Finite Group Databasebeta

← #21447481

Subgroups — #21447481

Order 7808.

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

normal subgroups only

This group has 258 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#16840310C211yesmaximal, characteristic
2#16839734C212yesmaximal, complemented
3#16839556C212yesmaximal, complemented
4#16839555C211yesmaximal, characteristic, complemented
5C61×#353C211yesmaximal, characteristic, complemented
6C2×#11758224C411yescharacteristic, complemented
7C2×#11758224C2211yescharacteristic
8#14519777C411yescharacteristic, complemented
9#14519764C411yescharacteristic, complemented
10#14519764C2211yescharacteristic
11#14519748—22no—
12D4×Dic61—22no—
13#14519733—22no—
14C42×D61C411yescharacteristic, complemented
15#14519692C2212yes—
16#14519691—22no—
17#127×C61C2211yescharacteristic
18#99×C61C2212yes—
19C2×D4×C61—22no—
20C2×D4×C61C2×C411yescharacteristic
21C2×D4×C61C2311yescharacteristic
22C2×C22⋊D61—21no—
23C2×C22⋊D61D412yes—
24C22×Dic61—21no—
25C22×Dic61D412yes—
26#11758224—41no—
27#11758224—41no—
28#11758224—41no—
29#11758224—41no—
30C2×C4×D61—21no—
31C2×C4×D61C2×C411yescharacteristic
32C2×Dic122C2×C411yescharacteristic
33C2×Dic122C2×C411yescharacteristic
34C22⋊C4×C61—22no—
35C42×C61C2×C411yescharacteristic
36C22⋊Dic61—22no—
37C22⋊Dic61—22no—
38C22⋊Dic61—22no—
39C4⋊Dic61—22no—
40#11758196—42no—
41C4×Dic61—21no—
42C4×Dic61—42no—
43C4×Dic61C2×C411yescharacteristic
44C23×C61—21no—
45C23×C61C2×D412yes—
46C22×D61C22⋊C411yescharacteristic
47D4×C61—41no—
48D4×C61—41no—
49D4×C61—44no—
50C2×C4×C61—21no—
51C2×C4×C61—42no—
52C2×C4×C61C22×C411yescharacteristic
53C22⋊D61—42no—
54C22⋊D61—42no—
55C2×Dic61—22no—
56C2×Dic61—22no—
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—41no—
60C2×Dic61—41no—
61C2×Dic61—42no—
62C2×Dic61C22⋊C412yes—
63C2×Dic61C22⋊C411yescharacteristic
64C4×D61—21no—
65C4×D61—21no—
66C4×D61—42no—
67Dic122—41no—
68Dic122—41no—
69C22×C61—22no—
70C22×C61—42no—
71C22×C61—42no—
72C22×C61—41no—
73C22×C61C2×C22⋊C411yescharacteristic
74C2×D61—21no—
75C2×D61—41no—
76C4×C61—22no—
77C4×C61—21no—
78C4×C61—82no—
79Dic61—22no—
80Dic61—41no—
81Dic61—41no—
82Dic61—82no—
83Dic61#9911yescharacteristic
84Dic61#9911yescharacteristic
85#2126—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—42no—
88C2×C61—81no—
89C2×C61C2×#9911yescharacteristic
90D61—41no—
91#532—611no—
92#410—612no—
93#354—612no—
94#353—611no—
95#353D6111yescharacteristic, complemented
96C61#212611yescharacteristic, complemented, Sylow
97C2×#41—611no—
98C2×#41—611no—
99C4⋊Q8—611no—
100#127C2×D6111yescharacteristic
101#124—611no—
102#124—611no—
103#121—1222no—
104C4×D4—1222no—
105#117—1222no—
106C2×C42—611no—
107#99—612no—
108#99—1222no—
109#99C2×D6112yes—
110#41—2441no—
111#41—2441no—
112#41—2441no—
113#41—2441no—
114C2×Q8—611no—
115C2×Q8—611no—
116C2×D4—22no—
117C2×D4—612no—
118C2×D4—1221no—
119C2×D4C4×D6111yescharacteristic
120C2×D4C22×D6111yescharacteristic
121C22×C4—612no—
122C22×C4—611no—
123C22×C4—1221no—
124C22×C4—1221no—
125C4⋊C4—1222no—
126C4⋊C4—2442no—
127C22⋊C4—22no—
128C22⋊C4—1222no—
129C22⋊C4—1222no—
130C22⋊C4—1222no—
131C42—611no—
132C42—1221no—
133C42—2442no—
134C42C4×D6111yescharacteristic
135C23—21no—
136C23—611no—
137C23D4×D6112yes—
138Q8—2441no—
139Q8—2441no—
140D4—41no—
141D4—41no—
142D4—44no—
143D4—2442no—
144D4—2442no—
145C2×C4—21no—
146C2×C4—42no—
147C2×C4—611no—
148C2×C4—612no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—2442no—
156C2×C4—2441no—
157C2×C4—2441no—
158C2×C4—2442no—
159C2×C4C2×C4×D6111yescharacteristic
160C22—22no—
161C22—42no—
162C22—42no—
163C22—41no—
164C22—1221no—
165C22—2441no—
166C22C22⋊C4×D6111yescharacteristic
167C4—22no—
168C4—21no—
169C4—82no—
170C4—611no—
171C4—611no—
172C4—1222no—
173C4—4882no—
174C4—2441no—
175C4—2441no—
176C2—21no—
177C2—42no—
178C2—81no—
179C2—2441no—
180C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#353C2
socleC2×C61C2×#99
hypercenter#353D61
hypocenterC61#2126
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #16839734C2semidirect
3. #16839556C2semidirect
4. #16839555C2semidirect
5. C61×#353C2semidirect
6. C2×#11758224C4semidirect
8. #14519777C4semidirect
9. #14519764C4semidirect
14. C42×D61C4semidirect
95. #353D61semidirect
96. C61#2126semidirect