Finite Group Databasebeta

← C61×#3125 #21443166

Subgroups — C61×#3125 #21443166

Order 7808.

384 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#542C211yesmaximal, characteristic, complemented
2C61×#520C211yesmaximal, characteristic, complemented
3C61×#483C211yesmaximal, characteristic, complemented
4C61×#481C211yesmaximal, characteristic, complemented
5C61×#476C211yesmaximal, characteristic, complemented
6C61×#475C211yesmaximal, characteristic, complemented
7C61×#464C211yesmaximal, characteristic, complemented
8C61×#463C211yesmaximal, characteristic, complemented
9C61×#452C211yesmaximal, characteristic, complemented
10C61×#449C211yesmaximal, characteristic
11C61×#442C211yesmaximal, characteristic, complemented
12C61×#441C211yesmaximal, characteristic, complemented
13C4×SD16×C61C211yesmaximal, characteristic, complemented
14C4×SD16×C61C211yesmaximal, characteristic, complemented
15C61×#433C211yesmaximal, characteristic, complemented
16C2×#41×C61C2211yescharacteristic
17C2×Q16×C61C2211yescharacteristic
18C2×SD16×C61C2211yescharacteristic
19C2×SD16×C61C2211yescharacteristic
20C2×D8×C61C2211yescharacteristic
21C4⋊Q8×C61C2211yescharacteristic
22#126×C61—21no—
23#124×C61—21no—
24#124×C61C2211yescharacteristic
25#123×C61—21no—
26C22⋊Q8×C61—21no—
27C22⋊Q8×C61C2211yescharacteristic
28#121×C61C2211yescharacteristic
29C4×Q8×C61C2211yescharacteristic
30C4×Q8×C61C2211yescharacteristic
31C4×Q8×C61C2211yescharacteristic
32C4×D4×C61—21no—
33C4×D4×C61—21no—
34C4×D4×C61C2211yescharacteristic
35C4×D4×C61C2211yescharacteristic
36C4×D4×C61C2211yescharacteristic
37#117×C61—21no—
38#117×C61C2211yescharacteristic
39C2×C4⋊C4×C61—21no—
40C2×C4⋊C4×C61C2211yescharacteristic
41#106×C61C2211yescharacteristic
42#106×C61C2211yescharacteristic
43#106×C61C2211yescharacteristic
44#106×C61C2211yescharacteristic
45C4⋊C8×C61C2211yescharacteristic
46C4⋊C8×C61C2211yescharacteristic
47#103×C61C2211yescharacteristic
48#103×C61C2211yescharacteristic
49#103×C61C2211yescharacteristic
50#103×C61C2211yescharacteristic
51#102×C61C2211yescharacteristic
52#102×C61C2211yescharacteristic
53#102×C61C2211yescharacteristic
54#102×C61C2211yescharacteristic
55C22⋊C8×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57#97×C61C2211yescharacteristic
58C4×C8×C61C2211yescharacteristic
59#41×C61—22no—
60#41×C61—22no—
61C2×Q8×C61—21no—
62C2×Q8×C61C2311yescharacteristic
63C2×Q8×C61C2311yescharacteristic
64C2×D4×C61—21no—
65C2×D4×C61—21no—
66C2×D4×C61C2311yescharacteristic
67C2×D4×C61C2311yescharacteristic
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C2311yescharacteristic
74Q16×C61—22no—
75SD16×C61—22no—
76SD16×C61—22no—
77D8×C61—22no—
78C2×C8×C61C2311yescharacteristic
79C2×C8×C61C2311yescharacteristic
80C2×C8×C61C2311yescharacteristic
81C2×C8×C61C2311yescharacteristic
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61D411yescharacteristic
89C4⋊C4×C61D411yescharacteristic
90C4⋊C4×C61C2311yescharacteristic
91C4⋊C4×C61C2311yescharacteristic
92C4⋊C4×C61C2311yescharacteristic
93C4⋊C4×C61C2311yescharacteristic
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C22⋊C4×C61—21no—
99C22⋊C4×C61—21no—
100C22⋊C4×C61—21no—
101C22⋊C4×C61D411yescharacteristic
102C22⋊C4×C61D411yescharacteristic
103C42×C61—21no—
104C42×C61—21no—
105C42×C61—21no—
106C42×C61C2311yescharacteristic
107C42×C61C2311yescharacteristic
108C23×C61—21no—
109C23×C61—21no—
110C23×C61C2×D411yescharacteristic
111Q8×C61—21no—
112Q8×C61—21no—
113Q8×C61—21no—
114Q8×C61—81no—
115Q8×C61#4112yes—
116D4×C61—24no—
117D4×C61—21no—
118D4×C61—21no—
119D4×C61—21no—
120D4×C61—81no—
121D4×C61#4112yes—
122C2×C4×C61—24no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2×D411yescharacteristic
137C2×C4×C61C2×D411yescharacteristic
138C2×C4×C61C2×D411yescharacteristic
139C2×C4×C61C2×D411yescharacteristic
140C2×C4×C61C2411yescharacteristic
141C8×C61—21no—
142C8×C61—21no—
143C8×C61—21no—
144C8×C61—21no—
145C22×C61—21no—
146C22×C61—22no—
147C22×C61—21no—
148C22×C61—21no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C22×D411yescharacteristic
155C4×C61—21no—
156C4×C61—22no—
157C4×C61—21no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61C2×#4111yescharacteristic
167C4×C61C2×#4111yescharacteristic
168#3125C6111yesmaximal, characteristic, direct product factor, Sylow
169C2×C61—41no—
170C2×C61—42no—
171C2×C61—81no—
172C2×C61#52511yescharacteristic
173C2×C61#57711yescharacteristic
174C2×C61#57711yescharacteristic
175#542C2×C6111yescharacteristic, complemented
176#520C2×C6111yescharacteristic, complemented
177#483C2×C6111yescharacteristic, complemented
178#481C2×C6111yescharacteristic, complemented
179#476C2×C6111yescharacteristic, complemented
180#475C2×C6111yescharacteristic, complemented
181#464C2×C6111yescharacteristic, complemented
182#463C2×C6111yescharacteristic, complemented
183#452C2×C6111yescharacteristic, complemented
184#449C2×C6111yescharacteristic
185#442C2×C6111yescharacteristic, complemented
186#441C2×C6111yescharacteristic, complemented
187C4×SD16C2×C6111yescharacteristic, complemented
188C4×SD16C2×C6111yescharacteristic, complemented
189#433C2×C6111yescharacteristic, complemented
190C61#312511yescharacteristic, direct product factor, Sylow
191C2×#41C22×C6111yescharacteristic
192C2×Q16C22×C6111yescharacteristic
193C2×SD16C22×C6111yescharacteristic
194C2×SD16C22×C6111yescharacteristic
195C2×D8C22×C6111yescharacteristic
196C4⋊Q8C22×C6111yescharacteristic
197#126—21no—
198#124—21no—
199#124C22×C6111yescharacteristic
200#123—21no—
201C22⋊Q8—21no—
202C22⋊Q8C22×C6111yescharacteristic
203#121C22×C6111yescharacteristic
204C4×Q8C22×C6111yescharacteristic
205C4×Q8C22×C6111yescharacteristic
206C4×Q8C22×C6111yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209C4×D4C22×C6111yescharacteristic
210C4×D4C22×C6111yescharacteristic
211C4×D4C22×C6111yescharacteristic
212#117—21no—
213#117C22×C6111yescharacteristic
214C2×C4⋊C4—21no—
215C2×C4⋊C4C22×C6111yescharacteristic
216#106C22×C6111yescharacteristic
217#106C22×C6111yescharacteristic
218#106C22×C6111yescharacteristic
219#106C22×C6111yescharacteristic
220C4⋊C8C22×C6111yescharacteristic
221C4⋊C8C22×C6111yescharacteristic
222#103C22×C6111yescharacteristic
223#103C22×C6111yescharacteristic
224#103C22×C6111yescharacteristic
225#103C22×C6111yescharacteristic
226#102C22×C6111yescharacteristic
227#102C22×C6111yescharacteristic
228#102C22×C6111yescharacteristic
229#102C22×C6111yescharacteristic
230C22⋊C8C22×C6111yescharacteristic
231C22⋊C8C22×C6111yescharacteristic
232#97C22×C6111yescharacteristic
233C4×C8C22×C6111yescharacteristic
234#41—22no—
235#41—22no—
236C2×Q8—21no—
237C2×Q8C23×C6111yescharacteristic
238C2×Q8C23×C6111yescharacteristic
239C2×D4—21no—
240C2×D4—21no—
241C2×D4C23×C6111yescharacteristic
242C2×D4C23×C6111yescharacteristic
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4C23×C6111yescharacteristic
249Q16—22no—
250SD16—22no—
251SD16—22no—
252D8—22no—
253C2×C8C23×C6111yescharacteristic
254C2×C8C23×C6111yescharacteristic
255C2×C8C23×C6111yescharacteristic
256C2×C8C23×C6111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4D4×C6111yescharacteristic
264C4⋊C4D4×C6111yescharacteristic
265C4⋊C4C23×C6111yescharacteristic
266C4⋊C4C23×C6111yescharacteristic
267C4⋊C4C23×C6111yescharacteristic
268C4⋊C4C23×C6111yescharacteristic
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4D4×C6111yescharacteristic
277C22⋊C4D4×C6111yescharacteristic
278C42—21no—
279C42—21no—
280C42—21no—
281C42C23×C6111yescharacteristic
282C42C23×C6111yescharacteristic
283C23—21no—
284C23—21no—
285C23C2×D4×C6111yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—81no—
290Q8#41×C6112yes—
291D4—24no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—81no—
296D4#41×C6112yes—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4C2×D4×C6111yescharacteristic
311C2×C4C2×D4×C6111yescharacteristic
312C2×C4C2×D4×C6111yescharacteristic
313C2×C4C2×D4×C6111yescharacteristic
314C2×C4C2×D4×C6111yescharacteristic
315C2×C4C24×C6111yescharacteristic
316C8—21no—
317C8—21no—
318C8—21no—
319C8—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—22no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22C22×D4×C6111yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4C2×#41×C6111yescharacteristic
342C4C2×#41×C6111yescharacteristic
343C2—41no—
344C2—42no—
345C2—81no—
346C2C61×#52511yescharacteristic
347C2C61×#57711yescharacteristic
348C2C61×#57711yescharacteristic
subgroupG/H
center, socleC22×C61C22×D4
commutator, Frattini, cosocleC2×C4C24×C61
prime radicalC61×#449C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ #117×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#542C2semidirect
2. C61×#520C2semidirect
3. C61×#483C2semidirect
4. C61×#481C2semidirect
5. C61×#476C2semidirect
6. C61×#475C2semidirect
7. C61×#464C2semidirect
8. C61×#463C2semidirect
9. C61×#452C2semidirect
11. C61×#442C2semidirect
12. C61×#441C2semidirect
13. C4×SD16×C61C2semidirect
14. C4×SD16×C61C2semidirect
15. C61×#433C2semidirect
168. #3125C61direct (N × H)
175. #542C2×C61semidirect
176. #520C2×C61semidirect
177. #483C2×C61semidirect
178. #481C2×C61semidirect
179. #476C2×C61semidirect
180. #475C2×C61semidirect
181. #464C2×C61semidirect
182. #463C2×C61semidirect
183. #452C2×C61semidirect
185. #442C2×C61semidirect
186. #441C2×C61semidirect
187. C4×SD16C2×C61semidirect
188. C4×SD16C2×C61semidirect
189. #433C2×C61semidirect
190. C61#3125direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#5422
C61×#5202
C61×#4832
C61×#4812
C61×#4762
C61×#4752
C61×#4642
C61×#4632
C61×#4522
C61×#4492
C61×#4422
C61×#4412
C4×SD16×C612
C61×#4332
#312561