Finite Group Databasebeta

← #21444214

Subgroups — #21444214

Order 7808.

248 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 113 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#16839815C211yesmaximal, characteristic
2#16839815C211yesmaximal, characteristic
3Q8⋊#92418C214yesmaximal, complemented
4C2×C4×Q8×C61C211yesmaximal, characteristic
5C4⋊#92418—21no—
6C4⋊#92418C2212yes—
7C22⋊#92418—21no—
8C22⋊#92418—21no—
9C4×#92418—21no—
10C4×#92418C2212yes—
11C22×Q8×C61C411yescharacteristic
12C4×Q8×C61—21no—
13C4×Q8×C61—21no—
14C4×Q8×C61C412yes—
15C4×Q8×C61C2212yes—
16C2×C4⋊C4×C61—21no—
17C2×C4⋊C4×C61C411yescharacteristic
18C2×C42×C61—21no—
19C2×C42×C61C2211yescharacteristic
20C2×Q8×C61—21no—
21C2×Q8×C61—22no—
22C2×Q8×C61C814yescomplemented
23C2×Q8×C61C2×C412yes—
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61C2×C411yescharacteristic
27C22×C4×C61D411yescharacteristic
28C22×C4×C61D411yescharacteristic
29C4⋊C4×C61—22no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61—22no—
32C4⋊C4×C61C2×C412yes—
33C42×C61—22no—
34C42×C61—22no—
35C42×C61C2×C411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61D411yescharacteristic
38C42×C61C2311yescharacteristic
39C2×#92418—22no—
40C2×#92418—22no—
41C23×C61C22⋊C411yescharacteristic
42Q8×C61—24no—
43Q8×C61—22no—
44Q8×C61C2×C814yes—
45C2×C4×C61—24no—
46C2×C4×C61—22no—
47C2×C4×C61—22no—
48C2×C4×C61—22no—
49C2×C4×C61—41no—
50C2×C4×C61—42no—
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C2×C812yes—
55C2×C4×C61M1612yes—
56C2×C4×C61C22×C411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59#92418—42no—
60#92418—42no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61C22⋊C812yes—
64C22×C61C2×C22⋊C411yescharacteristic
65C4×C61—24no—
66C4×C61—21no—
67C4×C61—21no—
68C4×C61—21no—
69C4×C61—42no—
70C4×C61C22⋊C812yes—
71C4×C61C22×C811yescharacteristic
72C4×C61C2×M1611yescharacteristic
73C4×C61#13712yes—
74#1479—611nomaximal, Sylow
75C2×C61—22no—
76C2×C61C2×C22⋊C811yescharacteristic
77C2×C61#41911yescharacteristic
78C2×C61#42111yescharacteristic
79C2×C4×Q8D6111yescharacteristic
80#431—611no—
81#431—611no—
82Q8⋊C8—614no—
83C61#147911yescharacteristic, complemented, Sylow
84C22×Q8Dic6111yescharacteristic
85C4×Q8—21no—
86C4×Q8—21no—
87C4×Q8Dic6112yes—
88C4×Q8C2×D6112yes—
89C2×C4⋊C4—21no—
90C2×C4⋊C4Dic6111yescharacteristic
91C2×C42—21no—
92C2×C42C2×D6111yescharacteristic
93C4⋊C8—612no—
94C4⋊C8—1221no—
95C22⋊C8—1221no—
96C22⋊C8—1221no—
97C4×C8—612no—
98C4×C8—1221no—
99C2×Q8—22no—
100C2×Q8—21no—
101C2×Q8#9241814yescomplemented
102C2×Q8C2×Dic6112yes—
103C22×C4—21no—
104C22×C4—21no—
105C22×C4C2×Dic6111yescharacteristic
106C22×C4C22⋊D6111yescharacteristic
107C22×C4C22⋊D6111yescharacteristic
108C2×C8—1222no—
109C2×C8—1222no—
110C4⋊C4—22no—
111C4⋊C4—21no—
112C4⋊C4—22no—
113C4⋊C4C2×Dic6112yes—
114C42—22no—
115C42—22no—
116C42C2×Dic6111yescharacteristic
117C42C22⋊D6111yescharacteristic
118C42C22⋊D6111yescharacteristic
119C42C22×D6111yescharacteristic
120C23C22⋊Dic6111yescharacteristic
121Q8—24no—
122Q8—22no—
123Q8C2×#9241814yes—
124C2×C4—24no—
125C2×C4—22no—
126C2×C4—22no—
127C2×C4—22no—
128C2×C4—41no—
129C2×C4—42no—
130C2×C4C2×#9241812yes—
131C2×C4#1175819412yes—
132C2×C4C22⋊Dic6111yescharacteristic
133C2×C4C22⋊Dic6111yescharacteristic
134C2×C4C22⋊Dic6111yescharacteristic
135C2×C4C22×Dic6111yescharacteristic
136C2×C4C2×C22⋊D6111yescharacteristic
137C2×C4C2×C22⋊D6111yescharacteristic
138C8—2442no—
139C8—2442no—
140C22—21no—
141C22—21no—
142C22C22⋊#9241812yes—
143C22C2×C22⋊Dic6111yescharacteristic
144C4—24no—
145C4—21no—
146C4—21no—
147C4—21no—
148C4—42no—
149C4C22⋊#9241812yes—
150C4C22×#9241811yescharacteristic
151C4C2×#1175819411yescharacteristic
152C4#1451980812yes—
153C2—22no—
154C2C2×C22⋊#9241811yescharacteristic
155C2#1683977111yescharacteristic
156C2#1683977911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC4×C61C22×C8
FrattiniC42C22×D61
FittingC2×C4×Q8×C61C2
socleC22×C61C2×C22⋊C4
hypercenterC2×C4×Q8D61
hypocenterC61#1479
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. Q8⋊#92418C2semidirect
22. C2×Q8×C61C8semidirect
83. C61#1479semidirect
101. C2×Q8#92418semidirect