Finite Group Databasebeta

← #21444441

Subgroups — #21444441

Order 7808.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D61C211yesmaximal, characteristic
2#16839817C212yesmaximal, complemented
3#16839502C211yesmaximal, characteristic, complemented
4#16839501C212yesmaximal, complemented
5C61×#329C211yesmaximal, characteristic, complemented
6C2×Q8×D61C411yescharacteristic
7C2×D4×D61C411yescharacteristic
8#14519766C411yescharacteristic
9#14519765C2211yescharacteristic
10#14519764C411yescharacteristic
11#14519763—22no—
12C22⋊C4×D61—22no—
13C42×D61C2211yescharacteristic
14#14519706—22no—
15#14519689—22no—
16#14519688C2212yescomplemented
17#124×C61C2211yescharacteristic
18#97×C61C2212yescomplemented
19C23×D61—21no—
20C2×Q8×C61C2×C411yescharacteristic
21C2×D4×C61C2×C411yescharacteristic
22C2×C22⋊D61—21no—
23Q8×D61—42no—
24D4×D61—42no—
25C2×D244C2×C411yescharacteristic
26C2×C4×D61—21no—
27C2×C4×D61C2×C411yescharacteristic
28C2×C4×D61D412yes—
29C2×Dic122—21no—
30C2×Dic122C2×C411yescharacteristic
31C2×C8×C61—22no—
32C22⋊C4×C61—22no—
33C42×C61C2311yescharacteristic
34C22⋊Dic61—22no—
35#11758198—22no—
36#11758198—22no—
37C4×Dic61C2×C411yescharacteristic
38C4×Dic61D412yes—
39C2×#92418—22no—
40C23×C61—21no—
41C22×D61—21no—
42C22×D61—44no—
43C22×D61—42no—
44C22×D61C22⋊C411yescharacteristic
45Q8×C61—41no—
46D4×C61—41no—
47C2×C4×C61—21no—
48C2×C4×C61C22×C411yescharacteristic
49C2×C4×C61C2×D412yes—
50C22⋊D61—42no—
51C2×Dic61—21no—
52C2×Dic61C22⋊C412yes—
53C2×Dic61C22⋊C411yescharacteristic
54D244—41no—
55C4×D61—22no—
56C4×D61—42no—
57C4×D61—42no—
58Dic122—42no—
59Dic122—41no—
60C8×C61—42no—
61#92418—42no—
62C22×C61—41no—
63C22×C61—42no—
64C22×C61C2×C22⋊C411yescharacteristic
65C2×D61—22no—
66C2×D61—41no—
67C2×D61—42no—
68C2×D61—84no—
69C2×D61#10012yes—
70C4×C61—21no—
71C4×C61—22no—
72C4×C61—41no—
73Dic61—21no—
74Dic61—22no—
75Dic61—41no—
76#1533—611nomaximal, Sylow
77C2×C61—81no—
78C2×C61C2×#10011yescharacteristic
79C2×C61#42112yes—
80D61—22no—
81D61—81no—
82C2×#124—611no—
83#432—612no—
84#329—611no—
85#329—612no—
86#329D6111yescharacteristic, complemented
87C61#153311yescharacteristic, complemented, Sylow
88C22×Q8—611no—
89C22×D4—611no—
90#124—611no—
91#124—611no—
92#124—611no—
93#124—1222no—
94#124C2×D6111yescharacteristic
95C2×C22⋊C4—1222no—
96C2×C42—611no—
97C4⋊C8—1222no—
98C22⋊C8—1222no—
99#97—612no—
100#97C2×D6112yescomplemented
101C24—1221no—
102C2×Q8—611no—
103C2×Q8—1221no—
104C2×Q8—2442no—
105C2×Q8C4×D6111yescharacteristic
106C2×D4—611no—
107C2×D4—1221no—
108C2×D4—2442no—
109C2×D4C4×D6111yescharacteristic
110C22×C4—611no—
111C22×C4—612no—
112C22×C4—1221no—
113C2×C8—22no—
114C2×C8—1222no—
115C22⋊C4—22no—
116C22⋊C4—1222no—
117C22⋊C4—1222no—
118C22⋊C4—1222no—
119C42—611no—
120C42—612no—
121C42C22×D6111yescharacteristic
122C23—21no—
123C23—611no—
124C23—1221no—
125C23—2442no—
126C23—2444no—
127Q8—41no—
128Q8—2441no—
129Q8—2442no—
130D4—41no—
131D4—2441no—
132D4—2442no—
133C2×C4—21no—
134C2×C4—612no—
135C2×C4—611no—
136C2×C4—1222no—
137C2×C4—1221no—
138C2×C4—2442no—
139C2×C4—2442no—
140C2×C4C2×C4×D6111yescharacteristic
141C2×C4D4×D6112yes—
142C8—42no—
143C8—2442no—
144C22—41no—
145C22—42no—
146C22—612no—
147C22—1222no—
148C22—4884no—
149C22—2441no—
150C22—2442no—
151C22C22⋊C4×D6111yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—1221no—
156C4—1222no—
157C4—2441no—
158C2—81no—
159C2—1222no—
160C2—4881no—
161C2#100×D6111yescharacteristic
162C2#1683977712yes—
subgroupG/H
centerC22C22⋊C4×D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#329C2
socleC22×C61C2×C22⋊C4
hypercenter#329D61
hypocenterC61#1533
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #16839817C2semidirect
3. #16839502C2semidirect
4. #16839501C2semidirect
5. C61×#329C2semidirect
16. #14519688C22semidirect
18. #97×C61C22semidirect
86. #329D61semidirect
87. C61#1533semidirect
100. #97C2×D61semidirect