Finite Group Databasebeta

← #21445006

Subgroups — #21445006

Order 7808.

212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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#16840498C211yesmaximal, characteristic
2#16840108C211yesmaximal, characteristic
3#16840048C211yesmaximal, characteristic, complemented
4#16839973C211yesmaximal, characteristic, complemented
5#16839492C211yesmaximal, characteristic, complemented
6#16839492C211yesmaximal, characteristic, complemented
7C61×#331C211yesmaximal, characteristic
8C2×Dic244—21no—
9#14519777C2211yescharacteristic
10#14519764—21no—
11#14519764—21no—
12#14519758—22no—
13C4×Dic122C2211yescharacteristic
14C4×Dic122C2211yescharacteristic
15D4×Dic61—21no—
16D4×Dic61—21no—
17#14519709—21no—
18#14519702—21no—
19#14519702—21no—
20#14519698—22no—
21C4×#92418C2211yescharacteristic
22#127×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4⋊C8×C61C2211yescharacteristic
25C2×D4×C61—21no—
26C2×D4×C61—21no—
27C2×D4×C61D412yes—
28C22×Dic61—22no—
29C2×Dic122—21no—
30C2×Dic122D411yescharacteristic
31C2×Dic122D411yescharacteristic
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C42×C61C2311yescharacteristic
35C22⋊Dic61—22no—
36C22⋊Dic61—22no—
37C22⋊Dic61—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61D411yescharacteristic
41C4⋊Dic61D411yescharacteristic
42#11758196—21no—
43#11758196—21no—
44C4×Dic61—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47Dic244—42no—
48C23×C61—22no—
49D4×C61—42no—
50D4×C61—41no—
51D4×C61—41no—
52D4×C61—41no—
53D4×C61—41no—
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—41no—
62C2×Dic61—82no—
63Dic122—21no—
64Dic122—21no—
65Dic122—21no—
66Dic122—21no—
67Dic122—41no—
68Dic122—41no—
69C8×C61—41no—
70C8×C61—41no—
71#92418—41no—
72C22×C61—42no—
73C22×C61—42no—
74C22×C61—42no—
75C22×C61#12011yescharacteristic
76C4×C61—21no—
77C4×C61#13511yescharacteristic
78C4×C61#13511yescharacteristic
79C4×C61AGL(1,ℤ/8)11yescharacteristic
80C4×C61#13711yescharacteristic
81Dic61—41no—
82Dic61—41no—
83Dic61—41no—
84Dic61—41no—
85Dic61—81no—
86#1640—611nomaximal, Sylow
87C2×C61—82no—
88C2×C61#44911yescharacteristic
89C2×C61#45211yescharacteristic
90C2×C61#45511yescharacteristic
91#559—611no—
92#486—611no—
93#475—611no—
94#462—611no—
95#331D6111yescharacteristic
96Q8⋊C8—611no—
97Q8⋊C8—611no—
98C61#164011yescharacteristic, complemented, Sylow
99C2×Q16—1221no—
100C4⋊Q8—611no—
101#127C2×D6111yescharacteristic
102#124—1221no—
103#124—1221no—
104#123—1222no—
105C4×Q8—611no—
106C4×Q8—611no—
107C4×D4—1221no—
108C4×D4—1221no—
109#106—1221no—
110C4⋊C8C2×D6111yescharacteristic
111C4⋊C8C2×D6111yescharacteristic
112#103—1221no—
113#103—1221no—
114#102—1222no—
115C4×C8—611no—
116C2×Q8—611no—
117C2×Q8—611no—
118C2×Q8—1221no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4D24412yes—
122C22×C4—1222no—
123Q16—2442no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—1221no—
127C4⋊C4—611no—
128C4⋊C4—611no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C22⋊C4—1222no—
134C22⋊C4—1222no—
135C22⋊C4—1222no—
136C42—1221no—
137C42—1221no—
138C42C22×D6111yescharacteristic
139C23—22no—
140Q8—1221no—
141Q8—1221no—
142Q8—1221no—
143Q8—1221no—
144Q8—2441no—
145Q8—2441no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—1221no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—1221no—
155C2×C4—4882no—
156C2×C4—2441no—
157C2×C4C2×D24411yescharacteristic
158C2×C4D4×D6111yescharacteristic
159C2×C4D4×D6111yescharacteristic
160C8—41no—
161C8—41no—
162C8—2441no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22#1451974711yescharacteristic
167C4—21no—
168C4—4881no—
169C4—2441no—
170C4—2441no—
171C4—2441no—
172C4—2441no—
173C4#1451979611yescharacteristic
174C4#1451979811yescharacteristic
175C4#1451980111yescharacteristic
176C4#1451980611yescharacteristic
177C2—82no—
178C2#1683990811yescharacteristic
179C2#1683992511yescharacteristic
180C2#1683994211yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#331C2
socleC22×C61#120
hypercenter#331D61
hypocenterC61#1640
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #16840048C2semidirect
4. #16839973C2semidirect
5. #16839492C2semidirect
6. #16839492C2semidirect
98. C61#1640semidirect