Finite Group Databasebeta

← #21447850

Subgroups — #21447850

Order 7808.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#16840492C211yesmaximal, characteristic, complemented
2#16839947C212yesmaximal
3#16839944C211yesmaximal, characteristic
4#16839560C212yesmaximal, complemented
5C61×#356C211yesmaximal, characteristic, complemented
6#14519825C2211yescharacteristic
7#14519810—22no—
8#14519808—21no—
9#14519776—22no—
10#14519775—21no—
11#14519775C2212yes—
12C4×Dic122—21no—
13#14519742—22no—
14#14519705—21no—
15#14519703—22no—
16#14519696C2211yescharacteristic
17C4⋊Q8×C61C2211yescharacteristic
18#101×C61C2212yes—
19C2×Q8×C61D411yescharacteristic
20C2×Q8×C61C2311yescharacteristic
21#11758226—41no—
22Q8×D61—41no—
23#11758222—21no—
24#11758222—22no—
25C2×Dic122—21no—
26C2×Dic122—21no—
27C2×Dic122D412yes—
28M16×C61—22no—
29C4⋊C4×C61—22no—
30C42×C61D411yescharacteristic
31#11758202—41no—
32#11758201—41no—
33C4⋊Dic61—21no—
34#11758196—22no—
35#11758196—22no—
36#11758196—22no—
37C4×Dic61—21no—
38C4×Dic61—22no—
39C4×Dic61D412yes—
40#11758194—21no—
41Dic244—42no—
42#11758190—42no—
43Q8×C61—41no—
44Q8×C61—41no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61C2×D411yescharacteristic
48C2×C4×C61C2×D412yes—
49C22⋊D61—41no—
50C2×Dic61—22no—
51C2×Dic61—22no—
52D244—22no—
53D244—21no—
54C4×D61—41no—
55C4×D61—42no—
56Dic122—24no—
57Dic122—22no—
58Dic122—21no—
59Dic122—42no—
60Dic122—81no—
61C8×C61—42no—
62#92418—41no—
63C22×C61#12011yescharacteristic
64C2×D61—41no—
65C4×C61—22no—
66C4×C61—21no—
67C4×C61—22no—
68C4×C61—41no—
69Dic61—24no—
70Dic61—41no—
71Dic61—42no—
72#2205—611nomaximal, Sylow
73C2×C61—21no—
74C2×C61B(4,𝔽2)11yescharacteristic
75D61—81no—
76Q82—611no—
77#456—611no—
78#456—612no—
79#356—612no—
80#356D6111yescharacteristic, complemented
81C61#220511yescharacteristic, complemented, Sylow
822−1+4—611no—
83#137—1222no—
84#137—1221no—
85C4⋊Q8—612no—
86C4⋊Q8—1222no—
87C4⋊Q8—1221no—
88C4⋊Q8C2×D6111yescharacteristic
89C4×Q8—1222no—
90C4×Q8—1221no—
91#104—1222no—
92#104—1221no—
93#101—611no—
94#101C2×D6112yes—
95#41—1221no—
96#41—1222no—
97#41—2441no—
98C2×Q8—612no—
99C2×Q8—1221no—
100C2×Q8—1221no—
101C2×Q8—2441no—
102C2×Q8D24411yescharacteristic
103C2×Q8C22×D6111yescharacteristic
104Q16—2442no—
105Q16—2441no—
106SD16—2442no—
107SD16—2441no—
108M16—22no—
109M16—1221no—
110C4⋊C4—22no—
111C4⋊C4—1222no—
112C4⋊C4—1221no—
113C4⋊C4—1222no—
114C4⋊C4—1222no—
115C42—612no—
116C42—1222no—
117C42—1221no—
118C42D24411yescharacteristic
119Q8—41no—
120Q8—41no—
121Q8—1224no—
122Q8—1222no—
123Q8—1221no—
124Q8—4881no—
125Q8—2442no—
126D4—1222no—
127D4—1221no—
128D4—2441no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—1222no—
132C2×C4—1222no—
133C2×C4—2442no—
134C2×C4—2441no—
135C2×C4C2×D24411yescharacteristic
136C2×C4D4×D6112yes—
137C8—42no—
138C8—2441no—
139C22—2441no—
140C22#1451974711yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—1224no—
146C4—2442no—
147C4—2441no—
148C2—21no—
149C2—4881no—
150C2#1683995011yescharacteristic
subgroupG/H
centerC2#16839950
commutatorC2×Q8×C61C23
FrattiniC2×Q8C22×D61
FittingC61×#356C2
socleC2×C61B(4,𝔽2)
hypercenter#356D61
hypocenterC61#2205
LCSG ▷ C2×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #16840492C2semidirect
4. #16839560C2semidirect
5. C61×#356C2semidirect
80. #356D61semidirect
81. C61#2205semidirect