Finite Group Databasebeta

← #29717676

Subgroups — #29717676

Order 15616.

1464 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840421C211yesmaximal, characteristic
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839922C211yesmaximal, characteristic, complemented
4C2×#16839917C211yesmaximal, characteristic, complemented
5C22×#14519700C211yesmaximal, characteristic, complemented
6#21447060C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21446912C211yesmaximal, characteristic, complemented
9#21446827C211yesmaximal, characteristic, complemented
10#21446163C211yesmaximal, characteristic, complemented
11#21446136C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446086C211yesmaximal, characteristic, complemented
14#21445757C211yesmaximal, characteristic, complemented
15C61×#2417C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×Dic122C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C22×#11758202C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C23×#92418C2211yescharacteristic
22#16840421—24no—
23#16840421—24no—
24C2×#14519765C2211yescharacteristic
25C2×#14519763—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519755—21no—
28C2×#14519751C2211yescharacteristic
29C2×#14519749—21no—
30C2×C4×Dic122C2211yescharacteristic
31C2×#14519737—21no—
32#16839993—24no—
33#16839922—24no—
34#16839917—24no—
35C2×#14519708C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519700—24no—
38C2×#14519700C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519700C2211yescharacteristic
43C2×#14519700C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519697C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×C22⋊#92418C2211yescharacteristic
49C2×C22⋊#92418C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic
56C2×C4×D4×C61C2211yescharacteristic
57C22×C4⋊C4×C61C2211yescharacteristic
58C61×#398—21no—
59C61×#396—21no—
60C61×#391C2211yescharacteristic
61C61×#389C2211yescharacteristic
62C61×#386—21no—
63C61×#380—21no—
64C61×#380C2211yescharacteristic
65C2×#11758222—22no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—41no—
70C2×#11758222—41no—
71C22×Dic122—22no—
72C22×Dic122—22no—
73C22×Dic122—21no—
74C22×Dic122—22no—
75C22×Dic122—41no—
76C22×Dic122—41no—
77C22×Dic122D414yes—
78C22×Dic122C2311yescharacteristic
79C22×Dic122C2311yescharacteristic
80C22×D244C2311yescharacteristic
81C22×C22⋊D61—21no—
82C22×C22⋊D61—21no—
83C23×Dic61—21no—
84C22×C4×D61—21no—
85C2×#11758202—22no—
86C2×#11758202—22no—
87C2×#11758202—22no—
88C2×#11758202—22no—
89C2×#11758202—41no—
90C2×#11758202—41no—
91C2×#11758201—22no—
92C2×#11758201—22no—
93C2×#11758201—41no—
94C22×#92418—22no—
95C22×#92418—22no—
96C22×#92418—41no—
97C22×#92418C2311yescharacteristic
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101#14519765—22no—
102#14519765—22no—
103#14519763—28no—
104#14519756—22no—
105#14519756—22no—
106#14519755—28no—
107#14519751—22no—
108#14519751D414yes—
109#14519749—28no—
110C4×Dic122—22no—
111C4×Dic122—22no—
112#14519737—28no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196—21no—
115C2×#11758196—21no—
116C2×C22⋊Dic61—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×C4×Dic61—21no—
121#14519708—22no—
122#14519701—22no—
123#14519700—22no—
124#14519700—22no—
125#14519700—22no—
126#14519700—22no—
127#14519700—22no—
128#14519700D414yescomplemented
129#14519697—22no—
130#14519697—22no—
131#14519697—41no—
132C22⋊#92418—22no—
133C22⋊#92418—22no—
134C22⋊#92418—41no—
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61D411yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C22⋊Q8×C61—22no—
141C22⋊Q8×C61—22no—
142C22⋊Q8×C61—22no—
143C22⋊Q8×C61—41no—
144C4×D4×C61—22no—
145C4×D4×C61—22no—
146C2×C4⋊C4×C61—22no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61—41no—
152C2×C4⋊C4×C61D411yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61D411yescharacteristic
160C2×C22⋊C4×C61D411yescharacteristic
161C2×C42×C61C2311yescharacteristic
162#95×C61—21no—
163#95×C61—21no—
164#95×C61—21no—
165#95×C61—21no—
166C24×C61C2×D411yescharacteristic
167C24×C61C2×D411yescharacteristic
168C23×D61—21no—
169C2×Q8×C61—21no—
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×D4×C61—22no—
176C2×D4×C61—22no—
177C2×D4×C61—22no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—42no—
193C22×C4×C61—42no—
194C22×C4×C61—81no—
195C22×C4×C61C2×D411yescharacteristic
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2411yescharacteristic
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—42no—
208C22×Dic61—21no—
209C22×Dic61—24no—
210C22×Dic61—21no—
211C22×Dic61—21no—
212C22×Dic61—42no—
213C22×Dic61—42no—
214#11758222—44no—
215#11758222—44no—
216#11758222—44no—
217#11758222—44no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244C2×D412yes—
224C2×C4×D61—24no—
225C2×C4×D61—42no—
226C2×C4×D61—42no—
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—28no—
235C2×Dic122—24no—
236C2×Dic122—21no—
237C2×Dic122—44no—
238C2×Dic122—44no—
239C2×Dic122—44no—
240C2×Dic122—42no—
241C2×Dic122—42no—
242C2×Dic122C2×D412yes—
243C2×Dic122C2×D412yes—
244C2×Dic122C2×D412yes—
245C2×Dic122#4112yes—
246C4⋊C4×C61—22no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—42no—
253C4⋊C4×C61—42no—
254C4⋊C4×C61—42no—
255C4⋊C4×C61—81no—
256C4⋊C4×C61C2×D412yes—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—42no—
260C22⋊C4×C61—42no—
261C22⋊C4×C61—81no—
262C42×C61—21no—
263C42×C61—21no—
264C22⋊Dic61—24no—
265#11758202—44no—
266#11758202—44no—
267#11758201—44no—
268#11758198—24no—
269#11758198—24no—
270#11758198—24no—
271C4⋊Dic61—21no—
272C4⋊Dic61C2×D412yes—
273#11758196—24no—
274#11758196—24no—
275C4×Dic61—24no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—44no—
288C2×#92418C2×D412yes—
289C23×C61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61#12012yes—
301C23×C61#13512yes—
302C23×C61#13712yes—
303C23×C61C22×D411yescharacteristic
304C22×D61—22no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311Q8×C61—41no—
312Q8×C61—41no—
313Q8×C61—41no—
314Q8×C61—41no—
315D4×C61—44no—
316C2×C4×C61—21no—
317C2×C4×C61—21no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—21no—
323C2×C4×C61—21no—
324C2×C4×C61—21no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—84no—
348C2×C4×C61#12012yes—
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C2×C4×C61H(5,𝔽2)11yescharacteristic
354C2×C4×C61H(5,𝔽2)11yescharacteristic
355C22⋊D61—48no—
356C22⋊D61—48no—
357C2×Dic61—22no—
358C2×Dic61—22no—
359C2×Dic61—22no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—48no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367D244—22no—
368D244—22no—
369D244—41no—
370D244—41no—
371C4×D61—48no—
372Dic122—22no—
373Dic122—22no—
374Dic122—22no—
375Dic122—22no—
376Dic122—22no—
377Dic122—48no—
378Dic122—41no—
379Dic122—41no—
380Dic122#12114yes—
381#92418—22no—
382#92418—41no—
383#92418—41no—
384#92418—41no—
385#24431—611nomaximal, Sylow
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—41no—
393C22×C61—41no—
394C22×C61—41no—
395C22×C61—41no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61#45214yescomplemented
400C22×C61C2×#12011yescharacteristic
401C22×C61D4211yescharacteristic
402C22×C61#54611yescharacteristic
403C22×C61C2×#13511yescharacteristic
404C22×C61C2×#13711yescharacteristic
405C22×C61#57711yescharacteristic
406C22×C61#57811yescharacteristic
407C2×D61—42no—
408C2×D61—42no—
409C2×D61—42no—
410C2×D61—81no—
411C2×D61—81no—
412C2×D61—81no—
413C2×D61—81no—
414C4×C61—22no—
415C4×C61—41no—
416C4×C61—41no—
417C4×C61—41no—
418C4×C61—42no—
419C4×C61—81no—
420C4×C61—81no—
421C4×C61—81no—
422C4×C61C2×#12111yescharacteristic
423C4×C61#53411yescharacteristic
424C4×C61D4211yescharacteristic
425C4×C61#54611yescharacteristic
426Dic61—24no—
427Dic61—42no—
428Dic61—42no—
429C2×#548—611no—
430C2×#465—611no—
431C2×#452—611no—
432C2×#451—611no—
433C22×#103—611no—
434#2417D6111yescharacteristic, complemented
435#2042—611no—
436#2035—611no—
437#2015—611no—
438#2001—611no—
439#1878—611no—
440#1874—611no—
441#1869—611no—
442#1865—611no—
443#1788—611no—
444C2×C61—24no—
445C2×C61—81no—
446C2×C61#241011yescharacteristic
447C2×C61C2×#45211yescharacteristic
448C2×C61#301311yescharacteristic
449C2×C61#327011yescharacteristic
450C2×C61#328211yescharacteristic
451C2×C61#330011yescharacteristic
452C2×C61#331611yescharacteristic
453D61—82no—
454C22×#41—611no—
455C23×Q8—611no—
456C22×Q16—611no—
457C22×Q16—611no—
458C22×SD16—611no—
459C23×C8—611no—
460#548—1224no—
461#548—1224no—
462C2×#124—611no—
463C2×#124—1221no—
464C2×C22⋊Q8—611no—
465C2×C22⋊Q8—1221no—
466C2×C22⋊Q8C2×D6111yescharacteristic
467C2×C22⋊Q8C2×D6111yescharacteristic
468C2×#121—611no—
469C2×#121—1221no—
470C2×C4×Q8—611no—
471C2×C4×D4—1221no—
472C2×C4×D4C2×D6111yescharacteristic
473C22×C4⋊C4C2×D6111yescharacteristic
474#465—1224no—
475#452—1224no—
476#451—1224no—
477C2×#106—611no—
478C2×#103—611no—
479C2×#103—611no—
480C2×#103—611no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103—611no—
485C2×#103—1224no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×C22⋊C8—611no—
490C2×C22⋊C8—611no—
491C2×C22⋊C8—611no—
492#398—21no—
493#396—21no—
494#391C2×D6111yescharacteristic
495#389C2×D6111yescharacteristic
496#386—21no—
497#380—21no—
498#380C2×D6111yescharacteristic
499#340—611no—
500#340—611no—
501#336—611no—
502#336—611no—
503C61#2443111yescharacteristic, complemented, Sylow
504C2×#41—1222no—
505C2×#41—1222no—
506C2×#41—1222no—
507C2×#41—1222no—
508C2×#41—2441no—
509C2×#41—2441no—
510C22×Q8—614no—
511C22×Q8—611no—
512C22×Q8—611no—
513C22×Q8—1222no—
514C22×Q8—1222no—
515C22×Q8—1222no—
516C22×Q8—1221no—
517C22×Q8—2441no—
518C22×Q8—2441no—
519C22×Q8C22×D6111yescharacteristic
520C22×D4—611no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4C22⋊D6111yescharacteristic
524C23×C4—21no—
525C23×C4—1221no—
526C23×C4—1221no—
527C23×C4C22×D6111yescharacteristic
528C23×C4C22×D6111yescharacteristic
529C2×Q16—1222no—
530C2×Q16—1222no—
531C2×Q16—1222no—
532C2×Q16—1222no—
533C2×Q16—2441no—
534C2×Q16—2441no—
535C2×SD16—1222no—
536C2×SD16—1222no—
537C2×SD16—2441no—
538C22×C8—611no—
539C22×C8—611no—
540C22×C8—611no—
541C22×C8—611no—
542C22×C8—1222no—
543C22×C8—1222no—
544C22×C8—2441no—
545#124—1222no—
546#124—1222no—
547#124—1228no—
548C22⋊Q8—22no—
549C22⋊Q8—22no—
550C22⋊Q8—22no—
551C22⋊Q8—41no—
552C22⋊Q8—1228no—
553C22⋊Q8—1222no—
554C22⋊Q8—1222no—
555#121—614no—
556#121—1228no—
557#121—1222no—
558C4×Q8—1222no—
559C4×Q8—1222no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—1228no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4C22⋊D6111yescharacteristic
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C4⋊C4C22×D6111yescharacteristic
575C2×C4⋊C4C22×D6111yescharacteristic
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4C22⋊D6111yescharacteristic
584C2×C22⋊C4C22⋊D6111yescharacteristic
585C2×C42—1221no—
586C2×C42C22×D6111yescharacteristic
587#106—1222no—
588#103—614no—
589#103—1222no—
590#103—1222no—
591#103—1222no—
592#103—1222no—
593#103—1222no—
594#103—1222no—
595#102—1222no—
596#102—1222no—
597#102—2441no—
598C22⋊C8—1222no—
599C22⋊C8—1222no—
600C22⋊C8—2441no—
601#95—21no—
602#95—21no—
603#95—21no—
604#95—21no—
605C24—1221no—
606C24C2×C22⋊D6111yescharacteristic
607C24C2×C22⋊D6111yescharacteristic
608#41—2444no—
609#41—2444no—
610#41—2444no—
611#41—2444no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—612no—
619C2×Q8—612no—
620C2×Q8—612no—
621C2×Q8—612no—
622C2×Q8—1228no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×Q8—1224no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×Q8—1221no—
631C2×Q8—1221no—
632C2×Q8—2442no—
633C2×Q8—2442no—
634C2×Q8—2444no—
635C2×Q8—2444no—
636C2×Q8—2444no—
637C2×D4—22no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—612no—
641C2×D4—1224no—
642C2×D4—1224no—
643C2×D4—1221no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—2442no—
649C2×D4—2442no—
650C2×D4—2442no—
651C2×D4—2442no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—81no—
669C22×C4—1224no—
670C22×C4—1221no—
671C22×C4—1221no—
672C22×C4—1221no—
673C22×C4—1224no—
674C22×C4—2442no—
675C22×C4—2442no—
676C22×C4—2442no—
677C22×C4—2442no—
678C22×C4D4×D6112yes—
679C22×C4D4×D6112yes—
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C2×C22⋊D6111yescharacteristic
684C22×C4C23×D6111yescharacteristic
685Q16—2444no—
686Q16—2444no—
687SD16—2444no—
688C2×C8—612no—
689C2×C8—1221no—
690C2×C8—1221no—
691C2×C8—1221no—
692C2×C8—1221no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—1221no—
699C2×C8—1221no—
700C2×C8—2444no—
701C4⋊C4—21no—
702C4⋊C4—22no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—42no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—81no—
711C4⋊C4—612no—
712C4⋊C4—1224no—
713C4⋊C4—1224no—
714C4⋊C4—1221no—
715C4⋊C4D4×D6112yes—
716C22⋊C4—22no—
717C22⋊C4—22no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4—1224no—
722C22⋊C4—1224no—
723C22⋊C4—1224no—
724C22⋊C4—1224no—
725C42—21no—
726C42—21no—
727C42—1224no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—1222no—
740C23—2441no—
741C23—2441no—
742C23—2441no—
743C23—2441no—
744C23—2441no—
745C23—2441no—
746C23#1451974512yes—
747C23#1451979712yes—
748C23#1451980812yes—
749C23C22×C22⋊D6111yescharacteristic
750Q8—41no—
751Q8—41no—
752Q8—41no—
753Q8—41no—
754Q8—614no—
755Q8—1222no—
756Q8—1222no—
757Q8—1222no—
758Q8—1222no—
759Q8—1222no—
760Q8—2448no—
761Q8—2441no—
762Q8—2441no—
763D4—44no—
764D4—1222no—
765D4—1222no—
766D4—2448no—
767D4—2448no—
768D4—2441no—
769D4—2441no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—84no—
802C2×C4—1222no—
803C2×C4—1222no—
804C2×C4—1222no—
805C2×C4—1222no—
806C2×C4—1222no—
807C2×C4—2448no—
808C2×C4—2448no—
809C2×C4—2441no—
810C2×C4—2441no—
811C2×C4—2441no—
812C2×C4—2441no—
813C2×C4#1451974512yes—
814C2×C4C2×D4×D6111yescharacteristic
815C2×C4C2×D4×D6111yescharacteristic
816C2×C4C2×D4×D6111yescharacteristic
817C2×C4#41×D6111yescharacteristic
818C2×C4#1451982211yescharacteristic
819C2×C4#1451982311yescharacteristic
820C8—1222no—
821C8—2441no—
822C8—2441no—
823C8—2441no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—22no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—41no—
837C22—4881no—
838C22—4881no—
839C22—4881no—
840C22—4881no—
841C22—2442no—
842C22—2442no—
843C22—2442no—
844C22#1683992214yescomplemented
845C22C2×#1451974511yescharacteristic
846C22D4×C22⋊D6111yescharacteristic
847C22#1684040011yescharacteristic
848C22C2×#1451979711yescharacteristic
849C22C2×#1451980811yescharacteristic
850C22#1684057311yescharacteristic
851C22#1684057711yescharacteristic
852C4—22no—
853C4—41no—
854C4—42no—
855C4—41no—
856C4—41no—
857C4—81no—
858C4—81no—
859C4—81no—
860C4—1224no—
861C4—2442no—
862C4—2442no—
863C4#121×D6111yescharacteristic
864C4#1684032011yescharacteristic
865C4#1684039611yescharacteristic
866C4#1684040111yescharacteristic
867C2—24no—
868C2—81no—
869C2—4882no—
870C2#2144919011yescharacteristic
871C2C2×#1683992211yescharacteristic
872C2#2145513111yescharacteristic
873C2#2145739011yescharacteristic
874C2#2145752211yescharacteristic
875C2#2145770011yescharacteristic
876C2#2145792411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2417C2
socleC23×C61C22×D4
prime radicalC2×#16840421C2
hypercenter#2417D61
hypocenterC61#24431
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
2. C2×#16839993C2semidirect
3. C2×#16839922C2semidirect
4. C2×#16839917C2semidirect
5. C22×#14519700C2semidirect
6. #21447060C2semidirect
7. #21447015C2semidirect
8. #21446912C2semidirect
9. #21446827C2semidirect
10. #21446163C2semidirect
11. #21446136C2semidirect
12. #21446112C2semidirect
13. #21446086C2semidirect
14. #21445757C2semidirect
15. C61×#2417C2semidirect
128. #14519700D4semidirect
399. C22×C61#452semidirect
434. #2417D61semidirect
503. C61#24431semidirect
844. C22#16839922semidirect

Maximal subgroups

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

subgroupindex
C2×#168404212
C2×#168399932
C2×#168399222
C2×#168399172
C22×#145197002
#214470602
#214470152
#214469122
#214468272
#214461632
#214461362
#214461122
#214460862
#214457572
C61×#24172
#2443161