Finite Group Databasebeta

← C61×#61798 #29565231

Subgroups — C61×#61798 #29565231

Order 15616.

1674 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3550C211yesmaximal, characteristic, complemented
2C61×#3512C211yesmaximal, characteristic
3C61×#3350C214yesmaximal, complemented
4C61×#3349C214yesmaximal, complemented
5C61×#3320C214yesmaximal, complemented
6C61×#3312C214yesmaximal, complemented
7C61×#3236C212yesmaximal, complemented
8C61×#3201C214yesmaximal, complemented
9C61×#3116C212yesmaximal, complemented
10C61×#3097C214yesmaximal, complemented
11C61×#2980C211yesmaximal, characteristic, complemented
12C61×#563—22no—
13C61×#559—21no—
14Q82×C61—21no—
15C61×#556C2214yes—
16C61×#553—24no—
17C61×#553C2214yes—
18C61×#552C2214yes—
19D4×Q8×C61C2214yes—
20C61×#542—24no—
21C61×#541—21no—
22C61×#540—21no—
23C61×#537C2212yes—
24C61×#536C2214yes—
25C61×#533C2212yes—
26C61×#532C2211yescharacteristic
27C61×#529—22no—
28C2×#125×C61C2211yescharacteristic
29C61×#520C2212yes—
30C4×#41×C61C2211yescharacteristic
31C61×#501C2214yes—
32C61×#491C2214yes—
33C61×#485C2214yes—
34C61×#485C2214yes—
35C61×#485C2214yes—
36C61×#485C2214yes—
37C61×#484C2214yes—
38C61×#484C2214yes—
39C61×#483C2214yes—
40C61×#483C2214yes—
41C61×#482C2214yes—
42C61×#479C2214yes—
43C61×#479C2214yes—
44C61×#477C2212yes—
45C61×#476C2212yes—
46C61×#470C2214yes—
47C61×#468C2214yes—
48C61×#467C2214yes—
49C61×#465C2214yes—
50C61×#462C2212yes—
51C61×#461C2212yes—
52C61×#452C2214yes—
53C61×#451C2214yes—
54C61×#448C2214yes—
55C61×#441C2214yes—
56C61×#440C2214yes—
57C61×#435C2214yes—
58C61×#435C2214yes—
59C61×#432C2212yes—
60C61×#428C2214yes—
61C61×#427C2214yes—
62C61×#419C2214yes—
63C2×#103×C61C2214yes—
64C61×#408C2214yes—
65C2×#41×C61C2311yescharacteristic
66C2×#41×C61C2312yes—
67C22×Q8×C61C2314yes—
68C2×Q16×C61C2314yes—
69C2×SD16×C61C2314yes—
70C2×M16×C61C2314yes—
71C22×C8×C61C2314yes—
72C4⋊Q8×C61—24no—
73C4⋊Q8×C61—24no—
74C4⋊Q8×C61D411yescharacteristic
75C4⋊Q8×C61C2312yes—
76C4⋊Q8×C61C2312yes—
77#127×C61D411yescharacteristic
78#126×C61—24no—
79#126×C61—24no—
80#126×C61—24no—
81#126×C61—24no—
82#125×C61—24no—
83#125×C61—22no—
84#125×C61—21no—
85#125×C61—21no—
86#125×C61C2314yes—
87#124×C61—24no—
88#124×C61—24no—
89#124×C61D412yes—
90#123×C61—24no—
91#123×C61—24no—
92#123×C61—24no—
93#123×C61—24no—
94C22⋊Q8×C61—22no—
95C22⋊Q8×C61—22no—
96C22⋊Q8×C61—24no—
97C22⋊Q8×C61—24no—
98C22⋊Q8×C61C2314yes—
99C22⋊Q8×C61C2314yes—
100C22⋊Q8×C61C2314yes—
101C22⋊Q8×C61C2314yes—
102#121×C61—22no—
103#121×C61—24no—
104#121×C61—24no—
105#121×C61D414yes—
106#121×C61C2314yes—
107C4×Q8×C61—22no—
108C4×Q8×C61—24no—
109C4×Q8×C61—22no—
110C4×Q8×C61C2314yes—
111C4×Q8×C61C2312yes—
112C4×D4×C61—22no—
113C4×D4×C61—24no—
114C4×D4×C61—24no—
115C4×D4×C61—22no—
116C4×D4×C61—24no—
117C4×D4×C61C2312yes—
118C4×D4×C61C2314yes—
119#117×C61—22no—
120#117×C61—24no—
121#117×C61—21no—
122#117×C61C2314yes—
123#117×C61C2314yes—
124#117×C61C2311yescharacteristic
125C2×C4⋊C4×C61—22no—
126C2×C4⋊C4×C61C2312yes—
127C2×C4⋊C4×C61C2314yes—
128C2×C42×C61—21no—
129C2×C42×C61C2311yescharacteristic
130#107×C61C2314yes—
131#107×C61C2314yes—
132#107×C61C2314yes—
133#106×C61C2314yes—
134#106×C61C2314yes—
135#106×C61C2314yes—
136C4⋊C8×C61C2312yes—
137C4⋊C8×C61C2312yes—
138#103×C61C2314yes—
139#103×C61C2314yes—
140#103×C61C2314yes—
141#103×C61C2314yes—
142#103×C61C2314yes—
143#103×C61C2314yes—
144#103×C61C2314yes—
145#102×C61C2314yes—
146C22⋊C8×C61C2314yes—
147C22⋊C8×C61C2314yes—
148C22⋊C8×C61C2314yes—
149#97×C61C2314yes—
150#41×C61—42no—
151#41×C61—42no—
152#41×C61—42no—
153C2×Q8×C61—22no—
154C2×Q8×C61—24no—
155C2×Q8×C61—44no—
156C2×Q8×C61—44no—
157C2×Q8×C61C2×D412yes—
158C2×Q8×C61C2414yes—
159C2×Q8×C61C2411yescharacteristic
160C2×D4×C61—21no—
161C2×D4×C61—24no—
162C2×D4×C61C2×D414yes—
163C2×D4×C61C2×D414yes—
164C2×D4×C61C2×D412yes—
165C2×D4×C61C2411yescharacteristic
166C22×C4×C61—22no—
167C22×C4×C61—24no—
168C22×C4×C61—24no—
169C22×C4×C61—21no—
170C22×C4×C61—22no—
171C22×C4×C61C2×D412yes—
172C22×C4×C61C2411yescharacteristic
173C22×C4×C61C2414yes—
174Q16×C61—44no—
175SD16×C61—44no—
176M16×C61—44no—
177C2×C8×C61—44no—
178C2×C8×C61C2414yes—
179C2×C8×C61C2414yes—
180C4⋊C4×C61—24no—
181C4⋊C4×C61—24no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—24no—
184C4⋊C4×C61—22no—
185C4⋊C4×C61—24no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—22no—
189C4⋊C4×C61—24no—
190C4⋊C4×C61—24no—
191C4⋊C4×C61—24no—
192C4⋊C4×C61—24no—
193C4⋊C4×C61C2×D414yes—
194C4⋊C4×C61C2414yes—
195C4⋊C4×C61C2412yes—
196C4⋊C4×C61C2414yes—
197C22⋊C4×C61—24no—
198C22⋊C4×C61—24no—
199C22⋊C4×C61—21no—
200C22⋊C4×C61—24no—
201C22⋊C4×C61—24no—
202C22⋊C4×C61—24no—
203C22⋊C4×C61—24no—
204C22⋊C4×C61—22no—
205C22⋊C4×C61—24no—
206C22⋊C4×C61C2×D414yes—
207C22⋊C4×C61C2×D414yes—
208C42×C61—22no—
209C42×C61—21no—
210C42×C61—24no—
211C42×C61—24no—
212C42×C61—24no—
213C42×C61C2×D411yescharacteristic
214C42×C61C2×D411yescharacteristic
215C42×C61C2412yes—
216C23×C61—21no—
217C23×C61C22×D414yes—
218C23×C61C22×D411yescharacteristic
219Q8×C61—24no—
220Q8×C61—22no—
221Q8×C61—24no—
222Q8×C61—42no—
223Q8×C61—44no—
224Q8×C61—84no—
225D4×C61—22no—
226D4×C61—44no—
227D4×C61—42no—
228D4×C61—44no—
229D4×C61—42no—
230D4×C61—84no—
231C2×C4×C61—24no—
232C2×C4×C61—24no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—21no—
237C2×C4×C61—24no—
238C2×C4×C61—24no—
239C2×C4×C61—42no—
240C2×C4×C61—42no—
241C2×C4×C61—82no—
242C2×C4×C61—84no—
243C2×C4×C61—82no—
244C2×C4×C61—84no—
245C2×C4×C61C22×D412yes—
246C2×C4×C61C22×D414yes—
247C2×C4×C61C22×D411yescharacteristic
248C2×C4×C61C22×D412yes—
249C2×C4×C61C2511yescharacteristic
250C8×C61—24no—
251C8×C61—24no—
252#61798C6111yesmaximal, characteristic, direct product factor, Sylow
253C22×C61—22no—
254C22×C61—24no—
255C22×C61—24no—
256C22×C61—24no—
257C22×C61—21no—
258C22×C61—42no—
259C22×C61—41no—
260C22×C61C23×D411yescharacteristic
261C4×C61—22no—
262C4×C61—22no—
263C4×C61—21no—
264C4×C61—24no—
265C4×C61—42no—
266C4×C61—44no—
267C4×C61—44no—
268C4×C61—41no—
269C4×C61—44no—
270C4×C61#58512yes—
271#3550C2×C6111yescharacteristic, complemented
272#3512C2×C6111yescharacteristic
273#3350C2×C6114yescomplemented
274#3349C2×C6114yescomplemented
275#3320C2×C6114yescomplemented
276#3312C2×C6114yescomplemented
277#3236C2×C6112yescomplemented
278#3201C2×C6114yescomplemented
279#3116C2×C6112yescomplemented
280#3097C2×C6114yescomplemented
281#2980C2×C6111yescharacteristic, complemented
282C2×C61—41no—
283C2×C61—44no—
284C2×C61—81no—
285C2×C61#348511yescharacteristic
286C2×C61#358612yes—
287#563—22no—
288#559—21no—
289Q82—21no—
290#556C22×C6114yes—
291#553—24no—
292#553C22×C6114yes—
293#552C22×C6114yes—
294D4×Q8C22×C6114yes—
295#542—24no—
296#541—21no—
297#540—21no—
298#537C22×C6112yes—
299#536C22×C6114yes—
300#533C22×C6112yes—
301#532C22×C6111yescharacteristic
302#529—22no—
303C2×#125C22×C6111yescharacteristic
304#520C22×C6112yes—
305C4×#41C22×C6111yescharacteristic
306#501C22×C6114yes—
307#491C22×C6114yes—
308#485C22×C6114yes—
309#485C22×C6114yes—
310#485C22×C6114yes—
311#485C22×C6114yes—
312#484C22×C6114yes—
313#484C22×C6114yes—
314#483C22×C6114yes—
315#483C22×C6114yes—
316#482C22×C6114yes—
317#479C22×C6114yes—
318#479C22×C6114yes—
319#477C22×C6112yes—
320#476C22×C6112yes—
321#470C22×C6114yes—
322#468C22×C6114yes—
323#467C22×C6114yes—
324#465C22×C6114yes—
325#462C22×C6112yes—
326#461C22×C6112yes—
327#452C22×C6114yes—
328#451C22×C6114yes—
329#448C22×C6114yes—
330#441C22×C6114yes—
331#440C22×C6114yes—
332#435C22×C6114yes—
333#435C22×C6114yes—
334#432C22×C6112yes—
335#428C22×C6114yes—
336#427C22×C6114yes—
337#419C22×C6114yes—
338C2×#103C22×C6114yes—
339#408C22×C6114yes—
340C61#6179811yescharacteristic, direct product factor, Sylow
341C2×#41C23×C6111yescharacteristic
342C2×#41C23×C6112yes—
343C22×Q8C23×C6114yes—
344C2×Q16C23×C6114yes—
345C2×SD16C23×C6114yes—
346C2×M16C23×C6114yes—
347C22×C8C23×C6114yes—
348C4⋊Q8—24no—
349C4⋊Q8—24no—
350C4⋊Q8D4×C6111yescharacteristic
351C4⋊Q8C23×C6112yes—
352C4⋊Q8C23×C6112yes—
353#127D4×C6111yescharacteristic
354#126—24no—
355#126—24no—
356#126—24no—
357#126—24no—
358#125—24no—
359#125—21no—
360#125—21no—
361#125—22no—
362#125C23×C6114yes—
363#124—24no—
364#124—24no—
365#124D4×C6112yes—
366#123—24no—
367#123—24no—
368#123—24no—
369#123—24no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8C23×C6114yes—
375C22⋊Q8C23×C6114yes—
376C22⋊Q8C23×C6114yes—
377C22⋊Q8C23×C6114yes—
378#121—22no—
379#121—24no—
380#121—24no—
381#121D4×C6114yes—
382#121C23×C6114yes—
383C4×Q8—22no—
384C4×Q8—24no—
385C4×Q8—22no—
386C4×Q8C23×C6112yes—
387C4×Q8C23×C6114yes—
388C4×D4—22no—
389C4×D4—24no—
390C4×D4—24no—
391C4×D4—22no—
392C4×D4—24no—
393C4×D4C23×C6112yes—
394C4×D4C23×C6114yes—
395#117—22no—
396#117—24no—
397#117—21no—
398#117C23×C6111yescharacteristic
399#117C23×C6114yes—
400#117C23×C6114yes—
401C2×C4⋊C4—22no—
402C2×C4⋊C4C23×C6112yes—
403C2×C4⋊C4C23×C6114yes—
404C2×C42—21no—
405C2×C42C23×C6111yescharacteristic
406#107C23×C6114yes—
407#107C23×C6114yes—
408#107C23×C6114yes—
409#106C23×C6114yes—
410#106C23×C6114yes—
411#106C23×C6114yes—
412C4⋊C8C23×C6112yes—
413C4⋊C8C23×C6112yes—
414#103C23×C6114yes—
415#103C23×C6114yes—
416#103C23×C6114yes—
417#103C23×C6114yes—
418#103C23×C6114yes—
419#103C23×C6114yes—
420#103C23×C6114yes—
421#102C23×C6114yes—
422C22⋊C8C23×C6114yes—
423C22⋊C8C23×C6114yes—
424C22⋊C8C23×C6114yes—
425#97C23×C6114yes—
426#41—42no—
427#41—42no—
428#41—42no—
429C2×Q8—22no—
430C2×Q8—24no—
431C2×Q8—44no—
432C2×Q8—44no—
433C2×Q8C2×D4×C6112yes—
434C2×Q8C24×C6114yes—
435C2×Q8C24×C6111yescharacteristic
436C2×D4—21no—
437C2×D4—24no—
438C2×D4C2×D4×C6114yes—
439C2×D4C2×D4×C6114yes—
440C2×D4C2×D4×C6112yes—
441C2×D4C24×C6111yescharacteristic
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4C2×D4×C6112yes—
448C22×C4C24×C6111yescharacteristic
449C22×C4C24×C6114yes—
450Q16—44no—
451SD16—44no—
452M16—44no—
453C2×C8—44no—
454C2×C8C24×C6114yes—
455C2×C8C24×C6114yes—
456C4⋊C4—24no—
457C4⋊C4—24no—
458C4⋊C4—22no—
459C4⋊C4—24no—
460C4⋊C4—22no—
461C4⋊C4—24no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—22no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4C2×D4×C6114yes—
470C4⋊C4C24×C6114yes—
471C4⋊C4C24×C6112yes—
472C4⋊C4C24×C6114yes—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—21no—
476C22⋊C4—24no—
477C22⋊C4—24no—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—22no—
481C22⋊C4—24no—
482C22⋊C4C2×D4×C6114yes—
483C22⋊C4C2×D4×C6114yes—
484C42—22no—
485C42—21no—
486C42—24no—
487C42—24no—
488C42—24no—
489C42C2×D4×C6111yescharacteristic
490C42C2×D4×C6111yescharacteristic
491C42C24×C6112yes—
492C23—21no—
493C23C22×D4×C6114yes—
494C23C22×D4×C6111yescharacteristic
495Q8—24no—
496Q8—22no—
497Q8—24no—
498Q8—42no—
499Q8—44no—
500Q8—84no—
501D4—22no—
502D4—44no—
503D4—42no—
504D4—44no—
505D4—42no—
506D4—84no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—82no—
518C2×C4—84no—
519C2×C4—82no—
520C2×C4—84no—
521C2×C4C22×D4×C6112yes—
522C2×C4C22×D4×C6114yes—
523C2×C4C22×D4×C6111yescharacteristic
524C2×C4C22×D4×C6112yes—
525C2×C4C25×C6111yescharacteristic
526C8—24no—
527C8—24no—
528C22—22no—
529C22—24no—
530C22—24no—
531C22—24no—
532C22—21no—
533C22—42no—
534C22—41no—
535C22C23×D4×C6111yescharacteristic
536C4—22no—
537C4—22no—
538C4—21no—
539C4—24no—
540C4—42no—
541C4—44no—
542C4—44no—
543C4—41no—
544C4—44no—
545C4C61×#58512yes—
546C2—41no—
547C2—44no—
548C2—81no—
549C2C61×#348511yescharacteristic
550C2C61×#358612yes—
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
prime radicalC61×#3512C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C61×#532 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3550C2semidirect
3. C61×#3350C2semidirect
4. C61×#3349C2semidirect
5. C61×#3320C2semidirect
6. C61×#3312C2semidirect
7. C61×#3236C2semidirect
8. C61×#3201C2semidirect
9. C61×#3116C2semidirect
10. C61×#3097C2semidirect
11. C61×#2980C2semidirect
252. #61798C61direct (N × H)
271. #3550C2×C61semidirect
273. #3350C2×C61semidirect
274. #3349C2×C61semidirect
275. #3320C2×C61semidirect
276. #3312C2×C61semidirect
277. #3236C2×C61semidirect
278. #3201C2×C61semidirect
279. #3116C2×C61semidirect
280. #3097C2×C61semidirect
281. #2980C2×C61semidirect
340. C61#61798direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35502
C61×#35122
C61×#33502
C61×#33492
C61×#33202
C61×#33122
C61×#32362
C61×#32012
C61×#31162
C61×#30972
C61×#29802
#6179861