Finite Group Databasebeta

← #21446356

Subgroups — #21446356

Order 7808.

314 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 89 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#16840336C211yesmaximal, characteristic
2#16839780C212yesmaximal
3C2×#14519696C211yesmaximal, characteristic, complemented
4#16839518C212yesmaximal, complemented
5C61×#519C211yesmaximal, characteristic, complemented
6C2×#11758222C2211yescharacteristic
7C2×#11758194C2212yes—
8#14519775C412yescomplemented
9#14519766C412yescomplemented
10#14519760—22no—
11#14519753—22no—
12#14519736C2211yescharacteristic
13#14519705—24no—
14#14519696—22no—
15C22×Q8×C61C2211yescharacteristic
16C4×Q8×C61—24no—
17#117×C61—22no—
18#117×C61C2212yes—
19C2×Q8×C61—22no—
20C2×Q8×C61—22no—
21C2×Q8×C61C2×C412yes—
22C2×Q8×C61D412yes—
23C22×C4×C61D412yes—
24C22×C4×C61C2311yescharacteristic
25C2×C22⋊D61—21no—
26#11758222—22no—
27#11758222—22no—
28C2×D244C2×C411yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122C2×C411yescharacteristic
31C4⋊C4×C61—24no—
32C4⋊C4×C61—22no—
33C22⋊C4×C61—22no—
34C42×C61—24no—
35C42×C61D414yes—
36C22⋊Dic61—21no—
37#11758198—24no—
38C4⋊Dic61—21no—
39#11758196—24no—
40C4×Dic61C2×C412yes—
41#11758194—22no—
42#11758194—22no—
43C2×#92418—22no—
44C23×C61C2×D411yescharacteristic
45C22×D61—21no—
46Q8×C61—24no—
47Q8×C61—24no—
48C2×C4×C61—22no—
49C2×C4×C61—22no—
50C2×C4×C61—24no—
51C2×C4×C61C22⋊C414yes—
52C2×C4×C61C22×C411yescharacteristic
53C2×C4×C61C2×D412yes—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61#4112yes—
56C22⋊D61—41no—
57C22⋊D61—41no—
58C2×Dic61—22no—
59C2×Dic61—21no—
60D244—22no—
61C4×D61—42no—
62Dic122—22no—
63#92418—42no—
64C22×C61—41no—
65C22×C61C2×C22⋊C411yescharacteristic
66C22×C61#12011yescharacteristic
67C22×C61#12311yescharacteristic
68C2×D61—42no—
69C2×D61—41no—
70C4×C61—24no—
71C4×C61—44no—
72C4×C61C4×D412yes—
73C4×C61#12112yes—
74Dic61—42no—
75Dic61—41no—
76#1912—611nomaximal, Sylow
77C2×C61—21no—
78C2×C61—21no—
79C2×C61—21no—
80C2×C61#38611yescharacteristic
81D61—81no—
82#536—611no—
83#519D6111yescharacteristic, complemented
84#421—612no—
85C2×#101—611no—
86H(3,ℤ/4)—612no—
87C61#191211yescharacteristic, complemented, Sylow
88C2×#41—611no—
89C22×Q8C2×D6111yescharacteristic
90C2×M16—612no—
91C4⋊Q8—612no—
92#124—612no—
93#123—1222no—
94C22⋊Q8—1222no—
95C4×Q8—24no—
96#117—22no—
97#117—611no—
98#117C2×D6112yes—
99#104—1224no—
100#101—1222no—
101#41—1222no—
102#41—1222no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—611no—
106C2×Q8C4×D6112yes—
107C2×Q8D24412yes—
108C2×D4—611no—
109C2×D4—1221no—
110C22×C4—1221no—
111C22×C4C22⋊D6112yes—
112C22×C4C22×D6111yescharacteristic
113M16—1222no—
114M16—1222no—
115C2×C8—1222no—
116C4⋊C4—24no—
117C4⋊C4—22no—
118C4⋊C4—1224no—
119C4⋊C4—1221no—
120C22⋊C4—22no—
121C22⋊C4—1221no—
122C22⋊C4—1224no—
123C42—24no—
124C42—612no—
125C42C22⋊D6114yes—
126C23—1221no—
127C23C2×C22⋊D6111yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—1222no—
131D4—1222no—
132D4—2441no—
133D4—2441no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—24no—
137C2×C4—1222no—
138C2×C4—1221no—
139C2×C4—2442no—
140C2×C4#1175819814yes—
141C2×C4C2×C4×D6111yescharacteristic
142C2×C4C2×D24411yescharacteristic
143C2×C4#1175822212yes—
144C2×C4C2×C22⋊D6112yes—
145C8—2442no—
146C22—41no—
147C22—2442no—
148C22—2441no—
149C22C2×#1175819811yescharacteristic
150C22#1451974611yescharacteristic
151C22#1451976011yescharacteristic
152C4—24no—
153C4—44no—
154C4—2442no—
155C4—2441no—
156C4C4×C22⋊D6112yes—
157C4#1451975112yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—4881no—
162C2#1683964111yescharacteristic
subgroupG/H
centerC2#16839641
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#519C2
socleC2×C61#386
hypercenter#519D61
hypocenterC61#1912
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #519

Complements

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

NH ≅ G/Ntype
3. C2×#14519696C2semidirect
4. #16839518C2semidirect
5. C61×#519C2semidirect
8. #14519775C4semidirect
9. #14519766C4semidirect
83. #519D61semidirect
87. C61#1912semidirect