Finite Group Databasebeta

← #21445003

Subgroups — #21445003

Order 7808.

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

normal subgroups only

This group has 212 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#16840110C211yesmaximal, characteristic
3#16840044C211yesmaximal, characteristic, complemented
4#16839505C211yesmaximal, characteristic
5Q8⋊#92418C211yesmaximal, characteristic, complemented
6#16839492C211yesmaximal, characteristic, complemented
7C61×#462C211yesmaximal, characteristic, complemented
8#14519774C2211yescharacteristic
9#14519766—21no—
10#14519765—21no—
11#14519762—22no—
12C4×Dic122C2211yescharacteristic
13C4×D244—21no—
14#14519739—21no—
15#14519708—21no—
16C4⋊#92418C2211yescharacteristic
17#14519700—21no—
18#14519697—22no—
19C4×#92418C2211yescharacteristic
20C2×Q16×C61—21no—
21C4⋊Q8×C61C2211yescharacteristic
22C4×Q8×C61C2211yescharacteristic
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
32Q16×C61—42no—
33C2×C8×C61—21no—
34C4⋊C4×C61—21no—
35C4⋊C4×C61—21no—
36C4⋊C4×C61—21no—
37C4⋊C4×C61D411yescharacteristic
38C42×C61—21no—
39C42×C61C2311yescharacteristic
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—41no—
52Q8×C61—41no—
53C2×C4×C61—21no—
54C2×C4×C61—21no—
55C2×C4×C61—41no—
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×C4×C61C2×D411yescharacteristic
59C2×Dic61—21no—
60C2×Dic61—21no—
61D244—42no—
62D244—41no—
63D244—41no—
64D244—41no—
65D244—41no—
66C4×D61—82no—
67Dic122—21no—
68Dic122—21no—
69C8×C61—41no—
70#92418—41no—
71#92418—41no—
72C22×C61#12011yescharacteristic
73C2×D61—42no—
74C2×D61—42no—
75C2×D61—42no—
76C4×C61—21no—
77C4×C61—41no—
78C4×C61—41no—
79C4×C61—81no—
80C4×C61#13511yescharacteristic
81C4×C61#13511yescharacteristic
82C4×C61AGL(1,ℤ/8)11yescharacteristic
83C4×C61#13711yescharacteristic
84Dic61—41no—
85Dic61—41no—
86#1640—611nomaximal, Sylow
87C2×C61#44911yescharacteristic
88C2×C61#45211yescharacteristic
89C2×C61#45511yescharacteristic
90D61—82no—
91#559—611no—
92#486—611no—
93#475—611no—
94#462D6111yescharacteristic, complemented
95#331—611no—
96Q8⋊C8—611no—
97Q8⋊C8—611no—
98C61#164011yescharacteristic, complemented, Sylow
99C2×Q16—21no—
100C4⋊Q8C2×D6111yescharacteristic
101#127—611no—
102#124—1221no—
103#124—1221no—
104#123—1222no—
105C4×Q8—611no—
106C4×Q8C2×D6111yescharacteristic
107C4×D4—1221no—
108C4×D4—1221no—
109#106—1221no—
110C4⋊C8—611no—
111C4⋊C8C2×D6111yescharacteristic
112#103—21no—
113#103—1221no—
114#102—1222no—
115C4×C8—611no—
116C2×Q8—21no—
117C2×Q8—611no—
118C2×Q8C22⋊D6111yescharacteristic
119C2×D4—612no—
120C2×D4—1221no—
121C2×D4—1221no—
122C22×C4—1222no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—1221no—
126C2×C8—1221no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—611no—
131C4⋊C4—1221no—
132C4⋊C4C22⋊D6111yescharacteristic
133C22⋊C4—1222no—
134C22⋊C4—1222no—
135C22⋊C4—1222no—
136C42—21no—
137C42—1221no—
138C42C22×D6111yescharacteristic
139C23—1222no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—1221no—
145Q8—1221no—
146D4—2442no—
147D4—2441no—
148D4—2441no—
149D4—2441no—
150D4—2441no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—1221no—
155C2×C4—1221no—
156C2×C4—4882no—
157C2×C4D4×D6111yescharacteristic
158C2×C4D4×D6111yescharacteristic
159C2×C4C2×C22⋊D6111yescharacteristic
160C8—41no—
161C8—2441no—
162C8—2441no—
163C22—2442no—
164C22—2442no—
165C22—2442no—
166C22#1451974511yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—2441no—
172C4—2441no—
173C4#1451979711yescharacteristic
174C4#1451980011yescharacteristic
175C4#1451980311yescharacteristic
176C4#1451980911yescharacteristic
177C2—4882no—
178C2#1683990511yescharacteristic
179C2#1683992311yescharacteristic
180C2#1683993811yescharacteristic
subgroupG/H
centerC22#14519745
commutatorC42×C61C23
FrattiniC42C22×D61
FittingC61×#462C2
socleC22×C61#120
hypercenter#462D61
hypocenterC61#1640
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #16840044C2semidirect
5. Q8⋊#92418C2semidirect
6. #16839492C2semidirect
7. C61×#462C2semidirect
94. #462D61semidirect
98. C61#1640semidirect