Finite Group Databasebeta

← C61×#10249 #29513682

Subgroups — C61×#10249 #29513682

Order 15616.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#3230C211yesmaximal, characteristic, complemented
2C61×#3077C211yesmaximal, characteristic
3C61×#2563C211yesmaximal, characteristic
4C61×#1549C211yesmaximal, characteristic, complemented
5C61×#1503C211yesmaximal, characteristic, complemented
6C61×#1478C211yesmaximal, characteristic
7C61×#1303C211yesmaximal, characteristic, complemented
8C61×#533C2211yescharacteristic
9C2×C4⋊Q8×C61C2211yescharacteristic
10C2×C4×D4×C61C2211yescharacteristic
11C61×#500—21no—
12C61×#487—21no—
13C61×#484—22no—
14C61×#478—22no—
15C61×#477—22no—
16C61×#476—21no—
17C61×#474—21no—
18C61×#431C2211yescharacteristic
19C61×#431C2211yescharacteristic
20C61×#428—21no—
21C61×#423C2211yescharacteristic
22C61×#418—21no—
23C61×#393—22no—
24C61×#390—21no—
25C61×#382—21no—
26C61×#380—22no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C61×#332—22no—
29C61×#328—22no—
30C61×D4⋊C8—22no—
31C22×Q8×C61—21no—
32C22×D4×C61D411yescharacteristic
33C23×C4×C61—21no—
34C2×M16×C61—21no—
35C4⋊Q8×C61—21no—
36C4⋊Q8×C61—21no—
37C4⋊Q8×C61—21no—
38C4⋊Q8×C61—21no—
39C4⋊Q8×C61D411yescharacteristic
40C4⋊Q8×C61D411yescharacteristic
41#125×C61—21no—
42C22⋊Q8×C61—21no—
43C22⋊Q8×C61—21no—
44C4×Q8×C61—21no—
45C4×Q8×C61—21no—
46C4×D4×C61—21no—
47C4×D4×C61—21no—
48C4×D4×C61—21no—
49C4×D4×C61—21no—
50#117×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61D412yes—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C22⋊C4×C61—21no—
56C2×C22⋊C4×C61—24no—
57C2×C42×C61—21no—
58C2×C42×C61C2311yescharacteristic
59#107×C61—22no—
60#107×C61—24no—
61#106×C61—22no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61D412yes—
65C4⋊C8×C61D412yes—
66#103×C61—24no—
67#102×C61—22no—
68#102×C61—22no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71C4×C8×C61—21no—
72C4×C8×C61—21no—
73#95×C61—24no—
74#95×C61D412yes—
75C24×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—41no—
79C2×Q8×C61—41no—
80C2×Q8×C61—82no—
81C2×D4×C61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61Q1612yes—
87C22×C4×C61—21no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—44no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96M16×C61—41no—
97M16×C61—41no—
98C2×C8×C61—22no—
99C2×C8×C61—22no—
100C2×C8×C61—41no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61—22no—
104C4⋊C4×C61—21no—
105C4⋊C4×C61—21no—
106C4⋊C4×C61—21no—
107C4⋊C4×C61—22no—
108C4⋊C4×C61—21no—
109C4⋊C4×C61—42no—
110C4⋊C4×C61—41no—
111C4⋊C4×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊C4×C61—41no—
117C22⋊C4×C61—84no—
118C42×C61—41no—
119C42×C61—41no—
120C42×C61—41no—
121C42×C61C2×D411yescharacteristic
122C42×C61C2×D411yescharacteristic
123C42×C61C2×D411yescharacteristic
124C42×C61#4111yescharacteristic
125C23×C61—22no—
126C23×C61—42no—
127C23×C61—42no—
128C23×C61—41no—
129C23×C61—41no—
130C23×C61#12011yescharacteristic
131Q8×C61—42no—
132Q8×C61—82no—
133Q8×C61—82no—
134Q8×C61—81no—
135D4×C61—22no—
136D4×C61—22no—
137D4×C61—41no—
138D4×C61—41no—
139C2×C4×C61—22no—
140C2×C4×C61—41no—
141C2×C4×C61—42no—
142C2×C4×C61—44no—
143C2×C4×C61—42no—
144C2×C4×C61—42no—
145C2×C4×C61—41no—
146C2×C4×C61—41no—
147C2×C4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—42no—
150C2×C4×C61—82no—
151C2×C4×C61—82no—
152C2×C4×C61#12011yescharacteristic
153C2×C4×C61#12011yescharacteristic
154C2×C4×C61#12111yescharacteristic
155C2×C4×C61#12111yescharacteristic
156C2×C4×C61#12111yescharacteristic
157C2×C4×C61#12711yescharacteristic
158C2×C4×C61C2×Q1611yescharacteristic
159C2×C4×C61#13511yescharacteristic
160C2×C4×C61#13711yescharacteristic
161C2×C4×C61#13711yescharacteristic
162C8×C61—42no—
163C8×C61—42no—
164C8×C61—81no—
165#10249C6111yesmaximal, characteristic, direct product factor, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—44no—
169C22×C61—42no—
170C22×C61—82no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61#39211yescharacteristic
174C22×C61#45111yescharacteristic
175C22×C61#45211yescharacteristic
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—82no—
180C4×C61—81no—
181C4×C61—81no—
182C4×C61—82no—
183C4×C61—81no—
184C4×C61#45111yescharacteristic
185C4×C61#45211yescharacteristic
186C4×C61#45412yes—
187C4×C61#46711yescharacteristic
188C4×C61#47011yescharacteristic
189#3230C2×C6111yescharacteristic, complemented
190#3077C2×C6111yescharacteristic
191#2563C2×C6111yescharacteristic
192#1549C2×C6111yescharacteristic, complemented
193#1503C2×C6111yescharacteristic, complemented
194#1478C2×C6111yescharacteristic
195#1303C2×C6111yescharacteristic, complemented
196C2×C61—21no—
197C2×C61—21no—
198C2×C61—82no—
199C2×C61#200111yescharacteristic
200C2×C61#200311yescharacteristic
201C2×C61#200811yescharacteristic
202#533C22×C6111yescharacteristic
203C2×C4⋊Q8C22×C6111yescharacteristic
204C2×C4×D4C22×C6111yescharacteristic
205#500—21no—
206#487—21no—
207#484—22no—
208#478—22no—
209#477—22no—
210#476—21no—
211#474—21no—
212#431C22×C6111yescharacteristic
213#431C22×C6111yescharacteristic
214#428—21no—
215#423C22×C6111yescharacteristic
216#418—21no—
217#393—22no—
218#390—21no—
219#382—21no—
220#380—22no—
221C4×C4⋊C4C22×C6111yescharacteristic
222#332—22no—
223#328—22no—
224D4⋊C8—22no—
225C61#1024911yescharacteristic, direct product factor, Sylow
226C22×Q8—21no—
227C22×D4D4×C6111yescharacteristic
228C23×C4—21no—
229C2×M16—21no—
230C4⋊Q8—21no—
231C4⋊Q8—21no—
232C4⋊Q8—21no—
233C4⋊Q8—21no—
234C4⋊Q8D4×C6111yescharacteristic
235C4⋊Q8D4×C6111yescharacteristic
236#125—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C4×Q8—21no—
240C4×Q8—21no—
241C4×D4—21no—
242C4×D4—21no—
243C4×D4—21no—
244C4×D4—21no—
245#117—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C6111yescharacteristic
249C2×C4⋊C4D4×C6112yes—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—24no—
252C2×C42—21no—
253C2×C42C23×C6111yescharacteristic
254#107—22no—
255#107—24no—
256#106—22no—
257C4⋊C8—21no—
258C4⋊C8—21no—
259C4⋊C8D4×C6112yes—
260C4⋊C8D4×C6112yes—
261#103—24no—
262#102—22no—
263#102—22no—
264C22⋊C8—21no—
265C22⋊C8—21no—
266C4×C8—21no—
267C4×C8—21no—
268#95—24no—
269#95D4×C6112yes—
270C24—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—82no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—21no—
280C2×D4—21no—
281C2×D4Q16×C6112yes—
282C22×C4—21no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—44no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4C2×D4×C6111yescharacteristic
289C22×C4C2×D4×C6111yescharacteristic
290C22×C4C2×D4×C6111yescharacteristic
291M16—41no—
292M16—41no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—41no—
296C4⋊C4—21no—
297C4⋊C4—21no—
298C4⋊C4—22no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—22no—
303C4⋊C4—21no—
304C4⋊C4—42no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—84no—
313C42—41no—
314C42—41no—
315C42—41no—
316C42C2×D4×C6111yescharacteristic
317C42C2×D4×C6111yescharacteristic
318C42C2×D4×C6111yescharacteristic
319C42#41×C6111yescharacteristic
320C23—22no—
321C23—42no—
322C23—42no—
323C23—41no—
324C23—41no—
325C23#120×C6111yescharacteristic
326Q8—42no—
327Q8—81no—
328Q8—82no—
329Q8—82no—
330D4—22no—
331D4—22no—
332D4—41no—
333D4—41no—
334C2×C4—22no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4#120×C6111yescharacteristic
348C2×C4#120×C6111yescharacteristic
349C2×C4#121×C6111yescharacteristic
350C2×C4#121×C6111yescharacteristic
351C2×C4#121×C6111yescharacteristic
352C2×C4#127×C6111yescharacteristic
353C2×C4C2×Q16×C6111yescharacteristic
354C2×C4#135×C6111yescharacteristic
355C2×C4#137×C6111yescharacteristic
356C2×C4#137×C6111yescharacteristic
357C8—42no—
358C8—42no—
359C8—81no—
360C22—21no—
361C22—21no—
362C22—44no—
363C22—42no—
364C22—82no—
365C22—81no—
366C22—81no—
367C22C61×#39211yescharacteristic
368C22C61×#45111yescharacteristic
369C22C61×#45211yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—82no—
374C4—82no—
375C4—81no—
376C4—81no—
377C4—81no—
378C4C61×#45111yescharacteristic
379C4C61×#45211yescharacteristic
380C4C61×#45412yes—
381C4C61×#46711yescharacteristic
382C4C61×#47011yescharacteristic
383C2—21no—
384C2—21no—
385C2—82no—
386C2C61×#200111yescharacteristic
387C2C61×#200311yescharacteristic
388C2C61×#200811yescharacteristic
subgroupG/H
center, socleC22×C61#392
commutator, Frattini, cosocleC2×C42C23×C61
prime radicalC22×D4×C61D4
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C61 ◁ C2×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#3230C2semidirect
4. C61×#1549C2semidirect
5. C61×#1503C2semidirect
7. C61×#1303C2semidirect
165. #10249C61direct (N × H)
189. #3230C2×C61semidirect
192. #1549C2×C61semidirect
193. #1503C2×C61semidirect
195. #1303C2×C61semidirect
225. C61#10249direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#32302
C61×#30772
C61×#25632
C61×#15492
C61×#15032
C61×#14782
C61×#13032
#1024961