Finite Group Databasebeta

← C61×#60205 #29563638

Subgroups — C61×#60205 #29563638

Order 15616.

1950 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3444C211yesmaximal, characteristic
2C61×#2967C218yesmaximal, complemented
3C61×#2965C218yesmaximal, complemented
4C61×#2961C212yesmaximal, complemented
5C61×#2932C212yesmaximal, complemented
6C61×#2930C214yesmaximal, complemented
7C61×#2922C212yesmaximal, complemented
8C61×#2920C211yesmaximal, characteristic, complemented
9C4×#131×C61C212yesmaximal, complemented
10C2×C4×M16×C61C211yesmaximal, characteristic, complemented
11C2×#131×C61C2214yes—
12C22×M16×C61C2212yes—
13C61×#533C412yes—
14C61×#533C2211yescharacteristic
15C61×#532C412yes—
16C61×#532C2211yescharacteristic
17C61×#529C414yes—
18C61×#529C414yes—
19C61×#529C2214yes—
20C61×#525C414yes—
21C61×#525C2212yes—
22C4×#41×C61C2214yes—
23C4×#41×C61C2212yes—
24C22×C42×C61C2211yescharacteristic
25C61×#446C22116yescomplemented
26C61×#436C22116yes—
27C61×#435C22116yes—
28C61×#435C22116yescomplemented
29C61×#433C2218yescomplemented
30C61×#432C2214yes—
31C61×#431C2214yes—
32C61×#431C2218yescomplemented
33C61×#424C2214yes—
34C61×#423C2212yes—
35C61×#408C2214yes—
36C61×#407C2212yes—
37C61×#405C2214yes—
38C61×#405C2218yescomplemented
39C4×M16×C61C2214yes—
40C4×M16×C61C2214yes—
41C4×M16×C61C2212yes—
42C4×M16×C61C2214yescomplemented
43C2×#97×C61C2212yes—
44C2×C4×C8×C61C2211yescharacteristic
45C2×C4×C8×C61C2211yescharacteristic
46C2×C4×C8×C61C2214yescomplemented
47C2×#41×C61C2×C414yes—
48C2×#41×C61C2312yes—
49C23×C4×C61C2×C412yes—
50C23×C4×C61C2311yescharacteristic
51#131×C61—216no—
52C2×M16×C61—28no—
53C2×M16×C61C2318yes—
54C2×M16×C61C2314yes—
55C2×M16×C61C2318yes—
56C22×C8×C61C2312yes—
57C22×C8×C61C2318yes—
58C22×C8×C61C2312yes—
59C4⋊Q8×C61C2×C412yes—
60C4⋊Q8×C61C2×C411yescharacteristic
61#127×C61C2×C411yescharacteristic
62#126×C61C2×C418yes—
63#125×C61C2×C414yes—
64#125×C61C2×C412yes—
65#124×C61C2×C414yes—
66#124×C61C2×C412yes—
67#123×C61C2×C418yes—
68#123×C61C2×C414yes—
69C22⋊Q8×C61C2×C414yes—
70C22⋊Q8×C61C2×C414yes—
71C22⋊Q8×C61C2×C414yes—
72#121×C61C2×C414yes—
73#121×C61C2×C414yes—
74#121×C61C2×C414yes—
75#120×C61C2×C414yes—
76C4×Q8×C61C2×C414yes—
77C4×Q8×C61C2×C414yes—
78C4×Q8×C61C2314yes—
79C4×D4×C61C2×C414yes—
80C4×D4×C61C2×C414yes—
81C4×D4×C61C2×C418yes—
82C4×D4×C61C2×C418yes—
83C4×D4×C61C2314yes—
84C4×D4×C61C2318yes—
85#117×C61C2×C414yes—
86#117×C61C2×C418yes—
87#117×C61C2312yes—
88#117×C61C2314yes—
89C2×C42×C61C2×C412yes—
90C2×C42×C61C2×C412yes—
91C2×C42×C61C2×C412yes—
92C2×C42×C61C2311yescharacteristic
93C2×C42×C61C2312yes—
94C2×C42×C61C2311yescharacteristic
95C2×C42×C61C2314yes—
96C2×C42×C61C2312yes—
97C4⋊C8×C61C2318yes—
98C4⋊C8×C61C23116yes—
99C22⋊C8×C61C2318yes—
100C22⋊C8×C61C23116yes—
101#97×C61C2318yes—
102#97×C61C2314yes—
103#97×C61C2318yes—
104C4×C8×C61C2312yes—
105C4×C8×C61C2312yes—
106C4×C8×C61C2318yes—
107C4×C8×C61C2312yes—
108C4×C8×C61C2312yes—
109C4×C8×C61C2314yes—
110C24×C61C22×C411yescharacteristic
111#41×C61—28no—
112#41×C61—48no—
113C2×Q8×C61C22×C412yes—
114C2×Q8×C61C22×C414yes—
115C2×D4×C61C22×C414yes—
116C2×D4×C61C22×C412yes—
117C2×D4×C61C22×C418yes—
118C2×D4×C61C22×C414yes—
119C22×C4×C61—24no—
120C22×C4×C61—44no—
121C22×C4×C61C22×C412yes—
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C412yes—
124C22×C4×C61C22×C412yes—
125C22×C4×C61C22×C412yes—
126C22×C4×C61C22×C418yes—
127C22×C4×C61C22×C412yes—
128C22×C4×C61C22×C412yes—
129C22×C4×C61C22×C412yes—
130C22×C4×C61C2412yes—
131C22×C4×C61C2414yes—
132C22×C4×C61C2411yescharacteristic
133M16×C61—28no—
134M16×C61—216no—
135M16×C61—216no—
136C2×C8×C61—24no—
137C2×C8×C61—216no—
138C2×C8×C61#4118yescomplemented
139C2×C8×C61C2414yes—
140C2×C8×C61C2418yes—
141C2×C8×C61C2414yes—
142C4⋊C4×C61C22×C414yes—
143C4⋊C4×C61C22×C418yes—
144C4⋊C4×C61C22×C414yes—
145C4⋊C4×C61C22×C418yes—
146C4⋊C4×C61C22×C414yes—
147C4⋊C4×C61C22×C418yes—
148C22⋊C4×C61C22×C418yes—
149C22⋊C4×C61C22×C418yes—
150C22⋊C4×C61C22×C418yes—
151C22⋊C4×C61C22×C414yes—
152C22⋊C4×C61C22×C418yes—
153C42×C61C22×C412yes—
154C42×C61C22×C412yes—
155C42×C61C22×C412yes—
156C42×C61C22×C412yes—
157C42×C61C22×C411yescharacteristic
158C42×C61C22×C412yes—
159C42×C61C22×C411yescharacteristic
160C42×C61C22×C418yes—
161C42×C61C2411yescharacteristic
162C42×C61C2414yes—
163C42×C61C2412yes—
164C42×C61C2411yescharacteristic
165C23×C61—22no—
166C23×C61—42no—
167C23×C61C23×C414yes—
168C23×C61C23×C412yes—
169C23×C61C23×C411yescharacteristic
170Q8×C61—24no—
171Q8×C61—44no—
172D4×C61—28no—
173D4×C61—24no—
174D4×C61—44no—
175D4×C61—48no—
176C2×C4×C61—22no—
177C2×C4×C61—24no—
178C2×C4×C61—24no—
179C2×C4×C61—24no—
180C2×C4×C61—24no—
181C2×C4×C61—216no—
182C2×C4×C61—28no—
183C2×C4×C61—24no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61C23×C412yes—
188C2×C4×C61C23×C412yes—
189C2×C4×C61C23×C412yes—
190C2×C4×C61C23×C412yes—
191C2×C4×C61C23×C414yes—
192C2×C4×C61C23×C418yes—
193C2×C4×C61C23×C411yescharacteristic
194C2×C4×C61C23×C412yes—
195C2×C4×C61C2×#4114yes—
196C2×C4×C61C2511yescharacteristic
197C8×C61—24no—
198C8×C61—28no—
199C8×C61C2×#4118yes—
200#60205C6111yesmaximal, characteristic, direct product factor, Sylow
201C22×C61—22no—
202C22×C61—22no—
203C22×C61—24no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—28no—
207C22×C61—44no—
208C22×C61C4×#4112yes—
209C22×C61C24×C411yescharacteristic
210C4×C61—22no—
211C4×C61—24no—
212C4×C61—22no—
213C4×C61—22no—
214C4×C61—22no—
215C4×C61—28no—
216C4×C61C4×#4112yes—
217C4×C61#56814yes—
218C4×C61C22×#4112yes—
219#3444C2×C6111yescharacteristic
220#2967C2×C6118yescomplemented
221#2965C2×C6118yescomplemented
222#2961C2×C6112yescomplemented
223#2932C2×C6112yescomplemented
224#2930C2×C6114yescomplemented
225#2922C2×C6112yescomplemented
226#2920C2×C6111yescharacteristic, complemented
227C4×#131C2×C6112yescomplemented
228C2×C4×M16C2×C6111yescharacteristic, complemented
229C2×C61—22no—
230C2×C61—44no—
231C2×C61—42no—
232C2×C61C2×C4×#4111yescharacteristic
233C2×C61C2×#56812yes—
234C2×#131C22×C6114yes—
235C22×M16C22×C6112yes—
236#533C4×C6112yes—
237#533C22×C6111yescharacteristic
238#532C4×C6112yes—
239#532C22×C6111yescharacteristic
240#529C4×C6114yes—
241#529C4×C6114yes—
242#529C22×C6114yes—
243#525C4×C6114yes—
244#525C22×C6112yes—
245C4×#41C22×C6114yes—
246C4×#41C22×C6112yes—
247C22×C42C22×C6111yescharacteristic
248#446C22×C61116yescomplemented
249#436C22×C61116yes—
250#435C22×C61116yes—
251#435C22×C61116yescomplemented
252#433C22×C6118yescomplemented
253#432C22×C6114yes—
254#431C22×C6114yes—
255#431C22×C6118yescomplemented
256#424C22×C6114yes—
257#423C22×C6112yes—
258#408C22×C6114yes—
259#407C22×C6112yes—
260#405C22×C6114yes—
261#405C22×C6118yescomplemented
262C4×M16C22×C6114yes—
263C4×M16C22×C6114yes—
264C4×M16C22×C6112yes—
265C4×M16C22×C6114yescomplemented
266C2×#97C22×C6112yes—
267C2×C4×C8C22×C6111yescharacteristic
268C2×C4×C8C22×C6111yescharacteristic
269C2×C4×C8C22×C6114yescomplemented
270C61#6020511yescharacteristic, direct product factor, Sylow
271C2×#41C2×C4×C6114yes—
272C2×#41C23×C6112yes—
273C23×C4C2×C4×C6112yes—
274C23×C4C23×C6111yescharacteristic
275#131—216no—
276C2×M16—28no—
277C2×M16C23×C6118yes—
278C2×M16C23×C6114yes—
279C2×M16C23×C6118yes—
280C22×C8C23×C6112yes—
281C22×C8C23×C6118yes—
282C22×C8C23×C6112yes—
283C4⋊Q8C2×C4×C6112yes—
284C4⋊Q8C2×C4×C6111yescharacteristic
285#127C2×C4×C6111yescharacteristic
286#126C2×C4×C6118yes—
287#125C2×C4×C6112yes—
288#125C2×C4×C6114yes—
289#124C2×C4×C6112yes—
290#124C2×C4×C6114yes—
291#123C2×C4×C6118yes—
292#123C2×C4×C6114yes—
293C22⋊Q8C2×C4×C6114yes—
294C22⋊Q8C2×C4×C6114yes—
295C22⋊Q8C2×C4×C6114yes—
296#121C2×C4×C6114yes—
297#121C2×C4×C6114yes—
298#121C2×C4×C6114yes—
299#120C2×C4×C6114yes—
300C4×Q8C2×C4×C6114yes—
301C4×Q8C2×C4×C6114yes—
302C4×Q8C23×C6114yes—
303C4×D4C2×C4×C6118yes—
304C4×D4C2×C4×C6118yes—
305C4×D4C2×C4×C6114yes—
306C4×D4C2×C4×C6114yes—
307C4×D4C23×C6118yes—
308C4×D4C23×C6114yes—
309#117C2×C4×C6114yes—
310#117C2×C4×C6118yes—
311#117C23×C6112yes—
312#117C23×C6114yes—
313C2×C42C2×C4×C6112yes—
314C2×C42C2×C4×C6112yes—
315C2×C42C2×C4×C6112yes—
316C2×C42C23×C6114yes—
317C2×C42C23×C6111yescharacteristic
318C2×C42C23×C6112yes—
319C2×C42C23×C6112yes—
320C2×C42C23×C6111yescharacteristic
321C4⋊C8C23×C6118yes—
322C4⋊C8C23×C61116yes—
323C22⋊C8C23×C6118yes—
324C22⋊C8C23×C61116yes—
325#97C23×C6118yes—
326#97C23×C6114yes—
327#97C23×C6118yes—
328C4×C8C23×C6112yes—
329C4×C8C23×C6112yes—
330C4×C8C23×C6112yes—
331C4×C8C23×C6112yes—
332C4×C8C23×C6114yes—
333C4×C8C23×C6118yes—
334C24C22×C4×C6111yescharacteristic
335#41—28no—
336#41—48no—
337C2×Q8C22×C4×C6112yes—
338C2×Q8C22×C4×C6114yes—
339C2×D4C22×C4×C6114yes—
340C2×D4C22×C4×C6112yes—
341C2×D4C22×C4×C6118yes—
342C2×D4C22×C4×C6114yes—
343C22×C4—24no—
344C22×C4—44no—
345C22×C4C22×C4×C6112yes—
346C22×C4C22×C4×C6111yescharacteristic
347C22×C4C22×C4×C6112yes—
348C22×C4C22×C4×C6112yes—
349C22×C4C22×C4×C6112yes—
350C22×C4C22×C4×C6118yes—
351C22×C4C22×C4×C6112yes—
352C22×C4C22×C4×C6112yes—
353C22×C4C22×C4×C6112yes—
354C22×C4C24×C6112yes—
355C22×C4C24×C6114yes—
356C22×C4C24×C6111yescharacteristic
357M16—28no—
358M16—216no—
359M16—216no—
360C2×C8—24no—
361C2×C8—216no—
362C2×C8#41×C6118yescomplemented
363C2×C8C24×C6114yes—
364C2×C8C24×C6118yes—
365C2×C8C24×C6114yes—
366C4⋊C4C22×C4×C6114yes—
367C4⋊C4C22×C4×C6118yes—
368C4⋊C4C22×C4×C6114yes—
369C4⋊C4C22×C4×C6118yes—
370C4⋊C4C22×C4×C6114yes—
371C4⋊C4C22×C4×C6118yes—
372C22⋊C4C22×C4×C6118yes—
373C22⋊C4C22×C4×C6118yes—
374C22⋊C4C22×C4×C6118yes—
375C22⋊C4C22×C4×C6114yes—
376C22⋊C4C22×C4×C6118yes—
377C42C22×C4×C6112yes—
378C42C22×C4×C6112yes—
379C42C22×C4×C6112yes—
380C42C22×C4×C6112yes—
381C42C22×C4×C6111yescharacteristic
382C42C22×C4×C6112yes—
383C42C22×C4×C6111yescharacteristic
384C42C22×C4×C6118yes—
385C42C24×C6111yescharacteristic
386C42C24×C6111yescharacteristic
387C42C24×C6114yes—
388C42C24×C6112yes—
389C23—22no—
390C23—42no—
391C23C23×C4×C6114yes—
392C23C23×C4×C6112yes—
393C23C23×C4×C6111yescharacteristic
394Q8—24no—
395Q8—44no—
396D4—28no—
397D4—24no—
398D4—44no—
399D4—48no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—216no—
405C2×C4—28no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4C23×C4×C6112yes—
412C2×C4C23×C4×C6112yes—
413C2×C4C23×C4×C6112yes—
414C2×C4C23×C4×C6112yes—
415C2×C4C23×C4×C6114yes—
416C2×C4C23×C4×C6118yes—
417C2×C4C23×C4×C6112yes—
418C2×C4C23×C4×C6111yescharacteristic
419C2×C4C2×#41×C6114yes—
420C2×C4C25×C6111yescharacteristic
421C8—24no—
422C8—28no—
423C8C2×#41×C6118yes—
424C22—22no—
425C22—22no—
426C22—22no—
427C22—28no—
428C22—22no—
429C22—24no—
430C22—44no—
431C22C4×#41×C6112yes—
432C22C24×C4×C6111yescharacteristic
433C4—22no—
434C4—22no—
435C4—22no—
436C4—28no—
437C4—22no—
438C4—24no—
439C4C4×#41×C6112yes—
440C4C61×#56814yes—
441C4C22×#41×C6112yes—
442C2—22no—
443C2—42no—
444C2—44no—
445C2C2×C4×#41×C6111yescharacteristic
446C2C2×C61×#56812yes—
subgroupG/H
centerC42×C61C24
commutatorC22C24×C4×C61
Frattini, cosocleC2×C4C25×C61
socleC22×C61C24×C4
prime radicalC61×#3444C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2967C2semidirect
3. C61×#2965C2semidirect
4. C61×#2961C2semidirect
5. C61×#2932C2semidirect
6. C61×#2930C2semidirect
7. C61×#2922C2semidirect
8. C61×#2920C2semidirect
9. C4×#131×C61C2semidirect
10. C2×C4×M16×C61C2semidirect
25. C61×#446C22semidirect
28. C61×#435C22semidirect
29. C61×#433C22semidirect
32. C61×#431C22semidirect
38. C61×#405C22semidirect
42. C4×M16×C61C22semidirect
46. C2×C4×C8×C61C22semidirect
138. C2×C8×C61#41semidirect
200. #60205C61direct (N × H)
220. #2967C2×C61semidirect
221. #2965C2×C61semidirect
222. #2961C2×C61semidirect
223. #2932C2×C61semidirect
224. #2930C2×C61semidirect
225. #2922C2×C61semidirect
226. #2920C2×C61semidirect
227. C4×#131C2×C61semidirect
228. C2×C4×M16C2×C61semidirect
248. #446C22×C61semidirect
251. #435C22×C61semidirect
252. #433C22×C61semidirect
255. #431C22×C61semidirect
261. #405C22×C61semidirect
265. C4×M16C22×C61semidirect
269. C2×C4×C8C22×C61semidirect
270. C61#60205direct (N × H)
362. C2×C8#41×C61semidirect

Maximal subgroups

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

subgroupindex
C61×#34442
C61×#29672
C61×#29652
C61×#29612
C61×#29322
C61×#29302
C61×#29222
C61×#29202
C4×#131×C612
C2×C4×M16×C612
#6020561