Finite Group Databasebeta

← #21445146

Subgroups — #21445146

Order 7808.

172 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 45 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
1C61⋊#564C211yesmaximal, characteristic
2#16840168C211yesmaximal, characteristic
3#16840130C211yesmaximal, characteristic
4#16839504C211yesmaximal, characteristic
5#16839503C211yesmaximal, characteristic
6#16839503C211yesmaximal, characteristic
7C61×#501C211yesmaximal, characteristic
8#14519769C2211yescharacteristic
9#14519769C2211yescharacteristic
10#14519768—21no—
11#14519768—21no—
12#14519767—21no—
13#14519767—21no—
14#14519767—21no—
15#14519767—21no—
16#14519710—21no—
17#14519708—21no—
18#14519701—21no—
19#14519701—21no—
20#14519688C2211yescharacteristic
21#14519688C2211yescharacteristic
22C4⋊Q8×C61C2211yescharacteristic
23#125×C61C2211yescharacteristic
24#107×C61—21no—
25#106×C61—21no—
26#97×C61C2211yescharacteristic
27C2×Q8×C61—21no—
28C2×C8×C61—21no—
29C4⋊C4×C61—21no—
30C4⋊C4×C61—21no—
31C4⋊C4×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C4⋊C4×C61D411yescharacteristic
35C42×C61C2311yescharacteristic
36C4⋊Dic61—21no—
37C4⋊Dic61—21no—
38C4⋊Dic61D411yescharacteristic
39C4⋊Dic61D411yescharacteristic
40C4⋊Dic61D411yescharacteristic
41C4⋊Dic61D411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47#11758196—21no—
48#11758196—21no—
49#11758196—21no—
50C4×Dic61—21no—
51C4×Dic61—21no—
52C2×#92418—21no—
53C2×#92418—21no—
54Q8×C61—42no—
55C2×C4×C61—21no—
56C2×C4×C61—21no—
57C2×C4×C61—41no—
58C2×C4×C61C2×D411yescharacteristic
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×Dic61—21no—
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C8×C61—22no—
66#92418—22no—
67#92418—41no—
68C22×C61#12011yescharacteristic
69C4×C61—21no—
70C4×C61—21no—
71C4×C61—21no—
72C4×C61—41no—
73C4×C61—41no—
74C4×C61—81no—
75Dic61—41no—
76Dic61—41no—
77Dic61—41no—
78Dic61—41no—
79#1663—611nomaximal, Sylow
80C2×C61#45411yescharacteristic
81C2×C61#45611yescharacteristic
82C2×C61#45611yescharacteristic
83#564—611no—
84#501—611no—
85#501D6111yescharacteristic
86#491—611no—
87#330—611no—
88#330—611no—
89#330—611no—
90C61#166311yescharacteristic, complemented, Sylow
91C4⋊Q8C2×D6111yescharacteristic
92#125—611no—
93#125—611no—
94#125—1221no—
95#125—1221no—
96#125—1221no—
97#125—1221no—
98#125—1221no—
99#125—1221no—
100#125C2×D6111yescharacteristic
101#107—21no—
102#107—1221no—
103#106—21no—
104#106—1221no—
105#103—1221no—
106#103—1221no—
107#97—611no—
108#97—611no—
109#97C2×D6111yescharacteristic
110C2×Q8—21no—
111C2×C8—21no—
112C2×C8—1221no—
113C2×C8—1221no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—21no—
118C4⋊C4—611no—
119C4⋊C4—611no—
120C4⋊C4—611no—
121C4⋊C4—611no—
122C4⋊C4—1221no—
123C4⋊C4—1221no—
124C4⋊C4—1221no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4C22⋊D6111yescharacteristic
133C4⋊C4C22⋊D6111yescharacteristic
134C42—1221no—
135C42—1221no—
136C42C22×D6111yescharacteristic
137Q8—42no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—1221no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—1221no—
145C2×C4D4×D6111yescharacteristic
146C2×C4D4×D6111yescharacteristic
147C2×C4C2×C22⋊D6111yescharacteristic
148C8—22no—
149C8—1222no—
150C8—2441no—
151C22#1451974511yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—41no—
156C4—41no—
157C4—81no—
158C4—2441no—
159C4—2441no—
160C4—2441no—
161C4—2441no—
162C2#1683993311yescharacteristic
163C2#1683994311yescharacteristic
164C2#1683994411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#501C2
socleC22×C61#120
hypercenter#501D61
hypocenterC61#1663
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
90. C61#1663semidirect