Finite Group Databasebeta

← #29717751

Subgroups — #29717751

Order 15616.

1582 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840408C211yesmaximal, characteristic
2C2×#16839993C211yesmaximal, characteristic, complemented
3C2×#16839922C211yesmaximal, characteristic, complemented
4C2×#16839912C211yesmaximal, characteristic, complemented
5C2×#16839756C211yesmaximal, characteristic, complemented
6#21447060C211yesmaximal, characteristic, complemented
7#21447015C211yesmaximal, characteristic, complemented
8#21446912C211yesmaximal, characteristic, complemented
9#21446827C211yesmaximal, characteristic, complemented
10#21446156C211yesmaximal, characteristic, complemented
11#21446141C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446079C211yesmaximal, characteristic, complemented
14#21445749C211yesmaximal, characteristic, complemented
15C61×#2415C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic, complemented
19C22×#11758201C2211yescharacteristic
20C22×#11758201C2211yescharacteristic
21C23×#92418C2211yescharacteristic, complemented
22#16840408—24no—
23#16840408—24no—
24C2×#14519765C2211yescharacteristic
25C2×#14519762—21no—
26C2×#14519756C2211yescharacteristic
27C2×#14519751C2211yescharacteristic
28C2×#14519750—21no—
29C2×#14519745—21no—
30C2×C4×D244C2211yescharacteristic
31C2×C22⋊C4×D61—21no—
32#16839993—24no—
33#16839922—24no—
34#16839912—24no—
35C2×#14519708C2211yescharacteristic, complemented
36#16839756—24no—
37C2×#14519701C2211yescharacteristic, complemented
38C2×#14519700C2211yescharacteristic, complemented
39C2×#14519700C2211yescharacteristic, complemented
40C2×#14519700C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519697C2211yescharacteristic
46C2×#14519697C2211yescharacteristic
47C2×C22⋊#92418C2211yescharacteristic
48C2×C22⋊#92418C2211yescharacteristic
49C2×C22⋊#92418C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839517C2211yescharacteristic, complemented
53#16839517C2211yescharacteristic, complemented
54C2×C22⋊Q8×C61C2211yescharacteristic
55C2×C22⋊Q8×C61C2211yescharacteristic, complemented
56C2×C4×D4×C61C2211yescharacteristic
57C2×#117×C61C2211yescharacteristic, complemented
58C61×#397—21no—
59C61×#394—21no—
60C61×#391C2211yescharacteristic, complemented
61C61×#389—21no—
62C61×#389C2211yescharacteristic, complemented
63C61×#388—21no—
64C61×#380C2211yescharacteristic
65C24×D61—21no—
66C2×#11758222—22no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—41no—
70C2×#11758222—41no—
71C2×#11758222D414yes—
72C22×Dic122C2311yescharacteristic
73C22×D244—21no—
74C22×D244—22no—
75C22×D244—22no—
76C22×D244—22no—
77C22×D244—22no—
78C22×D244—41no—
79C22×D244—41no—
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61—21no—
83C22×C22⋊D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C2×#11758202—22no—
87C2×#11758202—41no—
88C2×#11758202—41no—
89C2×#11758201—22no—
90C2×#11758201—22no—
91C2×#11758201—22no—
92C2×#11758201—22no—
93C2×#11758201—22no—
94C2×#11758201—41no—
95C22×#92418—22no—
96C22×#92418—22no—
97C22×#92418—41no—
98C22×#92418C2311yescharacteristic
99C22×#92418C2311yescharacteristic
100C22×#92418C2311yescharacteristic
101C22×#92418C2311yescharacteristic
102#14519765—22no—
103#14519765—22no—
104#14519762—28no—
105#14519756—22no—
106#14519756—22no—
107#14519751—22no—
108#14519751D414yes—
109#14519750—28no—
110#14519745—28no—
111C4×D244—22no—
112C4×D244—22no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196—21no—
115C2×C22⋊Dic61—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C22⋊C4×D61—28no—
121#14519708—22no—
122#14519701—22no—
123#14519700—22no—
124#14519700—22no—
125#14519700—22no—
126#14519697—22no—
127#14519697—22no—
128#14519697—22no—
129#14519697—22no—
130#14519697—41no—
131#14519697D414yescomplemented
132C22⋊#92418—22no—
133C22⋊#92418—22no—
134C22⋊#92418—41no—
135C22×Q8×C61C2311yescharacteristic
136C22×D4×C61D411yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C22⋊Q8×C61—22no—
140C22⋊Q8×C61—22no—
141C22⋊Q8×C61—22no—
142C22⋊Q8×C61—41no—
143C4×D4×C61—22no—
144C4×D4×C61—22no—
145#117×C61—22no—
146#117×C61—41no—
147C2×C4⋊C4×C61—21no—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61—21no—
150C2×C4⋊C4×C61D411yescharacteristic
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C22⋊C4×C61—21no—
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61D411yescharacteristic
159C2×C22⋊C4×C61D411yescharacteristic
160C2×C42×C61—21no—
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—
169C23×D61—21no—
170C23×D61—24no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—81no—
176C23×D61—81no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×D4×C61—22no—
184C2×D4×C61—22no—
185C2×D4×C61—41no—
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—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61—21no—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D411yescharacteristic
203C22×C4×C61C2×D411yescharacteristic
204C22×C4×C61C2×D412yes—
205C22×C4×C61C2×D412yes—
206C22×C4×C61C2411yescharacteristic
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—42no—
211C2×C22⋊D61—81no—
212C2×C22⋊D61—81no—
213C22×Dic61—21no—
214C22×Dic61—21no—
215#11758222—28no—
216#11758222—44no—
217#11758222—44no—
218#11758222—44no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—21no—
225C2×D244—21no—
226C2×D244—24no—
227C2×D244—21no—
228C2×D244—44no—
229C2×D244—44no—
230C2×D244—44no—
231C2×D244—42no—
232C2×D244—42no—
233C2×D244—44no—
234C2×D244C2×D412yes—
235C2×D244C2×D412yes—
236C2×D244C2×D412yes—
237C2×D244#4112yes—
238C2×C4×D61—24no—
239C2×C4×D61—24no—
240C2×C4×D61—42no—
241C2×C4×D61—42no—
242C2×C4×D61—81no—
243C2×C4×D61—81no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122C2×D412yes—
250C4⋊C4×C61—22no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—42no—
257C4⋊C4×C61—42no—
258C4⋊C4×C61—42no—
259C4⋊C4×C61C2×D412yes—
260C22⋊C4×C61—22no—
261C22⋊C4×C61—22no—
262C22⋊C4×C61—42no—
263C22⋊C4×C61—42no—
264C22⋊C4×C61—42no—
265C22⋊C4×C61—42no—
266C42×C61—21no—
267C42×C61—21no—
268C42×C61—42no—
269C22⋊Dic61—24no—
270#11758202—44no—
271#11758201—44no—
272#11758201—44no—
273#11758198—24no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277C4⋊Dic61—21no—
278C4⋊Dic61C2×D412yes—
279#11758196—24no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—44no—
292C2×#92418C2×D412yes—
293C23×C61—21no—
294C23×C61—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61#12012yes—
306C23×C61#13512yes—
307C23×C61C22×D411yescharacteristic
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—22no—
312C22×D61—48no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—48no—
318C22×D61—41no—
319C22×D61—41no—
320C22×D61—41no—
321C22×D61—41no—
322C22×D61—41no—
323C22×D61—41no—
324C22×D61—84no—
325C22×D61—84no—
326C22×D61—84no—
327C22×D61—84no—
328C22×D61—84no—
329Q8×C61—41no—
330Q8×C61—41no—
331Q8×C61—41no—
332Q8×C61—41no—
333D4×C61—44no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—22no—
337C2×C4×C61—22no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—22no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—21no—
349C2×C4×C61—21no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—41no—
353C2×C4×C61—41no—
354C2×C4×C61—41no—
355C2×C4×C61—41no—
356C2×C4×C61—41no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61#12012yes—
366C2×C4×C61C22×D411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C2×#4111yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C22⋊D61—48no—
373C22⋊D61—84no—
374C2×Dic61—22no—
375C2×Dic61—22no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380D244—22no—
381D244—22no—
382D244—22no—
383D244—22no—
384D244—22no—
385D244—48no—
386D244—41no—
387D244—41no—
388D244#12114yes—
389C4×D61—48no—
390C4×D61—84no—
391Dic122—22no—
392Dic122—22no—
393Dic122—41no—
394Dic122—41no—
395#92418—22no—
396#92418—41no—
397#92418—41no—
398#92418—41no—
399#24436—611nomaximal, Sylow
400C22×C61—22no—
401C22×C61—22no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61C2×#12011yescharacteristic
415C22×C61D4211yescharacteristic
416C22×C61#54611yescharacteristic
417C22×C61C2×#13511yescharacteristic
418C22×C61#57511yescharacteristic
419C22×C61#57711yescharacteristic
420C22×C61#57711yescharacteristic
421C2×D61—24no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—42no—
426C2×D61—42no—
427C2×D61—42no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—816no—
432C2×D61—81no—
433C2×D61—81no—
434C2×D61—81no—
435C2×D61—81no—
436C4×C61—22no—
437C4×C61—41no—
438C4×C61—41no—
439C4×C61—41no—
440C4×C61—42no—
441C4×C61—81no—
442C4×C61—81no—
443C4×C61—81no—
444C4×C61C2×#12111yescharacteristic
445C4×C61#53411yescharacteristic
446C4×C61D4211yescharacteristic
447C4×C61#54611yescharacteristic
448Dic61—42no—
449Dic61—42no—
450C2×#546—611no—
451C2×#465—611no—
452C2×#452—611no—
453C2×#450—611no—
454C2×#416—611no—
455#2415D6111yescharacteristic, complemented
456#2042—611no—
457#2035—611no—
458#2015—611no—
459#2001—611no—
460#1877—611no—
461#1875—611no—
462#1869—611no—
463#1864—611no—
464#1786—611no—
465C2×C61—42no—
466C2×C61—42no—
467C2×C61#241011yescharacteristic
468C2×C61#300211yescharacteristic
469C2×C61#300911yescharacteristic
470C2×C61#326711yescharacteristic
471C2×C61#328211yescharacteristic
472C2×C61#329611yescharacteristic
473C2×C61#331111yescharacteristic
474D61—44no—
475D61—82no—
476C22×#41—611no—
477C23×D4—611no—
478C22×Q16—611no—
479C22×SD16—611no—
480C22×SD16—611no—
481C23×C8—611no—
482#546—1224no—
483#546—1224no—
484C2×#124—611no—
485C2×#123—1221no—
486C2×C22⋊Q8—611no—
487C2×C22⋊Q8C2×D6111yescharacteristic
488C2×C22⋊Q8C2×D6111yescharacteristic, complemented
489C2×#121—611no—
490C2×#121—1221no—
491C2×#120—1221no—
492C2×C4×D4—611no—
493C2×C4×D4C2×D6111yescharacteristic
494C2×#117C2×D6111yescharacteristic, complemented
495C22×C22⋊C4—1221no—
496#465—1224no—
497#452—1224no—
498#450—1224no—
499C2×#106—611no—
500#416—1224no—
501C2×#103—611no—
502C2×#103—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#102—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×C22⋊C8—611no—
512C2×C22⋊C8—611no—
513C2×C22⋊C8—611no—
514#397—21no—
515#394—21no—
516#391C2×D6111yescharacteristic, complemented
517#389—21no—
518#389C2×D6111yescharacteristic, complemented
519#388—21no—
520#380C2×D6111yescharacteristic
521#340—611no—
522#340—611no—
523#336—611no—
524#336—611no—
525C61#2443611yescharacteristic, complemented, Sylow
526C25—1221no—
527C2×#41—614no—
528C2×#41—1222no—
529C2×#41—1222no—
530C2×#41—1222no—
531C2×#41—2441no—
532C2×#41—2441no—
533C22×Q8—611no—
534C22×Q8C22×D6111yescharacteristic
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—1222no—
538C22×D4—1222no—
539C22×D4—1222no—
540C22×D4—1222no—
541C22×D4—1221no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—2441no—
545C22×D4—2441no—
546C22×D4C22⋊D6111yescharacteristic
547C23×C4—1221no—
548C23×C4—1221no—
549C23×C4C22×D6111yescharacteristic
550C23×C4C22×D6111yescharacteristic
551C2×Q16—1222no—
552C2×Q16—2441no—
553C2×Q16—2441no—
554C2×SD16—1222no—
555C2×SD16—1222no—
556C2×SD16—1222no—
557C2×SD16—1222no—
558C2×SD16—1222no—
559C2×SD16—2441no—
560C22×C8—611no—
561C22×C8—611no—
562C22×C8—611no—
563C22×C8—611no—
564C22×C8—1222no—
565C22×C8—1222no—
566C22×C8—2441no—
567#124—1222no—
568#124—1222no—
569#123—1228no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—41no—
574C22⋊Q8—1222no—
575C22⋊Q8—1222no—
576#121—614no—
577#121—1228no—
578#121—1222no—
579#120—1228no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—1222no—
583C4×D4—1222no—
584#117—22no—
585#117—41no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4C22⋊D6111yescharacteristic
592C2×C4⋊C4C22×D6111yescharacteristic
593C2×C4⋊C4C22×D6111yescharacteristic
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—1228no—
600C2×C22⋊C4—1221no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4C22⋊D6111yescharacteristic
606C2×C22⋊C4C22⋊D6111yescharacteristic
607C2×C42—21no—
608C2×C42C22×D6111yescharacteristic
609#106—1222no—
610#103—1222no—
611#103—1222no—
612#103—1222no—
613#103—1222no—
614#102—614no—
615#102—1222no—
616#102—1222no—
617#102—1222no—
618#102—1222no—
619#102—2441no—
620C22⋊C8—1222no—
621C22⋊C8—1222no—
622C22⋊C8—2441no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—1224no—
628C24—1221no—
629C24—1221no—
630C24—4881no—
631C24—4881no—
632C24—2442no—
633C24—2442no—
634C24—2442no—
635C24—2442no—
636C24C2×C22⋊D6111yescharacteristic
637C24C2×C22⋊D6111yescharacteristic
638#41—1228no—
639#41—2444no—
640#41—2444no—
641#41—2444no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—612no—
649C2×Q8—1221no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—41no—
657C2×D4—612no—
658C2×D4—612no—
659C2×D4—612no—
660C2×D4—612no—
661C2×D4—1224no—
662C2×D4—1224no—
663C2×D4—1224no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—4881no—
673C2×D4—4881no—
674C2×D4—2442no—
675C2×D4—2442no—
676C2×D4—2444no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4—2444no—
680C2×D4—2442no—
681C2×D4—2442no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—1224no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1224no—
700C22×C4—4881no—
701C22×C4—4881no—
702C22×C4—2442no—
703C22×C4—2442no—
704C22×C4D4×D6112yes—
705C22×C4D4×D6112yes—
706C22×C4C2×C22⋊D6111yescharacteristic
707C22×C4C2×C22⋊D6111yescharacteristic
708C22×C4C2×C22⋊D6111yescharacteristic
709C22×C4C2×C22⋊D6111yescharacteristic
710C22×C4C23×D6111yescharacteristic
711Q16—2444no—
712SD16—2444no—
713SD16—2444no—
714C2×C8—612no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—2444no—
727C4⋊C4—21no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—42no—
736C4⋊C4—612no—
737C4⋊C4—1224no—
738C4⋊C4—1221no—
739C4⋊C4D4×D6112yes—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—42no—
743C22⋊C4—42no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—1224no—
747C22⋊C4—1224no—
748C22⋊C4—1224no—
749C22⋊C4—1224no—
750C22⋊C4—1224no—
751C42—21no—
752C42—21no—
753C42—42no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—1222no—
767C23—1222no—
768C23—1222no—
769C23—1222no—
770C23—4884no—
771C23—4884no—
772C23—4884no—
773C23—4884no—
774C23—4884no—
775C23—2448no—
776C23—2448no—
777C23—2441no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781C23—2441no—
782C23—2441no—
783C23—2441no—
784C23—2441no—
785C23—2441no—
786C23—2441no—
787C23#1451974512yes—
788C23#1451979712yes—
789C23C22×C22⋊D6111yescharacteristic
790Q8—41no—
791Q8—41no—
792Q8—41no—
793Q8—41no—
794Q8—1222no—
795Q8—1222no—
796Q8—2441no—
797Q8—2441no—
798D4—44no—
799D4—614no—
800D4—1222no—
801D4—1222no—
802D4—1222no—
803D4—1222no—
804D4—1222no—
805D4—4884no—
806D4—2448no—
807D4—2448no—
808D4—2441no—
809D4—2441no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—1222no—
842C2×C4—1222no—
843C2×C4—4884no—
844C2×C4—2448no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4#1451974512yes—
850C2×C4C2×D4×D6111yescharacteristic
851C2×C4C2×D4×D6111yescharacteristic
852C2×C4C2×D4×D6111yescharacteristic
853C2×C4#41×D6111yescharacteristic
854C2×C4#1451982211yescharacteristic
855C2×C4#1451982311yescharacteristic
856C8—1222no—
857C8—2441no—
858C8—2441no—
859C8—2441no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—22no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—1224no—
875C22—48816no—
876C22—4881no—
877C22—4881no—
878C22—4881no—
879C22—4881no—
880C22—2442no—
881C22—2442no—
882C22—2442no—
883C22—2442no—
884C22—2442no—
885C22—2442no—
886C22—2442no—
887C22—2442no—
888C22—2442no—
889C22C2×#1451974511yescharacteristic
890C22D4×C22⋊D6111yescharacteristic
891C22#1684040011yescharacteristic
892C22C2×#1451979711yescharacteristic
893C22#1684056011yescharacteristic
894C22#1684057011yescharacteristic
895C22#1684057011yescharacteristic
896C4—22no—
897C4—41no—
898C4—42no—
899C4—41no—
900C4—41no—
901C4—81no—
902C4—81no—
903C4—81no—
904C4—2442no—
905C4—2442no—
906C4#121×D6111yescharacteristic
907C4#1684032011yescharacteristic
908C4#1684039611yescharacteristic
909C4#1684040111yescharacteristic
910C2—42no—
911C2—42no—
912C2—4882no—
913C2—2444no—
914C2#2144919011yescharacteristic
915C2#2145503511yescharacteristic
916C2#2145509411yescharacteristic
917C2#2145734511yescharacteristic
918C2#2145752711yescharacteristic
919C2#2145764811yescharacteristic
920C2#2145784911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2415C2
socleC23×C61C22×D4
prime radicalC2×#16840408C2
hypercenter#2415D61
hypocenterC61#24436
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2415

Complements

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

NH ≅ G/Ntype
2. C2×#16839993C2semidirect
3. C2×#16839922C2semidirect
4. C2×#16839912C2semidirect
5. C2×#16839756C2semidirect
6. #21447060C2semidirect
7. #21447015C2semidirect
8. #21446912C2semidirect
9. #21446827C2semidirect
10. #21446156C2semidirect
11. #21446141C2semidirect
12. #21446112C2semidirect
13. #21446079C2semidirect
14. #21445749C2semidirect
15. C61×#2415C2semidirect
18. C22×#11758202C22semidirect
21. C23×#92418C22semidirect
35. C2×#14519708C22semidirect
37. C2×#14519701C22semidirect
38. C2×#14519700C22semidirect
39. C2×#14519700C22semidirect
40. C2×#14519700C22semidirect
49. C2×C22⋊#92418C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839517C22semidirect
53. #16839517C22semidirect
55. C2×C22⋊Q8×C61C22semidirect
57. C2×#117×C61C22semidirect
60. C61×#391C22semidirect
62. C61×#389C22semidirect
131. #14519697D4semidirect
455. #2415D61semidirect
488. C2×C22⋊Q8C2×D61semidirect
494. C2×#117C2×D61semidirect
516. #391C2×D61semidirect
518. #389C2×D61semidirect
525. C61#24436semidirect

Maximal subgroups

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

subgroupindex
C2×#168404082
C2×#168399932
C2×#168399222
C2×#168399122
C2×#168397562
#214470602
#214470152
#214469122
#214468272
#214461562
#214461412
#214461122
#214460792
#214457492
C61×#24152
#2443661