Finite Group Databasebeta

← C2×C61×#2987 #29563680

Subgroups — C2×C61×#2987 #29563680

Order 15616.

1706 conjugacy classes of subgroups.

The subgroup lattice has 224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C61×#533C211yesmaximal, characteristic
2C61×#2987C2116yesmaximal, direct product factor
3C2×C61×#446C218yesmaximal, complemented
4C2×C61×#433C214yesmaximal
5C2×C61×#432C212yesmaximal
6C61×#533C418yes—
7C61×#533C2218yes—
8C2×C4⋊Q8×C61C412yes—
9C2×#125×C61C412yes—
10C2×C22⋊Q8×C61C414yes—
11C2×C4×Q8×C61C2214yes—
12C2×#117×C61C2212yes—
13C22×C42×C61C2211yescharacteristic
14C61×#446C22164yescomplemented
15C61×#433C22132yes—
16C61×#432C22116yes—
17C2×C4⋊C8×C61C2214yes—
18C2×C4⋊C8×C61C2218yes—
19C2×C22⋊C8×C61C2214yes—
20C2×#97×C61C2214yes—
21C2×#97×C61C2214yes—
22C2×C4×C8×C61C2214yes—
23C22×Q8×C61C2×C414yes—
24C23×C4×C61C2×C412yes—
25C23×C4×C61C2311yescharacteristic
26C22×C8×C61C2318yes—
27C4⋊Q8×C61C2×C4116yes—
28#125×C61C2×C4116yes—
29C22⋊Q8×C61C2×C4132yes—
30C4×Q8×C61C2×C4116yes—
31C4×Q8×C61C23116yes—
32#117×C61C2×C418yes—
33#117×C61C2318yes—
34C2×C4⋊C4×C61C2×C414yes—
35C2×C4⋊C4×C61C2×C414yes—
36C2×C4⋊C4×C61C2×C418yes—
37C2×C22⋊C4×C61C2×C414yes—
38C2×C42×C61C2×C411yescharacteristic
39C2×C42×C61C2×C414yes—
40C2×C42×C61C2×C411yescharacteristic
41C2×C42×C61C2314yes—
42C2×C42×C61C2314yes—
43C2×C42×C61C2312yes—
44C4⋊C8×C61C23116yes—
45C4⋊C8×C61C23132yes—
46C22⋊C8×C61C23116yes—
47#97×C61C23116yes—
48#97×C61C23116yes—
49C4×C8×C61C23116yes—
50C24×C61C22×C411yescharacteristic
51C2×Q8×C61—48no—
52C2×Q8×C61C22×C4116yes—
53C22×C4×C61—24no—
54C22×C4×C61—44no—
55C22×C4×C61C22×C411yescharacteristic
56C22×C4×C61C22×C412yes—
57C22×C4×C61C22×C412yes—
58C22×C4×C61C22×C412yes—
59C22×C4×C61C22×C418yes—
60C22×C4×C61C22×C418yes—
61C22×C4×C61C2412yes—
62C22×C4×C61C2411yescharacteristic
63C2×C8×C61—216no—
64C2×C8×C61C24116yes—
65C4⋊C4×C61C22×C4116yes—
66C4⋊C4×C61C22×C4132yes—
67C4⋊C4×C61C22×C4116yes—
68C22⋊C4×C61C22×C4116yes—
69C42×C61C22×C414yes—
70C42×C61C22×C414yes—
71C42×C61C22×C414yes—
72C42×C61C22×C418yes—
73C42×C61C2418yes—
74C42×C61C2414yes—
75C23×C61—22no—
76C23×C61—24no—
77C23×C61C23×C412yes—
78C23×C61C23×C411yescharacteristic
79Q8×C61—416no—
80C2×C4×C61—22no—
81C2×C4×C61—24no—
82C2×C4×C61—24no—
83C2×C4×C61—216no—
84C2×C4×C61—24no—
85C2×C4×C61—24no—
86C2×C4×C61—48no—
87C2×C4×C61C23×C412yes—
88C2×C4×C61C23×C414yes—
89C2×C4×C61C23×C414yes—
90C2×C4×C61C23×C4116yes—
91C2×C4×C61C23×C411yescharacteristic
92C2×C4×C612−1+414yes—
93C2×C4×C61C2511yescharacteristic
94C8×C61—216no—
95C2×#2987C6111yesmaximal, characteristic, direct product factor, Sylow
96C22×C61—22no—
97C22×C61—24no—
98C22×C61—44no—
99C22×C61#51912yes—
100C22×C61#56814yes—
101C22×C61C24×C411yescharacteristic
102C4×C61—22no—
103C4×C61—24no—
104C4×C61—24no—
105C4×C61—216no—
106C4×C61#51912yes—
107C4×C61C2×2−1+412yes—
108C2×#533C2×C6111yescharacteristic
109#2987C2×C61116yesdirect product factor
110C2×#446C2×C6118yescomplemented
111C2×#433C2×C6114yes—
112C2×#432C2×C6112yes—
113C2×C61—42no—
114C2×C61#298714yesdirect product factor
115C2×C61C2×#51911yescharacteristic
116C2×C61C2×#56812yes—
117#533C4×C6118yes—
118#533C22×C6118yes—
119C2×C4⋊Q8C4×C6112yes—
120C2×#125C4×C6112yes—
121C2×C22⋊Q8C4×C6114yes—
122C2×C4×Q8C22×C6114yes—
123C2×#117C22×C6112yes—
124C22×C42C22×C6111yescharacteristic
125#446C22×C61164yescomplemented
126#433C22×C61132yes—
127#432C22×C61116yes—
128C2×C4⋊C8C22×C6114yes—
129C2×C4⋊C8C22×C6118yes—
130C2×C22⋊C8C22×C6114yes—
131C2×#97C22×C6114yes—
132C2×#97C22×C6114yes—
133C2×C4×C8C22×C6114yes—
134C61C2×#298711yescharacteristic, direct product factor, Sylow
135C22×Q8C2×C4×C6114yes—
136C23×C4C2×C4×C6112yes—
137C23×C4C23×C6111yescharacteristic
138C22×C8C23×C6118yes—
139C4⋊Q8C2×C4×C61116yes—
140#125C2×C4×C61116yes—
141C22⋊Q8C2×C4×C61132yes—
142C4×Q8C2×C4×C61116yes—
143C4×Q8C23×C61116yes—
144#117C2×C4×C6118yes—
145#117C23×C6118yes—
146C2×C4⋊C4C2×C4×C6114yes—
147C2×C4⋊C4C2×C4×C6118yes—
148C2×C4⋊C4C2×C4×C6114yes—
149C2×C22⋊C4C2×C4×C6114yes—
150C2×C42C2×C4×C6111yescharacteristic
151C2×C42C2×C4×C6111yescharacteristic
152C2×C42C2×C4×C6114yes—
153C2×C42C23×C6114yes—
154C2×C42C23×C6112yes—
155C2×C42C23×C6114yes—
156C4⋊C8C23×C61116yes—
157C4⋊C8C23×C61132yes—
158C22⋊C8C23×C61116yes—
159#97C23×C61116yes—
160#97C23×C61116yes—
161C4×C8C23×C61116yes—
162C24C22×C4×C6111yescharacteristic
163C2×Q8—48no—
164C2×Q8C22×C4×C61116yes—
165C22×C4—24no—
166C22×C4—44no—
167C22×C4C22×C4×C6111yescharacteristic
168C22×C4C22×C4×C6112yes—
169C22×C4C22×C4×C6112yes—
170C22×C4C22×C4×C6112yes—
171C22×C4C22×C4×C6118yes—
172C22×C4C22×C4×C6118yes—
173C22×C4C24×C6112yes—
174C22×C4C24×C6111yescharacteristic
175C2×C8—216no—
176C2×C8C24×C61116yes—
177C4⋊C4C22×C4×C61116yes—
178C4⋊C4C22×C4×C61132yes—
179C4⋊C4C22×C4×C61116yes—
180C22⋊C4C22×C4×C61116yes—
181C42C22×C4×C6114yes—
182C42C22×C4×C6114yes—
183C42C22×C4×C6114yes—
184C42C22×C4×C6118yes—
185C42C24×C6118yes—
186C42C24×C6114yes—
187C23—24no—
188C23—22no—
189C23C23×C4×C6112yes—
190C23C23×C4×C6111yescharacteristic
191Q8—416no—
192C2×C4—24no—
193C2×C4—24no—
194C2×C4—216no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—48no—
199C2×C4C23×C4×C6112yes—
200C2×C4C23×C4×C6114yes—
201C2×C4C23×C4×C6114yes—
202C2×C4C23×C4×C61116yes—
203C2×C4C23×C4×C6111yescharacteristic
204C2×C42−1+4×C6114yes—
205C2×C4C25×C6111yescharacteristic
206C8—216no—
207C22—24no—
208C22—22no—
209C22—44no—
210C22C61×#51912yes—
211C22C61×#56814yes—
212C22C24×C4×C6111yescharacteristic
213C4—24no—
214C4—24no—
215C4—216no—
216C4—22no—
217C4C61×#51912yes—
218C4C2×2−1+4×C6112yes—
219C2—42no—
220C2C61×#298714yesdirect product factor
221C2C2×C61×#51911yescharacteristic
222C2C2×C61×#56812yes—
subgroupG/H
centerC22×C4×C61C24
commutatorC22C24×C4×C61
Frattini, cosocleC2×C4C25×C61
socleC23×C61C23×C4
prime radicalC24×C61C22×C4
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C4×C61 ◁ G

Complements

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

NH ≅ G/Ntype
2. C61×#2987C2direct (N × H)
3. C2×C61×#446C2semidirect
14. C61×#446C22semidirect
95. C2×#2987C61direct (N × H)
109. #2987C2×C61direct (N × H)
110. C2×#446C2×C61semidirect
114. C2×C61#2987direct (N × H)
125. #446C22×C61semidirect
134. C61C2×#2987direct (N × H)
220. C2C61×#2987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C61×#5332
C61×#29872
C2×C61×#4462
C2×C61×#4332
C2×C61×#4322
C2×#298761