Finite Group Databasebeta

← #30620357

Subgroups — #30620357

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#435C211yesmaximal, characteristic
2D4×C4⋊#6923C211yesmaximal, characteristic
3#21462002C211yesmaximal, characteristic, complemented
4#21461999C211yesmaximal, characteristic, complemented
5#21461834C211yesmaximal, characteristic, complemented
6#21461832C211yesmaximal, characteristic, complemented
7#21461804C211yesmaximal, characteristic, complemented
8#21461804C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461722C211yesmaximal, characteristic, complemented
11#21461688C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461508C211yesmaximal, characteristic, complemented
14C2×#16840635C211yesmaximal, characteristic, complemented
15#552×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×D4×#6923—21no—
19C22×C4⋊#6923C2211yescharacteristic
20C22×C4⋊#6923C2211yescharacteristic
21#16840794—21no—
22#16840793—21no—
23#16840792—21no—
24#16840791—21no—
25D61⋊(C4⋊C8)C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29C2×#14519840C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31D61⋊(C22⋊C8)C2211yescharacteristic
32#16840721C2211yescharacteristic
33#16840713—21no—
34#16840709—21no—
35#16840709—21no—
36#16840708C2211yescharacteristic
37#16840704C2211yescharacteristic
38#16840704C2211yescharacteristic
39C4×C4⋊#6923C2211yescharacteristic
40#16840635C2211yescharacteristic
41#16840635C2211yescharacteristic
42#16840635C2211yescharacteristic
43#16840635C2211yescharacteristic
44#16840635C2211yescharacteristic
45#16840635C2211yescharacteristic
46#16840635C2211yescharacteristic
47#16840635C2211yescharacteristic
48#16840635C2211yescharacteristic
49#16840635C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52#16840454C411yescharacteristic, complemented
53#16840453C411yescharacteristic, complemented
54#16840452C411yescharacteristic, complemented
55#16840451C411yescharacteristic, complemented
56#16840450C411yescharacteristic, complemented
57#16840449—21no—
58#16840448—21no—
59#16840447C411yescharacteristic, complemented
60#16840446C411yescharacteristic, complemented
61#16840445—21no—
62#16840444—21no—
63#126×D61—21no—
64#125×D61—21no—
65#125×D61C2211yescharacteristic
66#123×D61—21no—
67C22⋊Q8×D61C2211yescharacteristic
68C22⋊Q8×D61C2211yescharacteristic
69C4×Q8×D61C2211yescharacteristic
70C4×D4×D61C2211yescharacteristic
71#117×D61—21no—
72#117×D61C2211yescharacteristic
73C2×C4⋊C4×D61C2211yescharacteristic
74C61×#552C411yescharacteristic, complemented
75C23×#6923—21no—
76C23×#6923—21no—
77C2×#11758213—21no—
78D61⋊M16—22no—
79D61⋊M16—41no—
80C2×#11758217—21no—
81C2×D61⋊C8—22no—
82C2×D61⋊C8—21no—
83C2×D61⋊C8—41no—
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C2×D61⋊C8C2311yescharacteristic
88C22×#92420—21no—
89D4×#6923—44no—
90C2×C4⋊#6923—22no—
91C2×C4⋊#6923—22no—
92C2×C4⋊#6923—21no—
93C2×C4⋊#6923—21no—
94C2×C4⋊#6923—21no—
95C2×C4⋊#6923—21no—
96C2×C4⋊#6923—41no—
97C2×C4⋊#6923—41no—
98C2×C4⋊#6923C2311yescharacteristic
99C2×C4⋊#6923C2311yescharacteristic
100C2×C4⋊#6923C2311yescharacteristic
101C2×C4⋊#6923C2311yescharacteristic
102C2×C22⋊#6923—21no—
103C2×C22⋊#6923—21no—
104C2×C4×#6923—21no—
105#14519844—21no—
106C4⋊#92420—21no—
107#14519840—22no—
108#14519840—22no—
109#14519840—41no—
110#14519840—41no—
111#14519834—21no—
112#14519834—21no—
113C22⋊#92420—21no—
114C22⋊#92420—21no—
115#14519832—21no—
116#14519832—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119(C2×#6923)⋊C4—21no—
120C2×Q8×D61C2311yescharacteristic
121C2×D4×D61D411yescharacteristic
122C22×C4×D61—21no—
123C22×C4×D61C2311yescharacteristic
124C22×C4×D61C2311yescharacteristic
125#14519772—21no—
126#14519772—21no—
127#14519772—21no—
128#14519771—21no—
129#14519770—21no—
130#14519770—21no—
131#14519770—21no—
132#14519769—21no—
133#14519769C2×C411yescharacteristic, complemented
134#14519768—21no—
135#14519768—21no—
136#14519768C2×C411yescharacteristic, complemented
137#14519768C2×C411yescharacteristic, complemented
138#14519767—21no—
139#14519767—21no—
140#14519767—21no—
141#14519767—21no—
142#14519767—21no—
143#14519767—21no—
144#14519762—21no—
145#14519762—21no—
146#14519761—21no—
147#14519760—21no—
148#14519759—21no—
149#14519759—21no—
150#14519758—21no—
151#14519757C2×C411yescharacteristic, complemented
152#14519757C2×C411yescharacteristic, complemented
153#14519756C2×C411yescharacteristic, complemented
154#14519756C2×C411yescharacteristic, complemented
155#14519755—21no—
156#14519755—21no—
157#14519754—21no—
158#14519754—21no—
159#14519753C2×C411yescharacteristic, complemented
160#14519753C2×C411yescharacteristic, complemented
161Q8×Dic61C2×C411yescharacteristic, complemented
162C4×Dic122—21no—
163C4×Dic122C2×C411yescharacteristic, complemented
164#14519742—21no—
165#14519742C2×C411yescharacteristic, complemented
166C4×D244C2×C411yescharacteristic
167D4×Dic61D411yescharacteristic
168#14519739D411yescharacteristic
169C4×C22⋊D61C2×C411yescharacteristic
170C4×C22⋊D61C2×C411yescharacteristic
171#14519737D411yescharacteristic
172#14519737D411yescharacteristic
173#14519736—21no—
174#14519736C2×C411yescharacteristic, complemented
175#14519735—21no—
176#14519735—21no—
177#14519735C2×C411yescharacteristic, complemented
178#14519735C2×C411yescharacteristic, complemented
179#14519734—21no—
180#14519734—21no—
181#14519734—21no—
182#14519733—21no—
183#14519733—21no—
184#14519733—21no—
185C2×C4⋊Dic61C2×C411yescharacteristic, complemented
186C2×#11758196—21no—
187C4⋊C4×D61—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C4⋊C4×D61—21no—
193C4⋊C4×D61—21no—
194C4⋊C4×D61C2×C411yescharacteristic, complemented
195C4⋊C4×D61C2×C411yescharacteristic, complemented
196C4⋊C4×D61D411yescharacteristic
197C4⋊C4×D61C2311yescharacteristic
198C4⋊C4×D61C2311yescharacteristic
199C4⋊C4×D61C2311yescharacteristic
200C22⋊C4×D61—21no—
201C22⋊C4×D61—21no—
202C22⋊C4×D61—21no—
203C22⋊C4×D61D411yescharacteristic
204C22⋊C4×D61D411yescharacteristic
205C42×D61—21no—
206C42×D61—21no—
207C42×D61C2311yescharacteristic
208#126×C61—21no—
209#125×C61—21no—
210#125×C61C2×C411yescharacteristic, complemented
211#123×C61—21no—
212C22⋊Q8×C61C2×C411yescharacteristic, complemented
213C22⋊Q8×C61C2×C411yescharacteristic, complemented
214C4×Q8×C61C2×C411yescharacteristic, complemented
215C4×D4×C61C2×C411yescharacteristic
216#117×C61—21no—
217#117×C61C2×C411yescharacteristic, complemented
218C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
219C23×D61C2×D411yescharacteristic
220C23×D61C2×D411yescharacteristic
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—21no—
225C22×#6923—42no—
226C22×#6923—42no—
227C22×#6923—42no—
228C22×#6923—42no—
229C22×#6923—81no—
230C22×#6923—81no—
231C2×Q8×C61C22×C411yescharacteristic
232C2×D4×C61C22⋊C411yescharacteristic
233C22×C4×C61—21no—
234C22×C4×C61C22×C411yescharacteristic
235C22×C4×C61C22×C411yescharacteristic
236C2×C22⋊D61C22⋊C411yescharacteristic
237C2×C22⋊D61C22⋊C411yescharacteristic
238C22×Dic61—21no—
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241Q8×D61—21no—
242Q8×D61—21no—
243Q8×D61—21no—
244Q8×D61—21no—
245D4×D61—22no—
246D4×D61—22no—
247C2×D244C22⋊C411yescharacteristic
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—21no—
259C2×C4×D61—21no—
260C2×C4×D61—21no—
261C2×C4×D61—21no—
262C2×C4×D61—42no—
263C2×C4×D61—42no—
264C2×C4×D61C22×C411yescharacteristic
265C2×C4×D61C22×C411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2×D411yescharacteristic
269C2×C4×D61C2×D411yescharacteristic
270C2×C4×D61C2×D411yescharacteristic
271C2×C4×D61C2×D411yescharacteristic
272C2×C4×D61C2411yescharacteristic
273C2×Dic122—21no—
274C2×Dic122C22×C411yescharacteristic
275C22⋊#6923—42no—
276C22⋊#6923—42no—
277#11758217—42no—
278C2×#92420—21no—
279C2×#92420—21no—
280C2×#92420—21no—
281C2×#92420—21no—
282C2×#92420—42no—
283C4⋊#6923—21no—
284C4⋊#6923—21no—
285C4⋊#6923—21no—
286C4⋊#6923—21no—
287C4⋊#6923—21no—
288C4⋊#6923—21no—
289C4⋊#6923—21no—
290C4⋊#6923—42no—
291C4⋊#6923—42no—
292C4⋊#6923—42no—
293C4⋊#6923—81no—
294C4⋊#6923#4112yes—
295C4×#6923—42no—
296#11758213—42no—
297D61⋊C8—21no—
298D61⋊C8—21no—
299D61⋊C8—21no—
300D61⋊C8—21no—
301D61⋊C8—21no—
302D61⋊C8—21no—
303D61⋊C8—21no—
304D61⋊C8—42no—
305D61⋊C8#4112yes—
306C4⋊C4×C61—21no—
307C4⋊C4×C61—21no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61C22⋊C411yescharacteristic
313C4⋊C4×C61C22×C411yescharacteristic
314C4⋊C4×C61C22×C411yescharacteristic
315C4⋊C4×C61C22×C411yescharacteristic
316C22⋊C4×C61—21no—
317C22⋊C4×C61—21no—
318C22⋊C4×C61—21no—
319C22⋊C4×C61C22⋊C411yescharacteristic
320C22⋊C4×C61C22⋊C411yescharacteristic
321C42×C61—21no—
322C42×C61—21no—
323C42×C61C22×C411yescharacteristic
324C22⋊Dic61—21no—
325C22⋊Dic61—21no—
326C22⋊Dic61—21no—
327C22⋊Dic61C22⋊C411yescharacteristic
328C22⋊Dic61C22⋊C411yescharacteristic
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198C22⋊C411yescharacteristic
336#11758198C22⋊C411yescharacteristic
337#11758198C22⋊C411yescharacteristic
338#11758198C22⋊C411yescharacteristic
339C4⋊Dic61—21no—
340C4⋊Dic61—21no—
341C4⋊Dic61—21no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344C4⋊Dic61—21no—
345C4⋊Dic61C22⋊C411yescharacteristic
346C4⋊Dic61C22×C411yescharacteristic
347C4⋊Dic61C22×C411yescharacteristic
348C4⋊Dic61C22×C411yescharacteristic
349#11758196—21no—
350#11758196—21no—
351#11758196—21no—
352#11758196—21no—
353#11758196—21no—
354#11758196—21no—
355#11758196—21no—
356#11758196—21no—
357#11758196—21no—
358#11758196—21no—
359#11758196—21no—
360#11758196—21no—
361#11758196—21no—
362#11758196—21no—
363#11758196—21no—
364#11758196C22⋊C411yescharacteristic
365#11758196C22⋊C411yescharacteristic
366C4×Dic61—21no—
367C4×Dic61—21no—
368C4×Dic61—21no—
369C4×Dic61—21no—
370C4×Dic61—21no—
371C4×Dic61—21no—
372C4×Dic61C22×C411yescharacteristic
373C4×Dic61C2×D411yescharacteristic
374C4×Dic61C2×D411yescharacteristic
375C23×C61C2×C22⋊C411yescharacteristic
376C23×C61C2×C22⋊C411yescharacteristic
377C22×D61—21no—
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61—21no—
385C22×D61—21no—
386C22×D61—21no—
387C22×D61C2×C22⋊C411yescharacteristic
388C22×D61C2×C22⋊C411yescharacteristic
389C22×D61AGL(1,ℤ/8)12yes—
390C22×D61#13712yes—
391C22×D61C22×D411yescharacteristic
392C2×#6923—22no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398C2×#6923—41no—
399C2×#6923—41no—
400C2×#6923—41no—
401C2×#6923—41no—
402C2×#6923—41no—
403C2×#6923—41no—
404C2×#6923—84no—
405C2×#6923—84no—
406Q8×C61—21no—
407Q8×C61—21no—
408D4×C61—22no—
409C2×C4×C61—21no—
410C2×C4×C61—21no—
411C2×C4×C61—21no—
412C2×C4×C61—21no—
413C2×C4×C61—21no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—21no—
417C2×C4×C61—42no—
418C2×C4×C61C2×C22⋊C411yescharacteristic
419C2×C4×C61C2×C22⋊C411yescharacteristic
420C2×C4×C61C2×C22⋊C411yescharacteristic
421C2×C4×C61C2×C22⋊C411yescharacteristic
422C2×C4×C61C23×C411yescharacteristic
423C22⋊D61—22no—
424C22⋊D61—22no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61—21no—
428C2×Dic61—21no—
429C2×Dic61—21no—
430C2×Dic61—21no—
431C2×Dic61—21no—
432C2×Dic61—21no—
433C2×Dic61—42no—
434C2×Dic61C2×C22⋊C411yescharacteristic
435C2×Dic61C2×C22⋊C411yescharacteristic
436C2×Dic61C2×C22⋊C411yescharacteristic
437C2×Dic61C2×C22⋊C411yescharacteristic
438C2×Dic61C22×D411yescharacteristic
439D244—22no—
440C4×D61—21no—
441C4×D61—21no—
442C4×D61—21no—
443C4×D61—21no—
444C4×D61—21no—
445C4×D61—21no—
446C4×D61—21no—
447C4×D61—21no—
448C4×D61—21no—
449C4×D61—21no—
450C4×D61—21no—
451C4×D61—21no—
452C4×D61—21no—
453C4×D61—21no—
454C4×D61—21no—
455C4×D61—21no—
456C4×D61—41no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61—41no—
460C4×D61—41no—
461C4×D61—41no—
462C4×D61—41no—
463C4×D61—41no—
464C4×D61—42no—
465C4×D61—42no—
466C4×D61C2×#4111yescharacteristic
467C4×D61C2×#4111yescharacteristic
468C4×D61H(5,𝔽2)11yescharacteristic
469C4×D612−1+411yescharacteristic
470Dic122—21no—
471Dic122—21no—
472Dic122—41no—
473Dic122—41no—
474#92420—22no—
475#92420—41no—
476#92420—41no—
477#92420—41no—
478#22491—611nomaximal, Sylow
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—21no—
484C22×C61#41712yes—
485C22×C61C22×C22⋊C411yescharacteristic
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—22no—
489C2×D61—22no—
490C2×D61—22no—
491C2×D61—22no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—21no—
495C2×D61—41no—
496C2×D61—41no—
497C2×D61—41no—
498C2×D61—41no—
499C2×D61#41712yes—
500C2×D61#54611yescharacteristic
501C2×D61#54711yescharacteristic
502C2×D61C2×AGL(1,ℤ/8)11yescharacteristic
503C2×D61C2×#13711yescharacteristic
504C2×D61#57711yescharacteristic
505C2×D61#57811yescharacteristic
506#6923—42no—
507#6923—81no—
508#6923—81no—
509#6923—81no—
510C4×C61—21no—
511C4×C61—21no—
512C4×C61—21no—
513C4×C61—21no—
514C4×C61—41no—
515C4×C61—41no—
516C4×C61—41no—
517C4×C61—41no—
518C4×C61C4×#4111yescharacteristic
519C4×C61#52011yescharacteristic
520Dic61—21no—
521Dic61—21no—
522Dic61—21no—
523Dic61—21no—
524Dic61—41no—
525Dic61—41no—
526Dic61—41no—
527Dic61—41no—
528Dic61#54611yescharacteristic
529Dic61#54711yescharacteristic
530C2×#552—611no—
531C2×#435—611no—
532D4×C4⋊C4—611no—
533#1992—611no—
534#1989—611no—
535#1894—611no—
536#1892—611no—
537#1872—611no—
538#1872—611no—
539#1825—611no—
540#1823—611no—
541#1803—611no—
542#1763—611no—
543#1736—611no—
544C2×#340—611no—
545C2×C61—22no—
546C2×C61—41no—
547C2×C61#233911yescharacteristic
548C2×C61C2×#41711yescharacteristic
549C2×C61#289811yescharacteristic
550D61—22no—
551D61—41no—
552D61#331011yescharacteristic
553D61#331211yescharacteristic
554D61#334311yescharacteristic
555D61#334411yescharacteristic
556C22×M16—611no—
557C23×C8—611no—
558#552—611no—
559#552—611no—
560#552—611no—
561#552—611no—
562#552—611no—
563#552—611no—
564#552—611no—
565#552—1221no—
566#552—1221no—
567#552—1221no—
568#552—1221no—
569#552#692311yescharacteristic, complemented
570C2×#126—1221no—
571C2×#125—611no—
572C2×#125—1221no—
573C2×#123—1221no—
574C2×C22⋊Q8—611no—
575C2×C22⋊Q8—611no—
576C2×C4×Q8—611no—
577C2×C4×D4—611no—
578C2×C4×D4—1221no—
579C2×#117—611no—
580C2×#117—1221no—
581C22×C4⋊C4—611no—
582C22×C4⋊C4—611no—
583C22×C4⋊C4—611no—
584#435—1221no—
585#435—1221no—
586#435—1221no—
587#435—1221no—
588C2×C4⋊C8—611no—
589C2×#103—611no—
590C2×#103—611no—
591C2×#103—611no—
592C2×#103—611no—
593C2×C22⋊C8—611no—
594C2×C22⋊C8—611no—
595C2×#97—611no—
596#389—1221no—
597#385—1221no—
598#385—1221no—
599#384—611no—
600#380—611no—
601#380—611no—
602C4×C4⋊C4—611no—
603#340—611no—
604#340—611no—
605#340—611no—
606#340—611no—
607#340—611no—
608#340—611no—
609#340—611no—
610#340—611no—
611#340—611no—
612#340—611no—
613#340—611no—
614#340—611no—
615C61#2249111yescharacteristic, complemented, Sylow
616C22×Q8—611no—
617C22×D4—611no—
618C23×C4—611no—
619C23×C4—611no—
620C23×C4—1221no—
621C23×C4—1221no—
622C23×C4—1221no—
623C2×M16—1222no—
624C2×M16—1221no—
625C2×M16—1221no—
626C2×M16—2441no—
627C22×C8—611no—
628C22×C8—611no—
629C22×C8—611no—
630C22×C8—611no—
631C22×C8—1222no—
632C22×C8—1221no—
633C22×C8—1221no—
634C22×C8—2441no—
635#126—21no—
636#126—1221no—
637#126—1221no—
638#126—1221no—
639#126—1221no—
640#126—1221no—
641#126—1221no—
642#126—1221no—
643#125—21no—
644#125—611no—
645#125—611no—
646#125—611no—
647#125—1221no—
648#125—1221no—
649#125—1221no—
650#125—1221no—
651#125—1221no—
652#125—1221no—
653#125—1221no—
654#125—1221no—
655#125—1221no—
656#125C2×#692311yescharacteristic, complemented
657#123—21no—
658#123—1221no—
659#123—1221no—
660#123—1221no—
661#123—1221no—
662#123—1221no—
663#123—1221no—
664#123—1221no—
665C22⋊Q8—611no—
666C22⋊Q8—611no—
667C22⋊Q8—611no—
668C22⋊Q8—611no—
669C22⋊Q8—611no—
670C22⋊Q8—611no—
671C22⋊Q8—1221no—
672C22⋊Q8—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8C2×#692311yescharacteristic, complemented
676C22⋊Q8C2×#692311yescharacteristic, complemented
677C4×Q8—611no—
678C4×Q8—611no—
679C4×Q8—611no—
680C4×Q8—1221no—
681C4×Q8—1221no—
682C4×Q8C2×#692311yescharacteristic, complemented
683C4×D4—611no—
684C4×D4—611no—
685C4×D4—611no—
686C4×D4—611no—
687C4×D4—611no—
688C4×D4—611no—
689C4×D4—611no—
690C4×D4—2444no—
691C4×D4C2×#692311yescharacteristic
692#117—21no—
693#117—611no—
694#117—611no—
695#117—611no—
696#117—1221no—
697#117—1221no—
698#117—1221no—
699#117—1221no—
700#117—1221no—
701#117—1221no—
702#117—1221no—
703#117—1221no—
704#117—1221no—
705#117C2×#692311yescharacteristic, complemented
706C2×C4⋊C4—611no—
707C2×C4⋊C4—611no—
708C2×C4⋊C4—611no—
709C2×C4⋊C4—611no—
710C2×C4⋊C4—611no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—611no—
713C2×C4⋊C4—611no—
714C2×C4⋊C4—611no—
715C2×C4⋊C4—611no—
716C2×C4⋊C4—611no—
717C2×C4⋊C4—1221no—
718C2×C4⋊C4—1221no—
719C2×C4⋊C4—1221no—
720C2×C4⋊C4—1221no—
721C2×C4⋊C4—1221no—
722C2×C4⋊C4—1221no—
723C2×C4⋊C4—1221no—
724C2×C4⋊C4—1222no—
725C2×C4⋊C4—1222no—
726C2×C4⋊C4—1221no—
727C2×C4⋊C4—1221no—
728C2×C4⋊C4—1221no—
729C2×C4⋊C4—1221no—
730C2×C4⋊C4—1221no—
731C2×C4⋊C4—2441no—
732C2×C4⋊C4—2441no—
733C2×C4⋊C4C2×#692311yescharacteristic, complemented
734C2×C22⋊C4—611no—
735C2×C22⋊C4—611no—
736C2×C22⋊C4—1221no—
737C2×C22⋊C4—1221no—
738C2×C22⋊C4—1221no—
739C2×C22⋊C4—1221no—
740C2×C22⋊C4—1221no—
741C2×C42—611no—
742C2×C42—1221no—
743C2×C42—1221no—
744C2×C42—1221no—
745C4⋊C8—1221no—
746C4⋊C8—1221no—
747#103—1222no—
748#103—1222no—
749#103—2441no—
750#103—2441no—
751C22⋊C8—1221no—
752C22⋊C8—1221no—
753C22⋊C8—1221no—
754C22⋊C8—1221no—
755#97—1221no—
756#97—1221no—
757#95—1221no—
758#95—1221no—
759#95—1221no—
760C24—611no—
761C24—611no—
762C2×Q8—611no—
763C2×Q8—1221no—
764C2×Q8—1221no—
765C2×Q8—1221no—
766C2×Q8—1221no—
767C2×Q8—1221no—
768C2×Q8C22×#692311yescharacteristic
769C2×D4—611no—
770C2×D4—611no—
771C2×D4—611no—
772C2×D4—1222no—
773C2×D4—1222no—
774C2×D4C22⋊#692311yescharacteristic
775C22×C4—21no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—611no—
780C22×C4—611no—
781C22×C4—611no—
782C22×C4—611no—
783C22×C4—611no—
784C22×C4—611no—
785C22×C4—611no—
786C22×C4—611no—
787C22×C4—1221no—
788C22×C4—1221no—
789C22×C4—1221no—
790C22×C4—1221no—
791C22×C4—1221no—
792C22×C4—1221no—
793C22×C4—1221no—
794C22×C4—1221no—
795C22×C4—1221no—
796C22×C4—1221no—
797C22×C4—1221no—
798C22×C4—1221no—
799C22×C4—1221no—
800C22×C4—1221no—
801C22×C4—1221no—
802C22×C4—1221no—
803C22×C4—1221no—
804C22×C4—1221no—
805C22×C4—1221no—
806C22×C4—4881no—
807C22×C4—4881no—
808C22×C4—2442no—
809C22×C4—2442no—
810C22×C4—2442no—
811C22×C4—2442no—
812C22×C4—2442no—
813C22×C4—2442no—
814C22×C4C22×#692311yescharacteristic
815C22×C4C22×#692311yescharacteristic
816M16—2442no—
817M16—2442no—
818C2×C8—612no—
819C2×C8—1221no—
820C2×C8—1221no—
821C2×C8—1221no—
822C2×C8—1221no—
823C2×C8—1221no—
824C2×C8—1221no—
825C2×C8—1221no—
826C2×C8—1221no—
827C2×C8—1221no—
828C2×C8—1221no—
829C2×C8—1221no—
830C2×C8—2442no—
831C2×C8—2442no—
832C4⋊C4—21no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—611no—
839C4⋊C4—611no—
840C4⋊C4—611no—
841C4⋊C4—612no—
842C4⋊C4—611no—
843C4⋊C4—611no—
844C4⋊C4—611no—
845C4⋊C4—1221no—
846C4⋊C4—1221no—
847C4⋊C4—1221no—
848C4⋊C4—1221no—
849C4⋊C4—1221no—
850C4⋊C4—1221no—
851C4⋊C4—1221no—
852C4⋊C4—1221no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C4⋊C4—1221no—
856C4⋊C4—1221no—
857C4⋊C4—1221no—
858C4⋊C4—1221no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—1221no—
864C4⋊C4—1221no—
865C4⋊C4—1221no—
866C4⋊C4—1221no—
867C4⋊C4—1221no—
868C4⋊C4—1221no—
869C4⋊C4—1221no—
870C4⋊C4—1221no—
871C4⋊C4—1221no—
872C4⋊C4—1221no—
873C4⋊C4—4881no—
874C4⋊C4—2442no—
875C4⋊C4—2442no—
876C4⋊C4—2442no—
877C4⋊C4C22⋊#692311yescharacteristic
878C4⋊C4C22×#692311yescharacteristic
879C4⋊C4C22×#692311yescharacteristic
880C4⋊C4C22×#692311yescharacteristic
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—611no—
885C22⋊C4—611no—
886C22⋊C4—611no—
887C22⋊C4—611no—
888C22⋊C4—611no—
889C22⋊C4—611no—
890C22⋊C4—1221no—
891C22⋊C4—1221no—
892C22⋊C4—1221no—
893C22⋊C4—1221no—
894C22⋊C4—1221no—
895C22⋊C4—1221no—
896C22⋊C4—1221no—
897C22⋊C4—1221no—
898C22⋊C4—1221no—
899C22⋊C4—2442no—
900C22⋊C4—2442no—
901C22⋊C4C22⋊#692311yescharacteristic
902C22⋊C4C22⋊#692311yescharacteristic
903C42—21no—
904C42—21no—
905C42—611no—
906C42—611no—
907C42—611no—
908C42—1221no—
909C42—1221no—
910C42—1221no—
911C42—1221no—
912C42—1221no—
913C42—1221no—
914C42—2442no—
915C42C22×#692311yescharacteristic
916C23—611no—
917C23—612no—
918C23—612no—
919C23—611no—
920C23—611no—
921C23—1221no—
922C23—1221no—
923C23—1221no—
924C23—1221no—
925C23—1221no—
926C23—1221no—
927C23—1221no—
928C23—1221no—
929C23—1221no—
930C23—1221no—
931C23C2×C22⋊#692311yescharacteristic
932C23C2×C22⋊#692311yescharacteristic
933Q8—21no—
934Q8—21no—
935Q8—1221no—
936Q8—1221no—
937Q8—2441no—
938Q8—2441no—
939D4—22no—
940D4—1222no—
941D4—1222no—
942D4—1222no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—42no—
952C2×C4—611no—
953C2×C4—611no—
954C2×C4—611no—
955C2×C4—611no—
956C2×C4—611no—
957C2×C4—611no—
958C2×C4—611no—
959C2×C4—611no—
960C2×C4—611no—
961C2×C4—1221no—
962C2×C4—1221no—
963C2×C4—1221no—
964C2×C4—1221no—
965C2×C4—1221no—
966C2×C4—1221no—
967C2×C4—1221no—
968C2×C4—1221no—
969C2×C4—1221no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—1221no—
976C2×C4—1221no—
977C2×C4—1221no—
978C2×C4—1221no—
979C2×C4—1221no—
980C2×C4—1221no—
981C2×C4—1222no—
982C2×C4—1221no—
983C2×C4—1221no—
984C2×C4—1221no—
985C2×C4—1221no—
986C2×C4—4884no—
987C2×C4—4884no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2442no—
995C2×C4—2442no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4—2441no—
999C2×C4—2441no—
1000C2×C4—2441no—
1001C2×C4—2441no—
1002C2×C4—2441no—
1003C2×C4—2441no—
1004C2×C4—2441no—
1005C2×C4—2441no—
1006C2×C4—2441no—
1007C2×C4—2441no—
1008C2×C4—2441no—
1009C2×C4—2442no—
1010C2×C4C2×C22⋊#692311yescharacteristic
1011C2×C4C2×C22⋊#692311yescharacteristic
1012C2×C4C2×C22⋊#692311yescharacteristic
1013C2×C4C2×C22⋊#692311yescharacteristic
1014C2×C4C23×#692311yescharacteristic
1015C8—1222no—
1016C8—2441no—
1017C8—2441no—
1018C8—2441no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—611no—
1025C22—611no—
1026C22—611no—
1027C22—611no—
1028C22—611no—
1029C22—611no—
1030C22—612no—
1031C22—1222no—
1032C22—1222no—
1033C22—1222no—
1034C22—1222no—
1035C22—1221no—
1036C22—1221no—
1037C22—1221no—
1038C22—1221no—
1039C22—1221no—
1040C22—2441no—
1041C22—2441no—
1042C22—2441no—
1043C22—2441no—
1044C22#1684075312yes—
1045C22C22×C22⋊#692311yescharacteristic
1046C4—21no—
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—41no—
1051C4—41no—
1052C4—41no—
1053C4—41no—
1054C4—611no—
1055C4—611no—
1056C4—1221no—
1057C4—1221no—
1058C4—1221no—
1059C4—1221no—
1060C4—4881no—
1061C4—4881no—
1062C4—4881no—
1063C4—2442no—
1064C4—2441no—
1065C4—2441no—
1066C4—2441no—
1067C4—2441no—
1068C4#41×#692311yescharacteristic
1069C4#1684083111yescharacteristic
1070C2—22no—
1071C2—41no—
1072C2—611no—
1073C2—611no—
1074C2—611no—
1075C2—611no—
1076C2—1222no—
1077C2—2441no—
1078C2#2146232211yescharacteristic
1079C2C2×#1684075311yescharacteristic
1080C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#552C4
socleC22×C61C22×C22⋊C4
prime radicalC2×D4×D61D4
cosocleC2×C4×D61C24
hypercenter#552#6923
hypocenterC61#22491
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
3. #21462002C2semidirect
4. #21461999C2semidirect
5. #21461834C2semidirect
6. #21461832C2semidirect
7. #21461804C2semidirect
8. #21461804C2semidirect
9. #21461724C2semidirect
10. #21461722C2semidirect
11. #21461688C2semidirect
12. #21461591C2semidirect
13. #21461508C2semidirect
14. C2×#16840635C2semidirect
52. #16840454C4semidirect
53. #16840453C4semidirect
54. #16840452C4semidirect
55. #16840451C4semidirect
56. #16840450C4semidirect
59. #16840447C4semidirect
60. #16840446C4semidirect
74. C61×#552C4semidirect
133. #14519769C2×C4semidirect
136. #14519768C2×C4semidirect
137. #14519768C2×C4semidirect
151. #14519757C2×C4semidirect
152. #14519757C2×C4semidirect
153. #14519756C2×C4semidirect
154. #14519756C2×C4semidirect
159. #14519753C2×C4semidirect
160. #14519753C2×C4semidirect
161. Q8×Dic61C2×C4semidirect
163. C4×Dic122C2×C4semidirect
165. #14519742C2×C4semidirect
174. #14519736C2×C4semidirect
177. #14519735C2×C4semidirect
178. #14519735C2×C4semidirect
185. C2×C4⋊Dic61C2×C4semidirect
194. C4⋊C4×D61C2×C4semidirect
195. C4⋊C4×D61C2×C4semidirect
210. #125×C61C2×C4semidirect
212. C22⋊Q8×C61C2×C4semidirect
213. C22⋊Q8×C61C2×C4semidirect
214. C4×Q8×C61C2×C4semidirect
217. #117×C61C2×C4semidirect
218. C2×C4⋊C4×C61C2×C4semidirect
569. #552#6923semidirect
615. C61#22491semidirect
656. #125C2×#6923semidirect
675. C22⋊Q8C2×#6923semidirect
676. C22⋊Q8C2×#6923semidirect
682. C4×Q8C2×#6923semidirect
705. #117C2×#6923semidirect
733. 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
D4×C4⋊#69232
#214620022
#214619992
#214618342
#214618322
#214618042
#214617242
#214617222
#214616882
#214615912
#214615082
C2×#168406352
#552×D612
#2249161