Finite Group Databasebeta

← #21444980

Subgroups — #21444980

Order 7808.

188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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#16840491C211yesmaximal, characteristic
2#16840113C211yesmaximal, characteristic
3#16840058C211yesmaximal, characteristic
4#16840057C211yesmaximal, characteristic
5#16839509C211yesmaximal, characteristic
6#16839494C211yesmaximal, characteristic
7C61×Q8⋊C8C211yesmaximal, characteristic
8#14519777—21no—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519768—21no—
12#14519768—22no—
13Q8×Dic61—21no—
14C4×Dic122—21no—
15C4×Dic122C2211yescharacteristic
16#14519711—21no—
17#14519710—21no—
18C4⋊#92418C2211yescharacteristic
19#14519702—21no—
20#14519702—22no—
21#14519701—21no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26C2×Dic122—21no—
27C2×Dic122—21no—
28C2×Dic122D411yescharacteristic
29C2×C8×C61—21no—
30C2×C8×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61D411yescharacteristic
33C42×C61—21no—
34C42×C61C2311yescharacteristic
35C4⋊Dic61—22no—
36C4⋊Dic61—22no—
37C4⋊Dic61—21no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61D412yes—
41C4⋊Dic61D411yescharacteristic
42#11758196—22no—
43#11758196—21no—
44C4×Dic61—22no—
45C4×Dic61—21no—
46C2×#92418—21no—
47Q8×C61—21no—
48Q8×C61Q1612yes—
49C2×C4×C61—21no—
50C2×C4×C61—21no—
51C2×C4×C61C2×D411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C2×Dic61—21no—
55C2×Dic61—21no—
56C2×Dic61—22no—
57C2×Dic61—41no—
58Dic122—21no—
59Dic122—21no—
60Dic122—41no—
61Dic122—41no—
62Dic122—42no—
63C8×C61—41no—
64C8×C61—41no—
65#92418—41no—
66C22×C61#12011yescharacteristic
67C4×C61—22no—
68C4×C61—21no—
69C4×C61—41no—
70C4×C61C2×Q1611yescharacteristic
71C4×C61#13511yescharacteristic
72C4×C61#13711yescharacteristic
73C4×C61#13711yescharacteristic
74Dic61—41no—
75Dic61—42no—
76Dic61—41no—
77Dic61—81no—
78#1636—611nomaximal, Sylow
79C2×C61#45111yescharacteristic
80C2×C61#45211yescharacteristic
81C2×C61#45411yescharacteristic
82#557—611no—
83#487—611no—
84#477—611no—
85#477—611no—
86#332—611no—
87Q8⋊C8—611no—
88Q8⋊C8D6111yescharacteristic
89C61#163611yescharacteristic, complemented, Sylow
90C4⋊Q8—611no—
91C4⋊Q8—611no—
92C4⋊Q8—1221no—
93#125—1222no—
94#125—1221no—
95C4×Q8—611no—
96C4×Q8—1221no—
97C4×Q8—1221no—
98C4×Q8C2×D6111yescharacteristic
99#107—1221no—
100#107—1221no—
101C4⋊C8—611no—
102C4⋊C8C2×D6111yescharacteristic
103#103—1222no—
104#103—1221no—
105#103—1221no—
106C4×C8C2×D6111yescharacteristic
107C2×Q8—611no—
108C2×Q8—1221no—
109C2×Q8—1221no—
110C2×Q8D24411yescharacteristic
111C2×C8—21no—
112C2×C8—21no—
113C2×C8—1221no—
114C4⋊C4—21no—
115C4⋊C4—612no—
116C4⋊C4—611no—
117C4⋊C4—1222no—
118C4⋊C4—1222no—
119C4⋊C4—1222no—
120C4⋊C4—1221no—
121C4⋊C4—1221no—
122C4⋊C4—1221no—
123C4⋊C4—1221no—
124C4⋊C4D24411yescharacteristic
125C42—21no—
126C42—1222no—
127C42—1221no—
128C42C22×D6111yescharacteristic
129Q8—21no—
130Q8—1221no—
131Q8—1221no—
132Q8—2442no—
133Q8—2441no—
134Q8—2441no—
135Q8Dic24412yes—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—1221no—
139C2×C4—1222no—
140C2×C4—1221no—
141C2×C4—2441no—
142C2×C4C2×D24411yescharacteristic
143C2×C4D4×D6111yescharacteristic
144C2×C4D4×D6111yescharacteristic
145C8—41no—
146C8—41no—
147C8—2441no—
148C22#1451974711yescharacteristic
149C4—21no—
150C4—22no—
151C4—41no—
152C4—4881no—
153C4—2441no—
154C4—2441no—
155C4—2442no—
156C4C2×Dic24411yescharacteristic
157C4#1451979811yescharacteristic
158C4#1451980911yescharacteristic
159C4#1451981011yescharacteristic
160C2#1683992011yescharacteristic
161C2#1683992711yescharacteristic
162C2#1683993611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1636
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
89. C61#1636semidirect