Finite Group Databasebeta

← #30620365

Subgroups — #30620365

Order 15616.

1130 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#436C211yesmaximal, characteristic
2#21462335C211yesmaximal, characteristic
3#21462001C211yesmaximal, characteristic, complemented
4#21461999C211yesmaximal, characteristic, complemented
5#21461834C211yesmaximal, characteristic, complemented
6#21461834C211yesmaximal, characteristic, complemented
7#21461805C211yesmaximal, characteristic, complemented
8#21461804C211yesmaximal, characteristic, complemented
9#21461724C211yesmaximal, characteristic, complemented
10#21461723C211yesmaximal, characteristic, complemented
11#21461690C211yesmaximal, characteristic, complemented
12C4×#14519840C211yesmaximal, characteristic, complemented
13#21461508C211yesmaximal, characteristic, complemented
14#21461506C211yesmaximal, characteristic, complemented
15#552×D61C211yesmaximal, characteristic
16C2×D61⋊M16C2211yescharacteristic
17C2×D61⋊M16C2211yescharacteristic
18C2×#14519856C2211yescharacteristic
19C22×C4⋊#6923C2211yescharacteristic
20#16840797—21no—
21#16840796—21no—
22#16840795—21no—
23#16840795—21no—
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519840C2211yescharacteristic
26C2×#14519840C2211yescharacteristic
27C2×#14519840C2211yescharacteristic
28C2×#14519840C2211yescharacteristic
29D61⋊(C22⋊C8)C2211yescharacteristic
30D61⋊(C22⋊C8)C2211yescharacteristic
31C4×D61⋊C8C2211yescharacteristic
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
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—
76C2×#11758213—21no—
77C2×#11758213—21no—
78D61⋊M16—22no—
79D61⋊M16—22no—
80D61⋊M16—41no—
81D61⋊M16—41no—
82C2×#11758217—21no—
83C2×#11758217—21no—
84C2×D61⋊C8C2311yescharacteristic
85C2×D61⋊C8C2311yescharacteristic
86C2×D61⋊C8C2311yescharacteristic
87C2×D61⋊C8C2311yescharacteristic
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#14519840—22no—
105#14519840—22no—
106#14519840—41no—
107#14519840—41no—
108#14519834—21no—
109#14519834—21no—
110C22⋊#92420—21no—
111C22⋊#92420—21no—
112C4×#92420—21no—
113C4×#92420—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×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, complemented
133#14519768—21no—
134#14519768—21no—
135#14519768C2×C411yescharacteristic, complemented
136#14519768C2×C411yescharacteristic, complemented
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, complemented
152#14519756C2×C411yescharacteristic
153#14519756C2×C411yescharacteristic, complemented
154#14519755—21no—
155#14519755—21no—
156#14519754—21no—
157#14519754—21no—
158#14519753C2×C411yescharacteristic
159#14519753C2×C411yescharacteristic, complemented
160Q8×Dic61C2×C411yescharacteristic, complemented
161C4×Dic122—21no—
162C4×Dic122C2×C411yescharacteristic, complemented
163#14519742—21no—
164#14519742C2×C411yescharacteristic, complemented
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, complemented
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, complemented
194C4⋊C4×D61C2×C411yescharacteristic, complemented
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, complemented
210#123×C61—21no—
211C22⋊Q8×C61C2×C411yescharacteristic
212C22⋊Q8×C61C2×C411yescharacteristic, complemented
213C4×Q8×C61C2×C411yescharacteristic, complemented
214C4×D4×C61C2×C411yescharacteristic
215#117×C61—21no—
216#117×C61C2×C411yescharacteristic
217C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
218C23×D61C2×D411yescharacteristic
219C23×D61C2×D411yescharacteristic
220C22×#6923—21no—
221C22×#6923—21no—
222C22×#6923—21no—
223C22×#6923—21no—
224C22×#6923—42no—
225C22×#6923—42no—
226C22×#6923—81no—
227C2×Q8×C61C22×C411yescharacteristic
228C2×D4×C61C22⋊C411yescharacteristic
229C22×C4×C61—21no—
230C22×C4×C61C22×C411yescharacteristic
231C22×C4×C61C22×C411yescharacteristic
232C2×C22⋊D61C22⋊C411yescharacteristic
233C2×C22⋊D61C22⋊C411yescharacteristic
234C22×Dic61—21no—
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237Q8×D61—21no—
238Q8×D61—21no—
239Q8×D61—21no—
240Q8×D61—21no—
241D4×D61—41no—
242D4×D61—41no—
243C2×D244C22⋊C411yescharacteristic
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—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×C4×D61—42no—
259C2×C4×D61—42no—
260C2×C4×D61C22×C411yescharacteristic
261C2×C4×D61C22×C411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×C4×D61C2×D411yescharacteristic
267C2×C4×D61C2×D411yescharacteristic
268C2×C4×D61C2411yescharacteristic
269C2×Dic122—21no—
270C2×Dic122C22×C411yescharacteristic
271C22⋊#6923—42no—
272C22⋊#6923—42no—
273C22⋊#6923—81no—
274#11758217—42no—
275#11758217—42no—
276C2×#92420—21no—
277C2×#92420—21no—
278C2×#92420—21no—
279C2×#92420—21no—
280C4⋊#6923—21no—
281C4⋊#6923—21no—
282C4⋊#6923—21no—
283C4⋊#6923—21no—
284C4⋊#6923—21no—
285C4⋊#6923—21no—
286C4⋊#6923—21no—
287C4⋊#6923—42no—
288C4⋊#6923#4112yes—
289C4×#6923—42no—
290C4×#6923—81no—
291#11758213—42no—
292#11758213—42no—
293D61⋊C8—21no—
294D61⋊C8—21no—
295D61⋊C8—21no—
296D61⋊C8—21no—
297D61⋊C8—21no—
298D61⋊C8—21no—
299D61⋊C8—21no—
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—
399C2×#6923—84no—
400Q8×C61—21no—
401Q8×C61—21no—
402D4×C61—41no—
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—21no—
411C2×C4×C61—42no—
412C2×C4×C61C2×C22⋊C411yescharacteristic
413C2×C4×C61C2×C22⋊C411yescharacteristic
414C2×C4×C61C2×C22⋊C411yescharacteristic
415C2×C4×C61C2×C22⋊C411yescharacteristic
416C2×C4×C61C23×C411yescharacteristic
417C22⋊D61—41no—
418C22⋊D61—41no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—21no—
423C2×Dic61—21no—
424C2×Dic61—21no—
425C2×Dic61—21no—
426C2×Dic61—21no—
427C2×Dic61—42no—
428C2×Dic61C2×C22⋊C411yescharacteristic
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C22×D411yescharacteristic
433D244—41no—
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—21no—
450C4×D61—42no—
451C4×D61—42no—
452C4×D61—41no—
453C4×D61—41no—
454C4×D61—41no—
455C4×D61—41no—
456C4×D61—41no—
457C4×D61—41no—
458C4×D61—41no—
459C4×D61—41no—
460C4×D61C2×#4111yescharacteristic
461C4×D61C2×#4111yescharacteristic
462C4×D61H(5,𝔽2)11yescharacteristic
463C4×D612−1+411yescharacteristic
464Dic122—21no—
465Dic122—21no—
466Dic122—41no—
467Dic122—41no—
468#92420—22no—
469#92420—41no—
470#92420—41no—
471#92420—41no—
472#22499—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61C22×C22⋊C411yescharacteristic
480C2×D61—21no—
481C2×D61—21no—
482C2×D61—21no—
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—21no—
486C2×D61—41no—
487C2×D61—41no—
488C2×D61—41no—
489C2×D61—41no—
490C2×D61—41no—
491C2×D61—41no—
492C2×D61—41no—
493C2×D61—41no—
494C2×D61#54611yescharacteristic
495C2×D61#54711yescharacteristic
496C2×D61#57511yescharacteristic
497C2×D61#57511yescharacteristic
498C2×D61#57711yescharacteristic
499C2×D61#57811yescharacteristic
500#6923—42no—
501#6923—81no—
502#6923—81no—
503#6923—81no—
504C4×C61—21no—
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—21no—
508C4×C61—41no—
509C4×C61—41no—
510C4×C61—41no—
511C4×C61—41no—
512C4×C61C4×#4111yescharacteristic
513C4×C61#52011yescharacteristic
514Dic61—21no—
515Dic61—21no—
516Dic61—21no—
517Dic61—21no—
518Dic61—41no—
519Dic61—41no—
520Dic61—41no—
521Dic61—41no—
522Dic61#54611yescharacteristic
523Dic61#54711yescharacteristic
524C2×#552—611no—
525C2×#436—611no—
526#2352—611no—
527#1991—611no—
528#1989—611no—
529#1894—611no—
530#1894—611no—
531#1873—611no—
532#1872—611no—
533#1825—611no—
534#1824—611no—
535#1805—611no—
536C4×#103—611no—
537#1736—611no—
538#1736—611no—
539C2×C61—41no—
540C2×C61—41no—
541C2×C61#233911yescharacteristic
542C2×C61#289611yescharacteristic
543C2×C61#289811yescharacteristic
544D61—41no—
545D61—41no—
546D61#332311yescharacteristic
547D61#332711yescharacteristic
548D61#335111yescharacteristic
549D61#335211yescharacteristic
550C22×M16—611no—
551C22×M16—611no—
552#552—611no—
553#552—611no—
554#552—611no—
555#552—611no—
556#552—611no—
557#552—611no—
558#552—611no—
559#552—1221no—
560#552—1221no—
561#552—1221no—
562#552—1221no—
563#552#692311yescharacteristic, complemented
564C2×#126—1221no—
565C2×#125—611no—
566C2×#125—1221no—
567C2×#123—1221no—
568C2×C22⋊Q8—611no—
569C2×C22⋊Q8—611no—
570C2×C4×Q8—611no—
571C2×C4×D4—611no—
572C2×#117—611no—
573C2×#117—611no—
574C2×#117—1221no—
575C22×C4⋊C4—611no—
576C22×C4⋊C4—611no—
577#436—1221no—
578#436—1221no—
579#436—1221no—
580#436—1221no—
581C2×C4⋊C8—611no—
582C2×#103—611no—
583C2×#103—611no—
584C2×#103—611no—
585C2×#103—611no—
586C2×C22⋊C8—611no—
587C2×C22⋊C8—611no—
588C2×C4×C8—611no—
589#388—1221no—
590#387—1221no—
591#386—1221no—
592#382—611no—
593#380—611no—
594#380—611no—
595C4×C4⋊C4—611no—
596C4×C22⋊C4—1221no—
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—
608#340—611no—
609C61#2249911yescharacteristic, complemented, Sylow
610C22×Q8—611no—
611C22×D4—611no—
612C23×C4—611no—
613C23×C4—611no—
614C23×C4—1221no—
615C23×C4—1221no—
616C2×M16—1222no—
617C2×M16—1222no—
618C2×M16—1221no—
619C2×M16—1221no—
620C2×M16—1221no—
621C2×M16—1221no—
622C2×M16—2441no—
623C2×M16—2441no—
624C22×C8—611no—
625C22×C8—611no—
626C22×C8—611no—
627C22×C8—611no—
628#126—21no—
629#126—1221no—
630#126—1221no—
631#126—1221no—
632#126—1221no—
633#126—1221no—
634#126—1221no—
635#126—1221no—
636#125—21no—
637#125—611no—
638#125—611no—
639#125—611no—
640#125—1221no—
641#125—1221no—
642#125—1221no—
643#125—1221no—
644#125—1221no—
645#125—1221no—
646#125—1221no—
647#125—1221no—
648#125—1221no—
649#125C2×#692311yescharacteristic, complemented
650#123—21no—
651#123—1221no—
652#123—1221no—
653#123—1221no—
654#123—1221no—
655#123—1221no—
656#123—1221no—
657#123—1221no—
658C22⋊Q8—611no—
659C22⋊Q8—611no—
660C22⋊Q8—611no—
661C22⋊Q8—611no—
662C22⋊Q8—611no—
663C22⋊Q8—611no—
664C22⋊Q8—1221no—
665C22⋊Q8—1221no—
666C22⋊Q8—1221no—
667C22⋊Q8—1221no—
668C22⋊Q8C2×#692311yescharacteristic
669C22⋊Q8C2×#692311yescharacteristic, complemented
670C4×Q8—611no—
671C4×Q8—611no—
672C4×Q8—611no—
673C4×Q8—1221no—
674C4×Q8—1221no—
675C4×Q8C2×#692311yescharacteristic, complemented
676C4×D4—611no—
677C4×D4—611no—
678C4×D4—611no—
679C4×D4—611no—
680C4×D4—611no—
681C4×D4—611no—
682C4×D4—611no—
683C4×D4C2×#692311yescharacteristic
684#117—21no—
685#117—611no—
686#117—611no—
687#117—611no—
688#117—1221no—
689#117—1221no—
690#117—1221no—
691#117—1221no—
692#117—1221no—
693#117—1221no—
694#117—1221no—
695#117—1221no—
696#117—1221no—
697#117—1222no—
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—1222no—
719C2×C4⋊C4—1221no—
720C2×C4⋊C4—1221no—
721C2×C4⋊C4—2441no—
722C2×C4⋊C4C2×#692311yescharacteristic, complemented
723C2×C22⋊C4—611no—
724C2×C22⋊C4—611no—
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—
736C4⋊C8—1221no—
737C4⋊C8—1221no—
738#103—1222no—
739#103—1222no—
740#103—2441no—
741#103—2441no—
742C22⋊C8—1221no—
743C22⋊C8—1221no—
744C22⋊C8—1221no—
745C22⋊C8—1221no—
746C4×C8—1221no—
747C4×C8—1221no—
748#95—1221no—
749#95—1221no—
750#95—1221no—
751#95—1221no—
752#95—1221no—
753C24—611no—
754C24—611no—
755C2×Q8—611no—
756C2×Q8—1221no—
757C2×Q8—1221no—
758C2×Q8—1221no—
759C2×Q8—1221no—
760C2×Q8—1221no—
761C2×Q8C22×#692311yescharacteristic
762C2×D4—611no—
763C2×D4—611no—
764C2×D4—611no—
765C2×D4—2441no—
766C2×D4—2441no—
767C2×D4C22⋊#692311yescharacteristic
768C22×C4—21no—
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—611no—
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—1221no—
799C22×C4—4881no—
800C22×C4—2442no—
801C22×C4—2442no—
802C22×C4—2442no—
803C22×C4—2442no—
804C22×C4C22×#692311yescharacteristic
805C22×C4C22×#692311yescharacteristic
806M16—2442no—
807M16—2442no—
808M16—2442no—
809M16—2442no—
810C2×C8—612no—
811C2×C8—1221no—
812C2×C8—1221no—
813C2×C8—1221no—
814C2×C8—1221no—
815C2×C8—1221no—
816C2×C8—1221no—
817C2×C8—1221no—
818C2×C8—1221no—
819C2×C8—1221no—
820C2×C8—1221no—
821C2×C8—1221no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—611no—
829C4⋊C4—611no—
830C4⋊C4—611no—
831C4⋊C4—612no—
832C4⋊C4—611no—
833C4⋊C4—611no—
834C4⋊C4—611no—
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—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—2442no—
864C4⋊C4C22⋊#692311yescharacteristic
865C4⋊C4C22×#692311yescharacteristic
866C4⋊C4C22×#692311yescharacteristic
867C4⋊C4C22×#692311yescharacteristic
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—611no—
872C22⋊C4—611no—
873C22⋊C4—611no—
874C22⋊C4—611no—
875C22⋊C4—611no—
876C22⋊C4—611no—
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—4881no—
887C22⋊C4—2442no—
888C22⋊C4—2442no—
889C22⋊C4C22⋊#692311yescharacteristic
890C22⋊C4C22⋊#692311yescharacteristic
891C42—21no—
892C42—21no—
893C42—611no—
894C42—611no—
895C42—611no—
896C42—1221no—
897C42—1221no—
898C42—1221no—
899C42—1221no—
900C42—1221no—
901C42—1221no—
902C42—4881no—
903C42—2442no—
904C42C22×#692311yescharacteristic
905C23—611no—
906C23—611no—
907C23—611no—
908C23—1221no—
909C23—1221no—
910C23—1221no—
911C23—1221no—
912C23—1221no—
913C23—1221no—
914C23—1221no—
915C23—1221no—
916C23—1221no—
917C23—1221no—
918C23—1221no—
919C23—1221no—
920C23C2×C22⋊#692311yescharacteristic
921C23C2×C22⋊#692311yescharacteristic
922Q8—21no—
923Q8—21no—
924Q8—1221no—
925Q8—1221no—
926Q8—2441no—
927Q8—2441no—
928D4—41no—
929D4—2441no—
930D4—2441no—
931D4—2441no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—42no—
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—611no—
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—1221no—
970C2×C4—1222no—
971C2×C4—1221no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—4884no—
976C2×C4—2441no—
977C2×C4—2441no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2442no—
985C2×C4—2442no—
986C2×C4—2441no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2442no—
996C2×C4—2441no—
997C2×C4—2441no—
998C2×C4C2×C22⋊#692311yescharacteristic
999C2×C4C2×C22⋊#692311yescharacteristic
1000C2×C4C2×C22⋊#692311yescharacteristic
1001C2×C4C2×C22⋊#692311yescharacteristic
1002C2×C4C23×#692311yescharacteristic
1003C8—1222no—
1004C8—2441no—
1005C8—2441no—
1006C8—2441no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—611no—
1014C22—611no—
1015C22—611no—
1016C22—611no—
1017C22—611no—
1018C22—611no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—1221no—
1024C22—1221no—
1025C22—2441no—
1026C22—2441no—
1027C22—2441no—
1028C22—2441no—
1029C22—2441no—
1030C22—2441no—
1031C22—2441no—
1032C22—2441no—
1033C22C22×C22⋊#692311yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—41no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—611no—
1043C4—611no—
1044C4—1221no—
1045C4—1221no—
1046C4—1221no—
1047C4—1221no—
1048C4—4881no—
1049C4—4881no—
1050C4—4881no—
1051C4—2442no—
1052C4—2441no—
1053C4—2441no—
1054C4—2441no—
1055C4—2441no—
1056C4#41×#692311yescharacteristic
1057C4#1684083111yescharacteristic
1058C2—41no—
1059C2—41no—
1060C2—611no—
1061C2—611no—
1062C2—611no—
1063C2—611no—
1064C2—2441no—
1065C2—2441no—
1066C2#2146232211yescharacteristic
1067C2#2146243911yescharacteristic
1068C2#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#22499
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. #21462001C2semidirect
4. #21461999C2semidirect
5. #21461834C2semidirect
6. #21461834C2semidirect
7. #21461805C2semidirect
8. #21461804C2semidirect
9. #21461724C2semidirect
10. #21461723C2semidirect
11. #21461690C2semidirect
12. C4×#14519840C2semidirect
13. #21461508C2semidirect
14. #21461506C2semidirect
52. #16840454C4semidirect
53. #16840453C4semidirect
54. #16840452C4semidirect
55. #16840451C4semidirect
56. #16840450C4semidirect
59. #16840447C4semidirect
60. #16840446C4semidirect
74. C61×#552C4semidirect
132. #14519769C2×C4semidirect
135. #14519768C2×C4semidirect
136. #14519768C2×C4semidirect
151. #14519757C2×C4semidirect
153. #14519756C2×C4semidirect
159. #14519753C2×C4semidirect
160. Q8×Dic61C2×C4semidirect
162. C4×Dic122C2×C4semidirect
164. #14519742C2×C4semidirect
184. C2×C4⋊Dic61C2×C4semidirect
193. C4⋊C4×D61C2×C4semidirect
194. C4⋊C4×D61C2×C4semidirect
209. #125×C61C2×C4semidirect
212. C22⋊Q8×C61C2×C4semidirect
213. C4×Q8×C61C2×C4semidirect
217. C2×C4⋊C4×C61C2×C4semidirect
563. #552#6923semidirect
609. C61#22499semidirect
649. #125C2×#6923semidirect
669. C22⋊Q8C2×#6923semidirect
675. C4×Q8C2×#6923semidirect
722. 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⋊#4362
#214623352
#214620012
#214619992
#214618342
#214618052
#214618042
#214617242
#214617232
#214616902
C4×#145198402
#214615082
#214615062
#552×D612
#2249961