Finite Group Databasebeta

← #21445071

Subgroups — #21445071

Order 7808.

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

normal subgroups only

This group has 234 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#16840167C211yesmaximal, characteristic, complemented
3#16840042C211yesmaximal, characteristic
4#16839973C211yesmaximal, characteristic, complemented
5#16839509C211yesmaximal, characteristic, complemented
6#16839494C211yesmaximal, characteristic, complemented
7C61×D4⋊C8C211yesmaximal, characteristic
8C22×Dic122—21no—
9C2×Dic244—21no—
10#14519777C2211yescharacteristic
11#14519777C2211yescharacteristic
12#14519776—21no—
13#14519756—21no—
14#14519754—22no—
15C4×Dic122C2211yescharacteristic
16D4×Dic61—21no—
17#14519711—22no—
18#14519710—21no—
19C4⋊#92418C2211yescharacteristic
20#14519702—21no—
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⋊Dic61D411yescharacteristic
44C4⋊Dic61D412yes—
45#11758196—22no—
46#11758196—21no—
47C4×Dic61—21no—
48C2×#92418—21no—
49Dic244—42no—
50C23×C61—21no—
51D4×C61—21no—
52D4×C61Q1612yescomplemented
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61C2×Dic61—22no—
62C2×Dic61—44no—
63C2×Dic61—41no—
64Dic122—21no—
65Dic122—44no—
66Dic122—41no—
67Dic122—41no—
68Dic122—41no—
69Dic122—41no—
70Dic122D812yes—
71C8×C61—22no—
72C8×C61—41no—
73#92418—41no—
74C22×C61—22no—
75C22×C61—41no—
76C22×C61—41no—
77C22×C61#12011yescharacteristic
78C4×C61—21no—
79C4×C61—41no—
80C4×C61C2×D811yescharacteristic
81C4×C61C2×Q1611yescharacteristic
82C4×C61AGL(1,ℤ/8)11yescharacteristic
83C4×C61#13711yescharacteristic
84Dic61—22no—
85Dic61—42no—
86Dic61—41no—
87Dic61—81no—
88#1649—611nomaximal, Sylow
89C2×C61—42no—
90C2×C61#44711yescharacteristic
91C2×C61#45111yescharacteristic
92C2×C61#45611yescharacteristic
93D4×Q8—611no—
94#500—611no—
95#474—611no—
96#462—611no—
97#332—611no—
98Q8⋊C8—611no—
99D4⋊C8D6111yescharacteristic
100C61#164911yescharacteristic, complemented, Sylow
101C22×Q8—1221no—
102C2×Q16—1221no—
103C4⋊Q8—611no—
104C4⋊Q8—611no—
105C4⋊Q8—1221no—
106C22⋊Q8—1222no—
107C22⋊Q8—1221no—
108C4×Q8—611no—
109C4×D4—1221no—
110C4×D4C2×D6111yescharacteristic
111#107—1222no—
112#107—1221no—
113C4⋊C8—611no—
114C4⋊C8C2×D6111yescharacteristic
115#103—1221no—
116#102—1221no—
117C4×C8C2×D6111yescharacteristic
118C2×Q8—611no—
119C2×Q8—1222no—
120C2×Q8—1221no—
121C2×Q8—1221no—
122C2×Q8—2442no—
123C2×Q8—2442no—
124C2×D4D24411yescharacteristic
125C22×C4—21no—
126C22×C4—1222no—
127Q16—2442no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—1221no—
131C4⋊C4—611no—
132C4⋊C4—612no—
133C4⋊C4—1222no—
134C4⋊C4—1221no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4D24411yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—1222no—
141C42—1221no—
142C42C22×D6111yescharacteristic
143C23—21no—
144Q8—612no—
145Q8—1221no—
146Q8—2444no—
147Q8—2441no—
148Q8—2441no—
149Q8—2441no—
150Q8—2441no—
151D4—21no—
152D4Dic24412yescomplemented
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—1221no—
157C2×C4—1221no—
158C2×C4—1222no—
159C2×C4—2444no—
160C2×C4—2441no—
161C2×C4C2×D24411yescharacteristic
162C2×C4D4×D6111yescharacteristic
163C2×C4D4×D6111yescharacteristic
164C8—22no—
165C8—41no—
166C8—2441no—
167C22—22no—
168C22—41no—
169C22—41no—
170C22#1451974711yescharacteristic
171C4—21no—
172C4—41no—
173C4—1222no—
174C4—4881no—
175C4—2441no—
176C4—2442no—
177C4D8×D6111yescharacteristic
178C4C2×Dic24411yescharacteristic
179C4#1451980411yescharacteristic
180C4#1451981011yescharacteristic
181C2—42no—
182C2#1683989711yescharacteristic
183C2#1683992011yescharacteristic
184C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×D4⋊C8C2
socleC22×C61#120
hypercenterD4⋊C8D61
hypocenterC61#1649
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. #16840167C2semidirect
4. #16839973C2semidirect
5. #16839509C2semidirect
6. #16839494C2semidirect
52. D4×C61Q16semidirect
100. C61#1649semidirect
152. D4Dic244semidirect