Finite Group Databasebeta

← C61×#3346 #21443387

Subgroups — C61×#3346 #21443387

Order 7808.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#554C211yesmaximal, characteristic, complemented
2C61×#553C211yesmaximal, characteristic
3C61×#501C211yesmaximal, characteristic, complemented
4C61×#485C211yesmaximal, characteristic, complemented
5C61×#484C211yesmaximal, characteristic, complemented
6C61×#481C211yesmaximal, characteristic, complemented
7C61×#480C211yesmaximal, characteristic, complemented
8C61×#479C211yesmaximal, characteristic, complemented
9C61×#474C211yesmaximal, characteristic, complemented
10C61×#468C211yesmaximal, characteristic, complemented
11C61×#465C211yesmaximal, characteristic, complemented
12C61×#440C211yesmaximal, characteristic, complemented
13C61×#435C211yesmaximal, characteristic, complemented
14C61×#428C211yesmaximal, characteristic, complemented
15C2×#107×C61C211yesmaximal, characteristic, complemented
16C2×SD16×C61C2211yescharacteristic
17C2×M16×C61C2211yescharacteristic
18C22×C8×C61C2211yescharacteristic
19C4⋊Q8×C61C2211yescharacteristic
20#126×C61—21no—
21#125×C61—21no—
22#125×C61C2211yescharacteristic
23#123×C61—21no—
24C22⋊Q8×C61—21no—
25C22⋊Q8×C61—21no—
26C22⋊Q8×C61C2211yescharacteristic
27C22⋊Q8×C61C2211yescharacteristic
28#121×C61—21no—
29#121×C61C2211yescharacteristic
30#121×C61C2211yescharacteristic
31C4×Q8×C61C2211yescharacteristic
32C4×D4×C61—21no—
33C4×D4×C61—21no—
34C4×D4×C61C2211yescharacteristic
35C4×D4×C61C2211yescharacteristic
36#117×C61C2211yescharacteristic
37C2×C4⋊C4×C61C2211yescharacteristic
38C2×C4⋊C4×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2211yescharacteristic
41#107×C61C2211yescharacteristic
42#107×C61C2211yescharacteristic
43#107×C61C2211yescharacteristic
44#107×C61C2211yescharacteristic
45#107×C61C2211yescharacteristic
46#106×C61C2211yescharacteristic
47#106×C61C2211yescharacteristic
48#106×C61C2211yescharacteristic
49C4⋊C8×C61C2211yescharacteristic
50#103×C61C2211yescharacteristic
51#103×C61C2211yescharacteristic
52#103×C61C2211yescharacteristic
53#102×C61C2211yescharacteristic
54#102×C61C2211yescharacteristic
55#102×C61C2211yescharacteristic
56C22⋊C8×C61C2211yescharacteristic
57C22⋊C8×C61C2211yescharacteristic
58#97×C61C2211yescharacteristic
59C2×Q8×C61—21no—
60C2×Q8×C61C2311yescharacteristic
61C2×D4×C61—21no—
62C2×D4×C61—21no—
63C2×D4×C61D411yescharacteristic
64C2×D4×C61C2311yescharacteristic
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C2311yescharacteristic
70C22×C4×C61C2311yescharacteristic
71SD16×C61—22no—
72M16×C61—22no—
73C2×C8×C61—22no—
74C2×C8×C61C2311yescharacteristic
75C2×C8×C61C2311yescharacteristic
76C2×C8×C61C2311yescharacteristic
77C2×C8×C61C2311yescharacteristic
78C4⋊C4×C61—21no—
79C4⋊C4×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61—21no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61D411yescharacteristic
88C4⋊C4×C61C2311yescharacteristic
89C4⋊C4×C61C2311yescharacteristic
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×C61D411yescharacteristic
101C22⋊C4×C61D411yescharacteristic
102C42×C61—21no—
103C42×C61—21no—
104C42×C61C2311yescharacteristic
105C23×C61—21no—
106C23×C61C2×D411yescharacteristic
107C23×C61C2×D411yescharacteristic
108Q8×C61—21no—
109Q8×C61—21no—
110Q8×C61—81no—
111D4×C61—22no—
112D4×C61—21no—
113D4×C61—21no—
114D4×C61—42no—
115D4×C61—81no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
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—81no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2411yescharacteristic
136C8×C61—21no—
137C8×C61—21no—
138C8×C61—21no—
139C8×C61#4112yes—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—41no—
146C22×C61—41no—
147C22×C61—41no—
148C22×C61#13712yes—
149C22×C61C22×D411yescharacteristic
150C4×C61—21no—
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61—41no—
159C4×C61—41no—
160C4×C61—41no—
161C4×C61C2×#4111yescharacteristic
162C4×C612−1+411yescharacteristic
163#3346C6111yesmaximal, characteristic, direct product factor, Sylow
164C2×C61—22no—
165C2×C61—41no—
166C2×C61—81no—
167C2×C61#54711yescharacteristic
168C2×C61C2×#13711yescharacteristic
169C2×C61#57611yescharacteristic
170#554C2×C6111yescharacteristic, complemented
171#553C2×C6111yescharacteristic
172#501C2×C6111yescharacteristic, complemented
173#485C2×C6111yescharacteristic, complemented
174#484C2×C6111yescharacteristic, complemented
175#481C2×C6111yescharacteristic, complemented
176#480C2×C6111yescharacteristic, complemented
177#479C2×C6111yescharacteristic, complemented
178#474C2×C6111yescharacteristic, complemented
179#468C2×C6111yescharacteristic, complemented
180#465C2×C6111yescharacteristic, complemented
181#440C2×C6111yescharacteristic, complemented
182#435C2×C6111yescharacteristic, complemented
183#428C2×C6111yescharacteristic, complemented
184C2×#107C2×C6111yescharacteristic, complemented
185C61#334611yescharacteristic, direct product factor, Sylow
186C2×SD16C22×C6111yescharacteristic
187C2×M16C22×C6111yescharacteristic
188C22×C8C22×C6111yescharacteristic
189C4⋊Q8C22×C6111yescharacteristic
190#126—21no—
191#125—21no—
192#125C22×C6111yescharacteristic
193#123—21no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196C22⋊Q8C22×C6111yescharacteristic
197C22⋊Q8C22×C6111yescharacteristic
198#121—21no—
199#121C22×C6111yescharacteristic
200#121C22×C6111yescharacteristic
201C4×Q8C22×C6111yescharacteristic
202C4×D4—21no—
203C4×D4—21no—
204C4×D4C22×C6111yescharacteristic
205C4×D4C22×C6111yescharacteristic
206#117C22×C6111yescharacteristic
207C2×C4⋊C4C22×C6111yescharacteristic
208C2×C4⋊C4C22×C6111yescharacteristic
209C2×C4⋊C4C22×C6111yescharacteristic
210#107C22×C6111yescharacteristic
211#107C22×C6111yescharacteristic
212#107C22×C6111yescharacteristic
213#107C22×C6111yescharacteristic
214#107C22×C6111yescharacteristic
215#107C22×C6111yescharacteristic
216#106C22×C6111yescharacteristic
217#106C22×C6111yescharacteristic
218#106C22×C6111yescharacteristic
219C4⋊C8C22×C6111yescharacteristic
220#103C22×C6111yescharacteristic
221#103C22×C6111yescharacteristic
222#103C22×C6111yescharacteristic
223#102C22×C6111yescharacteristic
224#102C22×C6111yescharacteristic
225#102C22×C6111yescharacteristic
226C22⋊C8C22×C6111yescharacteristic
227C22⋊C8C22×C6111yescharacteristic
228#97C22×C6111yescharacteristic
229C2×Q8—21no—
230C2×Q8C23×C6111yescharacteristic
231C2×D4—21no—
232C2×D4—21no—
233C2×D4D4×C6111yescharacteristic
234C2×D4C23×C6111yescharacteristic
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4C23×C6111yescharacteristic
240C22×C4C23×C6111yescharacteristic
241SD16—22no—
242M16—22no—
243C2×C8—22no—
244C2×C8C23×C6111yescharacteristic
245C2×C8C23×C6111yescharacteristic
246C2×C8C23×C6111yescharacteristic
247C2×C8C23×C6111yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
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⋊C4D4×C6111yescharacteristic
271C22⋊C4D4×C6111yescharacteristic
272C42—21no—
273C42—21no—
274C42C23×C6111yescharacteristic
275C23—21no—
276C23C2×D4×C6111yescharacteristic
277C23C2×D4×C6111yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—81no—
281D4—22no—
282D4—21no—
283D4—21no—
284D4—42no—
285D4—81no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C2×D4×C6111yescharacteristic
302C2×C4C2×D4×C6111yescharacteristic
303C2×C4C2×D4×C6111yescharacteristic
304C2×C4C2×D4×C6111yescharacteristic
305C2×C4C24×C6111yescharacteristic
306C8—21no—
307C8—21no—
308C8—21no—
309C8#41×C6112yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—41no—
316C22—41no—
317C22—41no—
318C22#137×C6112yes—
319C22C22×D4×C6111yescharacteristic
320C4—21no—
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—41no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4C2×#41×C6111yescharacteristic
332C42−1+4×C6111yescharacteristic
333C2—22no—
334C2—41no—
335C2—81no—
336C2C61×#54711yescharacteristic
337C2C2×#137×C6111yescharacteristic
338C2C61×#57611yescharacteristic
subgroupG/H
center, socleC22×C61C22×D4
commutator, Frattini, cosocleC2×C4C24×C61
prime radicalC61×#553C2
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×#554C2semidirect
3. C61×#501C2semidirect
4. C61×#485C2semidirect
5. C61×#484C2semidirect
6. C61×#481C2semidirect
7. C61×#480C2semidirect
8. C61×#479C2semidirect
9. C61×#474C2semidirect
10. C61×#468C2semidirect
11. C61×#465C2semidirect
12. C61×#440C2semidirect
13. C61×#435C2semidirect
14. C61×#428C2semidirect
15. C2×#107×C61C2semidirect
163. #3346C61direct (N × H)
170. #554C2×C61semidirect
172. #501C2×C61semidirect
173. #485C2×C61semidirect
174. #484C2×C61semidirect
175. #481C2×C61semidirect
176. #480C2×C61semidirect
177. #479C2×C61semidirect
178. #474C2×C61semidirect
179. #468C2×C61semidirect
180. #465C2×C61semidirect
181. #440C2×C61semidirect
182. #435C2×C61semidirect
183. #428C2×C61semidirect
184. C2×#107C2×C61semidirect
185. C61#3346direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#5542
C61×#5532
C61×#5012
C61×#4852
C61×#4842
C61×#4812
C61×#4802
C61×#4792
C61×#4742
C61×#4682
C61×#4652
C61×#4402
C61×#4352
C61×#4282
C2×#107×C612
#334661