Finite Group Databasebeta

← C61×#61889 #29565322

Subgroups — C61×#61889 #29565322

Order 15616.

1706 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3502C211yesmaximal, characteristic, complemented
2C2×C61×#556C211yesmaximal, characteristic
3C61×#3398C218yesmaximal, complemented
4C61×#3369C218yesmaximal, complemented
5C61×#3215C214yesmaximal
6C61×#3209C212yesmaximal, complemented
7C61×#3113C214yesmaximal, complemented
8C61×#3101C212yesmaximal
9C61×#2983C211yesmaximal, characteristic, complemented
10Q82×C61C2214yescomplemented
11C61×#557—24no—
12C61×#557C2214yescomplemented
13C61×#556—24no—
14C61×#556C2218yes—
15C61×#544—21no—
16C61×#544—22no—
17C61×#533C2212yes—
18C61×#533C2214yes—
19C2×C4⋊Q8×C61C2211yescharacteristic
20C2×#126×C61—22no—
21C2×#124×C61C2212yes—
22C2×C22⋊Q8×C61—21no—
23C61×#519—21no—
24C2×C4×Q8×C61C2212yes—
25C2×C4×Q8×C61C2211yescharacteristic
26C2×C4×D4×C61C2211yescharacteristic
27C2×#117×C61—21no—
28C61×#497C2218yes—
29C61×#494C2214yescomplemented
30C61×#489C2218yes—
31C61×#487C2214yescomplemented
32C61×#483C2214yes—
33C61×#476C2214yes—
34C61×#475C2218yescomplemented
35C61×#464C22116yes—
36C61×#462C2218yescomplemented
37C61×#462C2218yescomplemented
38C61×#461C2214yes—
39C61×#451C2218yes—
40C61×#450C2214yes—
41C61×#446C2218yescomplemented
42C61×#441C22116yescomplemented
43C4×SD16×C61C2218yes—
44C61×#432C2214yes—
45C61×#431C2212yes—
46C22×Q8×C61D411yescharacteristic
47C22×Q8×C61C2312yes—
48C22×D4×C61C2311yescharacteristic
49C23×C4×C61—21no—
50C2×Q16×C61C23116yes—
51C2×SD16×C61C2318yes—
52C4⋊Q8×C61—24no—
53C4⋊Q8×C61—28no—
54C4⋊Q8×C61—22no—
55C4⋊Q8×C61C2314yes—
56C4⋊Q8×C61C2312yes—
57C4⋊Q8×C61C2314yes—
58C4⋊Q8×C61C2314yes—
59C4⋊Q8×C61C2312yes—
60#126×C61—216no—
61#125×C61—24no—
62#125×C61—28no—
63#125×C61—22no—
64#125×C61—24no—
65#124×C61—24no—
66#124×C61C2318yes—
67C22⋊Q8×C61—28no—
68C22⋊Q8×C61—24no—
69C22⋊Q8×C61—22no—
70C22⋊Q8×C61C2314yes—
71C4×Q8×C61—24no—
72C4×Q8×C61—24no—
73C4×Q8×C61—22no—
74C4×Q8×C61—24no—
75C4×Q8×C61—24no—
76C4×Q8×C61D414yes—
77C4×Q8×C61C2314yes—
78C4×Q8×C61C2318yes—
79C4×Q8×C61C2318yes—
80C4×Q8×C61C2314yes—
81C4×D4×C61—22no—
82C4×D4×C61C2314yes—
83#117×C61—24no—
84#117×C61—22no—
85#117×C61—28no—
86C2×C4⋊C4×C61—21no—
87C2×C4⋊C4×C61—21no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61D411yescharacteristic
90C2×C4⋊C4×C61D412yes—
91C2×C4⋊C4×C61C2311yescharacteristic
92C2×C22⋊C4×C61—22no—
93C2×C22⋊C4×C61—21no—
94C2×C22⋊C4×C61—22no—
95C2×C42×C61—22no—
96C2×C42×C61C2311yescharacteristic
97C2×C42×C61C2312yes—
98#106×C61C2318yes—
99C4⋊C8×C61C2314yes—
100C4⋊C8×C61C2318yes—
101#103×C61C2318yes—
102#103×C61C23116yes—
103#102×C61C2318yes—
104C22⋊C8×C61C2314yes—
105#97×C61C2318yes—
106C4×C8×C61C2314yes—
107C24×C61—21no—
108C2×Q8×C61—24no—
109C2×Q8×C61—22no—
110C2×Q8×C61—24no—
111C2×Q8×C61—22no—
112C2×Q8×C61—44no—
113C2×Q8×C61C2×D414yes—
114C2×Q8×C61C2414yes—
115C2×Q8×C61C2414yes—
116C2×D4×C61—21no—
117C2×D4×C61—42no—
118C2×D4×C61C2412yes—
119C22×C4×C61—21no—
120C22×C4×C61—22no—
121C22×C4×C61—24no—
122C22×C4×C61—44no—
123C22×C4×C61C2×D412yes—
124C22×C4×C61C2×D412yes—
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2411yescharacteristic
128Q16×C61—416no—
129SD16×C61—48no—
130C2×C8×C61C2418yes—
131C4⋊C4×C61—24no—
132C4⋊C4×C61—28no—
133C4⋊C4×C61—24no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—24no—
136C4⋊C4×C61—22no—
137C4⋊C4×C61—24no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—24no—
140C4⋊C4×C61—24no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—28no—
143C4⋊C4×C61—24no—
144C4⋊C4×C61C2×D414yes—
145C4⋊C4×C61C2×D418yes—
146C4⋊C4×C61C2414yes—
147C4⋊C4×C61C2412yes—
148C22⋊C4×C61—24no—
149C22⋊C4×C61—28no—
150C22⋊C4×C61—24no—
151C22⋊C4×C61—28no—
152C42×C61—28no—
153C42×C61—28no—
154C42×C61—24no—
155C42×C61C2×D412yes—
156C42×C61C2×D414yes—
157C42×C61C2412yes—
158C42×C61C2414yes—
159C23×C61—22no—
160C23×C61—42no—
161C23×C61—42no—
162C23×C61—42no—
163C23×C61C22×D411yescharacteristic
164Q8×C61—28no—
165Q8×C61—28no—
166Q8×C61—28no—
167Q8×C61—44no—
168Q8×C61—84no—
169Q8×C61—82no—
170D4×C61—24no—
171D4×C61—42no—
172C2×C4×C61—24no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—24no—
176C2×C4×C61—24no—
177C2×C4×C61—24no—
178C2×C4×C61—42no—
179C2×C4×C61—41no—
180C2×C4×C61—44no—
181C2×C4×C61—42no—
182C2×C4×C61—48no—
183C2×C4×C61#13714yes—
184C2×C4×C61C22×D414yes—
185C2×C4×C61C22×D414yes—
186C2×C4×C61C22×D411yescharacteristic
187C2×C4×C61C22×D412yes—
188C2×C4×C61C22×D412yes—
189C2×C4×C61C2511yescharacteristic
190C8×C61—28no—
191#61889C6111yesmaximal, characteristic, direct product factor, Sylow
192C22×C61—21no—
193C22×C61—21no—
194C22×C61—42no—
195C22×C61—42no—
196C22×C61—42no—
197C22×C61—84no—
198C22×C61C2×#13712yes—
199C22×C61C23×D411yescharacteristic
200C4×C61—24no—
201C4×C61—22no—
202C4×C61—21no—
203C4×C61—24no—
204C4×C61—44no—
205C4×C61—44no—
206C4×C61—44no—
207C4×C61—42no—
208C4×C61C2×#13714yes—
209C4×C61#58512yes—
210#3502C2×C6111yescharacteristic, complemented
211C2×#556C2×C6111yescharacteristic
212#3398C2×C6118yescomplemented
213#3369C2×C6118yescomplemented
214#3215C2×C6114yes—
215#3209C2×C6112yescomplemented
216#3113C2×C6114yescomplemented
217#3101C2×C6112yes—
218#2983C2×C6111yescharacteristic, complemented
219C2×C61—22no—
220C2×C61—82no—
221C2×C61#348711yescharacteristic
222C2×C61C22×#13711yescharacteristic
223C2×C61#358611yescharacteristic
224Q82C22×C6114yescomplemented
225#557—24no—
226#557C22×C6114yescomplemented
227#556—24no—
228#556C22×C6118yes—
229#544—21no—
230#544—22no—
231#533C22×C6112yes—
232#533C22×C6114yes—
233C2×C4⋊Q8C22×C6111yescharacteristic
234C2×#126—22no—
235C2×#124C22×C6112yes—
236C2×C22⋊Q8—21no—
237#519—21no—
238C2×C4×Q8C22×C6112yes—
239C2×C4×Q8C22×C6111yescharacteristic
240C2×C4×D4C22×C6111yescharacteristic
241C2×#117—21no—
242#497C22×C6118yes—
243#494C22×C6114yescomplemented
244#489C22×C6118yes—
245#487C22×C6114yescomplemented
246#483C22×C6114yes—
247#476C22×C6114yes—
248#475C22×C6118yescomplemented
249#464C22×C61116yes—
250#462C22×C6118yescomplemented
251#462C22×C6118yescomplemented
252#461C22×C6114yes—
253#451C22×C6118yes—
254#450C22×C6114yes—
255#446C22×C6118yescomplemented
256#441C22×C61116yescomplemented
257C4×SD16C22×C6118yes—
258#432C22×C6114yes—
259#431C22×C6112yes—
260C61#6188911yescharacteristic, direct product factor, Sylow
261C22×Q8D4×C6111yescharacteristic
262C22×Q8C23×C6112yes—
263C22×D4C23×C6111yescharacteristic
264C23×C4—21no—
265C2×Q16C23×C61116yes—
266C2×SD16C23×C6118yes—
267C4⋊Q8—24no—
268C4⋊Q8—28no—
269C4⋊Q8—22no—
270C4⋊Q8C23×C6114yes—
271C4⋊Q8C23×C6112yes—
272C4⋊Q8C23×C6114yes—
273C4⋊Q8C23×C6114yes—
274C4⋊Q8C23×C6112yes—
275#126—216no—
276#125—24no—
277#125—28no—
278#125—22no—
279#125—24no—
280#124—24no—
281#124C23×C6118yes—
282C22⋊Q8—28no—
283C22⋊Q8—24no—
284C22⋊Q8—22no—
285C22⋊Q8C23×C6114yes—
286C4×Q8—24no—
287C4×Q8—24no—
288C4×Q8—24no—
289C4×Q8—22no—
290C4×Q8—24no—
291C4×Q8D4×C6114yes—
292C4×Q8C23×C6118yes—
293C4×Q8C23×C6114yes—
294C4×Q8C23×C6118yes—
295C4×Q8C23×C6114yes—
296C4×D4—22no—
297C4×D4C23×C6114yes—
298#117—24no—
299#117—22no—
300#117—28no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4D4×C6111yescharacteristic
305C2×C4⋊C4D4×C6112yes—
306C2×C4⋊C4C23×C6111yescharacteristic
307C2×C22⋊C4—22no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—22no—
310C2×C42—22no—
311C2×C42C23×C6111yescharacteristic
312C2×C42C23×C6112yes—
313#106C23×C6118yes—
314C4⋊C8C23×C6114yes—
315C4⋊C8C23×C6118yes—
316#103C23×C6118yes—
317#103C23×C61116yes—
318#102C23×C6118yes—
319C22⋊C8C23×C6114yes—
320#97C23×C6118yes—
321C4×C8C23×C6114yes—
322C24—21no—
323C2×Q8—24no—
324C2×Q8—22no—
325C2×Q8—24no—
326C2×Q8—22no—
327C2×Q8—44no—
328C2×Q8C2×D4×C6114yes—
329C2×Q8C24×C6114yes—
330C2×Q8C24×C6114yes—
331C2×D4—21no—
332C2×D4—42no—
333C2×D4C24×C6112yes—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—24no—
337C22×C4—44no—
338C22×C4C2×D4×C6112yes—
339C22×C4C2×D4×C6112yes—
340C22×C4C2×D4×C6111yescharacteristic
341C22×C4C2×D4×C6111yescharacteristic
342C22×C4C24×C6111yescharacteristic
343Q16—416no—
344SD16—48no—
345C2×C8C24×C6118yes—
346C4⋊C4—24no—
347C4⋊C4—28no—
348C4⋊C4—24no—
349C4⋊C4—21no—
350C4⋊C4—24no—
351C4⋊C4—22no—
352C4⋊C4—24no—
353C4⋊C4—22no—
354C4⋊C4—24no—
355C4⋊C4—24no—
356C4⋊C4—22no—
357C4⋊C4—28no—
358C4⋊C4—24no—
359C4⋊C4C2×D4×C6114yes—
360C4⋊C4C2×D4×C6118yes—
361C4⋊C4C24×C6114yes—
362C4⋊C4C24×C6112yes—
363C22⋊C4—24no—
364C22⋊C4—28no—
365C22⋊C4—24no—
366C22⋊C4—28no—
367C42—28no—
368C42—28no—
369C42—24no—
370C42C2×D4×C6112yes—
371C42C2×D4×C6114yes—
372C42C24×C6112yes—
373C42C24×C6114yes—
374C23—22no—
375C23—42no—
376C23—42no—
377C23—42no—
378C23C22×D4×C6111yescharacteristic
379Q8—28no—
380Q8—28no—
381Q8—28no—
382Q8—44no—
383Q8—84no—
384Q8—82no—
385D4—24no—
386D4—42no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—42no—
394C2×C4—41no—
395C2×C4—44no—
396C2×C4—42no—
397C2×C4—48no—
398C2×C4#137×C6114yes—
399C2×C4C22×D4×C6114yes—
400C2×C4C22×D4×C6114yes—
401C2×C4C22×D4×C6111yescharacteristic
402C2×C4C22×D4×C6112yes—
403C2×C4C22×D4×C6112yes—
404C2×C4C25×C6111yescharacteristic
405C8—28no—
406C22—21no—
407C22—21no—
408C22—42no—
409C22—42no—
410C22—42no—
411C22—84no—
412C22C2×#137×C6112yes—
413C22C23×D4×C6111yescharacteristic
414C4—24no—
415C4—24no—
416C4—22no—
417C4—21no—
418C4—42no—
419C4—44no—
420C4—44no—
421C4—44no—
422C4C2×#137×C6114yes—
423C4C61×#58512yes—
424C2—22no—
425C2—82no—
426C2C61×#348711yescharacteristic
427C2C22×#137×C6111yescharacteristic
428C2C61×#358611yescharacteristic
subgroupG/H
center, socleC22×C61C23×D4
commutator, Frattini, cosocleC2×C4C25×C61
prime radicalC22×D4×C61C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C4×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3502C2semidirect
3. C61×#3398C2semidirect
4. C61×#3369C2semidirect
6. C61×#3209C2semidirect
7. C61×#3113C2semidirect
9. C61×#2983C2semidirect
10. Q82×C61C22semidirect
12. C61×#557C22semidirect
29. C61×#494C22semidirect
31. C61×#487C22semidirect
34. C61×#475C22semidirect
36. C61×#462C22semidirect
37. C61×#462C22semidirect
41. C61×#446C22semidirect
42. C61×#441C22semidirect
191. #61889C61direct (N × H)
210. #3502C2×C61semidirect
212. #3398C2×C61semidirect
213. #3369C2×C61semidirect
215. #3209C2×C61semidirect
216. #3113C2×C61semidirect
218. #2983C2×C61semidirect
224. Q82C22×C61semidirect
226. #557C22×C61semidirect
243. #494C22×C61semidirect
245. #487C22×C61semidirect
248. #475C22×C61semidirect
250. #462C22×C61semidirect
251. #462C22×C61semidirect
255. #446C22×C61semidirect
256. #441C22×C61semidirect
260. C61#61889direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#35022
C2×C61×#5562
C61×#33982
C61×#33692
C61×#32152
C61×#32092
C61×#31132
C61×#31012
C61×#29832
#6188961