Finite Group Databasebeta

← #21444397

Subgroups — #21444397

Order 7808.

218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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#16840296C211yesmaximal, characteristic
2#16839630C211yesmaximal, characteristic, complemented
3#16839500C212yesmaximal, complemented
4#16839497C212yesmaximal
5C61×#431C211yesmaximal, characteristic, complemented
6#14519771—21no—
7#14519769C411yescharacteristic, complemented
8#14519765C411yescharacteristic, complemented
9#14519760—21no—
10#14519756C2211yescharacteristic
11#14519751C2211yescharacteristic
12C4×Dic122C411yescharacteristic, complemented
13C4×D244C411yescharacteristic, complemented
14C4×C22⋊D61—21no—
15#14519734—21no—
16#14519684—21no—
17#14519684—21no—
18#14519684C2212yes—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61—21no—
21C22⋊C8×C61C2212yes—
22C4×C8×C61—21no—
23C22×C4×C61D411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61C2311yescharacteristic
26C2×C22⋊D61—21no—
27C22×Dic61—22no—
28C2×D244C2×C411yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122C2×C411yescharacteristic
31C2×C8×C61—22no—
32C42×C61C2×C411yescharacteristic
33C42×C61C2×C411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36C22⋊Dic61—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41C4⋊Dic61C2×C411yescharacteristic
42C4⋊Dic61C2×C411yescharacteristic
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47C4×Dic61—21no—
48C23×C61C2×D411yescharacteristic
49C22×D61—21no—
50C2×C4×C61—22no—
51C2×C4×C61—41no—
52C2×C4×C61—41no—
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22×C411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C22⋊D61—42no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—42no—
64C2×Dic61—42no—
65C2×Dic61—42no—
66D244—41no—
67C4×D61—42no—
68Dic122—41no—
69C8×C61—42no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61C2×C22⋊C411yescharacteristic
73C22×C61#13512yes—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61—41no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—21no—
83Dic61—41no—
84Dic61—41no—
85Dic61—41no—
86Dic61—82no—
87#1521—611nomaximal, Sylow
88C2×C61—22no—
89C2×C61#41011yescharacteristic
90C2×C61#41611yescharacteristic
91C2×C61#42111yescharacteristic
92D61—81no—
93#529—611no—
94#431D6111yescharacteristic, complemented
95#383—611no—
96#328—612no—
97#327—612no—
98C61#152111yescharacteristic, complemented, Sylow
99#126—1221no—
100#125—611no—
101#124—611no—
102#123—1221no—
103C22⋊Q8—611no—
104#121—611no—
105C4×Q8—611no—
106C4×D4—611no—
107C4×D4—1221no—
108#117—1221no—
109C2×C42C2×D6111yescharacteristic
110C4⋊C8—21no—
111C22⋊C8C2×D6112yes—
112C4×C8—21no—
113#95—612no—
114#95—1221no—
115#95—1221no—
116C2×Q8—611no—
117C2×D4—611no—
118C2×D4—1221no—
119C22×C4—1221no—
120C22×C4—1222no—
121C22×C4D24411yescharacteristic
122C22×C4D24411yescharacteristic
123C22×C4C22×D6111yescharacteristic
124C2×C8—22no—
125C4⋊C4—611no—
126C4⋊C4—611no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C42—1221no—
137C42C4×D6111yescharacteristic
138C42C4×D6111yescharacteristic
139C42C22⋊D6111yescharacteristic
140C42C22⋊D6111yescharacteristic
141C23—1221no—
142C23C2×D24411yescharacteristic
143Q8—2441no—
144D4—2441no—
145D4—2442no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—1221no—
152C2×C4—2442no—
153C2×C4—2442no—
154C2×C4—2442no—
155C2×C4—2442no—
156C2×C4#1175819811yescharacteristic
157C2×C4#1175819811yescharacteristic
158C2×C4#1175819811yescharacteristic
159C2×C4#1175819811yescharacteristic
160C2×C4C2×C4×D6111yescharacteristic
161C2×C4C2×C22⋊D6111yescharacteristic
162C8—42no—
163C22—21no—
164C22—21no—
165C22—2441no—
166C22—2441no—
167C22—2441no—
168C22C2×#1175819811yescharacteristic
169C22#1451979912yes—
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—4882no—
177C4—2441no—
178C4—2441no—
179C4—2441no—
180C2—22no—
181C2—4881no—
182C2#1683973511yescharacteristic
183C2#1683975911yescharacteristic
184C2#1683977811yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1521
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #16839630C2semidirect
3. #16839500C2semidirect
5. C61×#431C2semidirect
7. #14519769C4semidirect
8. #14519765C4semidirect
12. C4×Dic122C4semidirect
13. C4×D244C4semidirect
94. #431D61semidirect
98. C61#1521semidirect