Finite Group Databasebeta

← #21445078

Subgroups — #21445078

Order 7808.

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

normal subgroups only

This group has 200 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#16840485C211yesmaximal, characteristic
2#16840167C211yesmaximal, characteristic, complemented
3#16840047C211yesmaximal, characteristic, complemented
4#16839968C211yesmaximal, characteristic
5#16839509C211yesmaximal, characteristic, complemented
6#16839491C211yesmaximal, characteristic
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758190—21no—
9#14519777C2211yescharacteristic
10#14519777C2211yescharacteristic
11#14519772—22no—
12#14519765—21no—
13#14519753—21no—
14C4×Dic122—21no—
15C4×D244C2211yescharacteristic
16#14519735—21no—
17#14519711—22no—
18#14519708—21no—
19C4⋊#92418C2211yescharacteristic
20#14519702—21no—
21#14519701—21no—
22C4×Q8×C61C2211yescharacteristic
23C4⋊C8×C61C2211yescharacteristic
24C4×C8×C61C2211yescharacteristic
25C2×Q8×C61D411yescharacteristic
26C2×D244D411yescharacteristic
27C2×C4×D61—21no—
28C2×Dic122—21no—
29C2×Dic122—21no—
30C2×C8×C61—21no—
31C2×C8×C61—21no—
32C4⋊C4×C61—21no—
33C4⋊C4×C61D411yescharacteristic
34C42×C61—21no—
35C42×C61C2311yescharacteristic
36#11758198—22no—
37#11758198—22no—
38#11758198—21no—
39C4⋊Dic61—21no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61D411yescharacteristic
43C4⋊Dic61D412yes—
44#11758196—22no—
45C4×Dic61—22no—
46C2×#92418—21no—
47#11758190—42no—
48C22×D61—21no—
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—22no—
58C2×Dic61—41no—
59D244—21no—
60D244—21no—
61C4×D61—41no—
62C4×D61—41no—
63Dic122—41no—
64Dic122—41no—
65Dic122—41no—
66Dic122—41no—
67C8×C61—22no—
68C8×C61—41no—
69#92418—41no—
70C22×C61#12011yescharacteristic
71C2×D61—41no—
72C2×D61—41no—
73C2×D61—41no—
74C4×C61—21no—
75C4×C61—41no—
76C4×C61—41no—
77C4×C61#13511yescharacteristic
78C4×C61#13511yescharacteristic
79C4×C61AGL(1,ℤ/8)11yescharacteristic
80C4×C61#13711yescharacteristic
81Dic61—42no—
82Dic61—41no—
83Dic61—81no—
84#1650—611nomaximal, Sylow
85C2×C61#44911yescharacteristic
86C2×C61#45211yescharacteristic
87C2×C61#45611yescharacteristic
88D61—81no—
89#556—611no—
90#500—611no—
91#475—611no—
92#461—611no—
93#332—611no—
94Q8⋊C8D6111yescharacteristic, complemented
95D4⋊C8—611no—
96C61#165011yescharacteristic, complemented, Sylow
97C2×SD16—1221no—
98C4⋊Q8—611no—
99C4⋊Q8—611no—
100#126—1222no—
101#124—1221no—
102C22⋊Q8—1221no—
103C4×Q8—1221no—
104C4×Q8C2×D6111yescharacteristic
105C4×D4—611no—
106#117—1221no—
107#107—1222no—
108#106—1221no—
109C4⋊C8—611no—
110C4⋊C8C2×D6111yescharacteristic
111#103—1221no—
112#103—1221no—
113C4×C8C2×D6111yescharacteristic
114C2×Q8—1221no—
115C2×Q8—1221no—
116C2×Q8D24411yescharacteristic
117C2×D4—611no—
118C22×C4—1221no—
119SD16—2442no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—1221no—
123C4⋊C4—21no—
124C4⋊C4—611no—
125C4⋊C4—612no—
126C4⋊C4—1222no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4D24411yescharacteristic
131C22⋊C4—1222no—
132C22⋊C4—1222no—
133C22⋊C4—1221no—
134C42—21no—
135C42—1222no—
136C42C22×D6111yescharacteristic
137C23—1221no—
138Q8—21no—
139Q8—21no—
140Q8—2441no—
141Q8—2441no—
142Q8—2441no—
143Q8—2441no—
144D4—1221no—
145D4—1221no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—1221no—
149C2×C4—1222no—
150C2×C4—2441no—
151C2×C4—2441no—
152C2×C4—2441no—
153C2×C4C2×D24411yescharacteristic
154C2×C4D4×D6111yescharacteristic
155C2×C4D4×D6111yescharacteristic
156C8—22no—
157C8—41no—
158C8—2441no—
159C22—2441no—
160C22—2441no—
161C22—2441no—
162C22#1451974711yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—4881no—
167C4—2442no—
168C4—2441no—
169C4#1451979911yescharacteristic
170C4#1451980011yescharacteristic
171C4#1451980411yescharacteristic
172C4#1451981011yescharacteristic
173C2—4881no—
174C2#1683991011yescharacteristic
175C2#1683992611yescharacteristic
176C2#1683994611yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1650
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. #16840167C2semidirect
3. #16840047C2semidirect
5. #16839509C2semidirect
7. C61×Q8⋊C8C2semidirect
94. Q8⋊C8D61semidirect
96. C61#1650semidirect