Finite Group Databasebeta

← C61×#18542 #29521975

Subgroups — C61×#18542 #29521975

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#556C211yesmaximal, characteristic
2C61×#3165C211yesmaximal, characteristic, complemented
3C61×#3113C211yesmaximal, characteristic, complemented
4C61×#3110C211yesmaximal, characteristic
5C61×#1652C214yesmaximal, complemented
6C61×#1650C214yesmaximal, complemented
7C61×#1556C211yesmaximal, characteristic, complemented
8C61×#1491C211yesmaximal, characteristic, complemented
9C61×#1490C211yesmaximal, characteristic
10C61×#556—22no—
11C61×#556—22no—
12C61×#556—22no—
13C61×#556C2214yes—
14C61×#533C2211yescharacteristic
15C2×C4⋊Q8×C61C2211yescharacteristic
16C2×#126×C61—22no—
17C2×#124×C61—21no—
18C2×C22⋊Q8×C61—21no—
19C2×C4×Q8×C61—21no—
20C2×C4×Q8×C61C2211yescharacteristic
21C2×C4×D4×C61C2211yescharacteristic
22C2×#117×C61—21no—
23C61×#501—22no—
24C61×#500C2212yescomplemented
25C61×#498C2212yescomplemented
26C61×#484—21no—
27C61×#483—21no—
28C61×#475C2212yescomplemented
29C61×#474C2212yes—
30C61×#462C2212yescomplemented
31C61×#461C2212yes—
32C61×#451—21no—
33C61×#450—21no—
34C61×#441—22no—
35C61×#440—22no—
36C61×#432C2211yescharacteristic
37C61×#432C2211yescharacteristic
38C61×#428—22no—
39C4×M16×C61C2211yescharacteristic
40C61×#332C2214yescomplemented
41C61×Q8⋊C8C2214yescomplemented
42C61×D4⋊C8C2214yes—
43C22×Q8×C61—21no—
44C22×Q8×C61D411yescharacteristic
45C22×D4×C61D411yescharacteristic
46C23×C4×C61—21no—
47C2×Q16×C61—22no—
48C2×SD16×C61—22no—
49C2×M16×C61—21no—
50C4⋊Q8×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61D412yes—
53C4⋊Q8×C61C2311yescharacteristic
54C4⋊Q8×C61C2311yescharacteristic
55C4⋊Q8×C61C2312yes—
56#126×C61—28no—
57#126×C61—28no—
58#125×C61—21no—
59#124×C61—24no—
60#124×C61—24no—
61C22⋊Q8×C61—24no—
62C22⋊Q8×C61—24no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C4×Q8×C61—24no—
66C4×Q8×C61—24no—
67C4×Q8×C61—21no—
68C4×Q8×C61—21no—
69C4×Q8×C61—21no—
70C4×Q8×C61—21no—
71C4×Q8×C61D412yes—
72C4×Q8×C61C2312yes—
73C4×D4×C61—21no—
74C4×D4×C61—21no—
75C4×D4×C61D412yes—
76C4×D4×C61C2312yes—
77#117×C61—24no—
78#117×C61—24no—
79#117×C61—21no—
80C2×C4⋊C4×C61—22no—
81C2×C4⋊C4×C61—21no—
82C2×C4⋊C4×C61—21no—
83C2×C4⋊C4×C61D412yes—
84C2×C4⋊C4×C61D411yescharacteristic
85C2×C4⋊C4×C61D411yescharacteristic
86C2×C22⋊C4×C61—22no—
87C2×C22⋊C4×C61—22no—
88C2×C22⋊C4×C61—21no—
89C2×C42×C61—22no—
90C2×C42×C61—21no—
91C2×C42×C61C2311yescharacteristic
92#107×C61—24no—
93#107×C61—22no—
94#106×C61—24no—
95#106×C61—22no—
96C4⋊C8×C61C2312yes—
97C4⋊C8×C61C2312yes—
98#103×C61—22no—
99#103×C61—22no—
100#103×C61—22no—
101#102×C61—22no—
102C22⋊C8×C61—21no—
103C22⋊C8×C61—21no—
104#97×C61—21no—
105#97×C61—21no—
106#97×C61—21no—
107C4×C8×C61C2312yes—
108C24×C61—21no—
109C2×Q8×C61—21no—
110C2×Q8×C61—22no—
111C2×Q8×C61—22no—
112C2×Q8×C61—21no—
113C2×Q8×C61—21no—
114C2×Q8×C61—42no—
115C2×Q8×C61—44no—
116C2×Q8×C61C2×D412yes—
117C2×D4×C61—21no—
118C2×D4×C61—42no—
119C2×D4×C61C2×D412yes—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—22no—
124C22×C4×C61—22no—
125C22×C4×C61—22no—
126C22×C4×C61—44no—
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130Q16×C61—44no—
131SD16×C61—44no—
132M16×C61—24no—
133C2×C8×C61—22no—
134C2×C8×C61—22no—
135C2×C8×C61—22no—
136C4⋊C4×C61—28no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—22no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—22no—
142C4⋊C4×C61—22no—
143C4⋊C4×C61—22no—
144C4⋊C4×C61—21no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—21no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—41no—
149C4⋊C4×C61—41no—
150C4⋊C4×C61C2×D412yes—
151C4⋊C4×C61C2×D412yes—
152C4⋊C4×C61C2×D414yes—
153C22⋊C4×C61—28no—
154C22⋊C4×C61—28no—
155C22⋊C4×C61—22no—
156C22⋊C4×C61—22no—
157C22⋊C4×C61—41no—
158C42×C61—28no—
159C42×C61—22no—
160C42×C61—22no—
161C42×C61—41no—
162C42×C61C2×D411yescharacteristic
163C42×C61C2×D411yescharacteristic
164C42×C61C2×D411yescharacteristic
165C42×C61C2411yescharacteristic
166C23×C61—22no—
167C23×C61—42no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61#12011yescharacteristic
171Q8×C61—22no—
172Q8×C61—22no—
173Q8×C61—42no—
174Q8×C61—44no—
175Q8×C61—44no—
176Q8×C61—42no—
177Q8×C61—42no—
178D4×C61—22no—
179D4×C61—22no—
180D4×C61—42no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—24no—
188C2×C4×C61—44no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—44no—
192C2×C4×C61—42no—
193C2×C4×C61—44no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61#12011yescharacteristic
197C2×C4×C61#12011yescharacteristic
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C22×D411yescharacteristic
202C8×C61—24no—
203C8×C61—42no—
204C8×C61—42no—
205#18542C6111yesmaximal, characteristic, direct product factor, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—42no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—84no—
212C22×C61#45612yes—
213C22×C61C2×#12011yescharacteristic
214C4×C61—21no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—42no—
219C4×C61—42no—
220C4×C61—44no—
221C4×C61—42no—
222C4×C61—81no—
223C4×C61—81no—
224C4×C61#57512yes—
225C4×C61#57512yes—
226C2×#556C2×C6111yescharacteristic
227#3165C2×C6111yescharacteristic, complemented
228#3113C2×C6111yescharacteristic, complemented
229#3110C2×C6111yescharacteristic
230#1652C2×C6114yescomplemented
231#1650C2×C6114yescomplemented
232#1556C2×C6111yescharacteristic, complemented
233#1491C2×C6111yescharacteristic, complemented
234#1490C2×C6111yescharacteristic
235C2×C61—22no—
236C2×C61—82no—
237C2×C61#300511yescharacteristic
238C2×C61#300511yescharacteristic
239C2×C61C2×#45611yescharacteristic
240#556—22no—
241#556—22no—
242#556—22no—
243#556C22×C6114yes—
244#533C22×C6111yescharacteristic
245C2×C4⋊Q8C22×C6111yescharacteristic
246C2×#126—22no—
247C2×#124—21no—
248C2×C22⋊Q8—21no—
249C2×C4×Q8—21no—
250C2×C4×Q8C22×C6111yescharacteristic
251C2×C4×D4C22×C6111yescharacteristic
252C2×#117—21no—
253#501—22no—
254#500C22×C6112yescomplemented
255#498C22×C6112yescomplemented
256#484—21no—
257#483—21no—
258#475C22×C6112yescomplemented
259#474C22×C6112yes—
260#462C22×C6112yescomplemented
261#461C22×C6112yes—
262#451—21no—
263#450—21no—
264#441—22no—
265#440—22no—
266#432C22×C6111yescharacteristic
267#432C22×C6111yescharacteristic
268#428—22no—
269C4×M16C22×C6111yescharacteristic
270#332C22×C6114yescomplemented
271Q8⋊C8C22×C6114yescomplemented
272D4⋊C8C22×C6114yes—
273C61#1854211yescharacteristic, direct product factor, Sylow
274C22×Q8—21no—
275C22×Q8D4×C6111yescharacteristic
276C22×D4D4×C6111yescharacteristic
277C23×C4—21no—
278C2×Q16—22no—
279C2×SD16—22no—
280C2×M16—21no—
281C4⋊Q8—21no—
282C4⋊Q8—21no—
283C4⋊Q8D4×C6112yes—
284C4⋊Q8C23×C6111yescharacteristic
285C4⋊Q8C23×C6111yescharacteristic
286C4⋊Q8C23×C6112yes—
287#126—28no—
288#126—28no—
289#125—21no—
290#124—24no—
291#124—24no—
292C22⋊Q8—24no—
293C22⋊Q8—24no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C4×Q8—24no—
297C4×Q8—24no—
298C4×Q8—21no—
299C4×Q8—21no—
300C4×Q8—21no—
301C4×Q8—21no—
302C4×Q8D4×C6112yes—
303C4×Q8C23×C6112yes—
304C4×D4—21no—
305C4×D4—21no—
306C4×D4D4×C6112yes—
307C4×D4C23×C6112yes—
308#117—24no—
309#117—24no—
310#117—21no—
311C2×C4⋊C4—22no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4D4×C6111yescharacteristic
315C2×C4⋊C4D4×C6111yescharacteristic
316C2×C4⋊C4D4×C6112yes—
317C2×C22⋊C4—22no—
318C2×C22⋊C4—22no—
319C2×C22⋊C4—21no—
320C2×C42—22no—
321C2×C42—21no—
322C2×C42C23×C6111yescharacteristic
323#107—24no—
324#107—22no—
325#106—24no—
326#106—22no—
327C4⋊C8C23×C6112yes—
328C4⋊C8C23×C6112yes—
329#103—22no—
330#103—22no—
331#103—22no—
332#102—22no—
333C22⋊C8—21no—
334C22⋊C8—21no—
335#97—21no—
336#97—21no—
337#97—21no—
338C4×C8C23×C6112yes—
339C24—21no—
340C2×Q8—21no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—21no—
344C2×Q8—21no—
345C2×Q8—42no—
346C2×Q8—44no—
347C2×Q8C2×D4×C6112yes—
348C2×D4—21no—
349C2×D4—42no—
350C2×D4C2×D4×C6112yes—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—44no—
358C22×C4C2×D4×C6111yescharacteristic
359C22×C4C2×D4×C6111yescharacteristic
360C22×C4C2×D4×C6111yescharacteristic
361Q16—44no—
362SD16—44no—
363M16—24no—
364C2×C8—22no—
365C2×C8—22no—
366C2×C8—22no—
367C4⋊C4—28no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—22no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4C2×D4×C6112yes—
382C4⋊C4C2×D4×C6112yes—
383C4⋊C4C2×D4×C6114yes—
384C22⋊C4—28no—
385C22⋊C4—28no—
386C22⋊C4—22no—
387C22⋊C4—22no—
388C22⋊C4—41no—
389C42—28no—
390C42—22no—
391C42—22no—
392C42—41no—
393C42C2×D4×C6111yescharacteristic
394C42C2×D4×C6111yescharacteristic
395C42C2×D4×C6111yescharacteristic
396C42C24×C6111yescharacteristic
397C23—22no—
398C23—42no—
399C23—42no—
400C23—42no—
401C23#120×C6111yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—42no—
405Q8—44no—
406Q8—44no—
407Q8—42no—
408Q8—42no—
409D4—22no—
410D4—22no—
411D4—42no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—24no—
419C2×C4—44no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4#120×C6111yescharacteristic
428C2×C4#120×C6111yescharacteristic
429C2×C4#120×C6111yescharacteristic
430C2×C4C22×D4×C6111yescharacteristic
431C2×C4C22×D4×C6111yescharacteristic
432C2×C4C22×D4×C6111yescharacteristic
433C8—24no—
434C8—42no—
435C8—42no—
436C22—21no—
437C22—21no—
438C22—42no—
439C22—42no—
440C22—42no—
441C22—84no—
442C22C61×#45612yes—
443C22C2×#120×C6111yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—42no—
449C4—42no—
450C4—44no—
451C4—42no—
452C4—81no—
453C4—81no—
454C4C61×#57512yes—
455C4C61×#57512yes—
456C2—22no—
457C2—82no—
458C2C61×#300511yescharacteristic
459C2C61×#300511yescharacteristic
460C2C2×C61×#45611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#120
commutator, Frattini, cosocleC42C24×C61
prime radicalC22×D4×C61D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#3165C2semidirect
3. C61×#3113C2semidirect
5. C61×#1652C2semidirect
6. C61×#1650C2semidirect
7. C61×#1556C2semidirect
8. C61×#1491C2semidirect
24. C61×#500C22semidirect
25. C61×#498C22semidirect
28. C61×#475C22semidirect
30. C61×#462C22semidirect
40. C61×#332C22semidirect
41. C61×Q8⋊C8C22semidirect
205. #18542C61direct (N × H)
227. #3165C2×C61semidirect
228. #3113C2×C61semidirect
230. #1652C2×C61semidirect
231. #1650C2×C61semidirect
232. #1556C2×C61semidirect
233. #1491C2×C61semidirect
254. #500C22×C61semidirect
255. #498C22×C61semidirect
258. #475C22×C61semidirect
260. #462C22×C61semidirect
270. #332C22×C61semidirect
271. Q8⋊C8C22×C61semidirect
273. C61#18542direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5562
C61×#31652
C61×#31132
C61×#31102
C61×#16522
C61×#16502
C61×#15562
C61×#14912
C61×#14902
#1854261