Finite Group Databasebeta

← #21447487

Subgroups — #21447487

Order 7808.

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

normal subgroups only

This group has 286 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#16840330C211yesmaximal, characteristic
2#99×D61C212yesmaximal, complemented
3#16839557C211yesmaximal, characteristic, complemented
4#16839554C212yesmaximal, complemented
5C61×#354C211yesmaximal, characteristic, complemented
6C2×#11758226C411yescharacteristic, complemented
7C2×D4×D61C2211yescharacteristic
8#14519774C411yescharacteristic, complemented
9#14519773C2211yescharacteristic
10#14519766C411yescharacteristic, complemented
11#14519750—22no—
12#14519747—22no—
13#14519734C411yescharacteristic, complemented
14C22⋊C4×D61—22no—
15#14519692C2212yes—
16#14519691—22no—
17#124×C61C2211yescharacteristic
18#99×C61C2212yes—
19C23×D61D412yes—
20C2×Q8×C61C2×C411yescharacteristic, complemented
21C2×D4×C61C2311yescharacteristic
22C2×C22⋊D61—22no—
23C2×C22⋊D61D412yes—
24#11758226—42no—
25D4×D61—42no—
26C2×D244—21no—
27C2×D244—22no—
28C2×D244C2×C411yescharacteristic
29C2×D244C2×C411yescharacteristic, complemented
30C2×C4×D61—21no—
31C2×C4×D61—42no—
32C2×C4×D61C2×C411yescharacteristic
33C22⋊C4×C61—22no—
34C22⋊C4×C61—22no—
35C42×C61C2×C411yescharacteristic, complemented
36C22⋊Dic61—22no—
37#11758198—21no—
38#11758198—22no—
39#11758198—42no—
40#11758196—21no—
41C4×Dic61C2×C411yescharacteristic, complemented
42C23×C61C2×D412yes—
43C22×D61—22no—
44C22×D61—22no—
45C22×D61—21no—
46C22×D61—82no—
47C22×D61C22⋊C412yes—
48C22×D61C22⋊C411yescharacteristic
49Q8×C61—41no—
50D4×C61—41no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—42no—
54C2×C4×C61C22×C411yescharacteristic
55C22⋊D61—42no—
56C22⋊D61—82no—
57C2×Dic61—21no—
58C2×Dic61—42no—
59C2×Dic61C22⋊C411yescharacteristic
60D244—41no—
61D244—41no—
62D244—42no—
63D244—82no—
64C4×D61—22no—
65C4×D61—42no—
66C4×D61—84no—
67C22×C61—22no—
68C22×C61—42no—
69C22×C61C2×C22⋊C411yescharacteristic
70C2×D61—22no—
71C2×D61—41no—
72C2×D61—44no—
73C2×D61—42no—
74C2×D61—42no—
75C2×D61—41no—
76C2×D61—82no—
77C2×D61#9912yes—
78C4×C61—21no—
79C4×C61—41no—
80C4×C61—41no—
81C4×C61—82no—
82Dic61—21no—
83Dic61—41no—
84Dic61—82no—
85#2127—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—42no—
88C2×C61C2×#9911yescharacteristic
89D61—22no—
90D61—42no—
91D61—81no—
92#535—611no—
93C2×#99—612no—
94#354—611no—
95#354D6111yescharacteristic, complemented
96#353—612no—
97C61#212711yescharacteristic, complemented, Sylow
98C2×#41—611no—
99C22×D4—611no—
100#127—611no—
101#127—611no—
102#124—611no—
103#124C2×D6111yescharacteristic
104#121—1222no—
105#120—1222no—
106#117—611no—
107C2×C22⋊C4—1222no—
108#99—612no—
109#99—1222no—
110#99C2×D6112yes—
111C24—612no—
112#41—2442no—
113C2×Q8C4×D6111yescharacteristic, complemented
114C2×D4—612no—
115C2×D4—611no—
116C2×D4—611no—
117C2×D4—1222no—
118C2×D4—1221no—
119C2×D4—1222no—
120C2×D4—2442no—
121C2×D4C22×D6111yescharacteristic
122C22×C4—611no—
123C22×C4—1221no—
124C22×C4—2442no—
125C4⋊C4—1221no—
126C22⋊C4—22no—
127C22⋊C4—22no—
128C22⋊C4—1221no—
129C22⋊C4—1222no—
130C22⋊C4—1222no—
131C22⋊C4—2442no—
132C42—611no—
133C42C4×D6111yescharacteristic, complemented
134C23—611no—
135C23—612no—
136C23—1222no—
137C23—1222no—
138C23—1221no—
139C23—4882no—
140C23D4×D6112yes—
141Q8—41no—
142D4—41no—
143D4—4882no—
144D4—4882no—
145D4—2441no—
146D4—2441no—
147D4—2442no—
148D4—2442no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—42no—
152C2×C4—611no—
153C2×C4—1222no—
154C2×C4—1221no—
155C2×C4—4884no—
156C2×C4—2442no—
157C2×C4—2442no—
158C2×C4C2×C4×D6111yescharacteristic
159C22—22no—
160C22—42no—
161C22—612no—
162C22—1222no—
163C22—4882no—
164C22—2441no—
165C22—2442no—
166C22—2442no—
167C22—2444no—
168C22—2441no—
169C22C22⋊C4×D6111yescharacteristic
170C4—21no—
171C4—41no—
172C4—41no—
173C4—82no—
174C4—1221no—
175C4—4882no—
176C4—2441no—
177C2—21no—
178C2—42no—
179C2—1222no—
180C2—4881no—
181C2—2442no—
182C2#99×D6111yescharacteristic
subgroupG/H
centerC2#99×D61
commutatorC2×C4×C61C22×C4
FrattiniC2×D4C22×D61
FittingC61×#354C2
socleC2×C61C2×#99
hypercenter#354D61
hypocenterC61#2127
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
2. #99×D61C2semidirect
3. #16839557C2semidirect
4. #16839554C2semidirect
5. C61×#354C2semidirect
6. C2×#11758226C4semidirect
8. #14519774C4semidirect
10. #14519766C4semidirect
13. #14519734C4semidirect
20. C2×Q8×C61C2×C4semidirect
29. C2×D244C2×C4semidirect
35. C42×C61C2×C4semidirect
41. C4×Dic61C2×C4semidirect
95. #354D61semidirect
97. C61#2127semidirect
113. C2×Q8C4×D61semidirect
133. C42C4×D61semidirect