Finite Group Databasebeta

← #21444942

Subgroups — #21444942

Order 7808.

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

normal subgroups only

This group has 218 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#16840135C211yesmaximal, characteristic
3#16840058C211yesmaximal, characteristic, complemented
4#16840057C211yesmaximal, characteristic, complemented
5#16839505C211yesmaximal, characteristic
6#16839494C211yesmaximal, characteristic, complemented
7C61×Q8⋊C8C211yesmaximal, characteristic, complemented
8C2×#11758190—22no—
9#14519777C2211yescharacteristic
10#14519774C2211yescharacteristic
11#14519766—21no—
12#14519765—21no—
13#14519762—22no—
14C4×Dic122C2211yescharacteristic
15C4×D244—21no—
16#14519739—21no—
17#14519711—21no—
18#14519710—21no—
19C4⋊#92418C2211yescharacteristic
20#14519702—21no—
21#14519701—21no—
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#11758198—22no—
39#11758198—22no—
40#11758198—22no—
41C4⋊Dic61—21no—
42C4⋊Dic61—21no—
43C4⋊Dic61D411yescharacteristic
44#11758196—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47#11758190—44no—
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—42no—
68C8×C61—22no—
69C8×C61—41no—
70#92418—41no—
71C22×C61#12011yescharacteristic
72C2×D61—42no—
73C2×D61—42no—
74C2×D61—42no—
75C4×C61—21no—
76C4×C61—41no—
77C4×C61—41no—
78C4×C61#13511yescharacteristic
79C4×C61#13511yescharacteristic
80C4×C61#13711yescharacteristic
81C4×C61#13711yescharacteristic
82Dic61—41no—
83Dic61—41no—
84Dic61—81no—
85#1630—611nomaximal, Sylow
86C2×C61#45211yescharacteristic
87C2×C61#45211yescharacteristic
88C2×C61#45311yescharacteristic
89D61—82no—
90#559—611no—
91#492—611no—
92#477—611no—
93#477—611no—
94#331—611no—
95Q8⋊C8—611no—
96Q8⋊C8D6111yescharacteristic, complemented
97C61#163011yescharacteristic, complemented, Sylow
98C2×SD16—1222no—
99C4⋊Q8—611no—
100#127—611no—
101#124—1221no—
102#124—1221no—
103#123—1222no—
104C4×Q8—611no—
105C4×Q8C2×D6111yescharacteristic
106C4×D4—1221no—
107C4×D4—1221no—
108#107—1221no—
109#107—1221no—
110C4⋊C8—611no—
111C4⋊C8C2×D6111yescharacteristic
112#103—1221no—
113#103—1221no—
114C4×C8C2×D6111yescharacteristic
115C2×Q8—611no—
116C2×Q8—1221no—
117C2×Q8D24411yescharacteristic
118C2×D4—612no—
119C2×D4—1221no—
120C2×D4—1221no—
121C22×C4—1222no—
122SD16—2444no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—1221no—
126C4⋊C4—21no—
127C4⋊C4—611no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C4⋊C4D24411yescharacteristic
132C22⋊C4—1222no—
133C22⋊C4—1222no—
134C22⋊C4—1222no—
135C42—21no—
136C42—1221no—
137C42C22×D6111yescharacteristic
138C23—1222no—
139Q8—21no—
140Q8—21no—
141Q8—1221no—
142Q8—1221no—
143Q8—2442no—
144D4—2442no—
145D4—2441no—
146D4—2441no—
147D4—2441no—
148D4—2441no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—1221no—
152C2×C4—1221no—
153C2×C4—4882no—
154C2×C4—2441no—
155C2×C4C2×D24411yescharacteristic
156C2×C4D4×D6111yescharacteristic
157C2×C4D4×D6111yescharacteristic
158C8—22no—
159C8—41no—
160C8—2441no—
161C22—2442no—
162C22—2442no—
163C22—2442no—
164C22#1451974711yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—4881no—
169C4—2441no—
170C4—2441no—
171C4#1451979811yescharacteristic
172C4#1451979911yescharacteristic
173C4#1451980911yescharacteristic
174C4#1451981011yescharacteristic
175C2—4882no—
176C2#1683992611yescharacteristic
177C2#1683992711yescharacteristic
178C2#1683993111yescharacteristic
subgroupG/H
centerC22#14519747
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×Q8⋊C8C2
socleC22×C61#120
hypercenterQ8⋊C8D61
hypocenterC61#1630
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. #16840058C2semidirect
4. #16840057C2semidirect
6. #16839494C2semidirect
7. C61×Q8⋊C8C2semidirect
96. Q8⋊C8D61semidirect
97. C61#1630semidirect