Finite Group Databasebeta

← #21444987

Subgroups — #21444987

Order 7808.

228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×Dic122C211yesmaximal, characteristic
2#16840113C211yesmaximal, characteristic, complemented
3#16840058C211yesmaximal, characteristic, complemented
4#16840052C211yesmaximal, characteristic
5#16839509C211yesmaximal, characteristic, complemented
6#16839494C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic
8C22×Dic122—21no—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519776—21no—
12#14519756—21no—
13#14519754—22no—
14C4×Dic122C2211yescharacteristic
15D4×Dic61—21no—
16#14519711—21no—
17#14519708—21no—
18C4⋊#92418C2211yescharacteristic
19#14519702—21no—
20#14519702—22no—
21#14519698—21no—
22C4×D4×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×D4×C61D411yescharacteristic
26C22×C4×C61—21no—
27C22×Dic61—22no—
28C2×Dic122—22no—
29C2×Dic122—21no—
30C2×Dic122—21no—
31C2×Dic122—42no—
32C2×Dic122—42no—
33C2×Dic122D411yescharacteristic
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61D411yescharacteristic
37C22⋊C4×C61—21no—
38C42×C61C2311yescharacteristic
39C22⋊Dic61—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61D412yes—
44C4⋊Dic61D411yescharacteristic
45#11758196—22no—
46#11758196—21no—
47C4×Dic61—21no—
48C2×#92418—21no—
49C23×C61—21no—
50D4×C61—21no—
51D4×C61Q1612yes—
52C2×C4×C61—21no—
53C2×C4×C61—41no—
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—
61C2×Dic61—44no—
62C2×Dic61—41no—
63Dic122—21no—
64Dic122—44no—
65Dic122—41no—
66Dic122—41no—
67Dic122—42no—
68Dic122SD1612yes—
69C8×C61—41no—
70C8×C61—41no—
71#92418—41no—
72C22×C61—22no—
73C22×C61—41no—
74C22×C61—41no—
75C22×C61#12011yescharacteristic
76C4×C61—21no—
77C4×C61—41no—
78C4×C61C2×SD1611yescharacteristic
79C4×C61C2×Q1611yescharacteristic
80C4×C61AGL(1,ℤ/8)11yescharacteristic
81C4×C61#13711yescharacteristic
82Dic61—22no—
83Dic61—42no—
84Dic61—41no—
85Dic61—81no—
86#1637—611nomaximal, Sylow
87C2×C61—42no—
88C2×C61#45011yescharacteristic
89C2×C61#45111yescharacteristic
90C2×C61#45411yescharacteristic
91D4×Q8—611no—
92#487—611no—
93#477—611no—
94#476—611no—
95#332—611no—
96Q8⋊C8—611no—
97D4⋊C8D6111yescharacteristic
98C61#163711yescharacteristic, complemented, Sylow
99C22×Q8—1221no—
100C4⋊Q8—611no—
101C4⋊Q8—611no—
102C4⋊Q8—1221no—
103C22⋊Q8—1222no—
104C22⋊Q8—1221no—
105C4×Q8—611no—
106C4×D4—1221no—
107C4×D4C2×D6111yescharacteristic
108#107—1221no—
109#106—1221no—
110C4⋊C8—611no—
111C4⋊C8C2×D6111yescharacteristic
112#103—1222no—
113#103—1221no—
114#102—1221no—
115C4×C8C2×D6111yescharacteristic
116C2×Q8—611no—
117C2×Q8—1222no—
118C2×Q8—1221no—
119C2×Q8—1221no—
120C2×Q8—2442no—
121C2×Q8—2442no—
122C2×D4D24411yescharacteristic
123C22×C4—21no—
124C22×C4—1222no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—1221no—
128C4⋊C4—612no—
129C4⋊C4—611no—
130C4⋊C4—1222no—
131C4⋊C4—1221no—
132C4⋊C4—1221no—
133C4⋊C4—1221no—
134C4⋊C4—1221no—
135C4⋊C4D24411yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—1222no—
138C42—1221no—
139C42C22×D6111yescharacteristic
140C23—21no—
141Q8—612no—
142Q8—1221no—
143Q8—2442no—
144Q8—2444no—
145Q8—2441no—
146Q8—2441no—
147D4—21no—
148D4Dic24412yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—1222no—
155C2×C4—2444no—
156C2×C4—2441no—
157C2×C4C2×D24411yescharacteristic
158C2×C4D4×D6111yescharacteristic
159C2×C4D4×D6111yescharacteristic
160C8—41no—
161C8—41no—
162C8—2441no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1451974711yescharacteristic
167C4—21no—
168C4—41no—
169C4—1222no—
170C4—4881no—
171C4—2441no—
172C4—2442no—
173C4SD16×D6111yescharacteristic
174C4C2×Dic24411yescharacteristic
175C4#1451980111yescharacteristic
176C4#1451981011yescharacteristic
177C2—42no—
178C2#1683991411yescharacteristic
179C2#1683992011yescharacteristic
180C2#1683993611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1637
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #16840113C2semidirect
3. #16840058C2semidirect
5. #16839509C2semidirect
6. #16839494C2semidirect
98. C61#1637semidirect