Finite Group Databasebeta

← #21445129

Subgroups — #21445129

Order 7808.

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

normal subgroups only

This group has 196 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
1#16840516C211yesmaximal, characteristic
2#16840168C211yesmaximal, characteristic, complemented
3#16840154C211yesmaximal, characteristic
4#16839504C211yesmaximal, characteristic, complemented
5#16839503C211yesmaximal, characteristic, complemented
6#16839501C211yesmaximal, characteristic
7C61×#501C211yesmaximal, characteristic, complemented
8C2×#11758202—21no—
9C2×#11758201—21no—
10#14519776—21no—
11#14519772—21no—
12#14519772—21no—
13#14519769C2211yescharacteristic
14#14519765C2211yescharacteristic
15#14519762—21no—
16#14519757—21no—
17#14519755—21no—
18#14519710—21no—
19#14519708—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×D244D411yescharacteristic
29C2×C4×D61—21no—
30C2×Dic122—21no—
31C2×Dic122D411yescharacteristic
32C2×C8×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61D411yescharacteristic
38C4⋊C4×C61D411yescharacteristic
39C42×C61C2311yescharacteristic
40#11758202—42no—
41#11758201—42no—
42#11758198—21no—
43#11758198—21no—
44#11758198—21no—
45#11758198—21no—
46#11758198—21no—
47C4⋊Dic61—21no—
48C4⋊Dic61D411yescharacteristic
49C4⋊Dic61D411yescharacteristic
50#11758196—21no—
51#11758196—21no—
52#11758196—21no—
53C4×Dic61—21no—
54C2×#92418—21no—
55C2×#92418—21no—
56C22×D61—21no—
57Q8×C61—41no—
58Q8×C61—41no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—41no—
62C2×C4×C61C2×D411yescharacteristic
63C2×C4×C61C2×D411yescharacteristic
64C2×C4×C61C2×D411yescharacteristic
65C2×Dic61—21no—
66C2×Dic61—21no—
67C2×Dic61—21no—
68D244—41no—
69C4×D61—81no—
70Dic122—41no—
71Dic122—81no—
72C8×C61—22no—
73#92418—22no—
74#92418—22no—
75C22×C61#12011yescharacteristic
76C2×D61—41no—
77C2×D61—41no—
78C2×D61—41no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—41no—
83C4×C61—41no—
84C4×C61—81no—
85Dic61—41no—
86Dic61—41no—
87Dic61—41no—
88#1660—611nomaximal, Sylow
89C2×C61#45311yescharacteristic
90C2×C61#45611yescharacteristic
91C2×C61#45611yescharacteristic
92D61—81no—
93#563—611no—
94#501—611no—
95#501D6111yescharacteristic, complemented
96#497—611no—
97#330—611no—
98#330—611no—
99#329—611no—
100C61#166011yescharacteristic, complemented, Sylow
101C2×Q16—1221no—
102C2×SD16—1221no—
103C4⋊Q8—1221no—
104C4⋊Q8C2×D6111yescharacteristic
105#126—1221no—
106#126—1221no—
107#125—611no—
108#125C2×D6111yescharacteristic
109#124—611no—
110#123—1221no—
111C22⋊Q8—1221no—
112C22⋊Q8—1221no—
113#107—21no—
114#107—1221no—
115#106—21no—
116#106—1221no—
117#97—611no—
118#97—611no—
119#97C2×D6111yescharacteristic
120C2×Q8—21no—
121C2×Q8—611no—
122C2×Q8—1221no—
123C2×D4—611no—
124C22×C4—1221no—
125Q16—2442no—
126SD16—2442no—
127C2×C8—21no—
128C2×C8—1221no—
129C2×C8—1221no—
130C4⋊C4—21no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—611no—
135C4⋊C4—611no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4—1221no—
139C4⋊C4—1221no—
140C4⋊C4C22⋊D6111yescharacteristic
141C4⋊C4C22⋊D6111yescharacteristic
142C22⋊C4—1221no—
143C22⋊C4—1221no—
144C22⋊C4—1221no—
145C22⋊C4—1221no—
146C22⋊C4—1221no—
147C42—1221no—
148C42C22×D6111yescharacteristic
149C23—1221no—
150Q8—41no—
151Q8—41no—
152Q8—4881no—
153Q8—2441no—
154D4—2441no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—1221no—
159C2×C4—1221no—
160C2×C4—1221no—
161C2×C4—4881no—
162C2×C4D4×D6111yescharacteristic
163C2×C4D4×D6111yescharacteristic
164C2×C4C2×C22⋊D6111yescharacteristic
165C8—22no—
166C8—1222no—
167C8—1222no—
168C22—2441no—
169C22—2441no—
170C22—2441no—
171C22#1451974511yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—81no—
178C4—2441no—
179C4—2441no—
180C4—2441no—
181C2—4881no—
182C2#1683992811yescharacteristic
183C2#1683994311yescharacteristic
184C2#1683994411yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#501C2
socleC22×C61#120
hypercenter#501D61
hypocenterC61#1660
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #16840168C2semidirect
4. #16839504C2semidirect
5. #16839503C2semidirect
7. C61×#501C2semidirect
95. #501D61semidirect
100. C61#1660semidirect