Finite Group Databasebeta

← C61×#8227 #29511660

Subgroups — C61×#8227 #29511660

Order 15616.

488 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#125×C61C211yesmaximal, characteristic
2C61×#1745C211yesmaximal, characteristic
3C4×#97×C61C211yesmaximal, characteristic
4C2×C61×#330C212yesmaximal
5C61×#1295C212yesmaximal
6C2×#125×C61C2211yescharacteristic
7C2×#97×C61—21no—
8C2×#97×C61C2212yes—
9C2×#97×C61C2212yes—
10C2×C4×C8×C61—21no—
11C61×#389C411yescharacteristic
12C61×#389C411yescharacteristic
13C61×#387—21no—
14C61×#387—21no—
15C61×#382C2211yescharacteristic
16C4×C4⋊C4×C61—21no—
17C4×C4⋊C4×C61—21no—
18C4×C4⋊C4×C61C411yescharacteristic
19C4×C4⋊C4×C61C411yescharacteristic
20C43×C61C2211yescharacteristic
21C61×#336—21no—
22C61×#336—21no—
23C61×#330C418yescomplemented
24C22×C8×C61—22no—
25C22×C8×C61—22no—
26#125×C61—22no—
27#125×C61C2×C414yes—
28C2×C4⋊C4×C61—21no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61—21no—
31C2×C4⋊C4×C61—21no—
32C2×C4⋊C4×C61C2×C411yescharacteristic
33C2×C4⋊C4×C61C2×C411yescharacteristic
34C2×C4⋊C4×C61C2×C411yescharacteristic
35C2×C4⋊C4×C61C2×C411yescharacteristic
36C2×C42×C61—21no—
37C2×C42×C61—21no—
38C2×C42×C61C2×C411yescharacteristic
39C2×C42×C61C2×C411yescharacteristic
40C2×C42×C61D411yescharacteristic
41C2×C42×C61D411yescharacteristic
42C2×C42×C61D411yescharacteristic
43C2×C42×C61D411yescharacteristic
44C2×C42×C61C2311yescharacteristic
45#97×C61—24no—
46#97×C61—22no—
47#97×C61—22no—
48#97×C61C2×C414yes—
49#97×C61C2×C414yes—
50C4×C8×C61—24no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61—21no—
56#95×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C2×C8×C61—24no—
69C2×C8×C61—24no—
70C2×C8×C61—24no—
71C2×C8×C61—24no—
72C2×C8×C61—42no—
73C2×C8×C61—42no—
74C4⋊C4×C61—21no—
75C4⋊C4×C61—21no—
76C4⋊C4×C61—24no—
77C4⋊C4×C61—24no—
78C4⋊C4×C61—42no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—42no—
82C4⋊C4×C61C4212yes—
83C4⋊C4×C61C4212yes—
84C42×C61—22no—
85C42×C61—22no—
86C42×C61—22no—
87C42×C61—41no—
88C42×C61—41no—
89C42×C61—41no—
90C42×C61—42no—
91C42×C61—42no—
92C42×C61C22×C412yes—
93C42×C61#4112yes—
94C23×C61C2×C22⋊C411yescharacteristic
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—22no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61—41no—
115C2×C4×C61—41no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61#10112yes—
123C2×C4×C61#10412yes—
124C2×C4×C61#10412yes—
125C2×C4×C61C2×C4211yescharacteristic
126C2×C4×C61#11711yescharacteristic
127C2×C4×C61C4×D412yes—
128C2×C4×C61C4×D412yes—
129C8×C61—28no—
130C8×C61—44no—
131#8227C6111yesmaximal, characteristic, direct product factor, Sylow
132C22×C61C4×C22⋊C411yescharacteristic
133C22×C61C2×#10111yescharacteristic
134C22×C61#41311yescharacteristic
135C22×C61C2×#10411yescharacteristic
136C22×C61C2×#10411yescharacteristic
137C22×C61#42111yescharacteristic
138C22×C61#42111yescharacteristic
139C4×C61—21no—
140C4×C61—21no—
141C4×C61—22no—
142C4×C61—22no—
143C4×C61—22no—
144C4×C61—22no—
145C4×C61—22no—
146C4×C61—42no—
147C4×C61—42no—
148C4×C61—41no—
149C4×C61—81no—
150C4×C61—81no—
151C4×#125C2×C6111yescharacteristic
152#1745C2×C6111yescharacteristic
153C4×#97C2×C6111yescharacteristic
154C2×#330C2×C6112yes—
155#1295C2×C6112yes—
156C2×C61#152811yescharacteristic
157C2×C61#152911yescharacteristic
158C2×C61#153111yescharacteristic
159C2×C61#153211yescharacteristic
160C2×C61C4×#10111yescharacteristic
161C2×C61C4×#10411yescharacteristic
162C2×C61#175911yescharacteristic
163C2×#125C22×C6111yescharacteristic
164C2×#97—21no—
165C2×#97C22×C6112yes—
166C2×#97C22×C6112yes—
167C2×C4×C8—21no—
168#389C4×C6111yescharacteristic
169#389C4×C6111yescharacteristic
170#387—21no—
171#387—21no—
172#382C22×C6111yescharacteristic
173C4×C4⋊C4—21no—
174C4×C4⋊C4—21no—
175C4×C4⋊C4C4×C6111yescharacteristic
176C4×C4⋊C4C4×C6111yescharacteristic
177C43C22×C6111yescharacteristic
178#336—21no—
179#336—21no—
180#330C4×C6118yescomplemented
181C61#822711yescharacteristic, direct product factor, Sylow
182C22×C8—22no—
183C22×C8—22no—
184#125—22no—
185#125C2×C4×C6114yes—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×C4×C6111yescharacteristic
191C2×C4⋊C4C2×C4×C6111yescharacteristic
192C2×C4⋊C4C2×C4×C6111yescharacteristic
193C2×C4⋊C4C2×C4×C6111yescharacteristic
194C2×C42—21no—
195C2×C42—21no—
196C2×C42C2×C4×C6111yescharacteristic
197C2×C42C2×C4×C6111yescharacteristic
198C2×C42D4×C6111yescharacteristic
199C2×C42D4×C6111yescharacteristic
200C2×C42D4×C6111yescharacteristic
201C2×C42D4×C6111yescharacteristic
202C2×C42C23×C6111yescharacteristic
203#97—24no—
204#97—22no—
205#97—22no—
206#97C2×C4×C6114yes—
207#97C2×C4×C6114yes—
208C4×C8—24no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95—21no—
215C22×C4—21no—
216C22×C4—21no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4C22⋊C4×C6111yescharacteristic
220C22×C4C22⋊C4×C6111yescharacteristic
221C22×C4C22⋊C4×C6111yescharacteristic
222C22×C4C22⋊C4×C6111yescharacteristic
223C22×C4C22×C4×C6111yescharacteristic
224C22×C4C2×D4×C6111yescharacteristic
225C22×C4C2×D4×C6111yescharacteristic
226C2×C8—24no—
227C2×C8—24no—
228C2×C8—24no—
229C2×C8—24no—
230C2×C8—42no—
231C2×C8—42no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—24no—
235C4⋊C4—24no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4C42×C6112yes—
241C4⋊C4C42×C6112yes—
242C42—22no—
243C42—22no—
244C42—22no—
245C42—41no—
246C42—41no—
247C42—41no—
248C42—42no—
249C42—42no—
250C42C22×C4×C6112yes—
251C42#41×C6112yes—
252C23C2×C22⋊C4×C6111yescharacteristic
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4#101×C6112yes—
281C2×C4#104×C6112yes—
282C2×C4#104×C6112yes—
283C2×C4C2×C42×C6111yescharacteristic
284C2×C4#117×C6111yescharacteristic
285C2×C4C4×D4×C6112yes—
286C2×C4C4×D4×C6112yes—
287C8—28no—
288C8—44no—
289C22C4×C22⋊C4×C6111yescharacteristic
290C22C2×#101×C6111yescharacteristic
291C22C61×#41311yescharacteristic
292C22C2×#104×C6111yescharacteristic
293C22C2×#104×C6111yescharacteristic
294C22C61×#42111yescharacteristic
295C22C61×#42111yescharacteristic
296C4—21no—
297C4—21no—
298C4—22no—
299C4—22no—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—42no—
304C4—42no—
305C4—41no—
306C4—81no—
307C4—81no—
308C2C61×#152811yescharacteristic
309C2C61×#152911yescharacteristic
310C2C61×#153111yescharacteristic
311C2C61×#153211yescharacteristic
312C2C4×#101×C6111yescharacteristic
313C2C4×#104×C6111yescharacteristic
314C2C61×#175911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C61C2×C22⋊C4
commutatorC2×C4C2×C42×C61
Frattini, cosocleC2×C42C23×C61
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C43×C61 ◁ G

Complements

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

NH ≅ G/Ntype
23. C61×#330C4semidirect
131. #8227C61direct (N × H)
180. #330C4×C61semidirect
181. C61#8227direct (N × H)

Maximal subgroups

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

subgroupindex
C4×#125×C612
C61×#17452
C4×#97×C612
C2×C61×#3302
C61×#12952
#822761