Finite Group Databasebeta

← #30620362

Subgroups — #30620362

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 1068 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#435C211yesmaximal, characteristic
2#21462337C211yesmaximal, characteristic
3#21462002C211yesmaximal, characteristic, complemented
4#21461999C211yesmaximal, characteristic, complemented
5#21461834C211yesmaximal, characteristic, complemented
6#21461832C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic, complemented
8#21461805C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461723C211yesmaximal, characteristic, complemented
11#21461688C211yesmaximal, characteristic, complemented
12#21461591C211yesmaximal, characteristic, complemented
13#21461506C211yesmaximal, characteristic, complemented
14#21461504C211yesmaximal, characteristic, complemented
15#552×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C22×D61⋊C8C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C2×#14519856C2211yescharacteristic
20#16840794—21no—
21#16840793—21no—
22#16840792—21no—
23#16840791—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29D61⋊(C22⋊C8)C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31#16840721C2211yescharacteristic
32#16840714—21no—
33#16840712—21no—
34#16840712—21no—
35#16840708C2211yescharacteristic
36#16840704C2211yescharacteristic
37#16840704C2211yescharacteristic
38C4⋊C4×#6923—21no—
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
75C2×#11758213—21no—
76D61⋊M16—22no—
77D61⋊M16—41no—
78C2×#11758217—21no—
79C2×D61⋊C8—22no—
80C2×D61⋊C8—21no—
81C2×D61⋊C8—41no—
82C2×D61⋊C8C2311yescharacteristic
83C2×D61⋊C8C2311yescharacteristic
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C22×#92420—21no—
87#14519856—22no—
88#14519856—22no—
89#14519856—41no—
90#14519856—41no—
91C2×C4⋊#6923—21no—
92C2×C4⋊#6923—21no—
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×C22⋊#6923—21no—
101C2×C4×#6923—21no—
102C2×C4×#6923—21no—
103C2×C4×#6923—21no—
104#14519844—21no—
105C4⋊#92420—21no—
106#14519840—22no—
107#14519840—22no—
108#14519840—41no—
109#14519840—41no—
110#14519834—21no—
111#14519834—21no—
112C22⋊#92420—21no—
113C22⋊#92420—21no—
114#14519832—21no—
115#14519832—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4—21no—
118(C2×#6923)⋊C4—21no—
119C2×Q8×D61C2311yescharacteristic
120C2×D4×D61D411yescharacteristic
121C22×C4×D61—21no—
122C22×C4×D61C2311yescharacteristic
123C22×C4×D61C2311yescharacteristic
124#14519772—21no—
125#14519772—21no—
126#14519772—21no—
127#14519771—21no—
128#14519770—21no—
129#14519770—21no—
130#14519770—21no—
131#14519769—21no—
132#14519769C2×C411yescharacteristic
133#14519768—21no—
134#14519768—21no—
135#14519768C2×C411yescharacteristic
136#14519768C2×C411yescharacteristic
137#14519767—21no—
138#14519767—21no—
139#14519767—21no—
140#14519767—21no—
141#14519767—21no—
142#14519767—21no—
143#14519762—21no—
144#14519762—21no—
145#14519761—21no—
146#14519760—21no—
147#14519759—21no—
148#14519759—21no—
149#14519758—21no—
150#14519757C2×C411yescharacteristic
151#14519757C2×C411yescharacteristic
152#14519756C2×C411yescharacteristic
153#14519756C2×C411yescharacteristic
154#14519755—21no—
155#14519755—21no—
156#14519754—21no—
157#14519754—21no—
158#14519753C2×C411yescharacteristic
159#14519753C2×C411yescharacteristic
160Q8×Dic61C2×C411yescharacteristic
161C4×Dic122—21no—
162C4×Dic122C2×C411yescharacteristic
163#14519742—21no—
164#14519742C2×C411yescharacteristic
165C4×D244C2×C411yescharacteristic
166D4×Dic61D411yescharacteristic
167#14519739D411yescharacteristic
168C4×C22⋊D61C2×C411yescharacteristic
169C4×C22⋊D61C2×C411yescharacteristic
170#14519737D411yescharacteristic
171#14519737D411yescharacteristic
172#14519736—21no—
173#14519736C2×C411yescharacteristic
174#14519735—21no—
175#14519735—21no—
176#14519735C2×C411yescharacteristic
177#14519735C2×C411yescharacteristic
178#14519734—21no—
179#14519734—21no—
180#14519734—21no—
181#14519733—21no—
182#14519733—21no—
183#14519733—21no—
184C2×C4⋊Dic61C2×C411yescharacteristic
185C2×#11758196—21no—
186C4⋊C4×D61—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×D61C2×C411yescharacteristic
194C4⋊C4×D61C2×C411yescharacteristic
195C4⋊C4×D61D411yescharacteristic
196C4⋊C4×D61C2311yescharacteristic
197C4⋊C4×D61C2311yescharacteristic
198C4⋊C4×D61C2311yescharacteristic
199C22⋊C4×D61—21no—
200C22⋊C4×D61—21no—
201C22⋊C4×D61—21no—
202C22⋊C4×D61D411yescharacteristic
203C22⋊C4×D61D411yescharacteristic
204C42×D61—21no—
205C42×D61—21no—
206C42×D61C2311yescharacteristic
207#126×C61—21no—
208#125×C61—21no—
209#125×C61C2×C411yescharacteristic
210#123×C61—21no—
211C22⋊Q8×C61C2×C411yescharacteristic
212C22⋊Q8×C61C2×C411yescharacteristic
213C4×Q8×C61C2×C411yescharacteristic
214C4×D4×C61C2×C411yescharacteristic
215#117×C61—21no—
216#117×C61C2×C411yescharacteristic
217C2×C4⋊C4×C61C2×C411yescharacteristic
218C23×D61C2×D411yescharacteristic
219C23×D61C2×D411yescharacteristic
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C2×Q8×C61C22×C411yescharacteristic
225C2×D4×C61C22⋊C411yescharacteristic
226C22×C4×C61—21no—
227C22×C4×C61C22×C411yescharacteristic
228C22×C4×C61C22×C411yescharacteristic
229C2×C22⋊D61C22⋊C411yescharacteristic
230C2×C22⋊D61C22⋊C411yescharacteristic
231C22×Dic61—21no—
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234Q8×D61—21no—
235Q8×D61—21no—
236Q8×D61—21no—
237Q8×D61—21no—
238D4×D61—41no—
239D4×D61—41no—
240C2×D244C22⋊C411yescharacteristic
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
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—42no—
256C2×C4×D61—42no—
257C2×C4×D61C22×C411yescharacteristic
258C2×C4×D61C22×C411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2411yescharacteristic
266C2×Dic122—21no—
267C2×Dic122C22×C411yescharacteristic
268C22⋊#6923—42no—
269C22⋊#6923—42no—
270C22⋊#6923—81no—
271C22⋊#6923—81no—
272#11758217—42no—
273C2×#92420—21no—
274C2×#92420—21no—
275C2×#92420—21no—
276C2×#92420—21no—
277C2×#92420—42no—
278C4⋊#6923—21no—
279C4⋊#6923—21no—
280C4⋊#6923—21no—
281C4⋊#6923—21no—
282C4⋊#6923—21no—
283C4⋊#6923—21no—
284C4⋊#6923—21no—
285C4⋊#6923—42no—
286C4⋊#6923—81no—
287C4⋊#6923#4112yes—
288C4×#6923—42no—
289C4×#6923—42no—
290C4×#6923—42no—
291#11758213—42no—
292D61⋊C8—21no—
293D61⋊C8—21no—
294D61⋊C8—21no—
295D61⋊C8—21no—
296D61⋊C8—21no—
297D61⋊C8—21no—
298D61⋊C8—21no—
299D61⋊C8—42no—
300D61⋊C8#4112yes—
301C4⋊C4×C61—21no—
302C4⋊C4×C61—21no—
303C4⋊C4×C61—21no—
304C4⋊C4×C61—21no—
305C4⋊C4×C61—21no—
306C4⋊C4×C61—21no—
307C4⋊C4×C61C22⋊C411yescharacteristic
308C4⋊C4×C61C22×C411yescharacteristic
309C4⋊C4×C61C22×C411yescharacteristic
310C4⋊C4×C61C22×C411yescharacteristic
311C22⋊C4×C61—21no—
312C22⋊C4×C61—21no—
313C22⋊C4×C61—21no—
314C22⋊C4×C61C22⋊C411yescharacteristic
315C22⋊C4×C61C22⋊C411yescharacteristic
316C42×C61—21no—
317C42×C61—21no—
318C42×C61C22×C411yescharacteristic
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321C22⋊Dic61—21no—
322C22⋊Dic61C22⋊C411yescharacteristic
323C22⋊Dic61C22⋊C411yescharacteristic
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198C22⋊C411yescharacteristic
331#11758198C22⋊C411yescharacteristic
332#11758198C22⋊C411yescharacteristic
333#11758198C22⋊C411yescharacteristic
334C4⋊Dic61—21no—
335C4⋊Dic61—21no—
336C4⋊Dic61—21no—
337C4⋊Dic61—21no—
338C4⋊Dic61—21no—
339C4⋊Dic61—21no—
340C4⋊Dic61C22⋊C411yescharacteristic
341C4⋊Dic61C22×C411yescharacteristic
342C4⋊Dic61C22×C411yescharacteristic
343C4⋊Dic61C22×C411yescharacteristic
344#11758196—21no—
345#11758196—21no—
346#11758196—21no—
347#11758196—21no—
348#11758196—21no—
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#11758196C22⋊C411yescharacteristic
360#11758196C22⋊C411yescharacteristic
361C4×Dic61—21no—
362C4×Dic61—21no—
363C4×Dic61—21no—
364C4×Dic61—21no—
365C4×Dic61—21no—
366C4×Dic61—21no—
367C4×Dic61C22×C411yescharacteristic
368C4×Dic61C2×D411yescharacteristic
369C4×Dic61C2×D411yescharacteristic
370C23×C61C2×C22⋊C411yescharacteristic
371C23×C61C2×C22⋊C411yescharacteristic
372C22×D61—21no—
373C22×D61—21no—
374C22×D61—21no—
375C22×D61—21no—
376C22×D61—21no—
377C22×D61—21no—
378C22×D61—21no—
379C22×D61—21no—
380C22×D61—21no—
381C22×D61—21no—
382C22×D61—21no—
383C22×D61—21no—
384C22×D61C2×C22⋊C411yescharacteristic
385C22×D61C2×C22⋊C411yescharacteristic
386C22×D61C22×D411yescharacteristic
387C2×#6923—22no—
388C2×#6923—41no—
389C2×#6923—41no—
390C2×#6923—41no—
391C2×#6923—41no—
392C2×#6923—41no—
393C2×#6923—41no—
394C2×#6923—41no—
395C2×#6923—41no—
396C2×#6923—41no—
397C2×#6923—41no—
398C2×#6923—41no—
399Q8×C61—21no—
400Q8×C61—21no—
401D4×C61—41no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—21no—
409C2×C4×C61—21no—
410C2×C4×C61—42no—
411C2×C4×C61C2×C22⋊C411yescharacteristic
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C23×C411yescharacteristic
416C22⋊D61—41no—
417C22⋊D61—41no—
418C2×Dic61—21no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—42no—
427C2×Dic61C2×C22⋊C411yescharacteristic
428C2×Dic61C2×C22⋊C411yescharacteristic
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C22×D411yescharacteristic
432D244—41no—
433C4×D61—21no—
434C4×D61—21no—
435C4×D61—21no—
436C4×D61—21no—
437C4×D61—21no—
438C4×D61—21no—
439C4×D61—21no—
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—42no—
450C4×D61—42no—
451C4×D61—41no—
452C4×D61—41no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61C2×#4111yescharacteristic
460C4×D61C2×#4111yescharacteristic
461C4×D61H(5,𝔽2)11yescharacteristic
462C4×D612−1+411yescharacteristic
463Dic122—21no—
464Dic122—21no—
465Dic122—41no—
466Dic122—41no—
467#92420—22no—
468#92420—41no—
469#92420—41no—
470#92420—41no—
471#22496—611nomaximal, Sylow
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61C22×C22⋊C411yescharacteristic
479C2×D61—21no—
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—41no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—41no—
489C2×D61—41no—
490C2×D61—41no—
491C2×D61—41no—
492C2×D61—41no—
493C2×D61#54611yescharacteristic
494C2×D61#54711yescharacteristic
495C2×D61#57511yescharacteristic
496C2×D61#57511yescharacteristic
497C2×D61#57711yescharacteristic
498C2×D61#57811yescharacteristic
499#6923—42no—
500#6923—81no—
501#6923—81no—
502#6923—81no—
503C4×C61—21no—
504C4×C61—21no—
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—41no—
508C4×C61—41no—
509C4×C61—41no—
510C4×C61—41no—
511C4×C61C4×#4111yescharacteristic
512C4×C61#52011yescharacteristic
513Dic61—21no—
514Dic61—21no—
515Dic61—21no—
516Dic61—21no—
517Dic61—41no—
518Dic61—41no—
519Dic61—41no—
520Dic61—41no—
521Dic61#54611yescharacteristic
522Dic61#54711yescharacteristic
523C2×#552—611no—
524C2×#435—611no—
525#2354—611no—
526#1992—611no—
527#1989—611no—
528#1894—611no—
529#1892—611no—
530#1873—611no—
531#1873—611no—
532#1825—611no—
533#1824—611no—
534#1803—611no—
535#1763—611no—
536#1736—611no—
537#1735—611no—
538C2×C61—41no—
539C2×C61—41no—
540C2×C61#233911yescharacteristic
541C2×C61#289611yescharacteristic
542C2×C61#289811yescharacteristic
543D61—41no—
544D61—41no—
545D61#331511yescharacteristic
546D61#331711yescharacteristic
547D61#334811yescharacteristic
548D61#334911yescharacteristic
549C22×M16—611no—
550C23×C8—611no—
551#552—611no—
552#552—611no—
553#552—611no—
554#552—611no—
555#552—611no—
556#552—611no—
557#552—611no—
558#552—1221no—
559#552—1221no—
560#552—1221no—
561#552—1221no—
562#552#692311yescharacteristic, complemented
563C2×#126—1221no—
564C2×#125—611no—
565C2×#125—1221no—
566C2×#123—1221no—
567C2×C22⋊Q8—611no—
568C2×C22⋊Q8—611no—
569C2×C4×Q8—611no—
570C2×C4×D4—611no—
571C2×#117—611no—
572C2×#117—611no—
573C2×#117—611no—
574C2×#117—1221no—
575C22×C4⋊C4—611no—
576#435—1221no—
577#435—1221no—
578#435—1221no—
579#435—1221no—
580C2×C4⋊C8—611no—
581C2×#103—611no—
582C2×#103—611no—
583C2×#103—611no—
584C2×#103—611no—
585C2×C22⋊C8—611no—
586C2×C22⋊C8—611no—
587C2×#97—611no—
588#390—1221no—
589#388—1221no—
590#388—1221no—
591#384—611no—
592#380—611no—
593#380—611no—
594C4×C4⋊C4—611no—
595C4×C4⋊C4—1221no—
596#340—611no—
597#340—611no—
598#340—611no—
599#340—611no—
600#340—611no—
601#340—611no—
602#340—611no—
603#340—611no—
604#340—611no—
605#340—611no—
606#340—611no—
607#340—611no—
608C61#2249611yescharacteristic, complemented, Sylow
609C22×Q8—611no—
610C22×D4—611no—
611C23×C4—611no—
612C23×C4—611no—
613C23×C4—1221no—
614C2×M16—1222no—
615C2×M16—1221no—
616C2×M16—1221no—
617C2×M16—2441no—
618C22×C8—611no—
619C22×C8—611no—
620C22×C8—611no—
621C22×C8—611no—
622C22×C8—1222no—
623C22×C8—1221no—
624C22×C8—1221no—
625C22×C8—2441no—
626#126—21no—
627#126—1221no—
628#126—1221no—
629#126—1221no—
630#126—1221no—
631#126—1221no—
632#126—1221no—
633#126—1221no—
634#125—21no—
635#125—611no—
636#125—611no—
637#125—611no—
638#125—1221no—
639#125—1221no—
640#125—1221no—
641#125—1221no—
642#125—1221no—
643#125—1221no—
644#125—1221no—
645#125—1221no—
646#125—1221no—
647#125C2×#692311yescharacteristic
648#123—21no—
649#123—1221no—
650#123—1221no—
651#123—1221no—
652#123—1221no—
653#123—1221no—
654#123—1221no—
655#123—1221no—
656C22⋊Q8—611no—
657C22⋊Q8—611no—
658C22⋊Q8—611no—
659C22⋊Q8—611no—
660C22⋊Q8—611no—
661C22⋊Q8—611no—
662C22⋊Q8—1221no—
663C22⋊Q8—1221no—
664C22⋊Q8—1221no—
665C22⋊Q8—1221no—
666C22⋊Q8C2×#692311yescharacteristic
667C22⋊Q8C2×#692311yescharacteristic
668C4×Q8—611no—
669C4×Q8—611no—
670C4×Q8—611no—
671C4×Q8—1221no—
672C4×Q8—1221no—
673C4×Q8C2×#692311yescharacteristic
674C4×D4—611no—
675C4×D4—611no—
676C4×D4—611no—
677C4×D4—611no—
678C4×D4—611no—
679C4×D4—611no—
680C4×D4—611no—
681C4×D4C2×#692311yescharacteristic
682#117—21no—
683#117—611no—
684#117—611no—
685#117—611no—
686#117—1221no—
687#117—1221no—
688#117—1221no—
689#117—1221no—
690#117—1221no—
691#117—1221no—
692#117—1221no—
693#117—1221no—
694#117—1221no—
695#117—1222no—
696#117—1222no—
697#117—2441no—
698#117—2441no—
699#117C2×#692311yescharacteristic
700C2×C4⋊C4—611no—
701C2×C4⋊C4—611no—
702C2×C4⋊C4—611no—
703C2×C4⋊C4—611no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—611no—
706C2×C4⋊C4—611no—
707C2×C4⋊C4—611no—
708C2×C4⋊C4—611no—
709C2×C4⋊C4—611no—
710C2×C4⋊C4—611no—
711C2×C4⋊C4—1221no—
712C2×C4⋊C4—1221no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4—1221no—
716C2×C4⋊C4—1221no—
717C2×C4⋊C4—1221no—
718C2×C4⋊C4—1221no—
719C2×C4⋊C4—1221no—
720C2×C4⋊C4—1221no—
721C2×C4⋊C4C2×#692311yescharacteristic
722C2×C22⋊C4—611no—
723C2×C22⋊C4—611no—
724C2×C22⋊C4—1221no—
725C2×C22⋊C4—1221no—
726C2×C22⋊C4—1221no—
727C2×C22⋊C4—1221no—
728C2×C22⋊C4—1221no—
729C2×C22⋊C4—1221no—
730C2×C22⋊C4—1221no—
731C2×C42—611no—
732C2×C42—1221no—
733C2×C42—1221no—
734C2×C42—1221no—
735C2×C42—1221no—
736C2×C42—1221no—
737C4⋊C8—1221no—
738C4⋊C8—1221no—
739#103—1222no—
740#103—1222no—
741#103—2441no—
742#103—2441no—
743C22⋊C8—1221no—
744C22⋊C8—1221no—
745C22⋊C8—1221no—
746C22⋊C8—1221no—
747#97—1221no—
748#97—1221no—
749#95—1221no—
750#95—1221no—
751#95—1221no—
752C24—611no—
753C24—611no—
754C2×Q8—611no—
755C2×Q8—1221no—
756C2×Q8—1221no—
757C2×Q8—1221no—
758C2×Q8—1221no—
759C2×Q8—1221no—
760C2×Q8C22×#692311yescharacteristic
761C2×D4—611no—
762C2×D4—611no—
763C2×D4—611no—
764C2×D4—2441no—
765C2×D4—2441no—
766C2×D4C22⋊#692311yescharacteristic
767C22×C4—21no—
768C22×C4—611no—
769C22×C4—611no—
770C22×C4—611no—
771C22×C4—611no—
772C22×C4—611no—
773C22×C4—611no—
774C22×C4—611no—
775C22×C4—611no—
776C22×C4—611no—
777C22×C4—611no—
778C22×C4—611no—
779C22×C4—1221no—
780C22×C4—1221no—
781C22×C4—1221no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4—1221no—
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—2442no—
799C22×C4—2442no—
800C22×C4C22×#692311yescharacteristic
801C22×C4C22×#692311yescharacteristic
802M16—2442no—
803M16—2442no—
804C2×C8—612no—
805C2×C8—1221no—
806C2×C8—1221no—
807C2×C8—1221no—
808C2×C8—1221no—
809C2×C8—1221no—
810C2×C8—1221no—
811C2×C8—1221no—
812C2×C8—1221no—
813C2×C8—1221no—
814C2×C8—1221no—
815C2×C8—1221no—
816C2×C8—2442no—
817C2×C8—2442no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—611no—
825C4⋊C4—611no—
826C4⋊C4—611no—
827C4⋊C4—612no—
828C4⋊C4—611no—
829C4⋊C4—611no—
830C4⋊C4—611no—
831C4⋊C4—1221no—
832C4⋊C4—1221no—
833C4⋊C4—1221no—
834C4⋊C4—1221no—
835C4⋊C4—1221no—
836C4⋊C4—1221no—
837C4⋊C4—1221no—
838C4⋊C4—1221no—
839C4⋊C4—1221no—
840C4⋊C4—1221no—
841C4⋊C4—1221no—
842C4⋊C4—1221no—
843C4⋊C4—1221no—
844C4⋊C4—1221no—
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—4881no—
860C4⋊C4—2442no—
861C4⋊C4C22⋊#692311yescharacteristic
862C4⋊C4C22×#692311yescharacteristic
863C4⋊C4C22×#692311yescharacteristic
864C4⋊C4C22×#692311yescharacteristic
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—611no—
869C22⋊C4—611no—
870C22⋊C4—611no—
871C22⋊C4—611no—
872C22⋊C4—611no—
873C22⋊C4—611no—
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—4881no—
884C22⋊C4—4881no—
885C22⋊C4—2442no—
886C22⋊C4—2442no—
887C22⋊C4C22⋊#692311yescharacteristic
888C22⋊C4C22⋊#692311yescharacteristic
889C42—21no—
890C42—21no—
891C42—611no—
892C42—611no—
893C42—611no—
894C42—1221no—
895C42—1221no—
896C42—1221no—
897C42—1221no—
898C42—1221no—
899C42—1221no—
900C42—2442no—
901C42—2442no—
902C42—2442no—
903C42C22×#692311yescharacteristic
904C23—611no—
905C23—611no—
906C23—611no—
907C23—1221no—
908C23—1221no—
909C23—1221no—
910C23—1221no—
911C23—1221no—
912C23—1221no—
913C23—1221no—
914C23—1221no—
915C23—1221no—
916C23—1221no—
917C23—1221no—
918C23—1221no—
919C23C2×C22⋊#692311yescharacteristic
920C23C2×C22⋊#692311yescharacteristic
921Q8—21no—
922Q8—21no—
923Q8—1221no—
924Q8—1221no—
925Q8—2441no—
926Q8—2441no—
927D4—41no—
928D4—2441no—
929D4—2441no—
930D4—2441no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—42no—
940C2×C4—611no—
941C2×C4—611no—
942C2×C4—611no—
943C2×C4—611no—
944C2×C4—611no—
945C2×C4—611no—
946C2×C4—611no—
947C2×C4—611no—
948C2×C4—611no—
949C2×C4—1221no—
950C2×C4—1221no—
951C2×C4—1221no—
952C2×C4—1221no—
953C2×C4—1221no—
954C2×C4—1221no—
955C2×C4—1221no—
956C2×C4—1221no—
957C2×C4—1221no—
958C2×C4—1221no—
959C2×C4—1221no—
960C2×C4—1221no—
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—1222no—
970C2×C4—1221no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—2441no—
975C2×C4—2441no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2442no—
983C2×C4—2442no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2442no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4C2×C22⋊#692311yescharacteristic
997C2×C4C2×C22⋊#692311yescharacteristic
998C2×C4C2×C22⋊#692311yescharacteristic
999C2×C4C2×C22⋊#692311yescharacteristic
1000C2×C4C23×#692311yescharacteristic
1001C8—1222no—
1002C8—2441no—
1003C8—2441no—
1004C8—2441no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—611no—
1012C22—611no—
1013C22—611no—
1014C22—611no—
1015C22—611no—
1016C22—611no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—2441no—
1024C22—2441no—
1025C22—2441no—
1026C22—2441no—
1027C22—2441no—
1028C22—2441no—
1029C22—2441no—
1030C22—2441no—
1031C22C22×C22⋊#692311yescharacteristic
1032C4—21no—
1033C4—21no—
1034C4—21no—
1035C4—21no—
1036C4—41no—
1037C4—41no—
1038C4—41no—
1039C4—41no—
1040C4—611no—
1041C4—611no—
1042C4—1221no—
1043C4—1221no—
1044C4—1221no—
1045C4—1221no—
1046C4—4881no—
1047C4—4881no—
1048C4—4881no—
1049C4—2442no—
1050C4—2441no—
1051C4—2441no—
1052C4—2441no—
1053C4—2441no—
1054C4#41×#692311yescharacteristic
1055C4#1684083111yescharacteristic
1056C2—41no—
1057C2—41no—
1058C2—611no—
1059C2—611no—
1060C2—611no—
1061C2—611no—
1062C2—2441no—
1063C2—2441no—
1064C2#2146232211yescharacteristic
1065C2#2146243911yescharacteristic
1066C2#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#22496
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. #21461805C2semidirect
8. #21461805C2semidirect
9. #21461724C2semidirect
10. #21461723C2semidirect
11. #21461688C2semidirect
12. #21461591C2semidirect
13. #21461506C2semidirect
14. #21461504C2semidirect
52. #16840454C4semidirect
53. #16840453C4semidirect
54. #16840452C4semidirect
55. #16840451C4semidirect
56. #16840450C4semidirect
59. #16840447C4semidirect
60. #16840446C4semidirect
74. C61×#552C4semidirect
562. #552#6923semidirect
608. C61#22496semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4352
#214623372
#214620022
#214619992
#214618342
#214618322
#214618052
#214617242
#214617232
#214616882
#214615912
#214615062
#214615042
#552×D612
#2249661