Finite Group Databasebeta

← #33096280

Subgroups — #33096280

Order 18688.

1010 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988554C211yesmaximal, characteristic
2#22612523C211yesmaximal, characteristic
3#22610130C211yesmaximal, characteristic, complemented
4#22610130C211yesmaximal, characteristic, complemented
5#22610128C211yesmaximal, characteristic, complemented
6#22610128C211yesmaximal, characteristic, complemented
7#22610124C211yesmaximal, characteristic, complemented
8#22610123C211yesmaximal, characteristic, complemented
9#22610119C211yesmaximal, characteristic, complemented
10#22610118C211yesmaximal, characteristic, complemented
11#22609962C211yesmaximal, characteristic, complemented
12#22609962C211yesmaximal, characteristic, complemented
13#22609958C211yesmaximal, characteristic, complemented
14#22609954C211yesmaximal, characteristic, complemented
15C73×#2311C211yesmaximal, characteristic
16C22×#11924012C2211yescharacteristic
17C23×#10596831C2211yescharacteristic
18C2×#14556550C2211yescharacteristic
19C22×C4⋊Dic73C2211yescharacteristic
20C2×#14556524C2211yescharacteristic
21C2×#14556524C2211yescharacteristic
22C2×#14556524C2211yescharacteristic
23C2×#14556524C2211yescharacteristic
24C2×#14556522C2211yescharacteristic
25C2×#14556522C2211yescharacteristic
26C2×#14556522C2211yescharacteristic
27C2×#14556522C2211yescharacteristic
28#17988554C418yescomplemented
29C2×C22⋊#10596831C2211yescharacteristic
30C2×C22⋊#10596831C2211yescharacteristic
31C2×C22⋊#10596831C2211yescharacteristic
32C2×C22⋊#10596831C2211yescharacteristic
33#17988494—21no—
34#17988490—21no—
35#17988467—21no—
36#17988467—21no—
37#17988447C2211yescharacteristic
38#17988447C2211yescharacteristic
39#17988447C2211yescharacteristic
40#17988447C2211yescharacteristic
41#17988349C2211yescharacteristic
42#17988349C2211yescharacteristic
43#17988349C2211yescharacteristic
44#17988349C2211yescharacteristic
45#17988349C2211yescharacteristic
46#17988349C2211yescharacteristic
47#17988349C2211yescharacteristic
48#17988349C2211yescharacteristic
49C22×#41×C73C2211yescharacteristic
50C2×#117×C73C2211yescharacteristic
51C22×C4⋊C4×C73C2211yescharacteristic
52#391×C73—21no—
53#390×C73—21no—
54#386×C73—21no—
55#386×C73—21no—
56#380×C73C2211yescharacteristic
57#380×C73C2211yescharacteristic
58#380×C73C2211yescharacteristic
59#380×C73C2211yescharacteristic
60C23×Dic73—21no—
61C2×#11924012—41no—
62C2×#11924012—41no—
63C2×#11924012C2×C414yescomplemented
64C22×#10596831—41no—
65C22×#10596831—41no—
66C22×#10596831C2×C414yescomplemented
67C22×#10596831C2311yescharacteristic
68C22×#10596831C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71#14556550—41no—
72#14556550—41no—
73C2×C4⋊Dic73—21no—
74C2×C4⋊Dic73—41no—
75C2×C4⋊Dic73—41no—
76C2×C4⋊Dic73C2311yescharacteristic
77C2×C4⋊Dic73C2311yescharacteristic
78C2×C4⋊Dic73C2311yescharacteristic
79C2×C4⋊Dic73C2311yescharacteristic
80C2×C22⋊Dic73—21no—
81C2×C22⋊Dic73—21no—
82C2×C22⋊Dic73—21no—
83C2×C22⋊Dic73—21no—
84C2×C22⋊Dic73—21no—
85C2×C4×Dic73—21no—
86#14556524—41no—
87#14556524—41no—
88#14556524—41no—
89#14556524—41no—
90#14556522—41no—
91#14556522—41no—
92#14556522—41no—
93#14556522—41no—
94C22⋊#10596831C2×C414yescomplemented
95C22⋊#10596831C2×C414yescomplemented
96C22⋊#10596831C2×C414yescomplemented
97C22⋊#10596831C2×C414yescomplemented
98#14556498—21no—
99#14556498—21no—
100#14556498—21no—
101#14556498—21no—
102C2×#41×C73—41no—
103C2×#41×C73—41no—
104C2×#41×C73—41no—
105C2×#41×C73—41no—
106C2×#41×C73C2×C414yes—
107C2×#41×C73Q814yes—
108C22×Q8×C73D411yescharacteristic
109C22×D4×C73D411yescharacteristic
110C22×D4×C73D411yescharacteristic
111C22×D4×C73D411yescharacteristic
112C23×C4×C73—21no—
113C23×C4×C73C2311yescharacteristic
114C23×C4×C73C2311yescharacteristic
115C23×C4×C73C2311yescharacteristic
116#117×C73—41no—
117#117×C73—41no—
118C2×C4⋊C4×C73—21no—
119C2×C4⋊C4×C73—41no—
120C2×C4⋊C4×C73—41no—
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C4⋊C4×C73C2311yescharacteristic
124C2×C4⋊C4×C73C2311yescharacteristic
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C42×C73—21no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135C22×Dic73—21no—
136C22×Dic73—21no—
137C22×Dic73—21no—
138C22×Dic73—21no—
139C22×Dic73—42no—
140C22×Dic73—81no—
141C22×Dic73—81no—
142#11924012—44no—
143C2×#10596831—21no—
144C2×#10596831—21no—
145C2×#10596831—21no—
146C2×#10596831—21no—
147C2×#10596831—21no—
148C2×#10596831—21no—
149C2×#10596831—21no—
150C2×#10596831—21no—
151C2×#10596831—44no—
152C2×#10596831C22×C412yes—
153C2×#10596831C22×C412yes—
154C2×#10596831C22×C412yes—
155C2×#10596831C22×C412yes—
156C4⋊Dic73—21no—
157C4⋊Dic73—21no—
158C4⋊Dic73—21no—
159C4⋊Dic73—21no—
160C4⋊Dic73—21no—
161C4⋊Dic73—21no—
162C4⋊Dic73—21no—
163C4⋊Dic73—21no—
164C4⋊Dic73—42no—
165C22⋊Dic73—42no—
166C22⋊Dic73—81no—
167C22⋊Dic73—81no—
168C22⋊Dic73—81no—
169C22⋊Dic73—81no—
170C4×Dic73—42no—
171C24×C73C2×D411yescharacteristic
172C24×C73C2×D411yescharacteristic
173C24×C73C2×D411yescharacteristic
174#41×C73—44no—
175#41×C73—44no—
176#41×C73—44no—
177#41×C73—44no—
178C2×Q8×C73—41no—
179C2×Q8×C73—41no—
180C2×Q8×C73C4⋊C414yes—
181C2×D4×C73—41no—
182C2×D4×C73—41no—
183C2×D4×C73—41no—
184C2×D4×C73—41no—
185C2×D4×C73—41no—
186C2×D4×C73—41no—
187C2×D4×C73C4⋊C414yes—
188C2×D4×C73C4⋊C414yes—
189C2×D4×C73C4⋊C414yes—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
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×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—42no—
207C22×C4×C73—81no—
208C22×C4×C73—81no—
209C22×C4×C73C22×C412yes—
210C22×C4×C73C22×C412yes—
211C22×C4×C73C22×C412yes—
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×Q812yes—
216C22×C4×C73C2×Q812yes—
217C22×C4×C73C2×Q812yes—
218C22×C4×C73C2411yescharacteristic
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—42no—
228C22⋊C4×C73—42no—
229C22⋊C4×C73—81no—
230C22⋊C4×C73—81no—
231C22⋊C4×C73—81no—
232C22⋊C4×C73—81no—
233C42×C73—42no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73—21no—
241C23×C73—21no—
242C23×C73—21no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—21no—
246C23×C73—21no—
247C23×C73—21no—
248C23×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—21no—
252C23×C73C2×C4⋊C412yes—
253C23×C73C2×C4⋊C412yes—
254C23×C73C2×C4⋊C412yes—
255C23×C73C22×D411yescharacteristic
256Q8×C73—44no—
257D4×C73—44no—
258D4×C73—44no—
259D4×C73—44no—
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—22no—
267C2×C4×C73—22no—
268C2×C4×C73—22no—
269C2×C4×C73—22no—
270C2×C4×C73—22no—
271C2×C4×C73—22no—
272C2×C4×C73—22no—
273C2×C4×C73—22no—
274C2×C4×C73—22no—
275C2×C4×C73—22no—
276C2×C4×C73—22no—
277C2×C4×C73—22no—
278C2×C4×C73—41no—
279C2×C4×C73—41no—
280C2×C4×C73—41no—
281C2×C4×C73—41no—
282C2×C4×C73—41no—
283C2×C4×C73—41no—
284C2×C4×C73—41no—
285C2×C4×C73—41no—
286C2×C4×C73—41no—
287C2×C4×C73—41no—
288C2×C4×C73—41no—
289C2×C4×C73—41no—
290C2×C4×C73—84no—
291C2×C4×C73C2×C4⋊C412yes—
292C2×C4×C73C2×C4⋊C412yes—
293C2×C4×C73C2×C4⋊C412yes—
294C2×C4×C73C23×C411yescharacteristic
295C2×C4×C73C22×Q811yescharacteristic
296C2×C4×C73H(5,𝔽2)11yescharacteristic
297C2×C4×C73H(5,𝔽2)11yescharacteristic
298C2×C4×C73H(5,𝔽2)11yescharacteristic
299C2×C4×C73H(5,𝔽2)11yescharacteristic
300C2×Dic73—41no—
301C2×Dic73—41no—
302C2×Dic73—41no—
303C2×Dic73—41no—
304C2×Dic73—41no—
305C2×Dic73—41no—
306C2×Dic73—41no—
307C2×Dic73—41no—
308C2×Dic73—41no—
309C2×Dic73—41no—
310C2×Dic73—41no—
311C2×Dic73—41no—
312C2×Dic73—84no—
313#10596831—22no—
314#10596831—22no—
315#10596831—22no—
316#10596831—22no—
317C22×C73—22no—
318C22×C73—22no—
319C22×C73—22no—
320C22×C73—22no—
321C22×C73—22no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—22no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—41no—
331C22×C73—41no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73C22×C4⋊C411yescharacteristic
339C22×C73#53411yescharacteristic
340C22×C73#53411yescharacteristic
341C22×C73#57611yescharacteristic
342C22×C73#57711yescharacteristic
343C22×C73#57711yescharacteristic
344C22×C73#57811yescharacteristic
345C4×C73—22no—
346C4×C73—22no—
347C4×C73—22no—
348C4×C73—81no—
349C4×C73—81no—
350C4×C73—81no—
351C4×C73—81no—
352C4×C73#51811yescharacteristic
353C4×C73#51811yescharacteristic
354C4×C73#54311yescharacteristic
355C4×C73#54311yescharacteristic
356Dic73—81no—
357Dic73—81no—
358Dic73—81no—
359Dic73—81no—
360#21945—731nomaximal, Sylow
361C2×C73—42no—
362C2×C73—42no—
363C2×C73—42no—
364C2×C73#231511yescharacteristic
365C2×C73#291211yescharacteristic
366C2×C73#291311yescharacteristic
367C2×C73#319811yescharacteristic
368C2×C73#319811yescharacteristic
369C2×C73#320111yescharacteristic
370C2×C73#320111yescharacteristic
371C2×#408—731no—
372#2311—731no—
373#2311D7311yescharacteristic
374#1854—731no—
375#1854—731no—
376#1854—731no—
377#1854—731no—
378#1853—731no—
379#1853—731no—
380#1852—731no—
381#1852—731no—
382#1809—731no—
383#1809—731no—
384#1808—731no—
385#1807—731no—
386C73#2194511yescharacteristic, complemented, Sylow
387C22×#41C2×D7311yescharacteristic
388C22×M16—731no—
389C23×C8—731no—
390C2×#117—731no—
391C2×#117C2×D7311yescharacteristic
392C22×C4⋊C4—731no—
393C22×C4⋊C4C2×D7311yescharacteristic
394C2×#107—731no—
395C2×#107—731no—
396C2×#107—731no—
397C2×#107—731no—
398C2×#106—731no—
399C2×#106—731no—
400C2×#106—731no—
401C2×#106—731no—
402#408—738no—
403C2×C22⋊C8—731no—
404C2×C22⋊C8—731no—
405C2×C22⋊C8—731no—
406C2×C22⋊C8—731no—
407#391—21no—
408#391—1461no—
409#390—21no—
410#390—1461no—
411#386—21no—
412#386—21no—
413#386—1461no—
414#386—1461no—
415#380—731no—
416#380—731no—
417#380—731no—
418#380—731no—
419#380C2×D7311yescharacteristic
420#380C2×D7311yescharacteristic
421#380C2×D7311yescharacteristic
422#380C2×D7311yescharacteristic
423#340—731no—
424#340—731no—
425#340—731no—
426#340—731no—
427#340—731no—
428#340—731no—
429#340—731no—
430#340—731no—
431C2×#41—41no—
432C2×#41—41no—
433C2×#41—41no—
434C2×#41—41no—
435C2×#41Dic14614yes—
436C2×#41C4×D7314yes—
437C22×Q8C22⋊D7311yescharacteristic
438C22×D4C22⋊D7311yescharacteristic
439C22×D4C22⋊D7311yescharacteristic
440C22×D4C22⋊D7311yescharacteristic
441C23×C4—21no—
442C23×C4—1461no—
443C23×C4C22×D7311yescharacteristic
444C23×C4C22×D7311yescharacteristic
445C23×C4C22×D7311yescharacteristic
446C2×M16—2921no—
447C2×M16—2921no—
448C2×M16—734no—
449C22×C8—2921no—
450C22×C8—2921no—
451C22×C8—734no—
452C22×C8—731no—
453C22×C8—731no—
454C22×C8—731no—
455C22×C8—731no—
456#117—41no—
457#117—41no—
458#117—2921no—
459#117—2921no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—41no—
463C2×C4⋊C4—2921no—
464C2×C4⋊C4—2921no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—731no—
467C2×C4⋊C4—731no—
468C2×C4⋊C4—731no—
469C2×C4⋊C4—1461no—
470C2×C4⋊C4C22×D7311yescharacteristic
471C2×C4⋊C4C22×D7311yescharacteristic
472C2×C4⋊C4C22×D7311yescharacteristic
473C2×C4⋊C4C22×D7311yescharacteristic
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—1461no—
480C2×C22⋊C4—1461no—
481C2×C22⋊C4—1461no—
482C2×C22⋊C4—1461no—
483C2×C22⋊C4—1461no—
484C2×C42—21no—
485C2×C42—1461no—
486#107—2921no—
487#107—2921no—
488#107—2921no—
489#107—2921no—
490#106—2921no—
491#106—2921no—
492#106—2921no—
493#106—2921no—
494C22⋊C8—734no—
495C22⋊C8—734no—
496C22⋊C8—734no—
497C22⋊C8—734no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—1461no—
503#95—1461no—
504#95—1461no—
505#95—1461no—
506C24C2×C22⋊D7311yescharacteristic
507C24C2×C22⋊D7311yescharacteristic
508C24C2×C22⋊D7311yescharacteristic
509#41—44no—
510#41—44no—
511#41—44no—
512#41—44no—
513C2×Q8—41no—
514C2×Q8—41no—
515C2×Q8#1192400714yes—
516C2×D4—41no—
517C2×D4—41no—
518C2×D4—41no—
519C2×D4—41no—
520C2×D4—41no—
521C2×D4—41no—
522C2×D4#1192400714yes—
523C2×D4#1192400714yes—
524C2×D4#1192400714yes—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—81no—
543C22×C4—81no—
544C22×C4—2922no—
545C22×C4—5841no—
546C22×C4—5841no—
547C22×C4—1461no—
548C22×C4—1461no—
549C22×C4—1461no—
550C22×C4—1461no—
551C22×C4C2×C4×D7312yes—
552C22×C4C2×C4×D7312yes—
553C22×C4C2×C4×D7312yes—
554C22×C4C2×C22⋊D7311yescharacteristic
555C22×C4C2×C22⋊D7311yescharacteristic
556C22×C4C2×C22⋊D7311yescharacteristic
557C22×C4C2×Dic14612yes—
558C22×C4C2×Dic14612yes—
559C22×C4C2×Dic14612yes—
560C22×C4C23×D7311yescharacteristic
561M16—2924no—
562C2×C8—2924no—
563C2×C8—732no—
564C2×C8—732no—
565C2×C8—732no—
566C2×C8—732no—
567C2×C8—1461no—
568C2×C8—1461no—
569C2×C8—1461no—
570C2×C8—1461no—
571C2×C8—1461no—
572C2×C8—1461no—
573C2×C8—1461no—
574C2×C8—1461no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—42no—
584C4⋊C4—2922no—
585C4⋊C4—1461no—
586C4⋊C4—1461no—
587C4⋊C4—1461no—
588C4⋊C4—1461no—
589C4⋊C4—1461no—
590C4⋊C4—1461no—
591C4⋊C4—1461no—
592C4⋊C4—1461no—
593C22⋊C4—42no—
594C22⋊C4—81no—
595C22⋊C4—81no—
596C22⋊C4—81no—
597C22⋊C4—81no—
598C22⋊C4—2922no—
599C22⋊C4—5841no—
600C22⋊C4—5841no—
601C22⋊C4—5841no—
602C22⋊C4—5841no—
603C42—42no—
604C42—2922no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23C2×#1192400712yes—
624C23C2×#1192400712yes—
625C23C2×#1192400712yes—
626C23C22×C22⋊D7311yescharacteristic
627Q8—44no—
628D4—44no—
629D4—44no—
630D4—44no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—84no—
662C2×C4—2921no—
663C2×C4—2921no—
664C2×C4—2921no—
665C2×C4—2921no—
666C2×C4—2921no—
667C2×C4—2921no—
668C2×C4—2921no—
669C2×C4—2921no—
670C2×C4—2921no—
671C2×C4—2921no—
672C2×C4—2921no—
673C2×C4—2921no—
674C2×C4—5844no—
675C2×C4C2×#1192400712yes—
676C2×C4C2×#1192400712yes—
677C2×C4C2×#1192400712yes—
678C2×C4C22×C4×D7311yescharacteristic
679C2×C4C22×Dic14611yescharacteristic
680C2×C4#1455663611yescharacteristic
681C2×C4#1455663611yescharacteristic
682C2×C4#1455663611yescharacteristic
683C2×C4#1455663611yescharacteristic
684C8—1462no—
685C8—1462no—
686C8—1462no—
687C8—1462no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22C22×#1192400711yescharacteristic
710C22#1798914611yescharacteristic
711C22#1798914611yescharacteristic
712C22#1798939011yescharacteristic
713C22#1798939511yescharacteristic
714C22#1798939811yescharacteristic
715C22#1798940211yescharacteristic
716C4—22no—
717C4—22no—
718C4—22no—
719C4—81no—
720C4—81no—
721C4—81no—
722C4—81no—
723C4—5841no—
724C4—5841no—
725C4—5841no—
726C4—5841no—
727C4#1798906011yescharacteristic
728C4#1798906011yescharacteristic
729C4#1798921311yescharacteristic
730C4#1798921311yescharacteristic
731C2—42no—
732C2—42no—
733C2—42no—
734C2#2261254311yescharacteristic
735C2#2261852411yescharacteristic
736C2#2261852911yescharacteristic
737C2#2262077711yescharacteristic
738C2#2262078311yescharacteristic
739C2#2262080711yescharacteristic
740C2#2262081311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2311C2
socleC23×C73C22×D4
prime radicalC22×#41×C73C22
cosocleC22×C4×C73C24
hypercenter#2311D73
hypocenterC73#21945
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×#41 ◁ #2311

Complements

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

NH ≅ G/Ntype
3. #22610130C2semidirect
4. #22610130C2semidirect
5. #22610128C2semidirect
6. #22610128C2semidirect
7. #22610124C2semidirect
8. #22610123C2semidirect
9. #22610119C2semidirect
10. #22610118C2semidirect
11. #22609962C2semidirect
12. #22609962C2semidirect
13. #22609958C2semidirect
14. #22609954C2semidirect
28. #17988554C4semidirect
63. C2×#11924012C2×C4semidirect
66. C22×#10596831C2×C4semidirect
94. C22⋊#10596831C2×C4semidirect
95. C22⋊#10596831C2×C4semidirect
96. C22⋊#10596831C2×C4semidirect
97. C22⋊#10596831C2×C4semidirect
386. C73#21945semidirect

Maximal subgroups

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

subgroupindex
C2×#179885542
#226125232
#226101302
#226101282
#226101242
#226101232
#226101192
#226101182
#226099622
#226099582
#226099542
C73×#23112
#2194573