Finite Group Databasebeta

← #21445095

Subgroups — #21445095

Order 7808.

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

normal subgroups only

This group has 194 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
2#16840158C211yesmaximal, characteristic
3#16839969C211yesmaximal, characteristic
4#16839509C211yesmaximal, characteristic
5Q8⋊#92418C211yesmaximal, characteristic
6#16839492C211yesmaximal, characteristic
7C61×#475C211yesmaximal, characteristic
8C2×#11758202—21no—
9#14519777C2211yescharacteristic
10#14519775—21no—
11#14519769—21no—
12#14519767—22no—
13C4×Dic122—21no—
14C4×Dic122C2211yescharacteristic
15#14519742—21no—
16#14519708—22no—
17C4⋊#92418C2211yescharacteristic
18#14519701—21no—
19C4×#92418C2211yescharacteristic
20C4⋊Q8×C61C2211yescharacteristic
21C4×Q8×C61C2211yescharacteristic
22#106×C61—21no—
23C4⋊C8×C61C2211yescharacteristic
24#103×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61D411yescharacteristic
27C2×Dic122—21no—
28C2×Dic122D411yescharacteristic
29C2×C8×C61—21no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C42×C61—21no—
35C42×C61C2311yescharacteristic
36#11758202—42no—
37C4⋊Dic61—21no—
38C4⋊Dic61D411yescharacteristic
39C4⋊Dic61D412yes—
40#11758196—22no—
41#11758196—22no—
42#11758196—22no—
43#11758196—21no—
44C4×Dic61—22no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48Q8×C61—21no—
49Q8×C61—21no—
50Q8×C61—41no—
51Q8×C61—41no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—22no—
61Dic122—21no—
62Dic122—41no—
63Dic122—41no—
64Dic122SD1612yes—
65C8×C61—41no—
66#92418—22no—
67#92418—41no—
68C22×C61#12011yescharacteristic
69C4×C61—21no—
70C4×C61—41no—
71C4×C61—41no—
72C4×C61—81no—
73C4×C61C2×SD1611yescharacteristic
74C4×C61#13511yescharacteristic
75C4×C61#13711yescharacteristic
76C4×C61#13711yescharacteristic
77Dic61—22no—
78Dic61—42no—
79Dic61—41no—
80#1653—611nomaximal, Sylow
81C2×C61#44811yescharacteristic
82C2×C61#45211yescharacteristic
83C2×C61#45611yescharacteristic
84#557—611no—
85#498—611no—
86#475D6111yescharacteristic
87#462—611no—
88#332—611no—
89Q8⋊C8—611no—
90Q8⋊C8—611no—
91C61#165311yescharacteristic, complemented, Sylow
92C2×Q16—1221no—
93C4⋊Q8—611no—
94C4⋊Q8—1221no—
95C4⋊Q8C2×D6111yescharacteristic
96#125—1221no—
97#125—1222no—
98C4×Q8—611no—
99C4×Q8—1221no—
100C4×Q8—1221no—
101C4×Q8C2×D6111yescharacteristic
102#106—21no—
103#106—1222no—
104C4⋊C8—611no—
105C4⋊C8C2×D6111yescharacteristic
106#103—21no—
107#103—1221no—
108C4×C8—611no—
109C2×Q8—21no—
110C2×Q8—611no—
111C2×Q8—1221no—
112C2×Q8C22⋊D6111yescharacteristic
113Q16—2442no—
114C2×C8—21no—
115C2×C8—1221no—
116C2×C8—1221no—
117C4⋊C4—21no—
118C4⋊C4—21no—
119C4⋊C4—21no—
120C4⋊C4—611no—
121C4⋊C4—612no—
122C4⋊C4—1222no—
123C4⋊C4—1222no—
124C4⋊C4—1222no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4C22⋊D6111yescharacteristic
128C42—21no—
129C42—1222no—
130C42—1221no—
131C42C22×D6111yescharacteristic
132Q8—21no—
133Q8—21no—
134Q8—41no—
135Q8—41no—
136Q8—612no—
137Q8—1221no—
138Q8—2441no—
139Q8—2441no—
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—41no—
143C2×C4—1221no—
144C2×C4—1221no—
145C2×C4—1222no—
146C2×C4D4×D6111yescharacteristic
147C2×C4D4×D6111yescharacteristic
148C2×C4C2×C22⋊D6111yescharacteristic
149C8—41no—
150C8—1222no—
151C8—2441no—
152C22#1451974511yescharacteristic
153C4—21no—
154C4—41no—
155C4—41no—
156C4—81no—
157C4—1222no—
158C4—2441no—
159C4—2442no—
160C4SD16×D6111yescharacteristic
161C4#1451979711yescharacteristic
162C4#1451980611yescharacteristic
163C4#1451980811yescharacteristic
164C2#1683989911yescharacteristic
165C2#1683992211yescharacteristic
166C2#1683994311yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#475C2
socleC22×C61#120
hypercenter#475D61
hypocenterC61#1653
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
91. C61#1653semidirect