Finite Group Databasebeta

← C61×#7573 #29511006

Subgroups — C61×#7573 #29511006

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#389C211yesmaximal, characteristic
2C61×#1797C211yesmaximal, characteristic
3C4×C22⋊C8×C61C211yesmaximal, characteristic
4C61×#1271C214yesmaximal, complemented
5C22×C4⋊C4×C61—21no—
6C22×C4⋊C4×C61C411yescharacteristic
7C22×C4⋊C4×C61C411yescharacteristic
8C22×C42×C61C2211yescharacteristic
9C2×C4⋊C8×C61—21no—
10C2×C22⋊C8×C61—21no—
11C2×C22⋊C8×C61—21no—
12C2×C4×C8×C61—21no—
13C61×#389—21no—
14C61×#389—21no—
15C61×#389C412yes—
16C61×#389C2212yes—
17C2×#95×C61—21no—
18C61×#336C2212yes—
19C61×#336C2212yes—
20C23×C4×C61—21no—
21C23×C4×C61—21no—
22C23×C4×C61C2×C411yescharacteristic
23C23×C4×C61D411yescharacteristic
24C23×C4×C61D411yescharacteristic
25C22×C8×C61—22no—
26C22×C8×C61—22no—
27C2×C4⋊C4×C61—21no—
28C2×C4⋊C4×C61—22no—
29C2×C4⋊C4×C61—21no—
30C2×C4⋊C4×C61—22no—
31C2×C4⋊C4×C61—22no—
32C2×C4⋊C4×C61—42no—
33C2×C4⋊C4×C61—42no—
34C2×C4⋊C4×C61—42no—
35C2×C4⋊C4×C61C814yescomplemented
36C2×C4⋊C4×C61C2×C412yes—
37C2×C4⋊C4×C61C2×C412yes—
38C2×C42×C61—42no—
39C2×C42×C61C2×C411yescharacteristic
40C2×C42×C61D411yescharacteristic
41C2×C42×C61D411yescharacteristic
42C2×C42×C61C2311yescharacteristic
43C4⋊C8×C61—42no—
44C22⋊C8×C61—24no—
45C22⋊C8×C61—42no—
46C4×C8×C61—42no—
47#95×C61—22no—
48#95×C61—22no—
49C24×C61C22⋊C411yescharacteristic
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—24no—
53C22×C4×C61—22no—
54C22×C4×C61—22no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61—41no—
58C22×C4×C61—41no—
59C22×C4×C61—41no—
60C22×C4×C61—42no—
61C22×C4×C61—42no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61—42no—
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C2×C812yes—
69C22×C4×C61M1612yes—
70C22×C4×C61D812yes—
71C22×C4×C61SD1612yes—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C2×C8×C61—24no—
76C2×C8×C61—42no—
77C2×C8×C61—42no—
78C2×C8×C61—42no—
79C2×C8×C61—42no—
80C2×C8×C61—42no—
81C4⋊C4×C61—24no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—42no—
85C4⋊C4×C61—44no—
86C4⋊C4×C61—42no—
87C4⋊C4×C61—42no—
88C4⋊C4×C61C2×C814yes—
89C42×C61—22no—
90C42×C61—22no—
91C42×C61—41no—
92C42×C61—41no—
93C23×C61—21no—
94C23×C61—21no—
95C23×C61—21no—
96C23×C61—21no—
97C23×C61C22⋊C812yes—
98C23×C61#10212yes—
99C23×C61#10412yes—
100C23×C61C2×C22⋊C411yescharacteristic
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—21no—
108C2×C4×C61—21no—
109C2×C4×C61—24no—
110C2×C4×C61—24no—
111C2×C4×C61—24no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—42no—
116C2×C4×C61—42no—
117C2×C4×C61—44no—
118C2×C4×C61—48no—
119C2×C4×C61—42no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—42no—
124C2×C4×C61—84no—
125C2×C4×C61C22⋊C812yes—
126C2×C4×C61#9912yes—
127C2×C4×C61#10112yes—
128C2×C4×C61#10212yes—
129C2×C4×C61C22×C811yescharacteristic
130C2×C4×C61C2×M1611yescharacteristic
131C2×C4×C61C2×D811yescharacteristic
132C2×C4×C61C2×SD1611yescharacteristic
133C2×C4×C61#13712yes—
134C8×C61—44no—
135C8×C61—82no—
136#7573C6111yesmaximal, characteristic, direct product factor, Sylow
137C22×C61—22no—
138C22×C61—22no—
139C22×C61—22no—
140C22×C61—22no—
141C22×C61—22no—
142C22×C61—22no—
143C22×C61D4⋊C814yes—
144C22×C61C2×C22⋊C811yescharacteristic
145C22×C61C2×#9911yescharacteristic
146C22×C61C2×#10111yescharacteristic
147C22×C61C2×#10211yescharacteristic
148C22×C61#41911yescharacteristic
149C22×C61C2×#10411yescharacteristic
150C22×C61#42111yescharacteristic
151C4×C61—21no—
152C4×C61—21no—
153C4×C61—22no—
154C4×C61—21no—
155C4×C61—22no—
156C4×C61—21no—
157C4×C61—44no—
158C4×C61—41no—
159C4×C61—82no—
160C4×C61#32414yes—
161C2×#389C2×C6111yescharacteristic
162#1797C2×C6111yescharacteristic
163C4×C22⋊C8C2×C6111yescharacteristic
164#1271C2×C6114yescomplemented
165C2×C61—24no—
166C2×C61C2×#32411yescharacteristic
167C2×C61C2×D4⋊C811yescharacteristic
168C2×C61#147911yescharacteristic
169C2×C61#150811yescharacteristic
170C2×C61#151911yescharacteristic
171C2×C61#152811yescharacteristic
172C2×C61#154611yescharacteristic
173C22×C4⋊C4—21no—
174C22×C4⋊C4C4×C6111yescharacteristic
175C22×C4⋊C4C4×C6111yescharacteristic
176C22×C42C22×C6111yescharacteristic
177C2×C4⋊C8—21no—
178C2×C22⋊C8—21no—
179C2×C22⋊C8—21no—
180C2×C4×C8—21no—
181#389—21no—
182#389—21no—
183#389C4×C6112yes—
184#389C22×C6112yes—
185C2×#95—21no—
186#336C22×C6112yes—
187#336C22×C6112yes—
188C61#757311yescharacteristic, direct product factor, Sylow
189C23×C4—21no—
190C23×C4—21no—
191C23×C4C2×C4×C6111yescharacteristic
192C23×C4D4×C6111yescharacteristic
193C23×C4D4×C6111yescharacteristic
194C22×C8—22no—
195C22×C8—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4C8×C6114yescomplemented
205C2×C4⋊C4C2×C4×C6112yes—
206C2×C4⋊C4C2×C4×C6112yes—
207C2×C42—42no—
208C2×C42C2×C4×C6111yescharacteristic
209C2×C42D4×C6111yescharacteristic
210C2×C42D4×C6111yescharacteristic
211C2×C42C23×C6111yescharacteristic
212C4⋊C8—42no—
213C22⋊C8—24no—
214C22⋊C8—42no—
215C4×C8—42no—
216#95—22no—
217#95—22no—
218C24C22⋊C4×C6111yescharacteristic
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—24no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—42no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4C22⋊C4×C6111yescharacteristic
235C22×C4C22⋊C4×C6111yescharacteristic
236C22×C4C22⋊C4×C6111yescharacteristic
237C22×C4C2×C8×C6112yes—
238C22×C4M16×C6112yes—
239C22×C4D8×C6112yes—
240C22×C4SD16×C6112yes—
241C22×C4C22×C4×C6111yescharacteristic
242C22×C4C2×D4×C6111yescharacteristic
243C22×C4C2×D4×C6111yescharacteristic
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C4⋊C4—24no—
251C4⋊C4—22no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—44no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4C2×C8×C6114yes—
258C42—22no—
259C42—22no—
260C42—41no—
261C42—41no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23C22⋊C8×C6112yes—
267C23#102×C6112yes—
268C23#104×C6112yes—
269C23C2×C22⋊C4×C6111yescharacteristic
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—24no—
279C2×C4—24no—
280C2×C4—24no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—44no—
287C2×C4—48no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—84no—
294C2×C4C22⋊C8×C6112yes—
295C2×C4#99×C6112yes—
296C2×C4#101×C6112yes—
297C2×C4#102×C6112yes—
298C2×C4C22×C8×C6111yescharacteristic
299C2×C4C2×M16×C6111yescharacteristic
300C2×C4C2×D8×C6111yescharacteristic
301C2×C4C2×SD16×C6111yescharacteristic
302C2×C4#137×C6112yes—
303C8—44no—
304C8—82no—
305C22—22no—
306C22—22no—
307C22—22no—
308C22—22no—
309C22—22no—
310C22—22no—
311C22C61×D4⋊C814yes—
312C22C2×C22⋊C8×C6111yescharacteristic
313C22C2×#99×C6111yescharacteristic
314C22C2×#101×C6111yescharacteristic
315C22C2×#102×C6111yescharacteristic
316C22C61×#41911yescharacteristic
317C22C2×#104×C6111yescharacteristic
318C22C61×#42111yescharacteristic
319C4—22no—
320C4—21no—
321C4—22no—
322C4—21no—
323C4—21no—
324C4—21no—
325C4—41no—
326C4—44no—
327C4—82no—
328C4C61×#32414yes—
329C2—24no—
330C2C2×C61×#32411yescharacteristic
331C2C2×C61×D4⋊C811yescharacteristic
332C2C61×#147911yescharacteristic
333C2C61×#150811yescharacteristic
334C2C61×#151911yescharacteristic
335C2C61×#152811yescharacteristic
336C2C61×#154611yescharacteristic
subgroupG/H
center, socleC23×C61C2×C22⋊C4
commutatorC2×C4C22×C8×C61
Frattini, cosocleC2×C42C23×C61
prime radicalC24×C61C22⋊C4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C61 ◁ C22×C42×C61 ◁ G

Complements

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

NH ≅ G/Ntype
4. C61×#1271C2semidirect
35. C2×C4⋊C4×C61C8semidirect
136. #7573C61direct (N × H)
164. #1271C2×C61semidirect
188. C61#7573direct (N × H)
204. C2×C4⋊C4C8×C61semidirect

Maximal subgroups

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

subgroupindex
C2×C61×#3892
C61×#17972
C4×C22⋊C8×C612
C61×#12712
#757361