Finite Group Databasebeta

← #21444228

Subgroups — #21444228

Order 7808.

212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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#16839815C211yesmaximal, characteristic, complemented
3#16839494C212yesmaximal, complemented
4#16839491C212yesmaximal, complemented
5C61×#431C211yesmaximal, characteristic, complemented
6#14519771—21no—
7#14519769C411yescharacteristic
8#14519765C411yescharacteristic
9#14519760—21no—
10#14519756C411yescharacteristic
11#14519751C411yescharacteristic
12C4×Dic122C2211yescharacteristic
13C4×D244C2211yescharacteristic
14C4×C22⋊D61—21no—
15#14519734—21no—
16C4⋊#92418C2212yes—
17C22⋊#92418—21no—
18C4×#92418—21no—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61—21no—
21C22⋊C8×C61—21no—
22C4×C8×C61C2212yes—
23C22×C4×C61C2×C411yescharacteristic
24C22×C4×C61D411yescharacteristic
25C22×C4×C61D411yescharacteristic
26C2×C22⋊D61—21no—
27C2×D244C2×C411yescharacteristic
28C2×C4×D61—21no—
29C2×Dic122C2×C411yescharacteristic
30C2×C8×C61—22no—
31C42×C61C2×C411yescharacteristic
32C42×C61D411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61C2311yescharacteristic
35C22⋊Dic61—21no—
36#11758198—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40C4⋊Dic61C2×C411yescharacteristic
41C4⋊Dic61C2×C411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46C4×Dic61—21no—
47C2×#92418—22no—
48C23×C61C22⋊C411yescharacteristic
49C22×D61—21no—
50C2×C4×C61—22no—
51C2×C4×C61—22no—
52C2×C4×C61—41no—
53C2×C4×C61C22⋊C411yescharacteristic
54C2×C4×C61C22⋊C411yescharacteristic
55C2×C4×C61C22⋊C411yescharacteristic
56C2×C4×C61C22×C411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C22⋊D61—42no—
60C2×Dic61—21no—
61C2×Dic61—21no—
62C2×Dic61—21no—
63D244—22no—
64C4×D61—42no—
65Dic122—22no—
66C8×C61—42no—
67#92418—42no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61—21no—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—41no—
73C2×D61—41no—
74C2×D61—41no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61#13112yes—
80C4×C61#13512yes—
81Dic61—41no—
82Dic61—41no—
83Dic61—41no—
84#1482—611nomaximal, Sylow
85C2×C61—41no—
86C2×C61#40811yescharacteristic
87C2×C61#41611yescharacteristic
88C2×C61#42111yescharacteristic
89D61—81no—
90#529—611no—
91#431—611no—
92#431D6111yescharacteristic, complemented
93Q8⋊C8—612no—
94D4⋊C8—612no—
95C61#148211yescharacteristic, complemented, Sylow
96#126—1221no—
97#125—611no—
98#124—611no—
99#123—1221no—
100C22⋊Q8—611no—
101#121—611no—
102C4×Q8—611no—
103C4×D4—611no—
104C4×D4—1221no—
105#117—1221no—
106C2×C42C2×D6111yescharacteristic
107C4⋊C8—21no—
108C4⋊C8—612no—
109C22⋊C8—21no—
110C22⋊C8—1221no—
111C4×C8—1221no—
112C4×C8C2×D6112yes—
113C2×Q8—611no—
114C2×D4—611no—
115C2×D4—1221no—
116C22×C4—1221no—
117C22×C4C4×D6111yescharacteristic
118C22×C4D24411yescharacteristic
119C22×C4C22⋊D6111yescharacteristic
120C2×C8—22no—
121C2×C8—1222no—
122C4⋊C4—611no—
123C4⋊C4—611no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C22⋊C4—1221no—
129C22⋊C4—1221no—
130C22⋊C4—1221no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C42—1221no—
134C42C4×D6111yescharacteristic
135C42D24411yescharacteristic
136C42C22⋊D6111yescharacteristic
137C42C22×D6111yescharacteristic
138C23—1221no—
139C23#1175819811yescharacteristic
140Q8—1222no—
141D4—1222no—
142D4—2442no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—41no—
146C2×C4—1221no—
147C2×C4—1221no—
148C2×C4—1221no—
149C2×C4—2442no—
150C2×C4#1175819811yescharacteristic
151C2×C4#1175819811yescharacteristic
152C2×C4#1175819811yescharacteristic
153C2×C4C2×C4×D6111yescharacteristic
154C2×C4C2×D24411yescharacteristic
155C2×C4C2×C22⋊D6111yescharacteristic
156C8—42no—
157C8—2442no—
158C22—21no—
159C22—21no—
160C22—21no—
161C22—2441no—
162C22—2441no—
163C22—2441no—
164C22C2×#1175819811yescharacteristic
165C4—21no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—2441no—
170C4—2441no—
171C4—2441no—
172C4#1451978512yes—
173C4#1451979912yes—
174C2—41no—
175C2—4881no—
176C2#1683973011yescharacteristic
177C2#1683975911yescharacteristic
178C2#1683978011yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1482
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #16839815C2semidirect
3. #16839494C2semidirect
4. #16839491C2semidirect
5. C61×#431C2semidirect
92. #431D61semidirect
95. C61#1482semidirect