Finite Group Databasebeta

← #21445007

Subgroups — #21445007

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#16840497C211yesmaximal, characteristic
2#16840109C211yesmaximal, characteristic
3#16840048C211yesmaximal, characteristic, complemented
4#16839972C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic
6#16839494C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758202—21no—
9#14519777C2211yescharacteristic
10#14519774C2211yescharacteristic
11#14519766—21no—
12#14519765—21no—
13#14519762—22no—
14C4×Dic122C2211yescharacteristic
15C4×D244—21no—
16#14519739—21no—
17#14519709—21no—
18C4⋊#92418C2211yescharacteristic
19#14519702—21no—
20#14519700—21no—
21#14519699—22no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26C2×D244—21no—
27C2×D244—21no—
28C2×D244D412yes—
29C2×C4×D61—22no—
30C2×Dic122—21no—
31C2×Dic122D411yescharacteristic
32C2×C8×C61—21no—
33C2×C8×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61D411yescharacteristic
36C42×C61—21no—
37C42×C61C2311yescharacteristic
38#11758202—42no—
39#11758198—22no—
40#11758198—22no—
41#11758198—22no—
42C4⋊Dic61—21no—
43C4⋊Dic61—21no—
44C4⋊Dic61D411yescharacteristic
45#11758196—21no—
46C4×Dic61—21no—
47C2×#92418—21no—
48C22×D61—22no—
49Q8×C61—21no—
50Q8×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61C2×D411yescharacteristic
54C2×C4×C61C2×D411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×Dic61—21no—
57C2×Dic61—21no—
58C2×Dic61—41no—
59D244—42no—
60D244—41no—
61D244—41no—
62D244—41no—
63D244—41no—
64C4×D61—82no—
65Dic122—21no—
66Dic122—21no—
67Dic122—41no—
68Dic122—41no—
69C8×C61—41no—
70C8×C61—41no—
71#92418—41no—
72C22×C61#12011yescharacteristic
73C2×D61—42no—
74C2×D61—42no—
75C2×D61—42no—
76C4×C61—21no—
77C4×C61—41no—
78C4×C61—41no—
79C4×C61#13511yescharacteristic
80C4×C61#13511yescharacteristic
81C4×C61AGL(1,ℤ/8)11yescharacteristic
82C4×C61#13711yescharacteristic
83Dic61—41no—
84Dic61—41no—
85Dic61—81no—
86#1640—611nomaximal, Sylow
87C2×C61#44911yescharacteristic
88C2×C61#45211yescharacteristic
89C2×C61#45511yescharacteristic
90D61—82no—
91#559—611no—
92#486—611no—
93#475—611no—
94#462—611no—
95#331—611no—
96Q8⋊C8—611no—
97Q8⋊C8D6111yescharacteristic, complemented
98C61#164011yescharacteristic, complemented, Sylow
99C2×Q16—1221no—
100C4⋊Q8—611no—
101#127—611no—
102#124—1221no—
103#124—1221no—
104#123—1222no—
105C4×Q8—611no—
106C4×Q8C2×D6111yescharacteristic
107C4×D4—1221no—
108C4×D4—1221no—
109#106—1221no—
110C4⋊C8—611no—
111C4⋊C8C2×D6111yescharacteristic
112#103—1221no—
113#103—1221no—
114#102—1222no—
115C4×C8C2×D6111yescharacteristic
116C2×Q8—611no—
117C2×Q8—1221no—
118C2×Q8D24411yescharacteristic
119C2×D4—612no—
120C2×D4—1221no—
121C2×D4—1221no—
122C22×C4—1222no—
123Q16—2442no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—1221no—
127C4⋊C4—21no—
128C4⋊C4—611no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4—1221no—
132C4⋊C4D24411yescharacteristic
133C22⋊C4—1222no—
134C22⋊C4—1222no—
135C22⋊C4—1222no—
136C42—21no—
137C42—1221no—
138C42C22×D6111yescharacteristic
139C23—1222no—
140Q8—21no—
141Q8—21no—
142Q8—1221no—
143Q8—1221no—
144Q8—2441no—
145Q8—2441no—
146D4—2442no—
147D4—2441no—
148D4—2441no—
149D4—2441no—
150D4—2441no—
151C2×C4—21no—
152C2×C4—21no—
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—2442no—
164C22—2442no—
165C22—2442no—
166C22#1451974711yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—4881no—
171C4—2441no—
172C4—2441no—
173C4#1451979811yescharacteristic
174C4#1451979911yescharacteristic
175C4#1451980511yescharacteristic
176C4#1451980911yescharacteristic
177C2—4882no—
178C2#1683990911yescharacteristic
179C2#1683992711yescharacteristic
180C2#1683994111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1640
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
3. #16840048C2semidirect
4. #16839972C2semidirect
6. #16839494C2semidirect
7. C61×Q8⋊C8C2semidirect
97. Q8⋊C8D61semidirect
98. C61#1640semidirect