Finite Group Databasebeta

← #21444699

Subgroups — #21444699

Order 7808.

166 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 63 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
1C8×Dic122C211yesmaximal, characteristic, complemented
2C4×#11758190C211yesmaximal, characteristic
3#16839841C211yesmaximal, characteristic
4#16839515C211yesmaximal, characteristic, complemented
5#16839494C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic
7C61×#322C211yesmaximal, characteristic, complemented
8C2×#11758190C411yescharacteristic
9C2×#11758189—21no—
10C4×Dic122C2211yescharacteristic
11C4×D244C2211yescharacteristic
12#14519709C411yescharacteristic
13C4⋊#92418C2211yescharacteristic
14C4⋊#92418C2211yescharacteristic
15#14519706—21no—
16#14519702C411yescharacteristic
17#14519699C411yescharacteristic
18#14519689—21no—
19C8×Dic61—21no—
20C4×C8×C61C2211yescharacteristic
21C4×C8×C61C2211yescharacteristic
22C4×C8×C61C2211yescharacteristic
23C2×D244C2×C411yescharacteristic
24C2×C4×D61—21no—
25C2×Dic122C2×C411yescharacteristic
26C2×C8×C61—21no—
27C2×C8×C61C2×C411yescharacteristic
28C2×C8×C61C2×C411yescharacteristic
29C2×C8×C61D411yescharacteristic
30C2×C8×C61D411yescharacteristic
31C42×C61C2311yescharacteristic
32#11758198—21no—
33C4⋊Dic61C2×C411yescharacteristic
34C4⋊Dic61C2×C411yescharacteristic
35#11758196—21no—
36C4×Dic61—21no—
37C2×#92418—21no—
38C2×#92418—21no—
39#11758190—22no—
40#11758189—42no—
41C22×D61—21no—
42C2×C4×C61C22×C411yescharacteristic
43C2×C4×C61C2×D411yescharacteristic
44C2×C4×C61#4111yescharacteristic
45C2×Dic61—21no—
46C2×Dic61—21no—
47C2×Dic61—21no—
48D244—21no—
49D244—21no—
50C4×D61—41no—
51C4×D61—41no—
52Dic122—21no—
53Dic122M1612yescomplemented
54C8×C61—22no—
55C8×C61—21no—
56C8×C61—21no—
57C8×C61—21no—
58C8×C61—21no—
59#92418—41no—
60#92418—41no—
61C22×C61C4×D411yescharacteristic
62C2×D61—41no—
63C2×D61—41no—
64C2×D61—41no—
65C4×C61—21no—
66C4×C61C2×M1611yescharacteristic
67C4×C61#13111yescharacteristic
68C4×C61AGL(1,ℤ/8)11yescharacteristic
69C4×C61#13711yescharacteristic
70Dic61—22no—
71Dic61—41no—
72Dic61—41no—
73#1588—611nomaximal, Sylow
74C2×C61#43511yescharacteristic
75C2×C61#44011yescharacteristic
76C2×C61#44311yescharacteristic
77D61—81no—
78C8×Q8—611no—
79C4×SD16—611no—
80#436—611no—
81#335—611no—
82Q8⋊C8—611no—
83D4⋊C8—611no—
84#322D6111yescharacteristic, complemented
85C61#158811yescharacteristic, complemented, Sylow
86C2×SD16—611no—
87C2×M16—1221no—
88C4×Q8—611no—
89C4×D4—611no—
90#106—611no—
91C4⋊C8—611no—
92C4⋊C8—611no—
93C4⋊C8—1221no—
94#103—611no—
95#102—611no—
96C22⋊C8—1221no—
97C4×C8—1221no—
98C4×C8C2×D6111yescharacteristic
99C4×C8C2×D6111yescharacteristic
100C4×C8C2×D6111yescharacteristic
101C2×Q8—611no—
102C2×D4—611no—
103C22×C4—1221no—
104SD16—1222no—
105M16—2442no—
106C2×C8—21no—
107C2×C8—1221no—
108C2×C8—1221no—
109C2×C8C4×D6111yescharacteristic
110C2×C8C4×D6111yescharacteristic
111C2×C8D24411yescharacteristic
112C2×C8D24411yescharacteristic
113C4⋊C4—611no—
114C4⋊C4—611no—
115C4⋊C4—1221no—
116C22⋊C4—1221no—
117C42—1221no—
118C42C22×D6111yescharacteristic
119C23—1221no—
120Q8—612no—
121Q8—1221no—
122D4—1221no—
123D4—1221no—
124C2×C4—1221no—
125C2×C4—1221no—
126C2×C4—1221no—
127C2×C4—2441no—
128C2×C4—2441no—
129C2×C4C2×C4×D6111yescharacteristic
130C2×C4C2×D24411yescharacteristic
131C2×C4#1175822211yescharacteristic
132C8—22no—
133C8—21no—
134C8—21no—
135C8—21no—
136C8—21no—
137C8—2441no—
138C8—2441no—
139C22—2441no—
140C22—2441no—
141C22—2441no—
142C22C4×D24411yescharacteristic
143C4—21no—
144C4—1222no—
145C4—2441no—
146C4—2441no—
147C4M16×D6111yescharacteristic
148C4#1451978511yescharacteristic
149C4#1451980511yescharacteristic
150C4#1451981011yescharacteristic
151C2—4881no—
152C2#1683983511yescharacteristic
153C2#1683986411yescharacteristic
154C2#1683988011yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#322C2
socleC22×C61C4×D4
hypercenter#322D61
hypocenterC61#1588
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #322

Complements

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

NH ≅ G/Ntype
1. C8×Dic122C2semidirect
4. #16839515C2semidirect
5. #16839494C2semidirect
7. C61×#322C2semidirect
53. Dic122M16semidirect
84. #322D61semidirect
85. C61#1588semidirect