Finite Group Databasebeta

← #21458784

Subgroups — #21458784

Order 7808.

320 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#16840488C212yesmaximal
2#16840170C212yesmaximal
3#16840164C211yesmaximal, characteristic
4#16840071C212yesmaximal
5#16840069C212yesmaximal
6#16840055C212yesmaximal
7#16839892C211yesmaximal, characteristic
8#16839869C212yesmaximal
9C4×Q16×C61C211yesmaximal, characteristic
10#14519776—22no—
11#14519776C2212yes—
12#14519769—22no—
13#14519769C2212yes—
14#14519768—22no—
15#14519768C2212yes—
16Q8×Dic61C2212yes—
17Q8×Dic61C2212yes—
18C4×Dic122—22no—
19C4×Dic122C2211yescharacteristic
20#14519711C2211yescharacteristic
21#14519711C2211yescharacteristic
22#14519710C2212yes—
23#14519709C2212yes—
24#14519708C2212yes—
25C4⋊#92418C2211yescharacteristic
26#14519706C2212yes—
27#14519701C2212yes—
28#14519701C2212yes—
29#14519687C2212yes—
30C2×Q16×C61C2211yescharacteristic
31C4×Q8×C61C2212yes—
32#107×C61C2211yescharacteristic
33#103×C61C2212yes—
34C4×C8×C61C2211yescharacteristic
35C2×Q8×C61C2312yes—
36C2×Dic122—22no—
37C2×Dic122D411yescharacteristic
38Q16×C61Q814yescomplemented
39C2×C8×C61C2311yescharacteristic
40C2×C8×C61C2311yescharacteristic
41C4⋊C4×C61—22no—
42C4⋊C4×C61C2312yes—
43C42×C61—22no—
44C42×C61C2311yescharacteristic
45C4⋊Dic61—22no—
46C4⋊Dic61—22no—
47C4⋊Dic61—22no—
48C4⋊Dic61D411yescharacteristic
49C4⋊Dic61C2312yes—
50C4⋊Dic61C2312yes—
51#11758196—22no—
52#11758196—22no—
53#11758196—22no—
54#11758196—22no—
55#11758196D412yes—
56C4×Dic61—22no—
57C4×Dic61—22no—
58C4×Dic61C2312yes—
59C2×#92418C2312yes—
60Q8×C61—22no—
61Q8×C61C2×Q814yes—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61C2×D411yescharacteristic
65C2×C4×C61C2×D411yescharacteristic
66C2×C4×C61C2411yescharacteristic
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61C2×D412yes—
70C2×Dic61C2×D412yes—
71Dic122—41no—
72Dic122—44no—
73C8×C61—21no—
74C8×C61C2×Q812yes—
75#92418—22no—
76C22×C61C22×D411yescharacteristic
77C4×C61—24no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—42no—
81C4×C61C22×Q811yescharacteristic
82C4×C612−1+411yescharacteristic
83Dic61—22no—
84Dic61—22no—
85Dic61—42no—
86Dic61—42no—
87#3390—611nomaximal, Sylow
88C2×C61D4×Q811yescharacteristic
89C2×C61#57511yescharacteristic
90C2×C61#57811yescharacteristic
91#557—612no—
92#501—612no—
93#499—611no—
94#479—612no—
95#479—612no—
96#477—612no—
97#446—611no—
98#441—612no—
99C4×Q16D6111yescharacteristic
100C61#339011yescharacteristic, complemented, Sylow
101C2×Q16C2×D6111yescharacteristic
102C4⋊Q8—612no—
103C4⋊Q8—1222no—
104#125—612no—
105#125—612no—
106#125—1222no—
107#125—1222no—
108C4×Q8—611no—
109C4×Q8—612no—
110C4×Q8—612no—
111C4×Q8—1222no—
112C4×Q8C2×D6112yes—
113#107—611no—
114#107—611no—
115#107—612no—
116#107C2×D6111yescharacteristic
117#106—612no—
118#106—612no—
119C4⋊C8—612no—
120C4⋊C8—611no—
121#103—612no—
122#103—612no—
123#103C2×D6112yes—
124#97—612no—
125C4×C8C2×D6111yescharacteristic
126C2×Q8—611no—
127C2×Q8—1222no—
128C2×Q8C22×D6112yes—
129Q16Dic12214yescomplemented
130C2×C8—612no—
131C2×C8C22×D6111yescharacteristic
132C2×C8C22×D6111yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—612no—
135C4⋊C4—611no—
136C4⋊C4—612no—
137C4⋊C4—612no—
138C4⋊C4—1222no—
139C4⋊C4—1222no—
140C4⋊C4—1222no—
141C4⋊C4—1222no—
142C4⋊C4—1222no—
143C4⋊C4—1222no—
144C4⋊C4—1222no—
145C4⋊C4C22×D6112yes—
146C42—22no—
147C42—612no—
148C42—1222no—
149C42—1222no—
150C42C22×D6111yescharacteristic
151Q8—22no—
152Q8—2441no—
153Q8—2444no—
154Q8C2×Dic12214yes—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—612no—
158C2×C4—612no—
159C2×C4—1222no—
160C2×C4—1222no—
161C2×C4D4×D6111yescharacteristic
162C2×C4D4×D6111yescharacteristic
163C2×C4C23×D6111yescharacteristic
164C8—21no—
165C8—1222no—
166C8C2×Dic12212yes—
167C22C2×D4×D6111yescharacteristic
168C4—21no—
169C4—21no—
170C4—24no—
171C4—42no—
172C4—1222no—
173C4—1222no—
174C4—2442no—
175C4—2442no—
176C4C22×Dic12211yescharacteristic
177C4#1451982411yescharacteristic
178C2D4×Dic12211yescharacteristic
179C2#1684055911yescharacteristic
180C2#1684057511yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC4×Q16×C61C2
socleC22×C61C22×D4
hypercenterC4×Q16D61
hypocenterC61#3390
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
38. Q16×C61Q8semidirect
100. C61#3390semidirect
129. Q16Dic122semidirect