Finite Group Databasebeta

← C61×#11782 #29515215

Subgroups — C61×#11782 #29515215

Order 15616.

414 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C61×#2546C211yesmaximal, characteristic
2C4×#101×C61C211yesmaximal, characteristic
3C61×#1467C211yesmaximal, characteristic
4C61×#1346C214yesmaximal
5C2×C4⋊Q8×C61—21no—
6C2×C4⋊Q8×C61C411yescharacteristic
7C2×C4×Q8×C61C2211yescharacteristic
8C61×#432—21no—
9C2×#101×C61—21no—
10C4×M16×C61—21no—
11C61×#398C412yes—
12C61×#398C2212yes—
13C61×#391—21no—
14C61×#389—21no—
15C61×#389—21no—
16C4×C4⋊C4×C61C411yescharacteristic
17C61×#343C2212yes—
18C61×#324—21no—
19C61×#324C2212yes—
20C22×Q8×C61—21no—
21C22×Q8×C61D411yescharacteristic
22C2×M16×C61—22no—
23C4⋊Q8×C61—41no—
24C4⋊Q8×C61—41no—
25C4⋊Q8×C61—44no—
26C4×Q8×C61—41no—
27C4×Q8×C61—41no—
28C2×C4⋊C4×C61—21no—
29C2×C4⋊C4×C61—22no—
30C2×C4⋊C4×C61—21no—
31C2×C4⋊C4×C61—22no—
32C2×C4⋊C4×C61C2×C412yes—
33C2×C4⋊C4×C61C2×C411yescharacteristic
34C2×C4⋊C4×C61D411yescharacteristic
35C2×C4⋊C4×C61C2311yescharacteristic
36C2×C42×C61—21no—
37C2×C42×C61C2×C411yescharacteristic
38C2×C42×C61D411yescharacteristic
39C2×C42×C61D411yescharacteristic
40C4⋊C8×C61—41no—
41#101×C61—24no—
42C22⋊C8×C61—22no—
43#97×C61—41no—
44#97×C61—41no—
45C4×C8×C61—41no—
46#95×C61—22no—
47#95×C61—22no—
48#95×C61C2×C412yes—
49C2×Q8×C61—22no—
50C2×Q8×C61—22no—
51C2×Q8×C61—41no—
52C2×Q8×C61—42no—
53C2×Q8×C61—42no—
54C2×Q8×C61—42no—
55C22×C4×C61—22no—
56C22×C4×C61—22no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64M16×C61—24no—
65M16×C61—42no—
66C2×C8×C61—42no—
67C2×C8×C61—42no—
68C4⋊C4×C61—24no—
69C4⋊C4×C61—41no—
70C4⋊C4×C61—41no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—44no—
73C4⋊C4×C61—42no—
74C4⋊C4×C61—41no—
75C4⋊C4×C61—41no—
76C4⋊C4×C61—44no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C42×C61—21no—
81C42×C61—21no—
82C42×C61—21no—
83C42×C61—42no—
84C23×C61C2×C22⋊C411yescharacteristic
85Q8×C61—44no—
86Q8×C61—84no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—22no—
92C2×C4×C61—24no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—42no—
105C2×C4×C61—42no—
106C2×C4×C61—42no—
107C2×C4×C61#9911yescharacteristic
108C2×C4×C61#9911yescharacteristic
109C2×C4×C61#10412yes—
110C2×C4×C61AGL(1,ℤ/8)12yes—
111C8×C61—44no—
112C8×C61—82no—
113#11782C6111yesmaximal, characteristic, direct product factor, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61C2×#9911yescharacteristic
117C22×C61#41811yescharacteristic
118C22×C61C2×#10411yescharacteristic
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—44no—
123C4×C61—41no—
124C4×C61—41no—
125C4×C61—41no—
126C4×C61—41no—
127C4×C61—82no—
128C4×C61#35612yes—
129#2546C2×C6111yescharacteristic
130C4×#101C2×C6111yescharacteristic
131#1467C2×C6111yescharacteristic
132#1346C2×C6114yes—
133C2×C61—21no—
134C2×C61—21no—
135C2×C61#150711yescharacteristic
136C2×C61#212311yescharacteristic
137C2×C61C2×#35611yescharacteristic
138C2×C4⋊Q8—21no—
139C2×C4⋊Q8C4×C6111yescharacteristic
140C2×C4×Q8C22×C6111yescharacteristic
141#432—21no—
142C2×#101—21no—
143C4×M16—21no—
144#398C4×C6112yes—
145#398C22×C6112yes—
146#391—21no—
147#389—21no—
148#389—21no—
149C4×C4⋊C4C4×C6111yescharacteristic
150#343C22×C6112yes—
151#324—21no—
152#324C22×C6112yes—
153C61#1178211yescharacteristic, direct product factor, Sylow
154C22×Q8—21no—
155C22×Q8D4×C6111yescharacteristic
156C2×M16—22no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C4⋊Q8—44no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C2×C4×C6112yes—
167C2×C4⋊C4C2×C4×C6111yescharacteristic
168C2×C4⋊C4D4×C6111yescharacteristic
169C2×C4⋊C4C23×C6111yescharacteristic
170C2×C42—21no—
171C2×C42C2×C4×C6111yescharacteristic
172C2×C42D4×C6111yescharacteristic
173C2×C42D4×C6111yescharacteristic
174C4⋊C8—41no—
175#101—24no—
176C22⋊C8—22no—
177#97—41no—
178#97—41no—
179C4×C8—41no—
180#95—22no—
181#95—22no—
182#95C2×C4×C6112yes—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—42no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C22⋊C4×C6111yescharacteristic
192C22×C4C22⋊C4×C6111yescharacteristic
193C22×C4C22⋊C4×C6111yescharacteristic
194C22×C4C22⋊C4×C6111yescharacteristic
195C22×C4C22×C4×C6111yescharacteristic
196C22×C4C2×D4×C6111yescharacteristic
197C22×C4C2×D4×C6111yescharacteristic
198M16—24no—
199M16—42no—
200C2×C8—42no—
201C2×C8—42no—
202C4⋊C4—24no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—44no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—42no—
218C23C2×C22⋊C4×C6111yescharacteristic
219Q8—44no—
220Q8—84no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4#99×C6111yescharacteristic
242C2×C4#99×C6111yescharacteristic
243C2×C4#104×C6112yes—
244C2×C4AGL(1,ℤ/8)×C6112yes—
245C8—44no—
246C8—82no—
247C22—21no—
248C22—21no—
249C22C2×#99×C6111yescharacteristic
250C22C61×#41811yescharacteristic
251C22C2×#104×C6111yescharacteristic
252C4—22no—
253C4—22no—
254C4—21no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4C61×#35612yes—
262C2—21no—
263C2—21no—
264C2C61×#150711yescharacteristic
265C2C61×#212311yescharacteristic
266C2C2×C61×#35611yescharacteristic
subgroupG/H
center, socleC22×C61C2×#99
commutatorC22×C4C22×C4×C61
Frattini, cosocleC2×C4⋊C4C23×C61
prime radicalC23×C61C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×C4×Q8×C61 ◁ G

Complements

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

NH ≅ G/Ntype
113. #11782C61direct (N × H)
153. C61#11782direct (N × H)

Maximal subgroups

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

subgroupindex
C61×#25462
C4×#101×C612
C61×#14672
C61×#13462
#1178261