Finite Group Databasebeta

← #30621756

Subgroups — #30621756

Order 15616.

1058 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q16×#6923C211yesmaximal, characteristic, complemented
2C2×#16840755C211yesmaximal, characteristic
3#21462345C211yesmaximal, characteristic
4Q8×C22⋊#6923C211yesmaximal, characteristic
5#21461967C211yesmaximal, characteristic, complemented
6#21461908C211yesmaximal, characteristic, complemented
7#21461899C211yesmaximal, characteristic, complemented
8#21461834C211yesmaximal, characteristic
9#21461813C211yesmaximal, characteristic, complemented
10#21461813C211yesmaximal, characteristic, complemented
11#21461785C211yesmaximal, characteristic, complemented
12#21461770C211yesmaximal, characteristic
13#21461592C211yesmaximal, characteristic, complemented
14#21461562C211yesmaximal, characteristic
15#451×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×Q8×#6923C2211yescharacteristic
18C2×Q8×#6923C2211yescharacteristic
19C2×Q8×#6923C2211yescharacteristic
20C2×#14519856C2211yescharacteristic
21Q16×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24#16840755—24no—
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30C2×#14519840C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33(C2×#6923)⋊Q8—21no—
34(C2×#6923)⋊Q8—21no—
35(C2×#6923)⋊Q8C2211yescharacteristic
36(C2×#6923)⋊Q8C2211yescharacteristic
37(C2×#6923)⋊Q8C2211yescharacteristic
38#16840713C2211yescharacteristic
39#16840712—21no—
40#16840712—21no—
41#16840711—21no—
42#16840704—21no—
43#16840704C2211yescharacteristic
44C4⋊C4×#6923—21no—
45C4⋊C4×#6923C2211yescharacteristic
46C4×C22⋊#6923—21no—
47C4×C22⋊#6923C2211yescharacteristic
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C22×Q8×D61C2211yescharacteristic
55C2×Q16×D61C2211yescharacteristic
56C2×Q16×D61C2211yescharacteristic
57C22⋊Q8×D61C2211yescharacteristic
58#16839920C411yescharacteristic, complemented
59#16839919C411yescharacteristic, complemented
60#16839919C411yescharacteristic, complemented
61#16839918C411yescharacteristic, complemented
62#16839917C411yescharacteristic, complemented
63#16839916C411yescharacteristic, complemented
64#16839916C411yescharacteristic, complemented
65#103×D61C2211yescharacteristic
66#103×D61C2211yescharacteristic
67C22⋊C8×D61C2211yescharacteristic
68C61×#451C411yescharacteristic, complemented
69C2×#11758213—21no—
70D61⋊M16—22no—
71D61⋊M16—41no—
72C2×#11758217—21no—
73C2×D61⋊C8C2311yescharacteristic
74C2×D61⋊C8C2311yescharacteristic
75Q8×#6923—22no—
76Q8×#6923—22no—
77Q8×#6923—22no—
78Q8×#6923—41no—
79Q8×#6923—41no—
80Q8×#6923—41no—
81#14519856—22no—
82#14519856—41no—
83C2×C4⋊#6923—21no—
84C2×C4⋊#6923—21no—
85C2×C4⋊#6923—21no—
86C2×C4⋊#6923—21no—
87C2×C4⋊#6923C2311yescharacteristic
88C2×C4⋊#6923C2311yescharacteristic
89C2×C4⋊#6923C2311yescharacteristic
90C2×C4⋊#6923C2311yescharacteristic
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923D411yescharacteristic
94C2×C22⋊#6923D411yescharacteristic
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923—21no—
99C2×C4×#6923—21no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102#14519846—22no—
103#14519845—41no—
104#14519840—22no—
105#14519840—22no—
106#14519840—22no—
107#14519840—22no—
108#14519840—41no—
109#14519840D414yes—
110#14519831—41no—
111C8×#6923—22no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120(C2×#6923)⋊C4—21no—
121(C2×#6923)⋊C4D411yescharacteristic
122(C2×#6923)⋊C4D411yescharacteristic
123C22×Dic122—21no—
124C22×Dic122C2×C411yescharacteristic
125C2×Q8×D61—21no—
126C2×Q8×D61—21no—
127C2×Q8×D61—22no—
128C2×Q8×D61—22no—
129C2×Q8×D61—41no—
130C2×Q8×D61—41no—
131C2×Q8×D61C2×C411yescharacteristic
132C2×Q8×D61C2×C411yescharacteristic
133C2×Q8×D61C2311yescharacteristic
134C2×Q8×D61C2311yescharacteristic
135C2×Q8×D61C2311yescharacteristic
136C22×C4×D61—21no—
137C22×C4×D61C2311yescharacteristic
138C2×Dic244C2×C411yescharacteristic
139C2×Dic244C2×C411yescharacteristic
140C2×#11758202C2×C411yescharacteristic
141C2×#11758202C2×C411yescharacteristic
142C2×#11758202C2×C411yescharacteristic
143C2×#11758202C2×C411yescharacteristic
144Q16×D61—22no—
145Q16×D61—22no—
146Q16×D61—41no—
147Q16×D61—41no—
148C2×C8×D61C2311yescharacteristic
149C2×C8×D61C2311yescharacteristic
150#14519757C2×C411yescharacteristic
151#14519756C2×C411yescharacteristic
152#14519755—21no—
153#14519754—21no—
154#14519753C2×C411yescharacteristic
155C4⋊C4×D61—21no—
156C4⋊C4×D61C2311yescharacteristic
157C22⋊C4×D61—21no—
158#14519702C2×C411yescharacteristic
159#14519702C2×C411yescharacteristic
160#14519701C2×C411yescharacteristic
161#14519701C2×C411yescharacteristic
162#14519700C2×C411yescharacteristic
163#14519700C2×C411yescharacteristic
164C22⋊#92418C2×C411yescharacteristic
165#14519689C2×C411yescharacteristic
166#14519689C2×C411yescharacteristic
167C22×Q8×C61C2×C411yescharacteristic
168C2×Q16×C61C2×C411yescharacteristic
169C2×Q16×C61C2×C411yescharacteristic
170C22⋊Q8×C61C2×C411yescharacteristic
171#103×C61C2×C411yescharacteristic
172#103×C61C2×C411yescharacteristic
173C22⋊C8×C61C2×C411yescharacteristic
174C23×D61C2×D411yescharacteristic
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—21no—
178C22×#6923—21no—
179C22×#6923C2×D411yescharacteristic
180C22×#6923C2×D411yescharacteristic
181C22×#6923C2×D411yescharacteristic
182C22×#6923C2×D411yescharacteristic
183C2×Q8×C61—21no—
184C2×Q8×C61—22no—
185C2×Q8×C61—41no—
186C2×Q8×C61C22×C411yescharacteristic
187C2×Q8×C61C22×C411yescharacteristic
188C2×Q8×C61C22×C411yescharacteristic
189C22×C4×C61—21no—
190C22×C4×C61C22×C411yescharacteristic
191C22×Dic61—21no—
192C22×Dic61#4111yescharacteristic
193Q8×D61—21no—
194Q8×D61—21no—
195Q8×D61—22no—
196Q8×D61—21no—
197Q8×D61—21no—
198Q8×D61—21no—
199Q8×D61—21no—
200Q8×D61—21no—
201Q8×D61—21no—
202Q8×D61—21no—
203Q8×D61—21no—
204Q8×D61—22no—
205Q8×D61—41no—
206Q8×D61—41no—
207Q8×D61—42no—
208Q8×D61—42no—
209Q8×D61—42no—
210Q8×D61—42no—
211Q8×D61C2×D412yes—
212Q8×D61#4112yes—
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—42no—
224C2×C4×D61—42no—
225C2×C4×D61C22×C411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×C4×D61#4111yescharacteristic
228C2×C4×D61C2411yescharacteristic
229C2×Dic122—21no—
230C2×Dic122—22no—
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—41no—
237C2×Dic122—42no—
238C2×Dic122—42no—
239C2×Dic122C22×C411yescharacteristic
240C2×Dic122C22×C411yescharacteristic
241C2×Dic122C22×C411yescharacteristic
242C22⋊#6923—22no—
243C22⋊#6923—41no—
244C22⋊#6923—42no—
245C22⋊#6923—42no—
246#11758217—42no—
247C2×#92420—21no—
248C2×#92420—21no—
249C4⋊#6923—21no—
250C4⋊#6923—21no—
251C4⋊#6923—21no—
252C4⋊#6923—21no—
253C4⋊#6923—21no—
254C4⋊#6923—21no—
255C4⋊#6923—21no—
256C4⋊#6923—42no—
257C4⋊#6923—42no—
258C4⋊#6923—42no—
259C4⋊#6923—42no—
260C4⋊#6923C2×D412yes—
261C4×#6923—21no—
262C4×#6923—21no—
263C4×#6923—21no—
264C4×#6923—21no—
265C4×#6923—42no—
266C4×#6923—42no—
267C4×#6923—42no—
268C4×#6923—42no—
269C4×#6923—42no—
270#11758213—42no—
271D61⋊C8—21no—
272D61⋊C8—21no—
273D61⋊C8—21no—
274D61⋊C8C2×D412yes—
275Q16×C61—22no—
276Q16×C61—41no—
277C2×C8×C61C22×C411yescharacteristic
278C2×C8×C61C22×C411yescharacteristic
279C4⋊C4×C61—21no—
280C4⋊C4×C61C22×C411yescharacteristic
281C22⋊C4×C61—21no—
282C22⋊Dic61—21no—
283#11758202—22no—
284#11758202—22no—
285#11758202—41no—
286#11758202—41no—
287#11758198—21no—
288#11758198—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61C22×C411yescharacteristic
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294C2×#92418C22×C411yescharacteristic
295C2×#92418C22×C411yescharacteristic
296Dic244—22no—
297Dic244—41no—
298C8×D61—21no—
299C8×D61—21no—
300C8×D61—21no—
301C8×D61—21no—
302C23×C61C4×D411yescharacteristic
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61C4×D411yescharacteristic
310C22×D61C22×D411yescharacteristic
311C2×#6923—21no—
312C2×#6923—21no—
313C2×#6923—21no—
314C2×#6923—22no—
315C2×#6923—21no—
316C2×#6923—21no—
317C2×#6923—21no—
318C2×#6923—21no—
319C2×#6923—21no—
320C2×#6923—21no—
321C2×#6923—21no—
322C2×#6923—21no—
323C2×#6923—41no—
324C2×#6923—41no—
325C2×#6923—41no—
326C2×#6923—41no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923#13712yes—
335Q8×C61—21no—
336Q8×C61—21no—
337Q8×C61—21no—
338Q8×C61—21no—
339Q8×C61—21no—
340Q8×C61—42no—
341Q8×C61C4×D412yes—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—42no—
349C2×C4×C61C4×D411yescharacteristic
350C2×C4×C61C23×C411yescharacteristic
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—42no—
358C2×Dic61C4×D411yescharacteristic
359C2×Dic61C2×#4111yescharacteristic
360C4×D61—21no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—21no—
364C4×D61—21no—
365C4×D61—21no—
366C4×D61—21no—
367C4×D61—21no—
368C4×D61—42no—
369C4×D61—42no—
370C4×D61—41no—
371C4×D61—41no—
372C4×D61—41no—
373C4×D61—41no—
374C4×D61—41no—
375C4×D61—41no—
376C4×D61C22×D411yescharacteristic
377C4×D61C2×#4111yescharacteristic
378C4×D61H(5,𝔽2)11yescharacteristic
379C4×D61H(5,𝔽2)11yescharacteristic
380Dic122—21no—
381Dic122—22no—
382Dic122—22no—
383Dic122—21no—
384Dic122—21no—
385Dic122—21no—
386Dic122—21no—
387Dic122—42no—
388Dic122—42no—
389Dic122—42no—
390Dic122—41no—
391Dic122—41no—
392Dic122—41no—
393Dic122—41no—
394Dic122C4×D412yes—
395#92420—22no—
396#92420—41no—
397C8×C61—21no—
398C8×C61—21no—
399#92418—21no—
400#92418—21no—
401#22881—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61C2×C4×D411yescharacteristic
406C2×D61—21no—
407C2×D61—21no—
408C2×D61—21no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—41no—
412C2×D61—41no—
413C2×D61D4211yescharacteristic
414C2×D61#54611yescharacteristic
415C2×D61C2×#13711yescharacteristic
416C2×D61#57511yescharacteristic
417C2×D61#57811yescharacteristic
418C2×D61#57811yescharacteristic
419#6923—22no—
420#6923—41no—
421#6923—41no—
422#6923—42no—
423#6923—41no—
424#6923—81no—
425#6923—81no—
426#6923—81no—
427C4×C61—22no—
428C4×C61—21no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61—41no—
432C4×C61C2×C4×D411yescharacteristic
433C4×C61#51811yescharacteristic
434Dic61—22no—
435Dic61—21no—
436Dic61—41no—
437Dic61—41no—
438Dic61—41no—
439Dic61#54611yescharacteristic
440Dic61#55111yescharacteristic
441C2×#451—611no—
442C2×C4×Q16—611no—
443C2×#419—611no—
444#2362—611no—
445Q8×C22⋊C4—611no—
446#1971—611no—
447#1933—611no—
448#1928—611no—
449#1894—611no—
450#1878—611no—
451#1878—611no—
452#1865—611no—
453#1854—611no—
454#1763—611no—
455#1753—611no—
456C2×C61—41no—
457C2×C61#235811yescharacteristic
458C2×C61C4×#13711yescharacteristic
459C2×C61#295011yescharacteristic
460D61—41no—
461D61#326911yescharacteristic
462D61#327011yescharacteristic
463D61#332711yescharacteristic
464D61#332811yescharacteristic
465C23×Q8—611no—
466C22×Q16—611no—
467C22×Q16—611no—
468C22×M16—611no—
469C2×C22⋊Q8—611no—
470C2×C4×Q8—611no—
471C2×C4×Q8—611no—
472C2×C4×Q8—611no—
473C2×#117—611no—
474#451—611no—
475#451—611no—
476#451—611no—
477#451—611no—
478#451—611no—
479#451—611no—
480#451—611no—
481#451#692311yescharacteristic, complemented
482C4×Q16—1224no—
483C2×#107—611no—
484C2×#106—611no—
485#419—1224no—
486C2×#103—611no—
487C2×#103—611no—
488C2×#103—611no—
489C2×#103—611no—
490C2×#103—611no—
491C2×#103—611no—
492C2×#103—611no—
493C2×#103—611no—
494C2×C22⋊C8—611no—
495C2×#97—611no—
496C2×C4×C8—611no—
497#391—611no—
498#391—611no—
499#391—611no—
500#391—1221no—
501#391—1221no—
502#389—611no—
503#388—1221no—
504#388—1221no—
505#387—1221no—
506#380—611no—
507#380—1221no—
508C4×C4⋊C4—611no—
509C4×C4⋊C4—1221no—
510C4×C22⋊C4—611no—
511C4×C22⋊C4—1221no—
512#340—611no—
513#340—611no—
514#340—611no—
515#340—611no—
516#336—611no—
517#336—611no—
518C61#2288111yescharacteristic, complemented, Sylow
519C22×Q8—611no—
520C22×Q8—611no—
521C22×Q8—611no—
522C22×Q8—611no—
523C22×Q8—611no—
524C22×Q8—611no—
525C22×Q8—1221no—
526C22×Q8—1221no—
527C22×Q8—1221no—
528C22×Q8—1222no—
529C22×Q8—1222no—
530C22×Q8—2441no—
531C22×Q8—2441no—
532C22×Q8C2×#692311yescharacteristic
533C23×C4—611no—
534C23×C4—1221no—
535C2×Q16—611no—
536C2×Q16—611no—
537C2×Q16—611no—
538C2×Q16—611no—
539C2×Q16—611no—
540C2×Q16—611no—
541C2×Q16—1222no—
542C2×Q16—1222no—
543C2×Q16—2441no—
544C2×Q16—2441no—
545C2×Q16C2×#692311yescharacteristic
546C2×Q16C2×#692311yescharacteristic
547C2×M16—1222no—
548C2×M16—1221no—
549C2×M16—1221no—
550C2×M16—2441no—
551C22×C8—611no—
552C22×C8—611no—
553C22×C8—611no—
554C22×C8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—611no—
557C22⋊Q8—611no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560C22⋊Q8C2×#692311yescharacteristic
561C4×Q8—1222no—
562C4×Q8—1222no—
563C4×Q8—1222no—
564C4×Q8—2441no—
565C4×Q8—2441no—
566C4×Q8—2441no—
567#117—1222no—
568#117—2441no—
569C2×C4⋊C4—611no—
570C2×C4⋊C4—611no—
571C2×C4⋊C4—611no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—1221no—
575C2×C4⋊C4—1221no—
576C2×C4⋊C4—1221no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C22⋊C4—611no—
580C2×C22⋊C4—611no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C42—611no—
585C2×C42—611no—
586C2×C42—1221no—
587C2×C42—1221no—
588C2×C42—1221no—
589C2×C42—1221no—
590C2×C42—1221no—
591#107—1222no—
592#106—2441no—
593#103—614no—
594#103—611no—
595#103—611no—
596#103—611no—
597#103—611no—
598#103—611no—
599#103—611no—
600#103—1222no—
601#103—1222no—
602#103—1222no—
603#103—1222no—
604#103—2441no—
605#103C2×#692311yescharacteristic
606#103C2×#692311yescharacteristic
607C22⋊C8—611no—
608C22⋊C8—611no—
609C22⋊C8—611no—
610C22⋊C8C2×#692311yescharacteristic
611#97—2441no—
612C4×C8—1222no—
613#95—611no—
614#95—611no—
615#95—1221no—
616#95—1221no—
617#95—1221no—
618#95—1221no—
619#95—1221no—
620#95—1221no—
621#95—1221no—
622#95—1221no—
623#95—1221no—
624C24—611no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—41no—
628C2×Q8—612no—
629C2×Q8—612no—
630C2×Q8—611no—
631C2×Q8—611no—
632C2×Q8—611no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×Q8—1221no—
637C2×Q8—1221no—
638C2×Q8—1222no—
639C2×Q8—1221no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8—1221no—
643C2×Q8—1221no—
644C2×Q8—1221no—
645C2×Q8—1221no—
646C2×Q8—1221no—
647C2×Q8—1221no—
648C2×Q8—1221no—
649C2×Q8—1221no—
650C2×Q8—1222no—
651C2×Q8—1222no—
652C2×Q8—2441no—
653C2×Q8—2442no—
654C2×Q8—2442no—
655C2×Q8—2442no—
656C2×Q8—2442no—
657C2×Q8—2441no—
658C2×Q8—2441no—
659C2×Q8—2442no—
660C2×Q8—2442no—
661C2×Q8C22×#692311yescharacteristic
662C2×Q8C22×#692311yescharacteristic
663C2×Q8C22×#692311yescharacteristic
664C22×C4—21no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—611no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—2442no—
690C22×C4—2442no—
691C22×C4C22×#692311yescharacteristic
692Q16—22no—
693Q16—41no—
694Q16—1222no—
695Q16—1222no—
696Q16—1222no—
697Q16—2441no—
698Q16—2441no—
699Q16—2441no—
700M16—2442no—
701M16—2442no—
702C2×C8—612no—
703C2×C8—611no—
704C2×C8—611no—
705C2×C8—1221no—
706C2×C8—1221no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8C22×#692311yescharacteristic
715C2×C8C22×#692311yescharacteristic
716C4⋊C4—21no—
717C4⋊C4—612no—
718C4⋊C4—611no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—2442no—
731C4⋊C4—2442no—
732C4⋊C4—2442no—
733C4⋊C4—2442no—
734C4⋊C4C22×#692311yescharacteristic
735C22⋊C4—21no—
736C22⋊C4—1221no—
737C22⋊C4—1221no—
738C22⋊C4—1222no—
739C22⋊C4—1221no—
740C22⋊C4—2441no—
741C22⋊C4—2442no—
742C22⋊C4—2442no—
743C42—1221no—
744C42—1221no—
745C42—1221no—
746C42—1221no—
747C42—2442no—
748C42—2442no—
749C42—2442no—
750C42—2442no—
751C42—2442no—
752C23—611no—
753C23—611no—
754C23—1221no—
755C23—1221no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23D4×#692311yescharacteristic
761Q8—21no—
762Q8—21no—
763Q8—21no—
764Q8—21no—
765Q8—21no—
766Q8—42no—
767Q8—612no—
768Q8—1222no—
769Q8—1222no—
770Q8—1221no—
771Q8—1221no—
772Q8—1221no—
773Q8—1221no—
774Q8—1221no—
775Q8—2442no—
776Q8—2442no—
777Q8—2441no—
778Q8—2441no—
779Q8—2441no—
780Q8—2441no—
781Q8—2442no—
782Q8D4×#692312yes—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—42no—
790C2×C4—611no—
791C2×C4—611no—
792C2×C4—611no—
793C2×C4—611no—
794C2×C4—611no—
795C2×C4—612no—
796C2×C4—611no—
797C2×C4—1221no—
798C2×C4—1221no—
799C2×C4—1221no—
800C2×C4—1222no—
801C2×C4—1222no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1221no—
808C2×C4—1221no—
809C2×C4—1221no—
810C2×C4—1221no—
811C2×C4—1221no—
812C2×C4—1221no—
813C2×C4—1222no—
814C2×C4—1221no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1221no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—2442no—
824C2×C4—2442no—
825C2×C4—2441no—
826C2×C4—2441no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2442no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4D4×#692311yescharacteristic
844C2×C4C23×#692311yescharacteristic
845C8—21no—
846C8—21no—
847C8—1222no—
848C8—1221no—
849C8—1221no—
850C8—2441no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—611no—
855C22—611no—
856C22—611no—
857C22—611no—
858C22—611no—
859C22—611no—
860C22—1221no—
861C22—1221no—
862C22—1221no—
863C22—2441no—
864C22—2441no—
865C22—2441no—
866C22—2441no—
867C22C2×D4×#692311yescharacteristic
868C4—21no—
869C4—22no—
870C4—41no—
871C4—41no—
872C4—41no—
873C4—611no—
874C4—611no—
875C4—1222no—
876C4—1221no—
877C4—1222no—
878C4—4881no—
879C4—4881no—
880C4—4881no—
881C4—2441no—
882C4—2441no—
883C4—2441no—
884C4—2442no—
885C4—2441no—
886C4—2441no—
887C4—2441no—
888C4C2×D4×#692311yescharacteristic
889C4#1684082911yescharacteristic
890C2—41no—
891C2—611no—
892C2—611no—
893C2—611no—
894C2—611no—
895C2—2441no—
896C2#2146234111yescharacteristic
897C2#137×#692311yescharacteristic
898C2#2146258011yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#451C4
socleC22×C61C2×C4×D4
prime radicalC23×D61C2×D4
cosocleC2×C4×D61C24
hypercenter#451#6923
hypocenterC61#22881
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×Q16×#6923C2semidirect
5. #21461967C2semidirect
6. #21461908C2semidirect
7. #21461899C2semidirect
9. #21461813C2semidirect
10. #21461813C2semidirect
11. #21461785C2semidirect
13. #21461592C2semidirect
58. #16839920C4semidirect
59. #16839919C4semidirect
60. #16839919C4semidirect
61. #16839918C4semidirect
62. #16839917C4semidirect
63. #16839916C4semidirect
64. #16839916C4semidirect
68. C61×#451C4semidirect
481. #451#6923semidirect
518. C61#22881semidirect

Maximal subgroups

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

subgroupindex
C2×Q16×#69232
C2×#168407552
#214623452
Q8×C22⋊#69232
#214619672
#214619082
#214618992
#214618342
#214618132
#214617852
#214617702
#214615922
#214615622
#451×D612
#2288161