Finite Group Databasebeta

← #21444917

Subgroups — #21444917

Order 7808.

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

normal subgroups only

This group has 210 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#16840490C211yesmaximal, characteristic, complemented
2#16840109C211yesmaximal, characteristic
3#16839963C211yesmaximal, characteristic
4#16839962C211yesmaximal, characteristic
5#16839507C211yesmaximal, characteristic, complemented
6#16839494C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758190—21no—
9C2×#11758201—21no—
10#14519777C2211yescharacteristic
11#14519775—21no—
12#14519774C2211yescharacteristic
13#14519769—21no—
14#14519767—22no—
15C4×Dic122—21no—
16C4×Dic122C2211yescharacteristic
17#14519742—21no—
18C4⋊#92418C2211yescharacteristic
19#14519699—21no—
20#14519699—22no—
21#14519697—21no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26C2×D244—21no—
27C2×D244—21no—
28C2×D244—21no—
29C2×Dic122—21no—
30C2×Dic122D411yescharacteristic
31C2×C8×C61—21no—
32C2×C8×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61D411yescharacteristic
35C42×C61—21no—
36C42×C61C2311yescharacteristic
37#11758201—42no—
38C4⋊Dic61—21no—
39C4⋊Dic61D411yescharacteristic
40C4⋊Dic61D412yes—
41#11758196—22no—
42#11758196—22no—
43#11758196—22no—
44#11758196—21no—
45C4×Dic61—22no—
46C4×Dic61—21no—
47C2×#92418—21no—
48#11758190—42no—
49C22×D61—41no—
50Q8×C61—21no—
51Q8×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—22no—
60D244—42no—
61D244—41no—
62D244—41no—
63D244—41no—
64D244—41no—
65Dic122—21no—
66Dic122—41no—
67Dic122—41no—
68Dic122SD1612yescomplemented
69C8×C61—41no—
70C8×C61—41no—
71#92418—41no—
72C22×C61#12011yescharacteristic
73C2×D61—81no—
74C2×D61—81no—
75C2×D61—81no—
76C4×C61—21no—
77C4×C61—41no—
78C4×C61—41no—
79C4×C61C2×SD1611yescharacteristic
80C4×C61#13511yescharacteristic
81C4×C61AGL(1,ℤ/8)11yescharacteristic
82C4×C61#13711yescharacteristic
83Dic61—22no—
84Dic61—42no—
85Dic61—41no—
86#1626—611nomaximal, Sylow
87C2×C61#44811yescharacteristic
88C2×C61#44911yescharacteristic
89C2×C61#45411yescharacteristic
90D61—161no—
91#557—611no—
92#486—611no—
93#460—611no—
94#460—611no—
95#332—611no—
96Q8⋊C8—611no—
97Q8⋊C8D6111yescharacteristic, complemented
98C61#162611yescharacteristic, complemented, Sylow
99C2×SD16—1221no—
100C2×SD16—1221no—
101C4⋊Q8—611no—
102C4⋊Q8—1221no—
103#127—611no—
104#125—1221no—
105#125—1222no—
106C4×Q8—611no—
107C4×Q8—1221no—
108C4×Q8—1221no—
109C4×Q8C2×D6111yescharacteristic
110C4⋊C8—611no—
111C4⋊C8C2×D6111yescharacteristic
112#102—1221no—
113#102—1222no—
114#102—1221no—
115C4×C8C2×D6111yescharacteristic
116C2×Q8—611no—
117C2×Q8—1221no—
118C2×Q8D24411yescharacteristic
119C2×D4—1221no—
120C2×D4—1221no—
121C2×D4—1221no—
122SD16—2442no—
123SD16—2442no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—1221no—
127C4⋊C4—21no—
128C4⋊C4—611no—
129C4⋊C4—612no—
130C4⋊C4—1222no—
131C4⋊C4—1222no—
132C4⋊C4—1222no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4D24411yescharacteristic
136C42—21no—
137C42—1222no—
138C42—1221no—
139C42C22×D6111yescharacteristic
140C23—2441no—
141Q8—21no—
142Q8—21no—
143Q8—612no—
144Q8—1221no—
145Q8—2441no—
146Q8—2441no—
147D4—2442no—
148D4—2441no—
149D4—2441no—
150D4—2441no—
151D4—2441no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—1222no—
157C2×C4C2×D24411yescharacteristic
158C2×C4D4×D6111yescharacteristic
159C2×C4D4×D6111yescharacteristic
160C8—41no—
161C8—41no—
162C8—2441no—
163C22—4881no—
164C22—4881no—
165C22—4881no—
166C22#1451974711yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—1222no—
171C4—2441no—
172C4—2442no—
173C4SD16×D6111yescharacteristic
174C4#1451979911yescharacteristic
175C4#1451980511yescharacteristic
176C4#1451980911yescharacteristic
177C2—9761no—
178C2#1683990211yescharacteristic
179C2#1683990911yescharacteristic
180C2#1683993611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1626
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #16840490C2semidirect
5. #16839507C2semidirect
6. #16839494C2semidirect
7. C61×Q8⋊C8C2semidirect
68. Dic122SD16semidirect
97. Q8⋊C8D61semidirect
98. C61#1626semidirect