—41no—
121C42×D73—41no—
122#14556498C2×C411yescharacteristic
123#14556498C2×C411yescharacteristic
124#14556498C2×C411yescharacteristic
125#14556498C2×C411yescharacteristic
126C2×C4⋊C4×C73C2×C411yescharacteristic
127C2×C22⋊C4×C73C2×C411yescharacteristic
128C2×C22⋊C4×C73C2×C411yescharacteristic
129C2×C22⋊C4×C73C2×C411yescharacteristic
130C2×C42×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132#95×C73C2×C411yescharacteristic
133#11924036—44no—
134C2×#10596833—21no—
135C2×#10596833—21no—
136C2×#10596833—21no—
137C2×#10596833—21no—
138C2×#10596833—21no—
139C2×#10596833—21no—
140C2×#10596833—21no—
141C2×#10596833—21no—
142C2×#10596833—21no—
143C2×#10596833—21no—
144C2×#10596833—21no—
145C2×#10596833—21no—
146C2×#10596833—21no—
147C2×#10596833—21no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—21no—
154C2×#10596833—21no—
155C2×#10596833—21no—
156C2×#10596833—21no—
157C2×#10596833—21no—
158C2×#10596833—44no—
159C23×D73C22×C411yescharacteristic
160C23×D73C22×C411yescharacteristic
161C2×D292—41no—
162C2×D292—41no—
163C2×D292C2×C814yescomplemented
164C2×C22⋊D73—41no—
165C2×C22⋊D73—41no—
166C2×C22⋊D73—41no—
167C2×C22⋊D73—41no—
168C2×C22⋊D73C2×C814yes—
169C2×C22⋊D73C2×C814yescomplemented
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—21no—
175C22×Dic73—21no—
176C22×Dic73C22×C411yescharacteristic
177C22×Dic73C22×C411yescharacteristic
178C22×Dic73C22×C411yescharacteristic
179C22×Dic73C22×C411yescharacteristic
180C22×Dic73C22×C411yescharacteristic
181C22×Dic73C2411yescharacteristic
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—21no—
191C2×C4×D73—21no—
192C2×C4×D73—21no—
193C2×C4×D73—21no—
194C2×C4×D73—41no—
195C2×C4×D73—41no—
196C2×C4×D73—41no—
197C2×C4×D73—41no—
198C2×C4×D73—41no—
199C2×C4×D73C2×C814yescomplemented
200#11924007—41no—
201#11924007—41no—
202#11924007—41no—
203#11924007C2×C814yescomplemented
204C22⋊Dic73—41no—
205#11924005—41no—
206#11924005—41no—
207#11924005—41no—
208#11924005—41no—
209#11924005—41no—
210#11924005C2×C814yescomplemented
211C4×Dic73—21no—
212C4×Dic73—21no—
213C4×Dic73—21no—
214C4×Dic73—21no—
215C4×Dic73—21no—
216C4×Dic73—21no—
217C4×Dic73—21no—
218C4×Dic73—21no—
219C4×Dic73—41no—
220C24×C73C22×C411yescharacteristic
221C22×C4×C73C22×C411yescharacteristic
222C22×C4×C73C22×C411yescharacteristic
223C22×C4×C73C22×C411yescharacteristic
224C22×C4×C73C22×C411yescharacteristic
225C22×C4×C73C22×C411yescharacteristic
226C22×C4×C73C22×C411yescharacteristic
227C4⋊C4×C73—41no—
228C22⋊C4×C73—41no—
229C22⋊C4×C73—41no—
230C22⋊C4×C73C2×C814yescomplemented
231C42×C73—41no—
232C23×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73C22×C812yes—
239C23×C73C23×C411yescharacteristic
240C22×D73—21no—
241C22×D73—21no—
242C22×D73—21no—
243C22×D73—21no—
244C22×D73—21no—
245C22×D73—21no—
246C22×D73—21no—
247C22×D73—21no—
248C22×D73—21no—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73C22×C812yes—
253C22×D73C22×C812yes—
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—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73C22×C812yes—
271C2×C4×C73C22×C812yes—
272C22⋊D73—44no—
273C22⋊D73—44no—
274C2×Dic73—21no—
275C2×Dic73—21no—
276C2×Dic73—21no—
277C2×Dic73—21no—
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—41no—
288C2×Dic73—41no—
289C2×Dic73—41no—
290C2×Dic73—41no—
291C2×Dic73C22×C812yes—
292C2×Dic73C22×C812yes—
293C2×Dic73H(5,𝔽2)11yescharacteristic
294C2×Dic73H(5,𝔽2)11yescharacteristic
295C2×Dic73H(5,𝔽2)11yescharacteristic
296C2×Dic73H(5,𝔽2)11yescharacteristic
297C2×Dic73H(5,𝔽2)11yescharacteristic
298C2×Dic732−1+411yescharacteristic
299D292—44no—
300C4×D73—44no—
301C4×D73—44no—
302C4×D73—41no—
303C4×D73—41no—
304C4×D73—41no—
305C4×D73—41no—
306C4×D73—41no—
307C4×D73—41no—
308C4×D73—41no—
309C4×D73—41no—
310#10596833—41no—
311#10596833—41no—
312#10596833—41no—
313#10596833—41no—
314#10596833—41no—
315#10596833—41no—
316#10596833—41no—
317#10596833—41no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73#51811yescharacteristic
326C22×C73#51811yescharacteristic
327C22×C73#52011yescharacteristic
328C22×C73C23×C811yescharacteristic
329C22×C73#56811yescharacteristic
330C22×C73#56811yescharacteristic
331C22×C73#56811yescharacteristic
332C2×D73—22no—
333C2×D73—22no—
334C2×D73—22no—
335C2×D73—22no—
336C2×D73—22no—
337C2×D73—22no—
338C2×D73—41no—
339C2×D73—41no—
340C2×D73—41no—
341C2×D73—41no—
342C2×D73—41no—
343C2×D73—41no—
344C2×D73—41no—
345C2×D73—41no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73—41no—
352Dic73—22no—
353Dic73—22no—
354Dic73—41no—
355Dic73—41no—
356Dic73—41no—
357Dic73#56011yescharacteristic
358Dic73#56011yescharacteristic
359Dic73#56211yescharacteristic
360Dic73#56211yescharacteristic
361#23326—731nomaximal, Sylow
362C2×C73—42no—
363C2×C73#237711yescharacteristic
364C2×C73#297211yescharacteristic
365C2×C73#297211yescharacteristic
366C2×C73#297811yescharacteristic
367C2×C73#298011yescharacteristic
368C2×C73#298811yescharacteristic
369C2×C73#299511yescharacteristic
370D73—42no—
371D73—42no—
372C4×#121—731no—
373#1954—731no—
374#1954—731no—
375#1923—731no—
376#1923—731no—
377#1916—731no—
378#1916—731no—
379#1869—731no—
380#1869—731no—
381#1869—731no—
382#1869—731no—
383#1850—731no—
384#1850—731no—
385#1817—731no—
386#1797—731no—
387C73#2332611yescharacteristic, complemented, Sylow
388C23×C8—731no—
389C23×C8—731no—
390C2×#121—731no—
391C2×C4×D4—731no—
392C2×C4×D4—731no—
393C2×C4×D4—731no—
394C22×C42—731no—
395C2×C4⋊C8—731no—
396C2×C4⋊C8—731no—
397C2×C4⋊C8—731no—
398C2×C4⋊C8—731no—
399C2×C22⋊C8—731no—
400C2×C22⋊C8—731no—
401C2×C22⋊C8—731no—
402C2×C22⋊C8—731no—
403C2×C22⋊C8—731no—
404C2×C22⋊C8—731no—
405C2×C22⋊C8—731no—
406C2×C22⋊C8—731no—
407C2×C22⋊C8—731no—
408C2×C22⋊C8—731no—
409C2×C4×C8—731no—
410C2×C4×C8—731no—
411#390—731no—
412#389—731no—
413#388—731no—
414#388#6440811yescharacteristic
415#386—731no—
416#386—731no—
417#380—731no—
418C4×C4⋊C4—731no—
419C4×C22⋊C4—731no—
420C4×C22⋊C4—731no—
421#336—731no—
422#336—731no—
423#336—731no—
424#336—731no—
425#336—731no—
426#336—731no—
427#336—731no—
428#336—731no—
429#336—731no—
430#336—731no—
431C22×D4—731no—
432C22×D4—731no—
433C22×D4—731no—
434C23×C4—731no—
435C23×C4—731no—
436C23×C4—731no—
437C23×C4—731no—
438C23×C4—731no—
439C22×C8—2921no—
440C22×C8—2921no—
441C22×C8—2921no—
442C22×C8—2921no—
443C22×C8—2921no—
444C22×C8—2921no—
445C22×C8—731no—
446C22×C8—731no—
447C22×C8—731no—
448C22×C8—731no—
449C22×C8—731no—
450C22×C8—731no—
451C22×C8—731no—
452C22×C8—731no—
453#121—738no—
454C4×D4—2921no—
455C4×D4—2921no—
456C4×D4—2921no—
457C4×D4—2921no—
458C4×D4—2921no—
459C4×D4—2921no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4C2×#6440811yescharacteristic
465C2×C22⋊C4—731no—
466C2×C22⋊C4—731no—
467C2×C22⋊C4—731no—
468C2×C22⋊C4—731no—
469C2×C22⋊C4—731no—
470C2×C22⋊C4—731no—
471C2×C22⋊C4—731no—
472C2×C22⋊C4C2×#6440811yescharacteristic
473C2×C22⋊C4C2×#6440811yescharacteristic
474C2×C22⋊C4C2×#6440811yescharacteristic
475C2×C42—2921no—
476C2×C42—2921no—
477C2×C42—731no—
478C2×C42—731no—
479C2×C42—731no—
480C2×C42—731no—
481C2×C42—731no—
482C2×C42C2×#6440811yescharacteristic
483C4⋊C8—2921no—
484C4⋊C8—2921no—
485C4⋊C8—2921no—
486C4⋊C8—2921no—
487C22⋊C8—2921no—
488C22⋊C8—2921no—
489C22⋊C8—2921no—
490C22⋊C8—2921no—
491C22⋊C8—2921no—
492C22⋊C8—2921no—
493C22⋊C8—2921no—
494C22⋊C8—2921no—
495C22⋊C8—2921no—
496C22⋊C8—2921no—
497C4×C8—2921no—
498C4×C8—2921no—
499#95—731no—
500#95—731no—
501#95—731no—
502#95—731no—
503#95C2×#6440811yescharacteristic
504#95C2×#6440811yescharacteristic
505C24—731no—
506C24—731no—
507C24C22×#6440811yescharacteristic
508C2×D4—2921no—
509C2×D4—2921no—
510C2×D4—2921no—
511C2×D4—2921no—
512C2×D4—2921no—
513C2×D4—2921no—
514C2×D4—734no—
515C2×D4—734no—
516C2×D4—734no—
517C22×C4—2921no—
518C22×C4—2921no—
519C22×C4—2921no—
520C22×C4—2921no—
521C22×C4—2921no—
522C22×C4—734no—
523C22×C4—731no—
524C22×C4—731no—
525C22×C4—731no—
526C22×C4—731no—
527C22×C4—731no—
528C22×C4—731no—
529C22×C4—1461no—
530C22×C4—1461no—
531C22×C4—1461no—
532C22×C4—1461no—
533C22×C4—1461no—
534C22×C4—1461no—
535C22×C4—1461no—
536C22×C4—1461no—
537C22×C4—1461no—
538C22×C4—1461no—
539C22×C4—1461no—
540C22×C4—1461no—
541C22×C4—1461no—
542C22×C4—1461no—
543C22×C4—1461no—
544C22×C4—1461no—
545C22×C4—1461no—
546C22×C4—1461no—
547C22×C4C22×#6440811yescharacteristic
548C22×C4C22×#6440811yescharacteristic
549C22×C4C22×#6440811yescharacteristic
550C22×C4C22×#6440811yescharacteristic
551C22×C4C22×#6440811yescharacteristic
552C22×C4C22×#6440811yescharacteristic
553C2×C8—2924no—
554C2×C8—2924no—
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—
565C2×C8—1461no—
566C2×C8—1461no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C4⋊C4—41no—
580C4⋊C4—2921no—
581C4⋊C4—2921no—
582C4⋊C4—2921no—
583C4⋊C4—734no—
584C22⋊C4—41no—
585C22⋊C4—41no—
586C22⋊C4—2921no—
587C22⋊C4—2921no—
588C22⋊C4—2921no—
589C22⋊C4—2921no—
590C22⋊C4—2921no—
591C22⋊C4—2921no—
592C22⋊C4—734no—
593C22⋊C4#1192403614yescomplemented
594C42—41no—
595C42—2921no—
596C42—1461no—
597C42—1461no—
598C42—1461no—
599C42—1461no—
600C42—1461no—
601C42—1461no—
602C42—1461no—
603C42—1461no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—732no—
611C23—732no—
612C23—1461no—
613C23—1461no—
614C23—1461no—
615C23—1461no—
616C23—1461no—
617C23—1461no—
618C23—1461no—
619C23—1461no—
620C23—1461no—
621C23—1461no—
622C23—1461no—
623C23—1461no—
624C23C2×#1192403612yes—
625C23C23×#6440811yescharacteristic
626D4—2924no—
627D4—2924no—
628D4—2924no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—2924no—
646C2×C4—2924no—
647C2×C4—2921no—
648C2×C4—2921no—
649C2×C4—2921no—
650C2×C4—2921no—
651C2×C4—2921no—
652C2×C4—2921no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—2921no—
657C2×C4—2921no—
658C2×C4—2921no—
659C2×C4—731no—
660C2×C4—731no—
661C2×C4—731no—
662C2×C4—731no—
663C2×C4—731no—
664C2×C4—731no—
665C2×C4—732no—
666C2×C4—732no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4—1461no—
676C2×C4—1461no—
677C2×C4—1461no—
678C2×C4—1461no—
679C2×C4—1461no—
680C2×C4C2×#1192403612yes—
681C2×C4C2×#1192403612yes—
682C8—2921no—
683C8—2921no—
684C8—2921no—
685C8—2921no—
686C8—2921no—
687C8—2921no—
688C8—2921no—
689C8—2921no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—41no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—2921no—
698C22—2921no—
699C22—2921no—
700C22—2921no—
701C22—2921no—
702C22—2921no—
703C22—2921no—
704C22—2921no—
705C22—1462no—
706C22—1462no—
707C22—1462no—
708C22—1462no—
709C22—1462no—
710C22—1462no—
711C22#1798965411yescharacteristic
712C22#1798965411yescharacteristic
713C22#1798965611yescharacteristic
714C22C22×#1192403611yescharacteristic
715C22#1798966611yescharacteristic
716C22#1798966611yescharacteristic
717C22#1798966611yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—41no—
724C4—2921no—
725C4—2921no—
726C4—2921no—
727C4—731no—
728C4—731no—
729C4—731no—
730C4—731no—
731C4—1462no—
732C4—1462no—
733C2—42no—
734C2—2922no—
735C2—2922no—
736C2#2262647211yescharacteristic
737C2#2262677911yescharacteristic
738C2#2262677911yescharacteristic
739C2#2262680911yescharacteristic
740C2#2262681711yescharacteristic
741C2#2262684811yescharacteristic
742C2#2262688611yescharacteristic
subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C23×C8
Fitting#388×C73C4
socleC23×C73C23×C4
prime radicalC2×#14556564C4
cosocleC22×Dic73C24
hypercenter#388#64408
hypocenterC73#23326
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. #22626054C2semidirect
2. #22626053C2semidirect
3. #22626003C2semidirect
4. #22626000C2semidirect
5. #22625986C2semidirect
6. #22625985C2semidirect
7. #22625907C2semidirect
8. #22625906C2semidirect
9. #22625906C2semidirect
10. #22625905C2semidirect
11. #22625876C2semidirect
12. #22625874C2semidirect
13. #22625823C2semidirect
14. #22625786C2semidirect
97. #14556564C8semidirect
163. C2×D292C2×C8semidirect
169. C2×C22⋊D73C2×C8semidirect
199. C2×C4×D73C2×C8semidirect
203. #11924007C2×C8semidirect
210. #11924005C2×C8semidirect
230. C22⋊C4×C73C2×C8semidirect
387. C73#23326semidirect
593. C22⋊C4#11924036semidirect

Maximal subgroups

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

subgroupindex
#226260542
#226260532
#226260032
#226260002
#226259862
#226259852
#226259072
#226259062
#226259052
#226258762
#226258742
#226258232
#226257862
#226124432
#2332673