Finite Group Databasebeta

← #30620186

Subgroups — #30620186

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×#16840759C211yesmaximal, characteristic, complemented
3C2×D61⋊#104C211yesmaximal, 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#21461693C211yesmaximal, characteristic, complemented
12#21461661C211yesmaximal, characteristic, complemented
13#21461661C211yesmaximal, characteristic, complemented
14#21461582C211yesmaximal, characteristic, complemented
15#21459306C211yesmaximal, 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#16840759—24no—
26C2×#14519842C2211yescharacteristic, complemented
27C2×#14519842C2211yescharacteristic, complemented
28C2×#14519842C2211yescharacteristic, complemented
29C2×#14519842C2211yescharacteristic, complemented
30C2×#14519842C2211yescharacteristic, complemented
31C2×#14519842C2211yescharacteristic, complemented
32C2×#14519842C2211yescharacteristic, complemented
33C2×#14519842C2211yescharacteristic, complemented
34D61⋊#104—24no—
35C2×#14519841C2211yescharacteristic
36C2×#14519841C2211yescharacteristic
37C2×#14519841C2211yescharacteristic
38C2×#14519841C2211yescharacteristic
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
54C2×#41×D61C2211yescharacteristic
55C2×#41×D61C2211yescharacteristic
56#16840433C411yescharacteristic, complemented
57#16840427C411yescharacteristic, complemented
58#16840422C411yescharacteristic, complemented
59#16840422C411yescharacteristic, complemented
60#16840413—21no—
61#16840404—21no—
62#16840404—21no—
63#16840400C411yescharacteristic, complemented
64#16840400C411yescharacteristic, complemented
65D4×D244C411yescharacteristic, complemented
66#16840396—21no—
67#16840313C2211yescharacteristic
68#16840307—21no—
69#16840275C2211yescharacteristic
70#16840275C2211yescharacteristic
71#16840270—21no—
72#16840270—21no—
73C4×#11758224C2211yescharacteristic
74C2×#14519739—21no—
75C4×D4×D61C2211yescharacteristic
76C61×#547C411yescharacteristic, 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—41no—
111#14519842—41no—
112#14519842—41no—
113#14519842—41no—
114#14519841—22no—
115#14519841—22no—
116#14519841—22no—
117#14519841D414yescomplemented
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×#11758226C2311yescharacteristic
130C2×#11758226C2311yescharacteristic
131C2×#11758222—21no—
132C2×#11758222—21no—
133C2×#11758222C2×C411yescharacteristic
134C2×#11758222C2×C411yescharacteristic, complemented
135C2×#11758224—21no—
136C2×#11758224—21no—
137C2×#11758224C2311yescharacteristic
138#41×D61—22no—
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142#41×D61—41no—
143#41×D61—41no—
144#41×D61—41no—
145#41×D61—41no—
146C2×Q8×D61C2×C411yescharacteristic
147C2×Q8×D61C2×C411yescharacteristic, complemented
148C22×D244—21no—
149C2×D4×D61—21no—
150C2×D4×D61—21no—
151C2×D4×D61C2×C411yescharacteristic
152C2×D4×D61C2×C411yescharacteristic, complemented
153C2×D4×D61D411yescharacteristic
154C22×C4×D61—21no—
155C22×C4×D61—21no—
156C22×C4×D61C2311yescharacteristic
157C22×C4×D61C2311yescharacteristic
158#14519776—21no—
159#14519774C2×C411yescharacteristic, complemented
160#14519773—21no—
161#14519766C2×C411yescharacteristic, complemented
162#14519766C2×C411yescharacteristic, complemented
163#14519763—21no—
164#14519763—21no—
165#14519762—21no—
166#14519762—21no—
167#14519760—21no—
168#14519760—21no—
169#14519755—21no—
170#14519755—21no—
171#14519755—21no—
172#14519755—21no—
173#14519753C2×C411yescharacteristic
174#14519753C2×C411yescharacteristic, complemented
175#14519752—21no—
176#14519752—21no—
177#14519752C2×C411yescharacteristic
178#14519752C2×C411yescharacteristic, complemented
179#14519751—21no—
180#14519751C2×C411yescharacteristic
181#14519751C2×C411yescharacteristic, complemented
182#14519750—21no—
183#14519750—21no—
184#14519750—21no—
185#14519750—21no—
186#14519749—21no—
187#14519749—21no—
188#14519747—21no—
189#14519747—21no—
190#14519747—21no—
191#14519747—21no—
192#14519745—21no—
193#14519745—21no—
194C4×Dic122C2×C411yescharacteristic, complemented
195#14519742C2×C411yescharacteristic, complemented
196C4×D244C2×C411yescharacteristic
197D4×Dic61C2×C411yescharacteristic, complemented
198D4×Dic61D411yescharacteristic
199#14519739—21no—
200#14519739—21no—
201#14519739—21no—
202#14519739—21no—
203#14519739—21no—
204#14519739—21no—
205#14519739—21no—
206#14519739—21no—
207#14519739D411yescharacteristic
208C4×C22⋊D61—21no—
209C4×C22⋊D61C2×C411yescharacteristic
210C4×C22⋊D61C2×C411yescharacteristic
211#14519737—21no—
212#14519737—21no—
213#14519737—21no—
214#14519737D411yescharacteristic
215#14519737D411yescharacteristic
216#14519735C2311yescharacteristic
217#14519733—21no—
218C4⋊C4×D61D411yescharacteristic
219C2×#11758198—21no—
220C2×#11758198—21no—
221C22⋊C4×D61D411yescharacteristic
222C22⋊C4×D61D411yescharacteristic
223C2×C4×Dic61—21no—
224C42×D61C2311yescharacteristic
225C2×#41×C61C2×C411yescharacteristic
226C2×#41×C61C2×C411yescharacteristic, complemented
227C4⋊Q8×C61C2×C411yescharacteristic, complemented
228#123×C61—21no—
229#123×C61—21no—
230C22⋊Q8×C61C2×C411yescharacteristic
231C22⋊Q8×C61C2×C411yescharacteristic, complemented
232#121×C61—21no—
233C4×D4×C61C2×C411yescharacteristic
234C4×D4×C61C2×C411yescharacteristic, complemented
235C2×C4⋊C4×C61—21no—
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—
247#41×C61—22no—
248#41×C61—22no—
249#41×C61—41no—
250#41×C61—41no—
251C2×Q8×C61C22×C411yescharacteristic
252C2×Q8×C61C22×C411yescharacteristic
253C2×D4×C61—21no—
254C2×D4×C61—21no—
255C2×D4×C61C22⋊C411yescharacteristic
256C2×D4×C61C22×C411yescharacteristic
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61C22×C411yescharacteristic
261C22×C4×C61C22×C411yescharacteristic
262C2×C22⋊D61—21no—
263C2×C22⋊D61—21no—
264C2×C22⋊D61—21no—
265C2×C22⋊D61—21no—
266C2×C22⋊D61—21no—
267C2×C22⋊D61—21no—
268C2×C22⋊D61—21no—
269C2×C22⋊D61C22⋊C411yescharacteristic
270C2×C22⋊D61C22⋊C411yescharacteristic
271C22×Dic61—21no—
272C22×Dic61—21no—
273C22×Dic61C2×D411yescharacteristic
274C22×Dic61C2×D411yescharacteristic
275#11758226—21no—
276#11758226—21no—
277#11758226—21no—
278#11758226—21no—
279#11758226—21no—
280#11758226—21no—
281#11758226—21no—
282#11758226—21no—
283Q8×D61—22no—
284Q8×D61—22no—
285Q8×D61—41no—
286Q8×D61—41no—
287#11758224—21no—
288#11758224—21no—
289#11758224—42no—
290#11758224—42no—
291#11758224—42no—
292#11758224—42no—
293#11758224C2×D412yes—
294#11758224#4112yes—
295D4×D61—22no—
296D4×D61—22no—
297D4×D61—41no—
298D4×D61—41no—
299D4×D61—42no—
300D4×D61—42no—
301D4×D61—42no—
302D4×D61—42no—
303D4×D61—42no—
304#11758222—22no—
305#11758222—22no—
306#11758222—41no—
307#11758222—41no—
308#11758222—42no—
309#11758222—42no—
310#11758222—42no—
311#11758222—42no—
312C2×D244—21no—
313C2×D244—21no—
314C2×D244—21no—
315C2×D244—21no—
316C2×D244—21no—
317C2×D244—21no—
318C2×D244—44no—
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—42no—
337C2×C4×D61—42no—
338C2×C4×D61—42no—
339C2×C4×D61—42no—
340C2×C4×D61C22×C411yescharacteristic
341C2×C4×D61C22×C411yescharacteristic
342C2×C4×D61C2×D411yescharacteristic
343C2×C4×D61C2×D411yescharacteristic
344C2×C4×D61C2×D411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×C4×D61C2×D411yescharacteristic
347C2×C4×D61C2×D411yescharacteristic
348C2×C4×D61C2411yescharacteristic
349C2×Dic122—21no—
350C2×Dic122—21no—
351C2×Dic122C22×C411yescharacteristic
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×C61C22⋊C411yescharacteristic
387C4⋊C4×C61C22×C411yescharacteristic
388C22⋊C4×C61—21no—
389C22⋊C4×C61—21no—
390C22⋊C4×C61—21no—
391C22⋊C4×C61C22⋊C411yescharacteristic
392C22⋊C4×C61C22⋊C411yescharacteristic
393C42×C61C22×C411yescharacteristic
394C22⋊Dic61—21no—
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#11758198C22⋊C411yescharacteristic
409#11758198C22⋊C411yescharacteristic
410#11758198C22⋊C411yescharacteristic
411#11758198C22⋊C411yescharacteristic
412C4⋊Dic61C22⋊C411yescharacteristic
413C4⋊Dic61C22×C411yescharacteristic
414#11758196—21no—
415#11758196—21no—
416#11758196—21no—
417#11758196—21no—
418#11758196C22⋊C411yescharacteristic
419#11758196C22⋊C411yescharacteristic
420C4×Dic61—21no—
421C4×Dic61—21no—
422C4×Dic61—21no—
423C4×Dic61C22×C411yescharacteristic
424C4×Dic61C2×D411yescharacteristic
425C4×Dic61C2×D411yescharacteristic
426C23×C61—21no—
427C23×C61C2×C22⋊C411yescharacteristic
428C23×C61C2×C22⋊C411yescharacteristic
429C22×D61—21no—
430C22×D61—21no—
431C22×D61—22no—
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—
465D4×C61—21no—
466D4×C61—41no—
467D4×C61—42no—
468D4×C61—42no—
469D4×C61C4×D412yes—
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—42no—
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—22no—
487C22⋊D61—22no—
488C22⋊D61—41no—
489C22⋊D61—42no—
490C22⋊D61—42no—
491C22⋊D61—42no—
492C22⋊D61—42no—
493C22⋊D61—81no—
494C22⋊D61—81no—
495C2×Dic61—21no—
496C2×Dic61—21no—
497C2×Dic61—21no—
498C2×Dic61—22no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—22no—
502C2×Dic61—21no—
503C2×Dic61—81no—
504C2×Dic61C2×C22⋊C411yescharacteristic
505C2×Dic61C2×C22⋊C411yescharacteristic
506C2×Dic61C2×C22⋊C411yescharacteristic
507C2×Dic61C2×C22⋊C411yescharacteristic
508C2×Dic61C22×D411yescharacteristic
509D244—22no—
510D244—21no—
511D244—21no—
512D244—21no—
513D244—21no—
514D244—42no—
515D244—42no—
516D244—41no—
517D244—41no—
518D244—41no—
519D244—41no—
520D244—42no—
521D244—81no—
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—21no—
533C4×D61—21no—
534C4×D61—41no—
535C4×D61—41no—
536C4×D61—42no—
537C4×D61—42no—
538C4×D61—42no—
539C4×D61—42no—
540C4×D61—41no—
541C4×D61—41no—
542C4×D61—41no—
543C4×D61—41no—
544C4×D61C22×D411yescharacteristic
545C4×D61C2×#4111yescharacteristic
546C4×D61H(5,𝔽2)11yescharacteristic
547C4×D61H(5,𝔽2)11yescharacteristic
548Dic122—21no—
549Dic122—42no—
550Dic122—42no—
551Dic122C4×D412yes—
552#92420—22no—
553#92420—41no—
554#92420—41no—
555#92420—41no—
556#22434—611nomaximal, Sylow
557C22×C61—22no—
558C22×C61—21no—
559C22×C61—21no—
560C22×C61—21no—
561C22×C61—21no—
562C22×C61—21no—
563C22×C61—21no—
564C22×C61—41no—
565C22×C61—41no—
566C22×C61C22×C22⋊C411yescharacteristic
567C2×D61—21no—
568C2×D61—21no—
569C2×D61—21no—
570C2×D61—21no—
571C2×D61—21no—
572C2×D61—21no—
573C2×D61—21no—
574C2×D61—42no—
575C2×D61—42no—
576C2×D61—41no—
577C2×D61—41no—
578C2×D61—41no—
579C2×D61—41no—
580C2×D61—41no—
581C2×D61—41no—
582C2×D61—81no—
583C2×D61—81no—
584C2×D61—84no—
585C2×D61—84no—
586C2×D61#42112yescomplemented
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—21no—
596C4×C61—21no—
597C4×C61—41no—
598C4×C61—41no—
599C4×C61—41no—
600C4×C61C2×C4×D411yescharacteristic
601C4×C61#51811yescharacteristic
602Dic61—22no—
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—41no—
626C2×C61—42no—
627C2×C61—41no—
628C2×C61D4×C22⋊C411yescharacteristic
629C2×C61C2×#42111yescharacteristic
630C2×C61#290111yescharacteristic
631D61—21no—
632D61—21no—
633D61—22no—
634D61—41no—
635D61—81no—
636D61—81no—
637C22×#41—611no—
638C22×#41—611no—
639C22×M16—611no—
640C22×M16—611no—
641#550—611no—
642D4×Q8—611no—
643#548—611no—
644#548—611no—
645#547—1221no—
646#547#692311yescharacteristic, complemented
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—1221no—
705C2×#41—1221no—
706C2×#41—1221no—
707C2×#41—1221no—
708C2×#41—1222no—
709C2×#41—1222no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—2441no—
713C2×#41—2441no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41C2×#692311yescharacteristic
717C2×#41C2×#692311yescharacteristic, complemented
718C22×Q8—611no—
719C22×Q8—611no—
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—1221no—
744C4⋊Q8C2×#692311yescharacteristic, complemented
745#127—611no—
746#127—1221no—
747#124—611no—
748#124—611no—
749#124—1221no—
750#124—1221no—
751#123—21no—
752#123—21no—
753#123—1221no—
754#123—1221no—
755#123—1221no—
756#123—1221no—
757C22⋊Q8—611no—
758C22⋊Q8—611no—
759C22⋊Q8—1221no—
760C22⋊Q8—1221no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8C2×#692311yescharacteristic
764C22⋊Q8C2×#692311yescharacteristic, complemented
765#121—21no—
766#121—611no—
767#121—611no—
768#121—611no—
769#121—611no—
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×Q8—611no—
787C4×D4—611no—
788C4×D4—611no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—611no—
792C4×D4—611no—
793C4×D4—611no—
794C4×D4—611no—
795C4×D4—1221no—
796C4×D4—1221no—
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×D4C2×#692311yescharacteristic
808C4×D4C2×#692311yescharacteristic, complemented
809#117—611no—
810#117—1221no—
811#117—1222no—
812#117—2441no—
813C2×C4⋊C4—21no—
814C2×C4⋊C4—611no—
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—22no—
863#41—22no—
864#41—41no—
865#41—41no—
866#41—612no—
867#41—612no—
868#41—1222no—
869#41—1222no—
870#41—1221no—
871#41—1221no—
872#41—1221no—
873#41—1221no—
874#41—1221no—
875#41—1221no—
876#41—1221no—
877#41—1221no—
878#41—1221no—
879#41—1221no—
880#41—2441no—
881#41—2441no—
882#41—2442no—
883#41—2442no—
884#41—2442no—
885#41—2442no—
886#41—2442no—
887#41—2442no—
888#41—2442no—
889#41—2442no—
890C2×Q8—611no—
891C2×Q8—1221no—
892C2×Q8—1221no—
893C2×Q8—1222no—
894C2×Q8—1222no—
895C2×Q8—2441no—
896C2×Q8—2441no—
897C2×Q8C22×#692311yescharacteristic
898C2×Q8C22×#692311yescharacteristic
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—611no—
902C2×D4—611no—
903C2×D4—611no—
904C2×D4—611no—
905C2×D4—611no—
906C2×D4—1221no—
907C2×D4—1221no—
908C2×D4—1221no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1221no—
913C2×D4—1222no—
914C2×D4—1222no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—2444no—
922C2×D4—2441no—
923C2×D4—2441no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2442no—
927C2×D4—2442no—
928C2×D4—2442no—
929C2×D4C22⋊#692311yescharacteristic
930C2×D4C22×#692311yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
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—611no—
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—611no—
995C4⋊C4—611no—
996C4⋊C4—611no—
997C4⋊C4—611no—
998C4⋊C4—1221no—
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—21no—
1009C22⋊C4—611no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
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—611no—
1033C42—611no—
1034C42—611no—
1035C42—612no—
1036C42—1221no—
1037C42—1221no—
1038C42—1221no—
1039C42—1221no—
1040C42—1221no—
1041C42—1221no—
1042C42—1221no—
1043C42—1221no—
1044C42—1221no—
1045C42—1221no—
1046C42—2442no—
1047C42C22×#692311yescharacteristic
1048C23—21no—
1049C23—611no—
1050C23—611no—
1051C23—611no—
1052C23—1221no—
1053C23—1221no—
1054C23—1222no—
1055C23—1221no—
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—612no—
1075Q8—1221no—
1076Q8—2442no—
1077Q8—2442no—
1078D4—21no—
1079D4—41no—
1080D4—42no—
1081D4—42no—
1082D4—1222no—
1083D4—1222no—
1084D4—1222no—
1085D4—1222no—
1086D4—1221no—
1087D4—1221no—
1088D4—1221no—
1089D4—1221no—
1090D4—4881no—
1091D4—4881no—
1092D4—4881no—
1093D4—2442no—
1094D4—2442no—
1095D4—2441no—
1096D4—2441no—
1097D4—2441no—
1098D4—2441no—
1099D4—2442no—
1100D4—2441no—
1101D4—2442no—
1102D4—2442no—
1103D4—2442no—
1104D4—2442no—
1105D4D4×#692312yes—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—42no—
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—1221no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1221no—
1136C2×C4—1221no—
1137C2×C4—1222no—
1138C2×C4—1222no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1221no—
1142C2×C4—1221no—
1143C2×C4—1221no—
1144C2×C4—1222no—
1145C2×C4—1222no—
1146C2×C4—1221no—
1147C2×C4—4881no—
1148C2×C4—2441no—
1149C2×C4—2441no—
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—22no—
1181C22—21no—
1182C22—21no—
1183C22—21no—
1184C22—21no—
1185C22—41no—
1186C22—41no—
1187C22—611no—
1188C22—611no—
1189C22—612no—
1190C22—1221no—
1191C22—1221no—
1192C22—1221no—
1193C22—1221no—
1194C22—1221no—
1195C22—1221no—
1196C22—1221no—
1197C22—4884no—
1198C22—4881no—
1199C22—4881no—
1200C22—4884no—
1201C22—2442no—
1202C22—2442no—
1203C22—2441no—
1204C22—2441no—
1205C22—2441no—
1206C22—2441no—
1207C22—2441no—
1208C22—2441no—
1209C22C22×C22⋊#692311yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—611no—
1218C4—611no—
1219C4—1221no—
1220C4—1221no—
1221C4—1222no—
1222C4—1221no—
1223C4—1221no—
1224C4—4881no—
1225C4—4881no—
1226C4—2442no—
1227C4—2442no—
1228C4—2441no—
1229C4C2×D4×#692311yescharacteristic
1230C4#1684082911yescharacteristic
1231C2—41no—
1232C2—41no—
1233C2—42no—
1234C2—1221no—
1235C2—1221no—
1236C2—1222no—
1237C2—4881no—
1238C2—4881no—
1239C2—2441no—
1240C2D4×C22⋊#692311yescharacteristic
1241C2D61⋊#42111yescharacteristic
1242C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#21459306C2
cosocleC2×C4×D61C24
hypercenter#547#6923
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #21462558C2semidirect
2. C2×#16840759C2semidirect
3. C2×D61⋊#104C2semidirect
4. #21462273C2semidirect
5. #21461982C2semidirect
6. #21461955C2semidirect
7. #21461838C2semidirect
8. #21461836C2semidirect
9. #21461801C2semidirect
10. #21461800C2semidirect
11. #21461693C2semidirect
12. #21461661C2semidirect
13. #21461661C2semidirect
14. #21461582C2semidirect
16. C22×#11758213C22semidirect
17. C2×D61⋊M16C22semidirect
18. C2×#14519856C22semidirect
19. C22×C4×#6923C22semidirect
24. #16840767C22semidirect
26. C2×#14519842C22semidirect
27. C2×#14519842C22semidirect
28. C2×#14519842C22semidirect
29. C2×#14519842C22semidirect
30. C2×#14519842C22semidirect
31. C2×#14519842C22semidirect
32. C2×#14519842C22semidirect
33. 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. #16840433C4semidirect
57. #16840427C4semidirect
58. #16840422C4semidirect
59. #16840422C4semidirect
63. #16840400C4semidirect
64. #16840400C4semidirect
65. D4×D244C4semidirect
76. C61×#547C4semidirect
117. #14519841D4semidirect
134. C2×#11758222C2×C4semidirect
147. C2×Q8×D61C2×C4semidirect
152. C2×D4×D61C2×C4semidirect
159. #14519774C2×C4semidirect
161. #14519766C2×C4semidirect
162. #14519766C2×C4semidirect
174. #14519753C2×C4semidirect
178. #14519752C2×C4semidirect
181. #14519751C2×C4semidirect
194. C4×Dic122C2×C4semidirect
195. #14519742C2×C4semidirect
197. D4×Dic61C2×C4semidirect
226. C2×#41×C61C2×C4semidirect
227. C4⋊Q8×C61C2×C4semidirect
231. C22⋊Q8×C61C2×C4semidirect
234. C4×D4×C61C2×C4semidirect
371. C4×#6923C2×D4semidirect
380. #11758213C2×D4semidirect
586. C2×D61#421semidirect
646. #547#6923semidirect
698. C61#22434semidirect
717. C2×#41C2×#6923semidirect
744. C4⋊Q8C2×#6923semidirect
764. C22⋊Q8C2×#6923semidirect
808. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625582
C2×#168407592
C2×D61⋊#1042
#214622732
#214619822
#214619552
#214618382
#214618362
#214618012
#214618002
#214616932
#214616612
#214615822
#214593062
#2243461