Finite Group Databasebeta

← #30620361

Subgroups — #30620361

Order 15616.

1390 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#435C211yesmaximal, characteristic, complemented
2#21462335C211yesmaximal, characteristic, complemented
3#21462003C211yesmaximal, characteristic, complemented
4#21461997C211yesmaximal, characteristic, complemented
5#21461835C211yesmaximal, characteristic, complemented
6#21461833C211yesmaximal, characteristic, complemented
7#21461807C211yesmaximal, characteristic, complemented
8#21461806C211yesmaximal, characteristic, complemented
9#21461723C211yesmaximal, characteristic, complemented
10#21461722C211yesmaximal, characteristic, complemented
11#21461689C211yesmaximal, characteristic, complemented
12#21461589C211yesmaximal, characteristic, complemented
13#21461506C211yesmaximal, characteristic, complemented
14C2×#16840635C211yesmaximal, characteristic, complemented
15#547×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840794—21no—
21#16840793—21no—
22#16840792—21no—
23#16840791—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29D61⋊(C22⋊C8)C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31#16840721C2211yescharacteristic
32#16840712—21no—
33#16840711—21no—
34#16840710—21no—
35#16840706C2211yescharacteristic
36#16840704C2211yescharacteristic
37#16840704C2211yescharacteristic
38C4×C4⋊#6923C2211yescharacteristic
39C22⋊C4×#6923—21no—
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52C2×#41×D61—21no—
53#16840417C411yescharacteristic, complemented
54#16840416C411yescharacteristic, complemented
55#16840415C411yescharacteristic, complemented
56#16840414—21no—
57#16840413C411yescharacteristic, complemented
58#16840413C411yescharacteristic, complemented
59#16840412C411yescharacteristic, complemented
60#16840412C411yescharacteristic, complemented
61#16840411—21no—
62#16840410—21no—
63#16840410—21no—
64C4⋊Q8×D61C2211yescharacteristic
65#123×D61—21no—
66#123×D61—21no—
67C22⋊Q8×D61—21no—
68#121×D61C2211yescharacteristic
69#121×D61C2211yescharacteristic
70C4×D4×D61C2211yescharacteristic
71C4×D4×D61C2211yescharacteristic
72C2×C4⋊C4×D61C2211yescharacteristic
73C2×C4⋊C4×D61C2211yescharacteristic
74C61×#547C411yescharacteristic, complemented
75C23×#6923—21no—
76C2×#11758213—21no—
77D61⋊M16—22no—
78D61⋊M16—41no—
79C2×#11758217—21no—
80C2×D61⋊C8—22no—
81C2×D61⋊C8—21no—
82C2×D61⋊C8—41no—
83C2×D61⋊C8C2311yescharacteristic
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C22×#92420—21no—
88#14519856—22no—
89#14519856—41no—
90C2×C4⋊#6923—22no—
91C2×C4⋊#6923—21no—
92C2×C4⋊#6923—41no—
93C2×C4⋊#6923C2311yescharacteristic
94C2×C4⋊#6923C2311yescharacteristic
95C2×C4⋊#6923C2311yescharacteristic
96C2×C4⋊#6923C2311yescharacteristic
97C2×C22⋊#6923—21no—
98C2×C22⋊#6923—21no—
99C2×C22⋊#6923—21no—
100C2×C4×#6923—21no—
101C2×C4×#6923—21no—
102#14519844—21no—
103C4⋊#92420—21no—
104#14519839—22no—
105#14519839—22no—
106#14519839—41no—
107#14519839—41no—
108#14519834—21no—
109#14519834—21no—
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112#14519832—21no—
113#14519832—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—
119C2×#11758226—21no—
120C2×#11758222—21no—
121C2×#11758222—21no—
122C2×#11758222—21no—
123C2×#11758224—21no—
124C2×#11758224—21no—
125C2×#11758224—21no—
126#41×D61—44no—
127#41×D61—44no—
128C2×Q8×D61—21no—
129C2×D4×D61—21no—
130C2×D4×D61—21no—
131C2×D4×D61D411yescharacteristic
132C2×D4×D61C2311yescharacteristic
133C22×C4×D61—21no—
134C22×C4×D61—21no—
135C22×C4×D61—21no—
136C22×C4×D61C2311yescharacteristic
137C22×C4×D61C2311yescharacteristic
138#14519777C2×C411yescharacteristic, complemented
139#14519776—21no—
140#14519776C2×C411yescharacteristic, complemented
141#14519776C2×C411yescharacteristic, complemented
142#14519775—21no—
143#14519762—21no—
144#14519762—21no—
145#14519762—21no—
146#14519762—21no—
147#14519761—21no—
148#14519761—21no—
149#14519760—21no—
150#14519760—21no—
151#14519759—21no—
152#14519759—21no—
153#14519759—21no—
154#14519759—21no—
155#14519758—21no—
156#14519758—21no—
157#14519757—21no—
158#14519756—21no—
159#14519755—21no—
160#14519755—21no—
161#14519754—21no—
162#14519754—21no—
163#14519753—21no—
164#14519752C2×C411yescharacteristic
165#14519752C2×C411yescharacteristic, complemented
166#14519751C2×C411yescharacteristic
167#14519751C2×C411yescharacteristic, complemented
168#14519750—21no—
169#14519750—21no—
170#14519749—21no—
171#14519749—21no—
172#14519748C2×C411yescharacteristic
173#14519748C2×C411yescharacteristic, complemented
174C4×D244C2×C411yescharacteristic
175C4×D244C2×C411yescharacteristic, complemented
176D4×Dic61C2×C411yescharacteristic, complemented
177D4×Dic61D411yescharacteristic
178#14519739C2×C411yescharacteristic, complemented
179#14519739D411yescharacteristic
180C4×C22⋊D61—21no—
181C4×C22⋊D61C2×C411yescharacteristic
182C4×C22⋊D61C2×C411yescharacteristic
183#14519737—21no—
184#14519737D411yescharacteristic
185#14519737D411yescharacteristic
186C2×C4⋊Dic61C2×C411yescharacteristic
187C2×C4⋊Dic61C2×C411yescharacteristic, complemented
188C2×#11758196—21no—
189C2×#11758196—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61—21no—
195C4⋊C4×D61C2×C411yescharacteristic
196C4⋊C4×D61C2×C411yescharacteristic
197C4⋊C4×D61C2×C411yescharacteristic, complemented
198C4⋊C4×D61C2×C411yescharacteristic, complemented
199C4⋊C4×D61D411yescharacteristic
200C4⋊C4×D61C2311yescharacteristic
201C4⋊C4×D61C2311yescharacteristic
202C4⋊C4×D61C2311yescharacteristic
203C22⋊C4×D61—21no—
204C22⋊C4×D61—21no—
205C22⋊C4×D61—21no—
206C22⋊C4×D61D411yescharacteristic
207C22⋊C4×D61D411yescharacteristic
208C42×D61C2311yescharacteristic
209C2×#41×C61—21no—
210C4⋊Q8×C61C2×C411yescharacteristic, complemented
211#123×C61—21no—
212#123×C61—21no—
213C22⋊Q8×C61—21no—
214#121×C61C2×C411yescharacteristic
215#121×C61C2×C411yescharacteristic, complemented
216C4×D4×C61C2×C411yescharacteristic
217C4×D4×C61C2×C411yescharacteristic, complemented
218C2×C4⋊C4×C61C2×C411yescharacteristic
219C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
220C23×D61—21no—
221C23×D61C2×D411yescharacteristic
222C23×D61C2×D411yescharacteristic
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—21no—
226C22×#6923—21no—
227C22×#6923—42no—
228C22×#6923—42no—
229C22×#6923—81no—
230#41×C61—44no—
231C2×Q8×C61—21no—
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61C22⋊C411yescharacteristic
235C2×D4×C61C22×C411yescharacteristic
236C22×C4×C61—21no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61C22×C411yescharacteristic
240C22×C4×C61C22×C411yescharacteristic
241C2×C22⋊D61—21no—
242C2×C22⋊D61—21no—
243C2×C22⋊D61—21no—
244C2×C22⋊D61—21no—
245C2×C22⋊D61—21no—
246C2×C22⋊D61C22⋊C411yescharacteristic
247C2×C22⋊D61C22⋊C411yescharacteristic
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—21no—
251C22×Dic61C2×D411yescharacteristic
252C22×Dic61C2×D411yescharacteristic
253#11758226—44no—
254Q8×D61—42no—
255Q8×D61—42no—
256#11758224—44no—
257#11758224—44no—
258#11758224—44no—
259D4×D61—22no—
260D4×D61—22no—
261D4×D61—21no—
262D4×D61—21no—
263D4×D61—21no—
264D4×D61—21no—
265D4×D61—42no—
266D4×D61—42no—
267D4×D61—42no—
268D4×D61—42no—
269#11758222—44no—
270#11758222—44no—
271#11758222—44no—
272C2×D244—21no—
273C2×D244—21no—
274C2×D244C22⋊C411yescharacteristic
275C2×D244C22×C411yescharacteristic
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—21no—
284C2×C4×D61—21no—
285C2×C4×D61—21no—
286C2×C4×D61—21no—
287C2×C4×D61—21no—
288C2×C4×D61—21no—
289C2×C4×D61—21no—
290C2×C4×D61—21no—
291C2×C4×D61—21no—
292C2×C4×D61—21no—
293C2×C4×D61—42no—
294C2×C4×D61—42no—
295C2×C4×D61—42no—
296C2×C4×D61—42no—
297C2×C4×D61—42no—
298C2×C4×D61—42no—
299C2×C4×D61C22×C411yescharacteristic
300C2×C4×D61C22×C411yescharacteristic
301C2×C4×D61C2×D411yescharacteristic
302C2×C4×D61C2×D411yescharacteristic
303C2×C4×D61C2×D411yescharacteristic
304C2×C4×D61C2×D411yescharacteristic
305C2×C4×D61C2×D411yescharacteristic
306C2×C4×D61C2×D411yescharacteristic
307C2×C4×D61C2411yescharacteristic
308C2×Dic122—21no—
309C2×Dic122—21no—
310C2×Dic122—21no—
311C22⋊#6923—42no—
312C22⋊#6923—42no—
313C22⋊#6923—81no—
314#11758217—42no—
315C2×#92420—21no—
316C2×#92420—21no—
317C2×#92420—21no—
318C2×#92420—21no—
319C2×#92420—42no—
320C4⋊#6923—21no—
321C4⋊#6923—21no—
322C4⋊#6923—21no—
323C4⋊#6923—21no—
324C4⋊#6923—21no—
325C4⋊#6923—21no—
326C4⋊#6923—21no—
327C4⋊#6923—42no—
328C4⋊#6923#4112yescomplemented
329C4×#6923—42no—
330C4×#6923—81no—
331#11758213—42no—
332D61⋊C8—21no—
333D61⋊C8—21no—
334D61⋊C8—21no—
335D61⋊C8—21no—
336D61⋊C8—21no—
337D61⋊C8—21no—
338D61⋊C8—21no—
339D61⋊C8—42no—
340D61⋊C8#4112yescomplemented
341C4⋊C4×C61—21no—
342C4⋊C4×C61—21no—
343C4⋊C4×C61—21no—
344C4⋊C4×C61C22⋊C411yescharacteristic
345C4⋊C4×C61C22×C411yescharacteristic
346C4⋊C4×C61C22×C411yescharacteristic
347C4⋊C4×C61C22×C411yescharacteristic
348C22⋊C4×C61—21no—
349C22⋊C4×C61—21no—
350C22⋊C4×C61—21no—
351C22⋊C4×C61C22⋊C411yescharacteristic
352C22⋊C4×C61C22⋊C411yescharacteristic
353C42×C61C22×C411yescharacteristic
354C22⋊Dic61—21no—
355C22⋊Dic61—21no—
356C22⋊Dic61—21no—
357C22⋊Dic61C22⋊C411yescharacteristic
358C22⋊Dic61C22⋊C411yescharacteristic
359#11758198—21no—
360#11758198—21no—
361#11758198—21no—
362#11758198—21no—
363#11758198—21no—
364#11758198—21no—
365#11758198C22⋊C411yescharacteristic
366#11758198C22⋊C411yescharacteristic
367#11758198C22⋊C411yescharacteristic
368#11758198C22⋊C411yescharacteristic
369C4⋊Dic61—21no—
370C4⋊Dic61—21no—
371C4⋊Dic61—21no—
372C4⋊Dic61C22⋊C411yescharacteristic
373C4⋊Dic61C22×C411yescharacteristic
374C4⋊Dic61C22×C411yescharacteristic
375C4⋊Dic61C22×C411yescharacteristic
376#11758196—21no—
377#11758196—21no—
378#11758196—21no—
379#11758196—21no—
380#11758196—21no—
381#11758196—21no—
382#11758196—21no—
383#11758196—21no—
384#11758196—21no—
385#11758196C22⋊C411yescharacteristic
386#11758196C22⋊C411yescharacteristic
387C4×Dic61C22×C411yescharacteristic
388C4×Dic61C2×D411yescharacteristic
389C4×Dic61C2×D411yescharacteristic
390C23×C61—21no—
391C23×C61C2×C22⋊C411yescharacteristic
392C23×C61C2×C22⋊C411yescharacteristic
393C22×D61—21no—
394C22×D61—21no—
395C22×D61—21no—
396C22×D61—21no—
397C22×D61—21no—
398C22×D61—21no—
399C22×D61—21no—
400C22×D61—21no—
401C22×D61—21no—
402C22×D61—21no—
403C22×D61—21no—
404C22×D61—41no—
405C22×D61—41no—
406C22×D61—41no—
407C22×D61—41no—
408C22×D61—41no—
409C22×D61—41no—
410C22×D61C2×C22⋊C411yescharacteristic
411C22×D61C2×C22⋊C411yescharacteristic
412C22×D61AGL(1,ℤ/8)12yes—
413C22×D61AGL(1,ℤ/8)12yes—
414C22×D61C22×D411yescharacteristic
415C2×#6923—22no—
416C2×#6923—41no—
417C2×#6923—41no—
418C2×#6923—41no—
419C2×#6923—41no—
420C2×#6923—41no—
421C2×#6923—41no—
422C2×#6923—41no—
423C2×#6923—41no—
424C2×#6923—41no—
425C2×#6923—41no—
426C2×#6923—41no—
427C2×#6923—84no—
428Q8×C61—42no—
429D4×C61—22no—
430D4×C61—21no—
431D4×C61—21no—
432D4×C61—42no—
433D4×C61—42no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—42no—
442C2×C4×C61—42no—
443C2×C4×C61—42no—
444C2×C4×C61C2×C22⋊C411yescharacteristic
445C2×C4×C61C2×C22⋊C411yescharacteristic
446C2×C4×C61C2×C22⋊C411yescharacteristic
447C2×C4×C61C2×C22⋊C411yescharacteristic
448C2×C4×C61C23×C411yescharacteristic
449C22⋊D61—22no—
450C22⋊D61—22no—
451C22⋊D61—42no—
452C22⋊D61—42no—
453C22⋊D61—42no—
454C22⋊D61—42no—
455C22⋊D61—41no—
456C22⋊D61—41no—
457C2×Dic61—21no—
458C2×Dic61—21no—
459C2×Dic61—21no—
460C2×Dic61—21no—
461C2×Dic61—21no—
462C2×Dic61—21no—
463C2×Dic61—21no—
464C2×Dic61—42no—
465C2×Dic61—42no—
466C2×Dic61—42no—
467C2×Dic61C2×C22⋊C411yescharacteristic
468C2×Dic61C2×C22⋊C411yescharacteristic
469C2×Dic61C2×C22⋊C411yescharacteristic
470C2×Dic61C2×C22⋊C411yescharacteristic
471C2×Dic61C22×D411yescharacteristic
472D244—22no—
473D244—21no—
474D244—21no—
475D244—42no—
476D244—42no—
477C4×D61—21no—
478C4×D61—21no—
479C4×D61—21no—
480C4×D61—21no—
481C4×D61—21no—
482C4×D61—21no—
483C4×D61—21no—
484C4×D61—21no—
485C4×D61—21no—
486C4×D61—21no—
487C4×D61—21no—
488C4×D61—21no—
489C4×D61—21no—
490C4×D61—21no—
491C4×D61—21no—
492C4×D61—21no—
493C4×D61—42no—
494C4×D61—42no—
495C4×D61—42no—
496C4×D61—42no—
497C4×D61—41no—
498C4×D61—41no—
499C4×D61—41no—
500C4×D61—41no—
501C4×D61—41no—
502C4×D61—41no—
503C4×D61—42no—
504C4×D61—42no—
505C4×D61C2×#4111yescharacteristic
506C4×D61C2×#4111yescharacteristic
507C4×D61H(5,𝔽2)11yescharacteristic
508C4×D612−1+411yescharacteristic
509Dic122—42no—
510Dic122—42no—
511Dic122—42no—
512#92420—22no—
513#92420—41no—
514#92420—41no—
515#92420—41no—
516#22495—611nomaximal, Sylow
517C22×C61—21no—
518C22×C61—21no—
519C22×C61—21no—
520C22×C61—21no—
521C22×C61—21no—
522C22×C61—41no—
523C22×C61—41no—
524C22×C61—41no—
525C22×C61#41812yes—
526C22×C61C22×C22⋊C411yescharacteristic
527C2×D61—21no—
528C2×D61—21no—
529C2×D61—22no—
530C2×D61—22no—
531C2×D61—22no—
532C2×D61—22no—
533C2×D61—21no—
534C2×D61—21no—
535C2×D61—21no—
536C2×D61—41no—
537C2×D61—41no—
538C2×D61—41no—
539C2×D61—41no—
540C2×D61—41no—
541C2×D61—41no—
542C2×D61—41no—
543C2×D61—81no—
544C2×D61—81no—
545C2×D61—81no—
546C2×D61—81no—
547C2×D61#41812yes—
548C2×D61#54611yescharacteristic
549C2×D61#54711yescharacteristic
550C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
551C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
552C2×D61#57711yescharacteristic
553C2×D61#57811yescharacteristic
554#6923—42no—
555#6923—81no—
556#6923—81no—
557#6923—81no—
558C4×C61—21no—
559C4×C61—21no—
560C4×C61—21no—
561C4×C61—21no—
562C4×C61—41no—
563C4×C61—41no—
564C4×C61—41no—
565C4×C61C4×#4111yescharacteristic
566C4×C61#52011yescharacteristic
567Dic61—21no—
568Dic61—21no—
569Dic61—21no—
570Dic61—21no—
571Dic61—41no—
572Dic61—41no—
573Dic61—41no—
574Dic61#54611yescharacteristic
575Dic61#54711yescharacteristic
576C2×#547—611no—
577C2×#435—611no—
578#2352—611no—
579#1993—611no—
580#1987—611no—
581#1895—611no—
582#1893—611no—
583#1875—611no—
584#1874—611no—
585#1824—611no—
586#1823—611no—
587#1804—611no—
588#1762—611no—
589#1736—611no—
590C2×#340—611no—
591C2×C61—22no—
592C2×C61—41no—
593C2×C61—81no—
594C2×C61#233911yescharacteristic
595C2×C61C2×#41811yescharacteristic
596C2×C61#289811yescharacteristic
597D61—22no—
598D61—41no—
599D61—81no—
600D61#330611yescharacteristic
601D61#330811yescharacteristic
602D61#334311yescharacteristic
603D61#334511yescharacteristic
604C22×#41—1221no—
605C22×M16—611no—
606C23×C8—611no—
607#547—611no—
608#547—611no—
609#547—611no—
610#547—611no—
611#547—611no—
612#547—611no—
613#547—611no—
614#547—1221no—
615#547—1221no—
616#547—1221no—
617#547—1221no—
618#547#692311yescharacteristic, complemented
619C2×C4⋊Q8—611no—
620C2×#123—1221no—
621C2×#123—1221no—
622C2×C22⋊Q8—1221no—
623C2×#121—611no—
624C2×#121—611no—
625C2×C4×D4—611no—
626C2×C4×D4—611no—
627C2×#117—611no—
628C22×C4⋊C4—611no—
629C22×C4⋊C4—611no—
630C22×C4⋊C4—611no—
631#435—1221no—
632#435—1221no—
633#435—1221no—
634#435—1221no—
635C2×C4⋊C8—611no—
636C2×#102—611no—
637C2×#102—611no—
638C2×#102—611no—
639C2×#102—611no—
640C2×C22⋊C8—611no—
641C2×C22⋊C8—611no—
642C2×#97—611no—
643#388—1221no—
644#387—1221no—
645#386—1221no—
646#382—611no—
647#380—611no—
648#380—611no—
649C4×C4⋊C4—611no—
650C4×C22⋊C4—1221no—
651#340—611no—
652#340—611no—
653#340—611no—
654#340—611no—
655#340—611no—
656#340—611no—
657#340—611no—
658#340—611no—
659#340—611no—
660#340—611no—
661#340—611no—
662#340—611no—
663C61#2249511yescharacteristic, complemented, Sylow
664C2×#41—21no—
665C2×#41—1221no—
666C2×#41—1221no—
667C2×#41—1221no—
668C2×#41—1221no—
669C2×#41—1221no—
670C2×#41—1221no—
671C2×#41—1221no—
672C2×#41—2444no—
673C2×#41—2444no—
674C22×Q8—1221no—
675C22×D4—611no—
676C22×D4—611no—
677C22×D4—1221no—
678C22×D4—1221no—
679C23×C4—611no—
680C23×C4—611no—
681C23×C4—1221no—
682C23×C4—1221no—
683C23×C4—1221no—
684C23×C4—1221no—
685C2×M16—1222no—
686C2×M16—1221no—
687C2×M16—1221no—
688C2×M16—2441no—
689C22×C8—611no—
690C22×C8—611no—
691C22×C8—611no—
692C22×C8—611no—
693C22×C8—1222no—
694C22×C8—1221no—
695C22×C8—1221no—
696C22×C8—2441no—
697C4⋊Q8—611no—
698C4⋊Q8—611no—
699C4⋊Q8—611no—
700C4⋊Q8—1221no—
701C4⋊Q8—1221no—
702C4⋊Q8C2×#692311yescharacteristic, complemented
703#123—21no—
704#123—21no—
705#123—1221no—
706#123—1221no—
707#123—1221no—
708#123—1221no—
709#123—1221no—
710#123—1221no—
711#123—1221no—
712#123—1221no—
713#123—1221no—
714#123—1221no—
715#123—1221no—
716#123—1221no—
717#123—1221no—
718#123—1221no—
719C22⋊Q8—21no—
720C22⋊Q8—1221no—
721C22⋊Q8—1221no—
722C22⋊Q8—1221no—
723C22⋊Q8—1221no—
724C22⋊Q8—1221no—
725C22⋊Q8—1221no—
726C22⋊Q8—1221no—
727#121—611no—
728#121—611no—
729#121—611no—
730#121—611no—
731#121—611no—
732#121—611no—
733#121—1221no—
734#121—1221no—
735#121—1221no—
736#121—1221no—
737#121C2×#692311yescharacteristic
738#121C2×#692311yescharacteristic, complemented
739C4×D4—611no—
740C4×D4—611no—
741C4×D4—611no—
742C4×D4—611no—
743C4×D4—611no—
744C4×D4—611no—
745C4×D4—611no—
746C4×D4—611no—
747C4×D4—611no—
748C4×D4—611no—
749C4×D4—1221no—
750C4×D4—1221no—
751C4×D4C2×#692311yescharacteristic
752C4×D4C2×#692311yescharacteristic, complemented
753#117—1222no—
754#117—2441no—
755C2×C4⋊C4—611no—
756C2×C4⋊C4—611no—
757C2×C4⋊C4—611no—
758C2×C4⋊C4—611no—
759C2×C4⋊C4—611no—
760C2×C4⋊C4—611no—
761C2×C4⋊C4—611no—
762C2×C4⋊C4—611no—
763C2×C4⋊C4—611no—
764C2×C4⋊C4—611no—
765C2×C4⋊C4—611no—
766C2×C4⋊C4—611no—
767C2×C4⋊C4—611no—
768C2×C4⋊C4—611no—
769C2×C4⋊C4—1221no—
770C2×C4⋊C4—1221no—
771C2×C4⋊C4—1221no—
772C2×C4⋊C4—1221no—
773C2×C4⋊C4—1221no—
774C2×C4⋊C4—1222no—
775C2×C4⋊C4—1221no—
776C2×C4⋊C4—1221no—
777C2×C4⋊C4—1221no—
778C2×C4⋊C4—2441no—
779C2×C4⋊C4C2×#692311yescharacteristic
780C2×C4⋊C4C2×#692311yescharacteristic, complemented
781C2×C22⋊C4—611no—
782C2×C22⋊C4—611no—
783C2×C22⋊C4—1221no—
784C2×C22⋊C4—1221no—
785C2×C22⋊C4—1221no—
786C2×C22⋊C4—1221no—
787C2×C22⋊C4—1221no—
788C2×C22⋊C4—1221no—
789C2×C42—611no—
790C2×C42—1221no—
791C2×C42—1221no—
792C4⋊C8—1221no—
793C4⋊C8—1221no—
794#102—1222no—
795#102—1222no—
796#102—2441no—
797#102—2441no—
798C22⋊C8—1221no—
799C22⋊C8—1221no—
800C22⋊C8—1221no—
801C22⋊C8—1221no—
802#97—1221no—
803#97—1221no—
804#95—1221no—
805#95—1221no—
806#95—1221no—
807#95—1221no—
808#95—1221no—
809C24—611no—
810C24—611no—
811C24—1221no—
812#41—44no—
813#41—2444no—
814#41—2444no—
815#41—2444no—
816#41—2444no—
817#41—2444no—
818#41—2444no—
819#41—2444no—
820C2×Q8—21no—
821C2×Q8—1221no—
822C2×Q8—1221no—
823C2×Q8—1221no—
824C2×Q8—2442no—
825C2×Q8—2442no—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—611no—
829C2×D4—611no—
830C2×D4—611no—
831C2×D4—611no—
832C2×D4—1221no—
833C2×D4—1221no—
834C2×D4—1221no—
835C2×D4—1221no—
836C2×D4—1221no—
837C2×D4—1221no—
838C2×D4—1221no—
839C2×D4—1222no—
840C2×D4—1222no—
841C2×D4—1221no—
842C2×D4—1221no—
843C2×D4—1221no—
844C2×D4—1221no—
845C2×D4—2442no—
846C2×D4—2442no—
847C2×D4—2442no—
848C2×D4—2442no—
849C2×D4C22⋊#692311yescharacteristic
850C2×D4C22×#692311yescharacteristic
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—611no—
855C22×C4—611no—
856C22×C4—611no—
857C22×C4—611no—
858C22×C4—611no—
859C22×C4—611no—
860C22×C4—611no—
861C22×C4—611no—
862C22×C4—611no—
863C22×C4—611no—
864C22×C4—611no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—1221no—
871C22×C4—1221no—
872C22×C4—1221no—
873C22×C4—1221no—
874C22×C4—1221no—
875C22×C4—1221no—
876C22×C4—1221no—
877C22×C4—1221no—
878C22×C4—1221no—
879C22×C4—1221no—
880C22×C4—1221no—
881C22×C4—1221no—
882C22×C4—1221no—
883C22×C4—1221no—
884C22×C4—1221no—
885C22×C4—1221no—
886C22×C4—1221no—
887C22×C4—1221no—
888C22×C4—1221no—
889C22×C4—4881no—
890C22×C4—2442no—
891C22×C4—2442no—
892C22×C4—2442no—
893C22×C4—2442no—
894C22×C4—2442no—
895C22×C4—2442no—
896C22×C4—2442no—
897C22×C4—2442no—
898C22×C4C22×#692311yescharacteristic
899C22×C4C22×#692311yescharacteristic
900M16—2442no—
901M16—2442no—
902C2×C8—612no—
903C2×C8—1221no—
904C2×C8—1221no—
905C2×C8—1221no—
906C2×C8—1221no—
907C2×C8—1221no—
908C2×C8—1221no—
909C2×C8—1221no—
910C2×C8—1221no—
911C2×C8—1221no—
912C2×C8—1221no—
913C2×C8—1221no—
914C2×C8—2442no—
915C2×C8—2442no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—611no—
920C4⋊C4—611no—
921C4⋊C4—611no—
922C4⋊C4—612no—
923C4⋊C4—611no—
924C4⋊C4—611no—
925C4⋊C4—611no—
926C4⋊C4—1221no—
927C4⋊C4—1221no—
928C4⋊C4—1221no—
929C4⋊C4—1221no—
930C4⋊C4—1221no—
931C4⋊C4—1221no—
932C4⋊C4—1221no—
933C4⋊C4—1221no—
934C4⋊C4—1221no—
935C4⋊C4—1221no—
936C4⋊C4—1221no—
937C4⋊C4—1221no—
938C4⋊C4—1221no—
939C4⋊C4—1221no—
940C4⋊C4—1221no—
941C4⋊C4—1221no—
942C4⋊C4—1221no—
943C4⋊C4—1221no—
944C4⋊C4—1221no—
945C4⋊C4—2442no—
946C4⋊C4C22⋊#692311yescharacteristic
947C4⋊C4C22×#692311yescharacteristic
948C4⋊C4C22×#692311yescharacteristic
949C4⋊C4C22×#692311yescharacteristic
950C22⋊C4—21no—
951C22⋊C4—21no—
952C22⋊C4—21no—
953C22⋊C4—611no—
954C22⋊C4—611no—
955C22⋊C4—611no—
956C22⋊C4—611no—
957C22⋊C4—611no—
958C22⋊C4—611no—
959C22⋊C4—1221no—
960C22⋊C4—1221no—
961C22⋊C4—1221no—
962C22⋊C4—1221no—
963C22⋊C4—1221no—
964C22⋊C4—1221no—
965C22⋊C4—1221no—
966C22⋊C4—1221no—
967C22⋊C4—1221no—
968C22⋊C4—4881no—
969C22⋊C4—2442no—
970C22⋊C4—2442no—
971C22⋊C4C22⋊#692311yescharacteristic
972C22⋊C4C22⋊#692311yescharacteristic
973C42—611no—
974C42—611no—
975C42—611no—
976C42—4881no—
977C42—2442no—
978C42C22×#692311yescharacteristic
979C23—21no—
980C23—611no—
981C23—612no—
982C23—612no—
983C23—611no—
984C23—611no—
985C23—1221no—
986C23—1221no—
987C23—1221no—
988C23—1221no—
989C23—1221no—
990C23—1221no—
991C23—1221no—
992C23—1221no—
993C23—1221no—
994C23—1221no—
995C23—1221no—
996C23—2441no—
997C23—2441no—
998C23—2441no—
999C23—2441no—
1000C23—2441no—
1001C23—2441no—
1002C23C2×C22⋊#692311yescharacteristic
1003C23C2×C22⋊#692311yescharacteristic
1004Q8—42no—
1005Q8—2442no—
1006Q8—2442no—
1007Q8—2442no—
1008D4—22no—
1009D4—21no—
1010D4—21no—
1011D4—42no—
1012D4—42no—
1013D4—1222no—
1014D4—1222no—
1015D4—1222no—
1016D4—1221no—
1017D4—1221no—
1018D4—2442no—
1019D4—2442no—
1020D4—2441no—
1021D4—2441no—
1022D4—2442no—
1023D4—2442no—
1024D4—2442no—
1025D4—2442no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—42no—
1034C2×C4—42no—
1035C2×C4—42no—
1036C2×C4—611no—
1037C2×C4—611no—
1038C2×C4—611no—
1039C2×C4—611no—
1040C2×C4—611no—
1041C2×C4—611no—
1042C2×C4—611no—
1043C2×C4—611no—
1044C2×C4—611no—
1045C2×C4—1221no—
1046C2×C4—1221no—
1047C2×C4—1221no—
1048C2×C4—1221no—
1049C2×C4—1221no—
1050C2×C4—1221no—
1051C2×C4—1221no—
1052C2×C4—1221no—
1053C2×C4—1221no—
1054C2×C4—1221no—
1055C2×C4—1221no—
1056C2×C4—1221no—
1057C2×C4—1221no—
1058C2×C4—1221no—
1059C2×C4—1221no—
1060C2×C4—1221no—
1061C2×C4—1221no—
1062C2×C4—1221no—
1063C2×C4—1221no—
1064C2×C4—1221no—
1065C2×C4—1222no—
1066C2×C4—1221no—
1067C2×C4—1221no—
1068C2×C4—1221no—
1069C2×C4—4884no—
1070C2×C4—2442no—
1071C2×C4—2442no—
1072C2×C4—2441no—
1073C2×C4—2441no—
1074C2×C4—2441no—
1075C2×C4—2441no—
1076C2×C4—2441no—
1077C2×C4—2441no—
1078C2×C4—2442no—
1079C2×C4—2442no—
1080C2×C4—2442no—
1081C2×C4—2442no—
1082C2×C4—2442no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2442no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2442no—
1096C2×C4C2×C22⋊#692311yescharacteristic
1097C2×C4C2×C22⋊#692311yescharacteristic
1098C2×C4C2×C22⋊#692311yescharacteristic
1099C2×C4C2×C22⋊#692311yescharacteristic
1100C2×C4C23×#692311yescharacteristic
1101C8—1222no—
1102C8—2441no—
1103C8—2441no—
1104C8—2441no—
1105C22—21no—
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—41no—
1111C22—41no—
1112C22—41no—
1113C22—611no—
1114C22—611no—
1115C22—611no—
1116C22—611no—
1117C22—611no—
1118C22—611no—
1119C22—612no—
1120C22—1222no—
1121C22—1222no—
1122C22—1222no—
1123C22—1222no—
1124C22—1221no—
1125C22—1221no—
1126C22—1221no—
1127C22—1221no—
1128C22—1221no—
1129C22—4881no—
1130C22—4881no—
1131C22—4881no—
1132C22—4881no—
1133C22—2441no—
1134C22—2441no—
1135C22—2441no—
1136C22—2441no—
1137C22—2441no—
1138C22—2441no—
1139C22—2441no—
1140C22#1684075412yes—
1141C22C22×C22⋊#692311yescharacteristic
1142C4—21no—
1143C4—21no—
1144C4—21no—
1145C4—21no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—611no—
1150C4—611no—
1151C4—1221no—
1152C4—1221no—
1153C4—1221no—
1154C4—1221no—
1155C4—4881no—
1156C4—4881no—
1157C4—4881no—
1158C4—2442no—
1159C4—2441no—
1160C4—2441no—
1161C4—2441no—
1162C4#41×#692311yescharacteristic
1163C4#1684083111yescharacteristic
1164C2—22no—
1165C2—41no—
1166C2—81no—
1167C2—611no—
1168C2—611no—
1169C2—611no—
1170C2—611no—
1171C2—1222no—
1172C2—4881no—
1173C2—2441no—
1174C2#2146232211yescharacteristic
1175C2C2×#1684075411yescharacteristic
1176C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#547×D61C2
cosocleC2×C4×D61C24
hypercenter#547#6923
hypocenterC61#22495
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. D61⋊#435C2semidirect
2. #21462335C2semidirect
3. #21462003C2semidirect
4. #21461997C2semidirect
5. #21461835C2semidirect
6. #21461833C2semidirect
7. #21461807C2semidirect
8. #21461806C2semidirect
9. #21461723C2semidirect
10. #21461722C2semidirect
11. #21461689C2semidirect
12. #21461589C2semidirect
13. #21461506C2semidirect
14. C2×#16840635C2semidirect
53. #16840417C4semidirect
54. #16840416C4semidirect
55. #16840415C4semidirect
57. #16840413C4semidirect
58. #16840413C4semidirect
59. #16840412C4semidirect
60. #16840412C4semidirect
74. C61×#547C4semidirect
138. #14519777C2×C4semidirect
140. #14519776C2×C4semidirect
141. #14519776C2×C4semidirect
165. #14519752C2×C4semidirect
167. #14519751C2×C4semidirect
173. #14519748C2×C4semidirect
175. C4×D244C2×C4semidirect
176. D4×Dic61C2×C4semidirect
178. #14519739C2×C4semidirect
187. C2×C4⋊Dic61C2×C4semidirect
197. C4⋊C4×D61C2×C4semidirect
198. C4⋊C4×D61C2×C4semidirect
210. C4⋊Q8×C61C2×C4semidirect
215. #121×C61C2×C4semidirect
217. C4×D4×C61C2×C4semidirect
219. C2×C4⋊C4×C61C2×C4semidirect
328. C4⋊#6923#41semidirect
340. D61⋊C8#41semidirect
618. #547#6923semidirect
663. C61#22495semidirect
702. C4⋊Q8C2×#6923semidirect
738. #121C2×#6923semidirect
752. C4×D4C2×#6923semidirect
780. C2×C4⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4352
#214623352
#214620032
#214619972
#214618352
#214618332
#214618072
#214618062
#214617232
#214617222
#214616892
#214615892
#214615062
C2×#168406352
#547×D612
#2249561