Finite Group Databasebeta

← #21444939

Subgroups — #21444939

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#16840136C211yesmaximal, characteristic
3#16840054C211yesmaximal, characteristic, complemented
4#16839505C211yesmaximal, characteristic
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839492C211yesmaximal, characteristic, complemented
7C61×#477C211yesmaximal, characteristic, complemented
8C2×#11758201—22no—
9#14519774C2211yescharacteristic
10#14519766—21no—
11#14519765—21no—
12#14519762—22no—
13C4×Dic122C2211yescharacteristic
14C4×D244—21no—
15#14519739—21no—
16#14519710—21no—
17C4⋊#92418C2211yescharacteristic
18#14519700—21no—
19C4×#92418C2211yescharacteristic
20C4⋊Q8×C61C2211yescharacteristic
21C4×Q8×C61C2211yescharacteristic
22#107×C61—21no—
23C4⋊C8×C61C2211yescharacteristic
24#103×C61—21no—
25C2×Q8×C61—21no—
26C2×Q8×C61D411yescharacteristic
27C2×D244—21no—
28C2×D244—21no—
29C2×D244D412yes—
30C2×C4×D61—22no—
31C2×Dic122D411yescharacteristic
32C2×C8×C61—21no—
33C4⋊C4×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61D411yescharacteristic
37C42×C61—21no—
38C42×C61C2311yescharacteristic
39#11758201—44no—
40#11758198—22no—
41#11758198—22no—
42#11758198—22no—
43C4⋊Dic61D411yescharacteristic
44#11758196—21no—
45C4×Dic61—21no—
46C2×#92418—21no—
47C2×#92418—21no—
48C22×D61—22no—
49Q8×C61—21no—
50Q8×C61—21no—
51Q8×C61—42no—
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—41no—
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×Dic61—21no—
59C2×Dic61—21no—
60D244—42no—
61D244—41no—
62D244—41no—
63D244—41no—
64D244—41no—
65C4×D61—82no—
66Dic122—21no—
67Dic122—21no—
68C8×C61—41no—
69#92418—22no—
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—81no—
79C4×C61#13511yescharacteristic
80C4×C61#13511yescharacteristic
81C4×C61#13711yescharacteristic
82C4×C61#13711yescharacteristic
83Dic61—41no—
84Dic61—41no—
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#477D6111yescharacteristic, complemented
94#331—611no—
95Q8⋊C8—611no—
96Q8⋊C8—611no—
97C61#163011yescharacteristic, complemented, Sylow
98C2×SD16—1222no—
99C4⋊Q8C2×D6111yescharacteristic
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—21no—
109#107—1221no—
110C4⋊C8—611no—
111C4⋊C8C2×D6111yescharacteristic
112#103—21no—
113#103—1221no—
114C4×C8—611no—
115C2×Q8—21no—
116C2×Q8—611no—
117C2×Q8C22⋊D6111yescharacteristic
118C2×D4—612no—
119C2×D4—1221no—
120C2×D4—1221no—
121C22×C4—1222no—
122SD16—2444no—
123C2×C8—21no—
124C2×C8—1221no—
125C2×C8—1221no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—611no—
130C4⋊C4—1221no—
131C4⋊C4C22⋊D6111yescharacteristic
132C22⋊C4—1222no—
133C22⋊C4—1222no—
134C22⋊C4—1222no—
135C42—21no—
136C42—1221no—
137C42C22×D6111yescharacteristic
138C23—1222no—
139Q8—21no—
140Q8—21no—
141Q8—42no—
142Q8—1221no—
143Q8—1221no—
144D4—2442no—
145D4—2441no—
146D4—2441no—
147D4—2441no—
148D4—2441no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—1221no—
153C2×C4—1221no—
154C2×C4—4882no—
155C2×C4D4×D6111yescharacteristic
156C2×C4D4×D6111yescharacteristic
157C2×C4C2×C22⋊D6111yescharacteristic
158C8—41no—
159C8—1222no—
160C8—2441no—
161C22—2442no—
162C22—2442no—
163C22—2442no—
164C22#1451974511yescharacteristic
165C4—21no—
166C4—41no—
167C4—41no—
168C4—81no—
169C4—2441no—
170C4—2441no—
171C4#1451979711yescharacteristic
172C4#1451980011yescharacteristic
173C4#1451980811yescharacteristic
174C4#1451980911yescharacteristic
175C2—4882no—
176C2#1683992211yescharacteristic
177C2#1683992311yescharacteristic
178C2#1683992811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#477C2
socleC22×C61#120
hypercenter#477D61
hypocenterC61#1630
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #477

Complements

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

NH ≅ G/Ntype
3. #16840054C2semidirect
5. Q8⋊#92418C2semidirect
6. #16839492C2semidirect
7. C61×#477C2semidirect
93. #477D61semidirect
97. C61#1630semidirect