Finite Group Databasebeta

← C61×#3347 #21443388

Subgroups — C61×#3347 #21443388

Order 7808.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#555C211yesmaximal, characteristic, complemented
2C61×#553C211yesmaximal, characteristic, complemented
3C61×#501C211yesmaximal, characteristic, complemented
4C61×#482C211yesmaximal, characteristic, complemented
5C61×#482C211yesmaximal, characteristic, complemented
6C61×#482C211yesmaximal, characteristic, complemented
7C61×#480C211yesmaximal, characteristic, complemented
8C61×#478C211yesmaximal, characteristic, complemented
9C61×#474C211yesmaximal, characteristic, complemented
10C61×#469C211yesmaximal, characteristic, complemented
11C61×#466C211yesmaximal, characteristic, complemented
12C61×#442C211yesmaximal, characteristic, complemented
13C61×#435C211yesmaximal, characteristic, complemented
14C61×#428C211yesmaximal, characteristic, complemented
15C61×#427C211yesmaximal, characteristic, complemented
16C2×D8×C61C2211yescharacteristic
17C2×M16×C61C2211yescharacteristic
18C22×C8×C61C2211yescharacteristic
19C4⋊Q8×C61C2211yescharacteristic
20#126×C61—21no—
21#125×C61C2211yescharacteristic
22#124×C61—21no—
23#124×C61—21no—
24#123×C61—21no—
25#121×C61—21no—
26#121×C61—21no—
27#121×C61C2211yescharacteristic
28#121×C61C2211yescharacteristic
29#121×C61C2211yescharacteristic
30#121×C61C2211yescharacteristic
31C4×D4×C61—21no—
32C4×D4×C61C2211yescharacteristic
33C4×D4×C61C2211yescharacteristic
34C4×D4×C61C2211yescharacteristic
35#117×C61—21no—
36#117×C61C2211yescharacteristic
37#117×C61C2211yescharacteristic
38#117×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2211yescharacteristic
41#107×C61C2211yescharacteristic
42#107×C61C2211yescharacteristic
43#107×C61C2211yescharacteristic
44#107×C61C2211yescharacteristic
45#106×C61C2211yescharacteristic
46#106×C61C2211yescharacteristic
47#106×C61C2211yescharacteristic
48#106×C61C2211yescharacteristic
49C4⋊C8×C61C2211yescharacteristic
50#102×C61C2211yescharacteristic
51#102×C61C2211yescharacteristic
52#102×C61C2211yescharacteristic
53#102×C61C2211yescharacteristic
54#102×C61C2211yescharacteristic
55#102×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×D4×C61—21no—
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61D411yescharacteristic
65C2×D4×C61C2311yescharacteristic
66C2×D4×C61C2311yescharacteristic
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61C2311yescharacteristic
71C22×C4×C61C2311yescharacteristic
72D8×C61—22no—
73M16×C61—22no—
74C2×C8×C61—22no—
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C2×C8×C61C2311yescharacteristic
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61D411yescharacteristic
84C4⋊C4×C61C2311yescharacteristic
85C4⋊C4×C61C2311yescharacteristic
86C4⋊C4×C61C2311yescharacteristic
87C4⋊C4×C61C2311yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
90C22⋊C4×C61—21no—
91C22⋊C4×C61—21no—
92C22⋊C4×C61—21no—
93C22⋊C4×C61—21no—
94C22⋊C4×C61—21no—
95C22⋊C4×C61—21no—
96C22⋊C4×C61—21no—
97C22⋊C4×C61—21no—
98C22⋊C4×C61—21no—
99C22⋊C4×C61D411yescharacteristic
100C22⋊C4×C61D411yescharacteristic
101C42×C61—21no—
102C42×C61—21no—
103C42×C61—21no—
104C42×C61C2311yescharacteristic
105C23×C61—21no—
106C23×C61—21no—
107C23×C61C2×D411yescharacteristic
108C23×C61C2×D411yescharacteristic
109Q8×C61—81no—
110D4×C61—21no—
111D4×C61—21no—
112D4×C61—21no—
113D4×C61—21no—
114D4×C61—41no—
115D4×C61—42no—
116D4×C61—81no—
117D4×C61—81no—
118D4×C61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
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—42no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C8×C61—21no—
138C8×C61—21no—
139C8×C61—21no—
140C8×C61#4112yes—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—21no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—41no—
153C22×C61C22×D411yescharacteristic
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164C4×C61C2×#4111yescharacteristic
165C4×C612−1+411yescharacteristic
166#3347C6111yesmaximal, characteristic, direct product factor, Sylow
167C2×C61—41no—
168C2×C61—41no—
169C2×C61—81no—
170C2×C61—81no—
171C2×C61#54711yescharacteristic
172C2×C61#57511yescharacteristic
173C2×C61#57611yescharacteristic
174#555C2×C6111yescharacteristic, complemented
175#553C2×C6111yescharacteristic, complemented
176#501C2×C6111yescharacteristic, complemented
177#482C2×C6111yescharacteristic, complemented
178#482C2×C6111yescharacteristic, complemented
179#482C2×C6111yescharacteristic, complemented
180#480C2×C6111yescharacteristic, complemented
181#478C2×C6111yescharacteristic, complemented
182#474C2×C6111yescharacteristic, complemented
183#469C2×C6111yescharacteristic, complemented
184#466C2×C6111yescharacteristic, complemented
185#442C2×C6111yescharacteristic, complemented
186#435C2×C6111yescharacteristic, complemented
187#428C2×C6111yescharacteristic, complemented
188#427C2×C6111yescharacteristic, complemented
189C61#334711yescharacteristic, direct product factor, Sylow
190C2×D8C22×C6111yescharacteristic
191C2×M16C22×C6111yescharacteristic
192C22×C8C22×C6111yescharacteristic
193C4⋊Q8C22×C6111yescharacteristic
194#126—21no—
195#125C22×C6111yescharacteristic
196#124—21no—
197#124—21no—
198#123—21no—
199#121—21no—
200#121—21no—
201#121C22×C6111yescharacteristic
202#121C22×C6111yescharacteristic
203#121C22×C6111yescharacteristic
204#121C22×C6111yescharacteristic
205C4×D4—21no—
206C4×D4C22×C6111yescharacteristic
207C4×D4C22×C6111yescharacteristic
208C4×D4C22×C6111yescharacteristic
209#117—21no—
210#117C22×C6111yescharacteristic
211#117C22×C6111yescharacteristic
212#117C22×C6111yescharacteristic
213C2×C4⋊C4C22×C6111yescharacteristic
214#107C22×C6111yescharacteristic
215#107C22×C6111yescharacteristic
216#107C22×C6111yescharacteristic
217#107C22×C6111yescharacteristic
218#107C22×C6111yescharacteristic
219#106C22×C6111yescharacteristic
220#106C22×C6111yescharacteristic
221#106C22×C6111yescharacteristic
222#106C22×C6111yescharacteristic
223C4⋊C8C22×C6111yescharacteristic
224#102C22×C6111yescharacteristic
225#102C22×C6111yescharacteristic
226#102C22×C6111yescharacteristic
227#102C22×C6111yescharacteristic
228#102C22×C6111yescharacteristic
229#102C22×C6111yescharacteristic
230C22⋊C8C22×C6111yescharacteristic
231C22⋊C8C22×C6111yescharacteristic
232#97C22×C6111yescharacteristic
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—21no—
237C2×D4—21no—
238C2×D4D4×C6111yescharacteristic
239C2×D4C23×C6111yescharacteristic
240C2×D4C23×C6111yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4C23×C6111yescharacteristic
245C22×C4C23×C6111yescharacteristic
246D8—22no—
247M16—22no—
248C2×C8—22no—
249C2×C8C23×C6111yescharacteristic
250C2×C8C23×C6111yescharacteristic
251C2×C8C23×C6111yescharacteristic
252C2×C8C23×C6111yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4D4×C6111yescharacteristic
258C4⋊C4C23×C6111yescharacteristic
259C4⋊C4C23×C6111yescharacteristic
260C4⋊C4C23×C6111yescharacteristic
261C4⋊C4C23×C6111yescharacteristic
262C4⋊C4C23×C6111yescharacteristic
263C4⋊C4C23×C6111yescharacteristic
264C22⋊C4—21no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—21no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4D4×C6111yescharacteristic
274C22⋊C4D4×C6111yescharacteristic
275C42—21no—
276C42—21no—
277C42—21no—
278C42C23×C6111yescharacteristic
279C23—21no—
280C23—21no—
281C23C2×D4×C6111yescharacteristic
282C23C2×D4×C6111yescharacteristic
283Q8—81no—
284D4—21no—
285D4—21no—
286D4—21no—
287D4—21no—
288D4—41no—
289D4—42no—
290D4—81no—
291D4—81no—
292D4—81no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—42no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4C2×D4×C6111yescharacteristic
307C2×C4C2×D4×C6111yescharacteristic
308C2×C4C2×D4×C6111yescharacteristic
309C2×C4C2×D4×C6111yescharacteristic
310C2×C4C24×C6111yescharacteristic
311C8—21no—
312C8—21no—
313C8—21no—
314C8#41×C6112yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22C22×D4×C6111yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4C2×#41×C6111yescharacteristic
339C42−1+4×C6111yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—81no—
344C2C61×#54711yescharacteristic
345C2C61×#57511yescharacteristic
346C2C61×#57611yescharacteristic
subgroupG/H
center, socleC22×C61C22×D4
commutator, Frattini, cosocleC2×C4C24×C61
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C4×D4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
1. C61×#555C2semidirect
2. C61×#553C2semidirect
3. C61×#501C2semidirect
4. C61×#482C2semidirect
5. C61×#482C2semidirect
6. C61×#482C2semidirect
7. C61×#480C2semidirect
8. C61×#478C2semidirect
9. C61×#474C2semidirect
10. C61×#469C2semidirect
11. C61×#466C2semidirect
12. C61×#442C2semidirect
13. C61×#435C2semidirect
14. C61×#428C2semidirect
15. C61×#427C2semidirect
166. #3347C61direct (N × H)
174. #555C2×C61semidirect
175. #553C2×C61semidirect
176. #501C2×C61semidirect
177. #482C2×C61semidirect
178. #482C2×C61semidirect
179. #482C2×C61semidirect
180. #480C2×C61semidirect
181. #478C2×C61semidirect
182. #474C2×C61semidirect
183. #469C2×C61semidirect
184. #466C2×C61semidirect
185. #442C2×C61semidirect
186. #435C2×C61semidirect
187. #428C2×C61semidirect
188. #427C2×C61semidirect
189. C61#3347direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#5552
C61×#5532
C61×#5012
C61×#4822
C61×#4802
C61×#4782
C61×#4742
C61×#4692
C61×#4662
C61×#4422
C61×#4352
C61×#4282
C61×#4272
#334761