Finite Group Databasebeta

← C61×#61289 #29564722

Subgroups — C61×#61289 #29564722

Order 15616.

1774 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3512C212yesmaximal, complemented
2C61×#3351C218yesmaximal, complemented
3C61×#3339C214yesmaximal, complemented
4C61×#3336C214yesmaximal, complemented
5C2×C61×#499C211yesmaximal, characteristic, complemented
6C61×#3099C214yesmaximal, complemented
7C61×#3080C212yesmaximal, complemented
8C61×#3061C212yesmaximal, complemented
9C4×#135×C61C211yesmaximal, characteristic, complemented
10C61×#2931C211yesmaximal, characteristic, complemented
11C61×#2913C212yesmaximal, complemented
12C2×#135×C61C2211yescharacteristic
13C2×#131×C61C2212yes—
14C61×#553—28no—
15C61×#553C2218yes—
16C61×#552C2218yes—
17C61×#541—22no—
18C61×#540—22no—
19C61×#537C2214yes—
20C61×#532C2211yescharacteristic
21C61×#529—24no—
22C2×#125×C61C2212yes—
23C61×#520C2214yes—
24C4×#41×C61C2212yes—
25C61×#499C2214yes—
26C61×#499C2214yes—
27C61×#485C2218yes—
28C61×#483C2218yes—
29C61×#482C2218yes—
30C61×#481C2218yes—
31C61×#479C2218yes—
32C61×#478C2218yes—
33C61×#468C2218yes—
34C61×#467C2214yes—
35C61×#466C2214yes—
36C4×Q16×C61C2212yes—
37C4×SD16×C61C2214yes—
38C4×D8×C61C2212yes—
39C61×#436C2214yes—
40C8×D4×C61C2214yes—
41C61×#428C2214yes—
42C61×#428C2218yes—
43C61×#427C2214yes—
44C61×#427C2211yescharacteristic
45C2×#107×C61C2212yes—
46C2×#107×C61C2214yes—
47C2×#106×C61C2212yes—
48C61×#423C2211yescharacteristic
49C61×#417C2214yes—
50C61×#416C2212yes—
51C61×#408C2212yes—
52C2×C4×C8×C61C2211yescharacteristic
53C2×#41×C61C2312yes—
54C2×#41×C61C2312yes—
55#135×C61—24no—
56C2×Q16×C61C2311yescharacteristic
57C2×SD16×C61C2312yes—
58C2×D8×C61C2311yescharacteristic
59#131×C61—28no—
60C2×M16×C61C2312yes—
61C2×M16×C61C2314yes—
62C22×C8×C61C2314yes—
63C22×C8×C61C2311yescharacteristic
64C22×C8×C61C2311yescharacteristic
65C4⋊Q8×C61D411yescharacteristic
66#127×C61D411yescharacteristic
67#126×C61—28no—
68#126×C61—28no—
69#125×C61—28no—
70#125×C61—22no—
71#125×C61—22no—
72#125×C61C2318yes—
73#124×C61D412yes—
74#123×C61—28no—
75#123×C61—28no—
76C22⋊Q8×C61—24no—
77C22⋊Q8×C61C2318yes—
78#121×C61—24no—
79#121×C61—28no—
80#121×C61—28no—
81#121×C61D414yes—
82#121×C61C2318yes—
83C4×Q8×C61—24no—
84C4×Q8×C61C2314yes—
85C4×D4×C61—24no—
86C4×D4×C61—28no—
87C4×D4×C61—24no—
88C4×D4×C61—28no—
89C4×D4×C61C2314yes—
90C4×D4×C61C2314yes—
91#117×C61—28no—
92#117×C61—22no—
93#117×C61C2318yes—
94#117×C61C2312yes—
95C2×C4⋊C4×C61—24no—
96C2×C4⋊C4×C61C2314yes—
97C2×C4⋊C4×C61C2318yes—
98C2×C42×C61—22no—
99C2×C42×C61C2311yescharacteristic
100#107×C61C2312yes—
101#107×C61C2314yes—
102#107×C61C2314yes—
103#107×C61C2318yes—
104#106×C61C2318yes—
105#106×C61C2312yes—
106#106×C61C2318yes—
107C4⋊C8×C61C2314yes—
108#103×C61C2314yes—
109#103×C61C2318yes—
110#102×C61C2314yes—
111#102×C61C2318yes—
112C22⋊C8×C61C2314yes—
113C22⋊C8×C61C2314yes—
114C4×C8×C61C2312yes—
115C4×C8×C61C2312yes—
116#41×C61—24no—
117#41×C61—24no—
118#41×C61—24no—
119#41×C61—24no—
120C2×Q8×C61C2×D412yes—
121C2×Q8×C61C2412yes—
122C2×D4×C61—22no—
123C2×D4×C61—28no—
124C2×D4×C61C2×D414yes—
125C2×D4×C61C2×D412yes—
126C2×D4×C61C2×D414yes—
127C2×D4×C61C2412yes—
128C22×C4×C61—24no—
129C22×C4×C61—28no—
130C22×C4×C61—22no—
131C22×C4×C61—24no—
132C22×C4×C61C2×D412yes—
133C22×C4×C61C2414yes—
134C22×C4×C61C2411yescharacteristic
135Q16×C61—22no—
136SD16×C61—24no—
137D8×C61—22no—
138M16×C61—24no—
139M16×C61—28no—
140C2×C8×C61—22no—
141C2×C8×C61—28no—
142C2×C8×C61#4114yes—
143C2×C8×C61C2412yes—
144C2×C8×C61C2414yes—
145C2×C8×C61C2411yescharacteristic
146C2×C8×C61C2411yescharacteristic
147C4⋊C4×C61—28no—
148C4⋊C4×C61—28no—
149C4⋊C4×C61—24no—
150C4⋊C4×C61—28no—
151C4⋊C4×C61—24no—
152C4⋊C4×C61—28no—
153C4⋊C4×C61C2×D414yes—
154C4⋊C4×C61C2414yes—
155C4⋊C4×C61C2418yes—
156C22⋊C4×C61—28no—
157C22⋊C4×C61—22no—
158C22⋊C4×C61—28no—
159C22⋊C4×C61—24no—
160C22⋊C4×C61—28no—
161C22⋊C4×C61C2×D414yes—
162C22⋊C4×C61C2×D414yes—
163C42×C61—24no—
164C42×C61—22no—
165C42×C61—28no—
166C42×C61C2×D411yescharacteristic
167C42×C61C2×D411yescharacteristic
168C42×C61C2412yes—
169C23×C61—22no—
170C23×C61C22×D414yes—
171C23×C61C22×D411yescharacteristic
172Q8×C61—24no—
173Q8×C61—22no—
174Q8×C61—22no—
175D4×C61—28no—
176D4×C61—24no—
177D4×C61—22no—
178D4×C61—22no—
179D4×C61—44no—
180D4×C61—44no—
181D4×C61—88no—
182C2×C4×C61—24no—
183C2×C4×C61—24no—
184C2×C4×C61—24no—
185C2×C4×C61—22no—
186C2×C4×C61—28no—
187C2×C4×C61—42no—
188C2×C4×C61—44no—
189C2×C4×C61—84no—
190C2×C4×C61—88no—
191C2×C4×C61—84no—
192C2×C4×C61C22×D412yes—
193C2×C4×C61C22×D414yes—
194C2×C4×C61C22×D412yes—
195C2×C4×C61C22×D411yescharacteristic
196C2×C4×C61C2×#4112yes—
197C2×C4×C612−1+412yes—
198C2×C4×C61C2511yescharacteristic
199C8×C61—24no—
200C8×C61—22no—
201C8×C61C2×#4112yes—
202C8×C61C2×#4112yes—
203#61289C6111yesmaximal, characteristic, direct product factor, Sylow
204C22×C61—22no—
205C22×C61—24no—
206C22×C61—24no—
207C22×C61—24no—
208C22×C61—44no—
209C22×C61—42no—
210C22×C61#54712yes—
211C22×C61C23×D411yescharacteristic
212C4×C61—22no—
213C4×C61—22no—
214C4×C61—24no—
215C4×C61—44no—
216C4×C61—48no—
217C4×C61—42no—
218C4×C61#54712yes—
219C4×C61C22×#4111yescharacteristic
220C4×C61C2×2−1+411yescharacteristic
221#3512C2×C6112yescomplemented
222#3351C2×C6118yescomplemented
223#3339C2×C6114yescomplemented
224#3336C2×C6114yescomplemented
225C2×#499C2×C6111yescharacteristic, complemented
226#3099C2×C6114yescomplemented
227#3080C2×C6112yescomplemented
228#3061C2×C6112yescomplemented
229C4×#135C2×C6111yescharacteristic, complemented
230#2931C2×C6111yescharacteristic, complemented
231#2913C2×C6112yescomplemented
232C2×C61—22no—
233C2×C61—44no—
234C2×C61—82no—
235C2×C61C2×#54711yescharacteristic
236C2×C61#358412yes—
237C2×#135C22×C6111yescharacteristic
238C2×#131C22×C6112yes—
239#553—28no—
240#553C22×C6118yes—
241#552C22×C6118yes—
242#541—22no—
243#540—22no—
244#537C22×C6114yes—
245#532C22×C6111yescharacteristic
246#529—24no—
247C2×#125C22×C6112yes—
248#520C22×C6114yes—
249C4×#41C22×C6112yes—
250#499C22×C6114yes—
251#499C22×C6114yes—
252#485C22×C6118yes—
253#483C22×C6118yes—
254#482C22×C6118yes—
255#481C22×C6118yes—
256#479C22×C6118yes—
257#478C22×C6118yes—
258#468C22×C6118yes—
259#467C22×C6114yes—
260#466C22×C6114yes—
261C4×Q16C22×C6112yes—
262C4×SD16C22×C6114yes—
263C4×D8C22×C6112yes—
264#436C22×C6114yes—
265C8×D4C22×C6114yes—
266#428C22×C6114yes—
267#428C22×C6118yes—
268#427C22×C6114yes—
269#427C22×C6111yescharacteristic
270C2×#107C22×C6114yes—
271C2×#107C22×C6112yes—
272C2×#106C22×C6112yes—
273#423C22×C6111yescharacteristic
274#417C22×C6114yes—
275#416C22×C6112yes—
276#408C22×C6112yes—
277C2×C4×C8C22×C6111yescharacteristic
278C61#6128911yescharacteristic, direct product factor, Sylow
279C2×#41C23×C6112yes—
280C2×#41C23×C6112yes—
281#135—24no—
282C2×Q16C23×C6111yescharacteristic
283C2×SD16C23×C6112yes—
284C2×D8C23×C6111yescharacteristic
285#131—28no—
286C2×M16C23×C6112yes—
287C2×M16C23×C6114yes—
288C22×C8C23×C6114yes—
289C22×C8C23×C6111yescharacteristic
290C22×C8C23×C6111yescharacteristic
291C4⋊Q8D4×C6111yescharacteristic
292#127D4×C6111yescharacteristic
293#126—28no—
294#126—28no—
295#125—28no—
296#125—22no—
297#125—22no—
298#125C23×C6118yes—
299#124D4×C6112yes—
300#123—28no—
301#123—28no—
302C22⋊Q8—24no—
303C22⋊Q8C23×C6118yes—
304#121—24no—
305#121—28no—
306#121—28no—
307#121D4×C6114yes—
308#121C23×C6118yes—
309C4×Q8—24no—
310C4×Q8C23×C6114yes—
311C4×D4—24no—
312C4×D4—28no—
313C4×D4—24no—
314C4×D4—28no—
315C4×D4C23×C6114yes—
316C4×D4C23×C6114yes—
317#117—28no—
318#117—22no—
319#117C23×C6112yes—
320#117C23×C6118yes—
321C2×C4⋊C4—24no—
322C2×C4⋊C4C23×C6114yes—
323C2×C4⋊C4C23×C6118yes—
324C2×C42—22no—
325C2×C42C23×C6111yescharacteristic
326#107C23×C6112yes—
327#107C23×C6114yes—
328#107C23×C6114yes—
329#107C23×C6118yes—
330#106C23×C6118yes—
331#106C23×C6112yes—
332#106C23×C6118yes—
333C4⋊C8C23×C6114yes—
334#103C23×C6114yes—
335#103C23×C6118yes—
336#102C23×C6114yes—
337#102C23×C6118yes—
338C22⋊C8C23×C6114yes—
339C22⋊C8C23×C6114yes—
340C4×C8C23×C6112yes—
341C4×C8C23×C6112yes—
342#41—24no—
343#41—24no—
344#41—24no—
345#41—24no—
346C2×Q8C2×D4×C6112yes—
347C2×Q8C24×C6112yes—
348C2×D4—22no—
349C2×D4—28no—
350C2×D4C2×D4×C6114yes—
351C2×D4C2×D4×C6112yes—
352C2×D4C2×D4×C6114yes—
353C2×D4C24×C6112yes—
354C22×C4—24no—
355C22×C4—28no—
356C22×C4—22no—
357C22×C4—24no—
358C22×C4C2×D4×C6112yes—
359C22×C4C24×C6114yes—
360C22×C4C24×C6111yescharacteristic
361Q16—22no—
362SD16—24no—
363D8—22no—
364M16—24no—
365M16—28no—
366C2×C8—22no—
367C2×C8—28no—
368C2×C8#41×C6114yes—
369C2×C8C24×C6112yes—
370C2×C8C24×C6114yes—
371C2×C8C24×C6111yescharacteristic
372C2×C8C24×C6111yescharacteristic
373C4⋊C4—28no—
374C4⋊C4—28no—
375C4⋊C4—24no—
376C4⋊C4—28no—
377C4⋊C4—24no—
378C4⋊C4—28no—
379C4⋊C4C2×D4×C6114yes—
380C4⋊C4C24×C6114yes—
381C4⋊C4C24×C6118yes—
382C22⋊C4—28no—
383C22⋊C4—22no—
384C22⋊C4—28no—
385C22⋊C4—24no—
386C22⋊C4—28no—
387C22⋊C4C2×D4×C6114yes—
388C22⋊C4C2×D4×C6114yes—
389C42—24no—
390C42—22no—
391C42—28no—
392C42C2×D4×C6111yescharacteristic
393C42C2×D4×C6111yescharacteristic
394C42C24×C6112yes—
395C23—22no—
396C23C22×D4×C6114yes—
397C23C22×D4×C6111yescharacteristic
398Q8—24no—
399Q8—22no—
400Q8—22no—
401D4—28no—
402D4—24no—
403D4—22no—
404D4—22no—
405D4—44no—
406D4—44no—
407D4—88no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—28no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—84no—
416C2×C4—88no—
417C2×C4—84no—
418C2×C4C22×D4×C6112yes—
419C2×C4C22×D4×C6114yes—
420C2×C4C22×D4×C6112yes—
421C2×C4C22×D4×C6111yescharacteristic
422C2×C4C2×#41×C6112yes—
423C2×C42−1+4×C6112yes—
424C2×C4C25×C6111yescharacteristic
425C8—24no—
426C8—22no—
427C8C2×#41×C6112yes—
428C8C2×#41×C6112yes—
429C22—22no—
430C22—24no—
431C22—24no—
432C22—24no—
433C22—44no—
434C22—42no—
435C22C61×#54712yes—
436C22C23×D4×C6111yescharacteristic
437C4—22no—
438C4—22no—
439C4—24no—
440C4—44no—
441C4—48no—
442C4—42no—
443C4C61×#54712yes—
444C4C22×#41×C6111yescharacteristic
445C4C2×2−1+4×C6111yescharacteristic
446C2—22no—
447C2—44no—
448C2—82no—
449C2C2×C61×#54711yescharacteristic
450C2C61×#358412yes—
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
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×#3512C2semidirect
2. C61×#3351C2semidirect
3. C61×#3339C2semidirect
4. C61×#3336C2semidirect
5. C2×C61×#499C2semidirect
6. C61×#3099C2semidirect
7. C61×#3080C2semidirect
8. C61×#3061C2semidirect
9. C4×#135×C61C2semidirect
10. C61×#2931C2semidirect
11. C61×#2913C2semidirect
203. #61289C61direct (N × H)
221. #3512C2×C61semidirect
222. #3351C2×C61semidirect
223. #3339C2×C61semidirect
224. #3336C2×C61semidirect
225. C2×#499C2×C61semidirect
226. #3099C2×C61semidirect
227. #3080C2×C61semidirect
228. #3061C2×C61semidirect
229. C4×#135C2×C61semidirect
230. #2931C2×C61semidirect
231. #2913C2×C61semidirect
278. C61#61289direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35122
C61×#33512
C61×#33392
C61×#33362
C2×C61×#4992
C61×#30992
C61×#30802
C61×#30612
C4×#135×C612
C61×#29312
C61×#29132
#6128961