Finite Group Databasebeta

← #21445085

Subgroups — #21445085

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
1Q8×D244C211yesmaximal, characteristic
2#16840160C211yesmaximal, characteristic, complemented
3#16840047C211yesmaximal, characteristic, complemented
4#16839968C211yesmaximal, characteristic
5#16839507C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×Q8×D61—21no—
9C2×#11758190—21no—
10#14519777—21no—
11#14519777C2211yescharacteristic
12#14519777C2211yescharacteristic
13#14519757—21no—
14#14519757—22no—
15C4×D244—21no—
16C4×D244C2211yescharacteristic
17#14519709—22no—
18#14519708—21no—
19C4⋊#92418C2211yescharacteristic
20#14519702—21no—
21#14519701—21no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26Q8×D61—42no—
27Q8×D61—42no—
28C2×D244D411yescharacteristic
29C2×C4×D61—22no—
30C2×C4×D61—21no—
31C2×Dic122—22no—
32C2×Dic122—21no—
33C2×Dic122—21no—
34C2×C8×C61—21no—
35C2×C8×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61D411yescharacteristic
38C42×C61—21no—
39C42×C61C2311yescharacteristic
40#11758198—22no—
41#11758198—21no—
42C4⋊Dic61—22no—
43C4⋊Dic61—21no—
44C4⋊Dic61—21no—
45C4⋊Dic61—21no—
46C4⋊Dic61D411yescharacteristic
47C4⋊Dic61D412yes—
48C2×#92418—21no—
49#11758190—42no—
50C22×D61—21no—
51Q8×C61—21no—
52Q8×C61SD1612yescomplemented
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×Dic61—21no—
59C2×Dic61—22no—
60C2×Dic61—41no—
61D244—21no—
62D244SD1612yes—
63C4×D61—44no—
64C4×D61—41no—
65C4×D61—41no—
66Dic122—44no—
67Dic122—41no—
68Dic122—41no—
69Dic122—41no—
70Dic122—41no—
71C8×C61—22no—
72C8×C61—41no—
73#92418—41no—
74C22×C61#12011yescharacteristic
75C2×D61—22no—
76C2×D61—41no—
77C2×D61—41no—
78C4×C61—22no—
79C4×C61—21no—
80C4×C61—41no—
81C4×C61C2×SD1611yescharacteristic
82C4×C61C2×SD1611yescharacteristic
83C4×C61AGL(1,ℤ/8)11yescharacteristic
84C4×C61#13711yescharacteristic
85Dic61—41no—
86Dic61—42no—
87Dic61—81no—
88#1651—611nomaximal, Sylow
89C2×C61#44811yescharacteristic
90C2×C61#45011yescharacteristic
91C2×C61#45611yescharacteristic
92D61—42no—
93D4×Q8—611no—
94#498—611no—
95#475—611no—
96#461—611no—
97#332—611no—
98Q8⋊C8D6111yescharacteristic, complemented
99D4⋊C8—611no—
100C61#165111yescharacteristic, complemented, Sylow
101C22×Q8—1221no—
102C2×SD16—1221no—
103C4⋊Q8—611no—
104C4⋊Q8—611no—
105C4⋊Q8—1221no—
106C22⋊Q8—1222no—
107C22⋊Q8—1221no—
108C4×Q8C2×D6111yescharacteristic
109C4×D4—611no—
110C4×D4—1221no—
111#106—1222no—
112#106—1221no—
113C4⋊C8—611no—
114C4⋊C8C2×D6111yescharacteristic
115#103—1221no—
116#103—1221no—
117C4×C8C2×D6111yescharacteristic
118C2×Q8—1222no—
119C2×Q8—1221no—
120C2×Q8—1221no—
121C2×Q8—2442no—
122C2×Q8—2442no—
123C2×Q8D24411yescharacteristic
124C2×D4—611no—
125C22×C4—1222no—
126C22×C4—1221no—
127SD16—2442no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—1221no—
131C4⋊C4—21no—
132C4⋊C4—611no—
133C4⋊C4—612no—
134C4⋊C4—1222no—
135C4⋊C4—1221no—
136C4⋊C4—1221no—
137C4⋊C4—1221no—
138C4⋊C4D24411yescharacteristic
139C22⋊C4—1222no—
140C22⋊C4—1221no—
141C42—21no—
142C42C22×D6111yescharacteristic
143C23—1221no—
144Q8—21no—
145Q8—2444no—
146Q8—2441no—
147Q8—2441no—
148Q8—2441no—
149Q8—2441no—
150Q8#1175819012yescomplemented
151D4—612no—
152D4—1221no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—1222no—
156C2×C4—1221no—
157C2×C4—2444no—
158C2×C4—2441no—
159C2×C4—2441no—
160C2×C4—2441no—
161C2×C4C2×D24411yescharacteristic
162C2×C4D4×D6111yescharacteristic
163C2×C4D4×D6111yescharacteristic
164C8—22no—
165C8—41no—
166C8—2441no—
167C22—1222no—
168C22—2441no—
169C22—2441no—
170C22#1451974711yescharacteristic
171C4—21no—
172C4—22no—
173C4—41no—
174C4—4881no—
175C4—2442no—
176C4—2441no—
177C4SD16×D6111yescharacteristic
178C4C2×#1175819011yescharacteristic
179C4#1451980511yescharacteristic
180C4#1451980911yescharacteristic
181C2—2442no—
182C2#1683990211yescharacteristic
183C2#1683991511yescharacteristic
184C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1651
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
2. #16840160C2semidirect
3. #16840047C2semidirect
5. #16839507C2semidirect
7. C61×Q8⋊C8C2semidirect
52. Q8×C61SD16semidirect
98. Q8⋊C8D61semidirect
100. C61#1651semidirect
150. Q8#11758190semidirect