Finite Group Databasebeta

← #30620191

Subgroups — #30620191

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462558C211yesmaximal, characteristic, complemented
2C2×#16840761C211yesmaximal, characteristic, complemented
3C22×#14519842C211yesmaximal, characteristic, complemented
4#21462273C211yesmaximal, characteristic, complemented
5#21461982C211yesmaximal, characteristic, complemented
6#21461955C211yesmaximal, characteristic, complemented
7#21461838C211yesmaximal, characteristic, complemented
8#21461836C211yesmaximal, characteristic, complemented
9#21461801C211yesmaximal, characteristic, complemented
10#21461800C211yesmaximal, characteristic, complemented
11#21461694C211yesmaximal, characteristic, complemented
12#21461662C211yesmaximal, characteristic, complemented
13#21461662C211yesmaximal, characteristic, complemented
14#21461583C211yesmaximal, characteristic, complemented
15D4×#11758226C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic, complemented
17C2×D61⋊M16C2211yescharacteristic, complemented
18C2×#14519856C2211yescharacteristic, complemented
19C22×C4×#6923C2211yescharacteristic, complemented
20#16840795—21no—
21#16840793—21no—
22#16840792—21no—
23#16840789—21no—
24#16840767C2211yescharacteristic, complemented
25#16840761—24no—
26C2×#14519842—24no—
27C2×#14519842C2211yescharacteristic
28C2×#14519842C2211yescharacteristic
29C2×#14519842C2211yescharacteristic
30C2×#14519842C2211yescharacteristic
31C2×#14519842C2211yescharacteristic, complemented
32C2×#14519842C2211yescharacteristic, complemented
33C2×#14519842C2211yescharacteristic, complemented
34C2×#14519842C2211yescharacteristic, complemented
35C2×#14519842C2211yescharacteristic, complemented
36C2×#14519842C2211yescharacteristic, complemented
37C2×#14519842C2211yescharacteristic, complemented
38C2×#14519842C2211yescharacteristic, complemented
39#16840733C2211yescharacteristic, complemented
40#16840733C2211yescharacteristic, complemented
41C4×#11758213C2211yescharacteristic, complemented
42#16840712—21no—
43#16840711—21no—
44#16840710—21no—
45#16840709—21no—
46C4×C4⋊#6923C2211yescharacteristic, complemented
47C4×C22⋊#6923C2211yescharacteristic, complemented
48C4×C22⋊#6923C2211yescharacteristic, complemented
49#16840698C2211yescharacteristic, complemented
50#16840632C2211yescharacteristic, complemented
51#16840632C2211yescharacteristic, complemented
52#16840632C2211yescharacteristic, complemented
53#16840632C2211yescharacteristic, complemented
54C22×#11758226C2211yescharacteristic
55C22×#11758226C2211yescharacteristic
56#16840434C411yescharacteristic, complemented
57#16840423C411yescharacteristic, complemented
58#16840423C411yescharacteristic, complemented
59#16840415—21no—
60#16840415C411yescharacteristic, complemented
61#16840403—21no—
62#16840403—21no—
63#16840403C411yescharacteristic, complemented
64#16840403C411yescharacteristic, complemented
65D4×D244—21no—
66D4×D244C411yescharacteristic, complemented
67#16840313—21no—
68#16840313C2211yescharacteristic
69#16840275—21no—
70#16840275—21no—
71#16840275C2211yescharacteristic
72#16840275C2211yescharacteristic
73C4×#11758226C2211yescharacteristic
74C4×D4×D61—21no—
75C4×D4×D61C2211yescharacteristic
76D4×Q8×C61C411yescharacteristic, complemented
77C23×#6923—21no—
78C2×#11758213—22no—
79C2×#11758213—21no—
80C2×#11758213—41no—
81C2×#11758213C2311yescharacteristic
82C2×#11758213C2311yescharacteristic
83C2×#11758213C2311yescharacteristic
84C2×#11758213C2311yescharacteristic
85D61⋊M16—22no—
86D61⋊M16—41no—
87C2×#11758217—21no—
88C2×D61⋊C8—21no—
89C22×#92420—21no—
90#14519856—22no—
91#14519856—41no—
92C2×C4⋊#6923—21no—
93C2×C4⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C22⋊#6923—21no—
96C2×C22⋊#6923—21no—
97C2×C4×#6923—22no—
98C2×C4×#6923—21no—
99C2×C4×#6923—41no—
100C2×C4×#6923C2311yescharacteristic
101C2×C4×#6923C2311yescharacteristic
102C2×C4×#6923C2311yescharacteristic
103C2×C4×#6923C2311yescharacteristic
104#14519844—21no—
105#14519844—21no—
106#14519842—22no—
107#14519842—22no—
108#14519842—22no—
109#14519842—22no—
110#14519842—22no—
111#14519842—22no—
112#14519842—22no—
113#14519842—41no—
114#14519842—41no—
115#14519842—41no—
116#14519842—41no—
117#14519842D414yescomplemented
118#14519834—21no—
119#14519834—21no—
120C22⋊#92420—21no—
121C22⋊#92420—21no—
122#14519832—21no—
123C4×#92420—21no—
124(C2×#6923)⋊C4—21no—
125(C2×#6923)⋊C4—21no—
126(C2×#6923)⋊C4—21no—
127(C2×#6923)⋊C4—21no—
128(C2×#6923)⋊C4—21no—
129C2×#11758226—21no—
130C2×#11758226—21no—
131C2×#11758226—21no—
132C2×#11758226—21no—
133C2×#11758226—22no—
134C2×#11758226—22no—
135C2×#11758226—22no—
136C2×#11758226—22no—
137C2×#11758226—41no—
138C2×#11758226—41no—
139C2×#11758226—41no—
140C2×#11758226—41no—
141C2×#11758226C2×C411yescharacteristic
142C2×#11758226C2×C411yescharacteristic
143C2×#11758226C2×C411yescharacteristic, complemented
144C2×#11758226C2×C411yescharacteristic, complemented
145C2×#11758226C2311yescharacteristic
146C2×#11758226C2311yescharacteristic
147C2×#11758226C2311yescharacteristic
148C22×D244—21no—
149C22×D244—21no—
150C22×D244C2×C411yescharacteristic
151C22×D244C2×C411yescharacteristic, complemented
152C2×D4×D61—21no—
153C2×D4×D61D411yescharacteristic
154C22×C4×D61—21no—
155C22×C4×D61—21no—
156C22×C4×D61C2311yescharacteristic
157C22×C4×D61C2311yescharacteristic
158#14519774—21no—
159#14519774C2×C411yescharacteristic, complemented
160#14519766—21no—
161#14519766—21no—
162#14519766C2×C411yescharacteristic, complemented
163#14519766C2×C411yescharacteristic, complemented
164#14519762—21no—
165#14519762—21no—
166#14519762—21no—
167#14519762—21no—
168#14519762—21no—
169#14519762—21no—
170#14519753—21no—
171#14519753—21no—
172#14519753C2×C411yescharacteristic
173#14519753C2×C411yescharacteristic, complemented
174#14519752—21no—
175#14519752—21no—
176#14519752—21no—
177#14519752—21no—
178#14519752—21no—
179#14519752—21no—
180#14519752—21no—
181#14519752—21no—
182#14519752C2×C411yescharacteristic
183#14519752C2×C411yescharacteristic, complemented
184#14519751—21no—
185#14519751—21no—
186#14519751C2×C411yescharacteristic
187#14519751C2×C411yescharacteristic, complemented
188#14519747—21no—
189#14519747—21no—
190#14519747—21no—
191#14519747—21no—
192#14519747—21no—
193#14519747—21no—
194Q8×Dic61C2×C411yescharacteristic, complemented
195C4×D244—21no—
196C4×D244—21no—
197C4×D244C2×C411yescharacteristic
198C4×D244C2×C411yescharacteristic, complemented
199D4×Dic61D411yescharacteristic
200#14519739—21no—
201#14519739—21no—
202#14519739—21no—
203#14519739—21no—
204#14519739—21no—
205#14519739C2×C411yescharacteristic, complemented
206#14519739D411yescharacteristic
207C4×C22⋊D61—21no—
208C4×C22⋊D61—21no—
209C4×C22⋊D61C2×C411yescharacteristic
210C4×C22⋊D61C2×C411yescharacteristic
211#14519737—21no—
212#14519737—21no—
213#14519737D411yescharacteristic
214#14519737D411yescharacteristic
215#14519735—21no—
216#14519735C2311yescharacteristic
217C4⋊C4×D61—21no—
218C4⋊C4×D61D411yescharacteristic
219C22⋊C4×D61—21no—
220C22⋊C4×D61—21no—
221C22⋊C4×D61D411yescharacteristic
222C22⋊C4×D61D411yescharacteristic
223C42×D61—21no—
224C42×D61C2311yescharacteristic
225C22×Q8×C61C2×C411yescharacteristic
226C22×Q8×C61C2×C411yescharacteristic, complemented
227C4⋊Q8×C61—21no—
228C4⋊Q8×C61C2×C411yescharacteristic, complemented
229C22⋊Q8×C61—21no—
230C22⋊Q8×C61—21no—
231C22⋊Q8×C61C2×C411yescharacteristic
232C22⋊Q8×C61C2×C411yescharacteristic, complemented
233C4×Q8×C61C2×C411yescharacteristic, complemented
234C4×D4×C61—21no—
235C4×D4×C61C2×C411yescharacteristic
236C23×D61—21no—
237C23×D61—21no—
238C23×D61C2×D411yescharacteristic
239C23×D61C2×D411yescharacteristic
240C22×#6923—21no—
241C22×#6923—21no—
242C22×#6923—21no—
243C22×#6923—21no—
244C22×#6923—42no—
245C22×#6923—42no—
246C22×#6923—42no—
247C2×Q8×C61—21no—
248C2×Q8×C61—21no—
249C2×Q8×C61—22no—
250C2×Q8×C61—22no—
251C2×Q8×C61—41no—
252C2×Q8×C61—41no—
253C2×Q8×C61C22×C411yescharacteristic
254C2×Q8×C61C22×C411yescharacteristic
255C2×Q8×C61C22×C411yescharacteristic
256C2×D4×C61C22⋊C411yescharacteristic
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61C22×C411yescharacteristic
260C22×C4×C61C22×C411yescharacteristic
261C2×C22⋊D61—21no—
262C2×C22⋊D61—21no—
263C2×C22⋊D61C22⋊C411yescharacteristic
264C2×C22⋊D61C22⋊C411yescharacteristic
265C22×Dic61C2×D411yescharacteristic
266C22×Dic61C2×D411yescharacteristic
267#11758226—21no—
268#11758226—21no—
269#11758226—22no—
270#11758226—22no—
271#11758226—22no—
272#11758226—22no—
273#11758226—21no—
274#11758226—21no—
275#11758226—21no—
276#11758226—21no—
277#11758226—21no—
278#11758226—21no—
279#11758226—21no—
280#11758226—21no—
281#11758226—42no—
282#11758226—42no—
283#11758226—42no—
284#11758226—42no—
285#11758226—41no—
286#11758226—41no—
287#11758226—41no—
288#11758226—41no—
289#11758226—42no—
290#11758226—42no—
291#11758226—42no—
292#11758226—42no—
293#11758226C2×D412yes—
294#11758226#4112yes—
295D4×D61—42no—
296D4×D61—44no—
297C2×D244—21no—
298C2×D244—22no—
299C2×D244—22no—
300C2×D244—21no—
301C2×D244—21no—
302C2×D244—21no—
303C2×D244—21no—
304C2×D244—21no—
305C2×D244—21no—
306C2×D244—21no—
307C2×D244—21no—
308C2×D244—21no—
309C2×D244—21no—
310C2×D244—21no—
311C2×D244—21no—
312C2×D244—41no—
313C2×D244—41no—
314C2×D244—42no—
315C2×D244—42no—
316C2×D244—42no—
317C2×D244—42no—
318C2×D244C22⋊C411yescharacteristic
319C2×D244C22×C411yescharacteristic
320C2×D244C22×C411yescharacteristic
321C2×D244C22×C411yescharacteristic
322C2×C4×D61—21no—
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—21no—
334C2×C4×D61—21no—
335C2×C4×D61—21no—
336C2×C4×D61—21no—
337C2×C4×D61—21no—
338C2×C4×D61—21no—
339C2×C4×D61—42no—
340C2×C4×D61—42no—
341C2×C4×D61—42no—
342C2×C4×D61—42no—
343C2×C4×D61C22×C411yescharacteristic
344C2×C4×D61C22×C411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×C4×D61C2×D411yescharacteristic
347C2×C4×D61C2×D411yescharacteristic
348C2×C4×D61C2×D411yescharacteristic
349C2×C4×D61C2×D411yescharacteristic
350C2×C4×D61C2×D411yescharacteristic
351C2×C4×D61C2411yescharacteristic
352C22⋊#6923—42no—
353C22⋊#6923—42no—
354C22⋊#6923—42no—
355#11758217—42no—
356C2×#92420—21no—
357C2×#92420—21no—
358C2×#92420—21no—
359C2×#92420—21no—
360C2×#92420—42no—
361C4⋊#6923—42no—
362C4⋊#6923—42no—
363C4×#6923—21no—
364C4×#6923—21no—
365C4×#6923—21no—
366C4×#6923—21no—
367C4×#6923—21no—
368C4×#6923—21no—
369C4×#6923—21no—
370C4×#6923—42no—
371C4×#6923C2×D412yescomplemented
372#11758213—21no—
373#11758213—21no—
374#11758213—21no—
375#11758213—21no—
376#11758213—21no—
377#11758213—21no—
378#11758213—21no—
379#11758213—42no—
380#11758213C2×D412yescomplemented
381D61⋊C8—42no—
382C4⋊C4×C61—21no—
383C4⋊C4×C61—21no—
384C4⋊C4×C61—21no—
385C4⋊C4×C61—21no—
386C4⋊C4×C61—21no—
387C4⋊C4×C61C22⋊C411yescharacteristic
388C4⋊C4×C61C22×C411yescharacteristic
389C22⋊C4×C61—21no—
390C22⋊C4×C61—21no—
391C22⋊C4×C61C22⋊C411yescharacteristic
392C22⋊C4×C61C22⋊C411yescharacteristic
393C42×C61—21no—
394C42×C61C22×C411yescharacteristic
395C22⋊Dic61C22⋊C411yescharacteristic
396C22⋊Dic61C22⋊C411yescharacteristic
397#11758198—21no—
398#11758198—21no—
399#11758198—21no—
400#11758198—21no—
401#11758198—21no—
402#11758198—21no—
403#11758198—21no—
404#11758198—21no—
405#11758198—21no—
406#11758198—21no—
407#11758198—21no—
408#11758198—21no—
409#11758198—21no—
410#11758198C22⋊C411yescharacteristic
411#11758198C22⋊C411yescharacteristic
412#11758198C22⋊C411yescharacteristic
413#11758198C22⋊C411yescharacteristic
414C4⋊Dic61—21no—
415C4⋊Dic61C22⋊C411yescharacteristic
416C4⋊Dic61C22×C411yescharacteristic
417#11758196—21no—
418#11758196—21no—
419#11758196C22⋊C411yescharacteristic
420#11758196C22⋊C411yescharacteristic
421C4×Dic61—21no—
422C4×Dic61—21no—
423C4×Dic61C22×C411yescharacteristic
424C4×Dic61C2×D411yescharacteristic
425C4×Dic61C2×D411yescharacteristic
426C23×C61C2×C22⋊C411yescharacteristic
427C23×C61C2×C22⋊C411yescharacteristic
428C22×D61—21no—
429C22×D61—22no—
430C22×D61—21no—
431C22×D61—21no—
432C22×D61—21no—
433C22×D61—21no—
434C22×D61—21no—
435C22×D61—21no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—41no—
439C22×D61—42no—
440C22×D61—42no—
441C22×D61—42no—
442C22×D61—42no—
443C22×D61—81no—
444C22×D61—81no—
445C22×D61C2×C22⋊C411yescharacteristic
446C22×D61C2×C22⋊C411yescharacteristic
447C22×D61C22×D411yescharacteristic
448C2×#6923—22no—
449C2×#6923—22no—
450C2×#6923—41no—
451C2×#6923—41no—
452C2×#6923—41no—
453C2×#6923—48no—
454C2×#6923—41no—
455C2×#6923—41no—
456C2×#6923—41no—
457C2×#6923—41no—
458C2×#6923—41no—
459C2×#6923—41no—
460C2×#6923—41no—
461Q8×C61—21no—
462Q8×C61—21no—
463Q8×C61—21no—
464Q8×C61—21no—
465Q8×C61—21no—
466Q8×C61—42no—
467Q8×C61—42no—
468Q8×C61C4×D412yes—
469D4×C61—22no—
470C2×C4×C61—21no—
471C2×C4×C61—21no—
472C2×C4×C61—21no—
473C2×C4×C61—21no—
474C2×C4×C61—21no—
475C2×C4×C61—21no—
476C2×C4×C61—21no—
477C2×C4×C61—21no—
478C2×C4×C61—42no—
479C2×C4×C61—42no—
480C2×C4×C61C2×C22⋊C411yescharacteristic
481C2×C4×C61C2×C22⋊C411yescharacteristic
482C2×C4×C61C2×C22⋊C411yescharacteristic
483C2×C4×C61C2×C22⋊C411yescharacteristic
484C2×C4×C61C23×C411yescharacteristic
485C22⋊D61—22no—
486C22⋊D61—41no—
487C22⋊D61—42no—
488C22⋊D61—42no—
489C2×Dic61—21no—
490C2×Dic61—21no—
491C2×Dic61—21no—
492C2×Dic61—21no—
493C2×Dic61—21no—
494C2×Dic61C2×C22⋊C411yescharacteristic
495C2×Dic61C2×C22⋊C411yescharacteristic
496C2×Dic61C2×C22⋊C411yescharacteristic
497C2×Dic61C2×C22⋊C411yescharacteristic
498C2×Dic61C22×D411yescharacteristic
499D244—22no—
500D244—22no—
501D244—21no—
502D244—21no—
503D244—21no—
504D244—21no—
505D244—21no—
506D244—41no—
507D244—42no—
508D244—42no—
509D244—42no—
510D244—42no—
511D244—42no—
512D244—42no—
513D244—42no—
514D244—41no—
515D244—41no—
516D244—41no—
517D244—41no—
518D244—81no—
519D244—81no—
520D244—81no—
521D244C4×D412yes—
522C4×D61—21no—
523C4×D61—21no—
524C4×D61—21no—
525C4×D61—21no—
526C4×D61—21no—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—22no—
533C4×D61—21no—
534C4×D61—21no—
535C4×D61—22no—
536C4×D61—41no—
537C4×D61—41no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—42no—
541C4×D61—42no—
542C4×D61—42no—
543C4×D61—41no—
544C4×D61—41no—
545C4×D61—41no—
546C4×D61—41no—
547C4×D61—81no—
548C4×D61C22×D411yescharacteristic
549C4×D61C2×#4111yescharacteristic
550C4×D61H(5,𝔽2)11yescharacteristic
551C4×D61H(5,𝔽2)11yescharacteristic
552#92420—22no—
553#92420—41no—
554#92420—41no—
555#92420—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61#42112yescomplemented
563C22×C61C22×C22⋊C411yescharacteristic
564C2×D61—21no—
565C2×D61—21no—
566C2×D61—21no—
567C2×D61—21no—
568C2×D61—22no—
569C2×D61—21no—
570C2×D61—21no—
571C2×D61—21no—
572C2×D61—21no—
573C2×D61—42no—
574C2×D61—42no—
575C2×D61—41no—
576C2×D61—41no—
577C2×D61—41no—
578C2×D61—41no—
579C2×D61—41no—
580C2×D61—41no—
581C2×D61—41no—
582C2×D61—41no—
583C2×D61—81no—
584C2×D61—81no—
585C2×D61—84no—
586C2×D61—84no—
587C2×D61D4211yescharacteristic
588C2×D61#54611yescharacteristic
589#6923—42no—
590#6923—42no—
591#6923—81no—
592#6923—81no—
593C4×C61—21no—
594C4×C61—21no—
595C4×C61—22no—
596C4×C61—21no—
597C4×C61—21no—
598C4×C61—41no—
599C4×C61—41no—
600C4×C61—41no—
601C4×C61C2×C4×D411yescharacteristic
602C4×C61#51811yescharacteristic
603Dic61—21no—
604Dic61—21no—
605Dic61—21no—
606Dic61—21no—
607Dic61—41no—
608Dic61D4211yescharacteristic
609Dic61#54611yescharacteristic
610D4×#41—611no—
611D4×M16—611no—
612C2×#421—611no—
613C22×#104—611no—
614#2290—611no—
615#1980—611no—
616#1963—611no—
617#1897—611no—
618#1896—611no—
619#1871—611no—
620#1871—611no—
621#1806—611no—
622#1789—611no—
623#1789—611no—
624#1759—611no—
625C2×C61—22no—
626C2×C61—41no—
627C2×C61D4×C22⋊C411yescharacteristic
628C2×C61C2×#42111yescharacteristic
629C2×C61#290111yescharacteristic
630D61—21no—
631D61—21no—
632D61—41no—
633D61—41no—
634D61—42no—
635D61—81no—
636D61—81no—
637C22×#41—611no—
638C22×#41—611no—
639C22×M16—611no—
640C22×M16—611no—
641#550—611no—
642D4×Q8#692311yescharacteristic, complemented
643#548—611no—
644#548—611no—
645#547—611no—
646#547—1221no—
647#546—611no—
648#546—611no—
649#546—1221no—
650#546—1221no—
651D42—611no—
652D42—1221no—
653#532—611no—
654#532—1221no—
655#525—611no—
656#525—611no—
657#525—1221no—
658#525—1221no—
659C4×#41—611no—
660C2×C4×D4—611no—
661C2×C4×D4—1221no—
662C2×#117—611no—
663C22×C42—611no—
664#436—1221no—
665#435—1221no—
666#435—1221no—
667C8×D4—1221no—
668#423—611no—
669#421—1224no—
670C2×#104—611no—
671C2×#104—611no—
672C2×#104—611no—
673C2×#104—611no—
674C2×#104—611no—
675C2×#104—611no—
676C2×#104—611no—
677C2×#104—611no—
678C2×#104—611no—
679C2×#104—611no—
680C2×#104—611no—
681C2×#104—611no—
682C2×#104—1224no—
683#407—611no—
684#407—611no—
685C4×M16—611no—
686#388—1221no—
687#387—1221no—
688#386—1221no—
689#385—1221no—
690C4×C4⋊C4—611no—
691C4×C22⋊C4—611no—
692C4×C22⋊C4—611no—
693#376—611no—
694#339—611no—
695#339—611no—
696#339—611no—
697#339—611no—
698C61#2243411yescharacteristic, complemented, Sylow
699C2×#41—611no—
700C2×#41—611no—
701C2×#41—611no—
702C2×#41—611no—
703C2×#41—611no—
704C2×#41—611no—
705C2×#41—611no—
706C2×#41—1221no—
707C2×#41—1221no—
708C2×#41—1221no—
709C2×#41—1221no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—1222no—
713C2×#41—1222no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41—2441no—
717C2×#41—2441no—
718C22×Q8C2×#692311yescharacteristic
719C22×Q8C2×#692311yescharacteristic, complemented
720C22×D4—611no—
721C22×D4—611no—
722C22×D4—611no—
723C22×D4—1221no—
724C22×D4—1221no—
725C22×D4—1221no—
726C23×C4—611no—
727C23×C4—611no—
728C23×C4—1221no—
729C23×C4—1221no—
730C23×C4—1221no—
731C2×M16—611no—
732C2×M16—611no—
733C2×M16—611no—
734C2×M16—611no—
735C2×M16—1221no—
736C2×M16—1221no—
737C2×M16—1222no—
738C2×M16—1222no—
739C2×M16—2441no—
740C2×M16—2441no—
741C22×C8—1221no—
742C22×C8—1221no—
743C4⋊Q8—21no—
744C4⋊Q8C2×#692311yescharacteristic, complemented
745#127—611no—
746#127—1221no—
747#124—611no—
748#124—611no—
749#124—1221no—
750#124—1221no—
751#123—1221no—
752#123—1221no—
753#123—1221no—
754#123—1221no—
755#123—1221no—
756#123—1221no—
757C22⋊Q8—21no—
758C22⋊Q8—21no—
759C22⋊Q8—611no—
760C22⋊Q8—611no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8C2×#692311yescharacteristic
764C22⋊Q8C2×#692311yescharacteristic, complemented
765#121—611no—
766#121—611no—
767#121—611no—
768#121—611no—
769#121—1221no—
770#121—1221no—
771#121—1221no—
772#121—1221no—
773#121—1221no—
774#121—1221no—
775#121—1221no—
776#121—1221no—
777#121—1221no—
778#121—1221no—
779#120—1221no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783#120—1221no—
784#120—1221no—
785C4×Q8—611no—
786C4×Q8C2×#692311yescharacteristic, complemented
787C4×D4—21no—
788C4×D4—611no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—611no—
792C4×D4—611no—
793C4×D4—611no—
794C4×D4—611no—
795C4×D4—611no—
796C4×D4—611no—
797C4×D4—1221no—
798C4×D4—1221no—
799C4×D4—1221no—
800C4×D4—1221no—
801C4×D4—1221no—
802C4×D4—1221no—
803C4×D4—1221no—
804C4×D4—1221no—
805C4×D4—1221no—
806C4×D4—1221no—
807C4×D4—1221no—
808C4×D4C2×#692311yescharacteristic
809#117—611no—
810#117—1221no—
811#117—1222no—
812#117—2441no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—1221no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C22⋊C4—611no—
818C2×C22⋊C4—611no—
819C2×C22⋊C4—1221no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C42—611no—
825C2×C42—611no—
826C2×C42—611no—
827C2×C42—611no—
828C2×C42—611no—
829C2×C42—1221no—
830C2×C42—1222no—
831C2×C42—1221no—
832C2×C42—2441no—
833C4⋊C8—1221no—
834C4⋊C8—1221no—
835#104—614no—
836#104—1222no—
837#104—1222no—
838#104—1222no—
839#104—1222no—
840#104—1222no—
841#104—1222no—
842#104—1222no—
843#104—2441no—
844#104—2441no—
845#104—2441no—
846#104—2441no—
847C22⋊C8—1221no—
848C22⋊C8—1221no—
849C22⋊C8—1221no—
850C22⋊C8—1221no—
851#97—1221no—
852C4×C8—1221no—
853#95—1221no—
854#95—1221no—
855#95—1221no—
856#95—1221no—
857#95—1221no—
858C24—611no—
859C24—611no—
860C24—1221no—
861C24—1221no—
862#41—612no—
863#41—612no—
864#41—1221no—
865#41—1221no—
866#41—1221no—
867#41—1221no—
868#41—1221no—
869#41—1221no—
870#41—1221no—
871#41—1221no—
872#41—1221no—
873#41—1221no—
874#41—1222no—
875#41—1222no—
876#41—1222no—
877#41—1222no—
878#41—2442no—
879#41—2442no—
880#41—2442no—
881#41—2442no—
882#41—2441no—
883#41—2441no—
884#41—2441no—
885#41—2441no—
886#41—2442no—
887#41—2442no—
888#41—2442no—
889#41—2442no—
890C2×Q8—21no—
891C2×Q8—21no—
892C2×Q8—22no—
893C2×Q8—22no—
894C2×Q8—41no—
895C2×Q8—41no—
896C2×Q8C22×#692311yescharacteristic
897C2×Q8C22×#692311yescharacteristic
898C2×Q8C22×#692311yescharacteristic
899C2×D4—611no—
900C2×D4—611no—
901C2×D4—611no—
902C2×D4—611no—
903C2×D4—611no—
904C2×D4—611no—
905C2×D4—1222no—
906C2×D4—1222no—
907C2×D4—1221no—
908C2×D4—1221no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1221no—
914C2×D4—1221no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—1221no—
922C2×D4—2441no—
923C2×D4—2441no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2442no—
927C2×D4—2442no—
928C2×D4—2442no—
929C2×D4—2444no—
930C2×D4C22⋊#692311yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—611no—
934C22×C4—611no—
935C22×C4—611no—
936C22×C4—611no—
937C22×C4—611no—
938C22×C4—611no—
939C22×C4—611no—
940C22×C4—611no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—1221no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—1221no—
965C22×C4—2442no—
966C22×C4—2442no—
967C22×C4—2442no—
968C22×C4—2442no—
969C22×C4—2442no—
970C22×C4—2442no—
971C22×C4—2442no—
972C22×C4C22×#692311yescharacteristic
973C22×C4C22×#692311yescharacteristic
974M16—612no—
975M16—1221no—
976M16—1221no—
977M16—1221no—
978M16—1221no—
979M16—1221no—
980M16—1221no—
981M16—1221no—
982M16—2442no—
983M16—2442no—
984C2×C8—1221no—
985C2×C8—1221no—
986C2×C8—1221no—
987C2×C8—1221no—
988C2×C8—2442no—
989C2×C8—2442no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—611no—
996C4⋊C4—611no—
997C4⋊C4—611no—
998C4⋊C4—611no—
999C4⋊C4—1221no—
1000C4⋊C4—1221no—
1001C4⋊C4—1221no—
1002C4⋊C4—2442no—
1003C4⋊C4—2442no—
1004C4⋊C4C22⋊#692311yescharacteristic
1005C4⋊C4C22×#692311yescharacteristic
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—611no—
1009C22⋊C4—611no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—1221no—
1015C22⋊C4—1221no—
1016C22⋊C4—1221no—
1017C22⋊C4—1221no—
1018C22⋊C4—1221no—
1019C22⋊C4—1221no—
1020C22⋊C4—1221no—
1021C22⋊C4—1221no—
1022C22⋊C4—1221no—
1023C22⋊C4—1221no—
1024C22⋊C4—1221no—
1025C22⋊C4—1221no—
1026C22⋊C4—1221no—
1027C22⋊C4—2442no—
1028C22⋊C4—2442no—
1029C22⋊C4—2442no—
1030C22⋊C4C22⋊#692311yescharacteristic
1031C22⋊C4C22⋊#692311yescharacteristic
1032C42—21no—
1033C42—611no—
1034C42—611no—
1035C42—611no—
1036C42—612no—
1037C42—1221no—
1038C42—1221no—
1039C42—1221no—
1040C42—1221no—
1041C42—1221no—
1042C42—1221no—
1043C42—1221no—
1044C42—1221no—
1045C42—1221no—
1046C42—2442no—
1047C42C22×#692311yescharacteristic
1048C23—611no—
1049C23—611no—
1050C23—611no—
1051C23—1221no—
1052C23—1221no—
1053C23—1221no—
1054C23—1221no—
1055C23—1222no—
1056C23—1221no—
1057C23—1221no—
1058C23—1221no—
1059C23—4881no—
1060C23—4881no—
1061C23—2441no—
1062C23—2441no—
1063C23—2441no—
1064C23—2442no—
1065C23—2442no—
1066C23—2442no—
1067C23—2442no—
1068C23C2×C22⋊#692311yescharacteristic
1069C23C2×C22⋊#692311yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—21no—
1075Q8—42no—
1076Q8—42no—
1077Q8D4×#692312yes—
1078D4—22no—
1079D4—612no—
1080D4—1222no—
1081D4—1222no—
1082D4—1222no—
1083D4—1221no—
1084D4—1221no—
1085D4—1221no—
1086D4—1221no—
1087D4—1221no—
1088D4—4881no—
1089D4—4881no—
1090D4—4881no—
1091D4—2441no—
1092D4—2442no—
1093D4—2442no—
1094D4—2442no—
1095D4—2442no—
1096D4—2442no—
1097D4—2441no—
1098D4—2441no—
1099D4—2441no—
1100D4—2441no—
1101D4—2442no—
1102D4—2442no—
1103D4—2441no—
1104D4—2442no—
1105D4—2442no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—42no—
1115C2×C4—42no—
1116C2×C4—611no—
1117C2×C4—611no—
1118C2×C4—611no—
1119C2×C4—611no—
1120C2×C4—611no—
1121C2×C4—611no—
1122C2×C4—611no—
1123C2×C4—611no—
1124C2×C4—611no—
1125C2×C4—1221no—
1126C2×C4—1221no—
1127C2×C4—1221no—
1128C2×C4—1221no—
1129C2×C4—1222no—
1130C2×C4—1222no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1221no—
1136C2×C4—1221no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1221no—
1143C2×C4—1222no—
1144C2×C4—1222no—
1145C2×C4—1221no—
1146C2×C4—4881no—
1147C2×C4—2441no—
1148C2×C4—2441no—
1149C2×C4—2442no—
1150C2×C4—2442no—
1151C2×C4—2442no—
1152C2×C4—2441no—
1153C2×C4—2441no—
1154C2×C4—2441no—
1155C2×C4—2441no—
1156C2×C4—2442no—
1157C2×C4—2442no—
1158C2×C4—2441no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4—2441no—
1165C2×C4—2441no—
1166C2×C4—2441no—
1167C2×C4—2441no—
1168C2×C4—2448no—
1169C2×C4C2×C22⋊#692311yescharacteristic
1170C2×C4C2×C22⋊#692311yescharacteristic
1171C2×C4C2×C22⋊#692311yescharacteristic
1172C2×C4C2×C22⋊#692311yescharacteristic
1173C2×C4C23×#692311yescharacteristic
1174C8—1222no—
1175C8—2441no—
1176C8—2441no—
1177C8—2441no—
1178C22—21no—
1179C22—21no—
1180C22—21no—
1181C22—21no—
1182C22—21no—
1183C22—611no—
1184C22—611no—
1185C22—1221no—
1186C22—1221no—
1187C22—1221no—
1188C22—1221no—
1189C22—1222no—
1190C22—1221no—
1191C22—1221no—
1192C22—1221no—
1193C22—1221no—
1194C22—4884no—
1195C22—4881no—
1196C22—4881no—
1197C22—4884no—
1198C22—2442no—
1199C22—2442no—
1200C22—2441no—
1201C22—2441no—
1202C22—2441no—
1203C22—2441no—
1204C22—2441no—
1205C22—2441no—
1206C22—2441no—
1207C22—2441no—
1208C22#1684076112yescomplemented
1209C22C22×C22⋊#692311yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—22no—
1213C4—21no—
1214C4—21no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—611no—
1219C4—611no—
1220C4—1221no—
1221C4—1221no—
1222C4—1221no—
1223C4—1221no—
1224C4—4881no—
1225C4—4881no—
1226C4—2442no—
1227C4—2442no—
1228C4—2441no—
1229C4C2×D4×#692311yescharacteristic
1230C4#1684082911yescharacteristic
1231C2—22no—
1232C2—41no—
1233C2—1221no—
1234C2—1221no—
1235C2—4881no—
1236C2—4881no—
1237C2—2441no—
1238C2—2441no—
1239C2—2442no—
1240C2D4×C22⋊#692311yescharacteristic
1241C2C2×#1684076111yescharacteristic
1242C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingD4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalD4×#11758226C2
cosocleC2×C4×D61C24
hypercenterD4×Q8#6923
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462558C2semidirect
2. C2×#16840761C2semidirect
3. C22×#14519842C2semidirect
4. #21462273C2semidirect
5. #21461982C2semidirect
6. #21461955C2semidirect
7. #21461838C2semidirect
8. #21461836C2semidirect
9. #21461801C2semidirect
10. #21461800C2semidirect
11. #21461694C2semidirect
12. #21461662C2semidirect
13. #21461662C2semidirect
14. #21461583C2semidirect
16. C22×#11758213C22semidirect
17. C2×D61⋊M16C22semidirect
18. C2×#14519856C22semidirect
19. C22×C4×#6923C22semidirect
24. #16840767C22semidirect
31. C2×#14519842C22semidirect
32. C2×#14519842C22semidirect
33. C2×#14519842C22semidirect
34. C2×#14519842C22semidirect
35. C2×#14519842C22semidirect
36. C2×#14519842C22semidirect
37. C2×#14519842C22semidirect
38. C2×#14519842C22semidirect
39. #16840733C22semidirect
40. #16840733C22semidirect
41. C4×#11758213C22semidirect
46. C4×C4⋊#6923C22semidirect
47. C4×C22⋊#6923C22semidirect
48. C4×C22⋊#6923C22semidirect
49. #16840698C22semidirect
50. #16840632C22semidirect
51. #16840632C22semidirect
52. #16840632C22semidirect
53. #16840632C22semidirect
56. #16840434C4semidirect
57. #16840423C4semidirect
58. #16840423C4semidirect
60. #16840415C4semidirect
63. #16840403C4semidirect
64. #16840403C4semidirect
66. D4×D244C4semidirect
76. D4×Q8×C61C4semidirect
117. #14519842D4semidirect
143. C2×#11758226C2×C4semidirect
144. C2×#11758226C2×C4semidirect
151. C22×D244C2×C4semidirect
159. #14519774C2×C4semidirect
162. #14519766C2×C4semidirect
163. #14519766C2×C4semidirect
173. #14519753C2×C4semidirect
183. #14519752C2×C4semidirect
187. #14519751C2×C4semidirect
194. Q8×Dic61C2×C4semidirect
198. C4×D244C2×C4semidirect
205. #14519739C2×C4semidirect
226. C22×Q8×C61C2×C4semidirect
228. C4⋊Q8×C61C2×C4semidirect
232. C22⋊Q8×C61C2×C4semidirect
233. C4×Q8×C61C2×C4semidirect
371. C4×#6923C2×D4semidirect
380. #11758213C2×D4semidirect
562. C22×C61#421semidirect
642. D4×Q8#6923semidirect
698. C61#22434semidirect
719. C22×Q8C2×#6923semidirect
744. C4⋊Q8C2×#6923semidirect
764. C22⋊Q8C2×#6923semidirect
786. C4×Q8C2×#6923semidirect
1208. C22#16840761semidirect

Maximal subgroups

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

subgroupindex
#214625582
C2×#168407612
C22×#145198422
#214622732
#214619822
#214619552
#214618382
#214618362
#214618012
#214618002
#214616942
#214616622
#214615832
D4×#117582262
#2243461