Finite Group Databasebeta

← #21446527

Subgroups — #21446527

Order 7808.

222 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 75 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#16839790C211yesmaximal, characteristic, complemented
2#16839758C211yesmaximal, characteristic
3#16839729C211yesmaximal, characteristic
4C2×#14519688C211yesmaximal, characteristic, complemented
5#16839526C211yesmaximal, characteristic, complemented
6#16839522C211yesmaximal, characteristic, complemented
7C2×#104×C61C211yesmaximal, characteristic
8C2×#11758194C2211yescharacteristic
9C22×#92418C2211yescharacteristic
10C22×#92418C2211yescharacteristic
11#14519736C2211yescharacteristic
12#14519706—22no—
13#14519701C412yescomplemented
14#14519698C412yescomplemented
15C22⋊#92418—22no—
16#14519688—22no—
17C2×#41×C61C2211yescharacteristic
18C2×M16×C61C2211yescharacteristic
19C2×C42×C61C2211yescharacteristic
20#104×C61—22no—
21#41×C61—21no—
22#41×C61—21no—
23#41×C61—21no—
24#41×C61—21no—
25C2×Q8×C61C2×C411yescharacteristic
26C2×D4×C61—21no—
27C2×D4×C61C2×C411yescharacteristic
28C22×C4×C61—21no—
29C22×C4×C61—21no—
30C22×C4×C61C2311yescharacteristic
31M16×C61—21no—
32M16×C61—21no—
33C2×C8×C61—21no—
34C42×C61—21no—
35C42×C61D412yes—
36C22⋊Dic61—21no—
37C4⋊Dic61C2×C412yes—
38C4×Dic61—21no—
39#11758194—21no—
40#11758194—21no—
41C2×#92418—21no—
42C2×#92418—21no—
43C2×#92418—21no—
44C2×#92418—21no—
45C2×#92418—21no—
46C2×#92418C2×C412yes—
47C2×#92418D412yes—
48C23×C61—21no—
49C23×C61#4111yescharacteristic
50Q8×C61—21no—
51Q8×C61—21no—
52D4×C61—21no—
53D4×C61—21no—
54D4×C61—41no—
55D4×C61—41no—
56C2×C4×C61—21no—
57C2×C4×C61—22no—
58C2×C4×C61—42no—
59C2×C4×C61—41no—
60C2×C4×C61—41no—
61C2×C4×C61C22×C411yescharacteristic
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61#4111yescharacteristic
65C2×C4×C61#4111yescharacteristic
66C2×C4×C61#4111yescharacteristic
67C2×Dic61—22no—
68C8×C61—41no—
69#92418—22no—
70#92418—22no—
71#92418—41no—
72C22×C61—22no—
73C22×C61—41no—
74C22×C61—42no—
75C22×C61C4×D411yescharacteristic
76C22×C61#12311yescharacteristic
77C22×C61#12611yescharacteristic
78C4×C61—42no—
79C4×C61—41no—
80C4×C61#11711yescharacteristic
81C4×C61C4×D411yescharacteristic
82C4×C61#12111yescharacteristic
83C4×C61#12411yescharacteristic
84Dic61—42no—
85#1938—611nomaximal, Sylow
86C2×C61—21no—
87C2×C61—21no—
88C2×C61—81no—
89C2×C61#38811yescharacteristic
90C2×C61#44412yes—
91#424—611no—
92C2×#104D6111yescharacteristic
93#416—611no—
94#408—611no—
95C2×#97—611no—
96#341—611no—
97#339—611no—
98C61#193811yescharacteristic, complemented, Sylow
99C2×#41C2×D6111yescharacteristic
100C2×M16—611no—
101C2×M16C2×D6111yescharacteristic
102C22×C8—611no—
103C22×C8—611no—
104#117—611no—
105C2×C42C2×D6111yescharacteristic
106C4⋊C8—1222no—
107#104—22no—
108#103—612no—
109#102—612no—
110C22⋊C8—1222no—
111#97—1222no—
112#41—21no—
113#41—21no—
114#41—21no—
115#41—21no—
116C2×Q8C4×D6111yescharacteristic
117C2×D4—21no—
118C2×D4C4×D6111yescharacteristic
119C22×C4—21no—
120C22×C4—21no—
121C22×C4C22×D6111yescharacteristic
122M16—21no—
123M16—21no—
124M16—1221no—
125M16—1221no—
126C2×C8—21no—
127C2×C8—612no—
128C2×C8—612no—
129C2×C8—1221no—
130C2×C8—1221no—
131C2×C8—1221no—
132C2×C8—1221no—
133C2×C8—1221no—
134C4⋊C4—612no—
135C22⋊C4—1221no—
136C42—21no—
137C42—1221no—
138C42C22⋊D6112yes—
139C23—21no—
140C23#1175822411yescharacteristic
141Q8—21no—
142Q8—21no—
143D4—21no—
144D4—21no—
145D4—41no—
146D4—41no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—1222no—
153C2×C4C2×C4×D6111yescharacteristic
154C2×C4#1175822211yescharacteristic
155C2×C4D4×D6111yescharacteristic
156C2×C4#1175822411yescharacteristic
157C2×C4#1175822411yescharacteristic
158C2×C4C2×C22⋊D6111yescharacteristic
159C8—41no—
160C8—1222no—
161C8—1222no—
162C8—2441no—
163C22—22no—
164C22—42no—
165C22—41no—
166C22#1451973711yescharacteristic
167C22#1451975811yescharacteristic
168C22#1451977011yescharacteristic
169C4—42no—
170C4—41no—
171C4—2442no—
172C4#1451973311yescharacteristic
173C4C4×C22⋊D6111yescharacteristic
174C4#1451974811yescharacteristic
175C4#1451976311yescharacteristic
176C2—21no—
177C2—21no—
178C2—81no—
179C2#1683965011yescharacteristic
180C2#1683988112yes—
subgroupG/H
centerC2×C4D4×D61
commutatorC2×C4×C61C22×C4
FrattiniC22×C4C22×D61
FittingC2×#104×C61C2
socleC22×C61C4×D4
hypercenterC2×#104D61
hypocenterC61#1938
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. #16839790C2semidirect
4. C2×#14519688C2semidirect
5. #16839526C2semidirect
6. #16839522C2semidirect
13. #14519701C4semidirect
14. #14519698C4semidirect
98. C61#1938semidirect