Finite Group Databasebeta

← #21461981

Subgroups — #21461981

Order 7808.

276 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 68 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
1D61⋊#108C211yesmaximal, characteristic
2#16840755C212yesmaximal
3D61⋊#101C212yesmaximal
4#16840725C211yesmaximal, characteristic
5C2×Q16×D61C211yesmaximal, characteristic
6D61⋊M16C2212yes—
7D61⋊M16C2211yescharacteristic
8#14519856C2211yescharacteristic
9#14519848—21no—
10#14519847—21no—
11#14519840—24no—
12#14519838—24no—
13#14519831—21no—
14C8×#6923—21no—
15C2×Q8×D61C2212yes—
16C2×Dic244C411yescharacteristic, complemented
17C2×#11758202C412yescomplemented
18Q16×D61—21no—
19Q16×D61—21no—
20Q16×D61—21no—
21Q16×D61—21no—
22C2×C8×D61C2211yescharacteristic
23C2×Q16×C61C411yescharacteristic, complemented
24C2×Q8×C61C2×C412yes—
25Q8×D61—22no—
26Q8×D61—22no—
27Q8×D61—22no—
28Q8×D61—22no—
29C2×C4×D61—22no—
30C2×C4×D61C2311yescharacteristic
31C2×Dic122—22no—
32C2×Dic122C2×C412yes—
33C22⋊#6923—21no—
34#11758217—22no—
35#11758217D412yes—
36C4⋊#6923D412yes—
37C4×#6923—21no—
38#11758213—21no—
39#11758213—22no—
40D61⋊C8—21no—
41D61⋊C8—22no—
42Q16×C61—21no—
43Q16×C61—21no—
44C2×C8×C61C2×C411yescharacteristic
45#11758202—22no—
46#11758202—22no—
47C2×#92418C2×C411yescharacteristic
48Dic244—21no—
49Dic244—21no—
50C8×D61D411yescharacteristic
51C8×D61D411yescharacteristic
52C8×D61D411yescharacteristic
53C8×D61D411yescharacteristic
54C22×D61#4111yescharacteristic
55C2×#6923—22no—
56Q8×C61—22no—
57Q8×C61—22no—
58C2×C4×C61—22no—
59C2×C4×C61C22×C411yescharacteristic
60C2×Dic61—22no—
61C2×Dic61C2×D411yescharacteristic
62C4×D61—42no—
63C4×D61—42no—
64C4×D61C2×D411yescharacteristic
65C4×D61C2×D411yescharacteristic
66C4×D61C2×D411yescharacteristic
67C4×D61#4111yescharacteristic
68Dic122—22no—
69Dic122—22no—
70Dic122—42no—
71Dic122—42no—
72#92420—22no—
73#92420—42no—
74C8×C61C22⋊C411yescharacteristic
75C8×C61C22⋊C411yescharacteristic
76#92418C22⋊C411yescharacteristic
77#92418C22⋊C411yescharacteristic
78C22×C61C4×D411yescharacteristic
79C2×D61—22no—
80C2×D61#12111yescharacteristic
81C2×D61#12411yescharacteristic
82#6923—42no—
83C4×C61—42no—
84C4×C61C2×C22⋊C411yescharacteristic
85C4×C61C4×D411yescharacteristic
86Dic61—42no—
87Dic61#12111yescharacteristic
88Dic61#12711yescharacteristic
89#1979—611nomaximal, Sylow
90C2×C61—21no—
91C2×C61#39011yescharacteristic
92D61—21no—
93D61#47312yes—
94C22×Q16—611no—
95C2×#108—611no—
96#419—612no—
97C2×#101—612no—
98#405—611no—
99C61#197911yescharacteristic, complemented, Sylow
100C22×Q8—612no—
101C2×Q16—612no—
102C2×Q16—611no—
103C2×Q16—1221no—
104C2×Q16—1221no—
105C2×Q16—1221no—
106C2×Q16—1221no—
107C2×Q16#692311yescharacteristic, complemented
108C2×M16—611no—
109C2×M16—612no—
110C22×C8—611no—
111#117—611no—
112#108—1221no—
113#108—1221no—
114#103—1224no—
115#101—1224no—
116#97—1221no—
117C4×C8—1221no—
118C2×Q8—612no—
119C2×Q8—1222no—
120C2×Q8—1222no—
121C2×Q8—1222no—
122C2×Q8—1222no—
123C2×Q8—1222no—
124C2×Q8C2×#692312yes—
125C22×C4—611no—
126C22×C4—1222no—
127Q16—21no—
128Q16—21no—
129Q16—1222no—
130Q16—1222no—
131Q16—1221no—
132Q16—1221no—
133M16—612no—
134M16—1221no—
135M16—1222no—
136M16—1222no—
137C2×C8—611no—
138C2×C8—611no—
139C2×C8—611no—
140C2×C8—611no—
141C2×C8—611no—
142C2×C8—1221no—
143C2×C8—1222no—
144C2×C8C2×#692311yescharacteristic
145C4⋊C4—612no—
146C22⋊C4—1221no—
147C42—1221no—
148C23—611no—
149Q8—22no—
150Q8—22no—
151Q8—1222no—
152Q8—1222no—
153Q8—2442no—
154Q8—2442no—
155C2×C4—22no—
156C2×C4—611no—
157C2×C4—611no—
158C2×C4—611no—
159C2×C4—611no—
160C2×C4—611no—
161C2×C4—1222no—
162C2×C4—1222no—
163C2×C4—2442no—
164C2×C4—2442no—
165C2×C4C22×#692311yescharacteristic
166C8—611no—
167C8—611no—
168C8—1222no—
169C8—2442no—
170C8C22⋊#692311yescharacteristic
171C8C22⋊#692311yescharacteristic
172C22—611no—
173C22—611no—
174C22—1222no—
175C22D4×#692311yescharacteristic
176C4—42no—
177C4—611no—
178C4—611no—
179C4—2442no—
180C4—2442no—
181C4C2×C22⋊#692311yescharacteristic
182C4D4×#692311yescharacteristic
183C2—21no—
184C2—612no—
185C2—1221no—
186C2#1684071411yescharacteristic
subgroupG/H
centerC2#16840714
commutatorC2×C4×C61C22×C4
FrattiniC2×C4C22×#6923
FittingC2×Q16×C61C4
socleC2×C61#390
hypercenterC2×Q16#6923
hypocenterC61#1979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
16. C2×Dic244C4semidirect
17. C2×#11758202C4semidirect
23. C2×Q16×C61C4semidirect
99. C61#1979semidirect
107. C2×Q16#6923semidirect