Finite Group Databasebeta

← #21447492

Subgroups — #21447492

Order 7808.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#16840332C211yesmaximal, characteristic
2#16839734C212yesmaximal
3#16839557C211yesmaximal, characteristic, complemented
4#16839556C212yesmaximal, complemented
5C61×#354C211yesmaximal, characteristic, complemented
6C2×#11758224C2211yescharacteristic
7C2×Q8×D61C411yescharacteristic, complemented
8#14519777C411yescharacteristic, complemented
9#14519775C411yescharacteristic, complemented
10#14519764C2211yescharacteristic
11#14519759—22no—
12#14519754—22no—
13#14519734C411yescharacteristic, complemented
14#14519733—22no—
15#14519692C2212yes—
16#14519691—22no—
17#124×C61C2211yescharacteristic
18#99×C61C2212yes—
19C2×Q8×C61C2×C411yescharacteristic
20C2×D4×C61C2311yescharacteristic
21C2×C22⋊D61D412yes—
22C22×Dic61D412yes—
23Q8×D61—42no—
24#11758224—42no—
25C2×C4×D61—21no—
26C2×C4×D61C2×C411yescharacteristic
27C2×Dic122—21no—
28C2×Dic122C2×C411yescharacteristic
29C2×Dic122C2×C411yescharacteristic
30C22⋊C4×C61—22no—
31C22⋊C4×C61—22no—
32C42×C61C2×C411yescharacteristic
33C22⋊Dic61—22no—
34C22⋊Dic61—22no—
35#11758198—21no—
36C4⋊Dic61—22no—
37#11758196—21no—
38#11758196—22no—
39#11758196—42no—
40C4×Dic61—42no—
41C4×Dic61C2×C411yescharacteristic
42C23×C61C2×D412yes—
43C22×D61C22⋊C411yescharacteristic
44Q8×C61—41no—
45D4×C61—41no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—42no—
49C2×C4×C61C22×C411yescharacteristic
50C22⋊D61—42no—
51C2×Dic61—22no—
52C2×Dic61—22no—
53C2×Dic61—21no—
54C2×Dic61—21no—
55C2×Dic61—42no—
56C2×Dic61C22⋊C412yes—
57C2×Dic61C22⋊C411yescharacteristic
58C4×D61—22no—
59C4×D61—42no—
60Dic122—41no—
61Dic122—42no—
62Dic122—41no—
63C22×C61—22no—
64C22×C61—42no—
65C22×C61C2×C22⋊C411yescharacteristic
66C2×D61—21no—
67C2×D61—41no—
68C4×C61—21no—
69C4×C61—41no—
70C4×C61—41no—
71C4×C61—82no—
72Dic61—22no—
73Dic61—41no—
74Dic61—41no—
75Dic61—82no—
76Dic61#9912yes—
77#2129—611nomaximal, Sylow
78C2×C61—21no—
79C2×C61—42no—
80C2×C61C2×#9911yescharacteristic
81D61—41no—
82#536—611no—
83#410—612no—
84#354—611no—
85#354—612no—
86#354D6111yescharacteristic, complemented
87C61#212911yescharacteristic, complemented, Sylow
88C2×#41—611no—
89C22×Q8—611no—
90C4⋊Q8—611no—
91C4⋊Q8—611no—
92#124—611no—
93#124C2×D6111yescharacteristic
94#123—1222no—
95C22⋊Q8—1222no—
96#117—611no—
97#117—1222no—
98#99—612no—
99#99—1222no—
100#99C2×D6112yes—
101#41—2442no—
102C2×Q8—611no—
103C2×Q8—611no—
104C2×Q8—1221no—
105C2×Q8—2442no—
106C2×Q8C4×D6111yescharacteristic
107C2×D4—612no—
108C2×D4C22×D6111yescharacteristic
109C22×C4—612no—
110C22×C4—611no—
111C22×C4—1221no—
112C4⋊C4—1221no—
113C4⋊C4—1222no—
114C4⋊C4—1222no—
115C4⋊C4—2442no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—1221no—
119C22⋊C4—1222no—
120C22⋊C4—1222no—
121C42—611no—
122C42—2442no—
123C42C4×D6111yescharacteristic
124C23—611no—
125C23D4×D6112yes—
126Q8—41no—
127Q8—2441no—
128Q8—2441no—
129Q8—2442no—
130D4—41no—
131D4—2442no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—611no—
136C2×C4—612no—
137C2×C4—1222no—
138C2×C4—1222no—
139C2×C4—1222no—
140C2×C4—1221no—
141C2×C4—1221no—
142C2×C4—2442no—
143C2×C4—2442no—
144C2×C4C2×C4×D6111yescharacteristic
145C22—22no—
146C22—42no—
147C22—1221no—
148C22—2441no—
149C22C22⋊C4×D6111yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—612no—
155C4—1222no—
156C4—4882no—
157C4—2441no—
158C4—2441no—
159C2—21no—
160C2—42no—
161C2—2441no—
162C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#354C2
socleC2×C61C2×#99
hypercenter#354D61
hypocenterC61#2129
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #16839557C2semidirect
4. #16839556C2semidirect
5. C61×#354C2semidirect
7. C2×Q8×D61C4semidirect
8. #14519777C4semidirect
9. #14519775C4semidirect
13. #14519734C4semidirect
86. #354D61semidirect
87. C61#2129semidirect