Finite Group Databasebeta

← #21455637

Subgroups — #21455637

Order 7808.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C4×#11758222C211yesmaximal, characteristic
2#16840066C214yesmaximal, complemented
3#16840059C214yesmaximal, complemented
4#16839802C212yesmaximal, complemented
5#16839786C211yesmaximal, characteristic, complemented
6#16839761C212yesmaximal
7C2×#125×C61C211yesmaximal, characteristic, complemented
8C2×#11758222C2211yescharacteristic
9C2×#11758194C2212yes—
10C4×Dic122C2212yes—
11C4×D244C2212yes—
12C4×C22⋊D61—22no—
13#14519736C2211yescharacteristic
14#14519734—21no—
15C42×D61—21no—
16#14519710C2214yes—
17#14519708C2214yes—
18C4⋊#92418C2214yes—
19#14519700C2214yes—
20#14519697C2214yes—
21#125×C61—21no—
22#125×C61—21no—
23#125×C61C2214yes—
24C2×C4⋊C4×C61—22no—
25C2×C4⋊C4×C61C2212yes—
26C2×C42×C61C2211yescharacteristic
27C22×C4×C61—22no—
28C22×C4×C61D412yes—
29C22×C4×C61C2311yescharacteristic
30C2×C22⋊D61—21no—
31#11758222—22no—
32#11758222Q814yes—
33C2×D244C2311yescharacteristic
34C2×C4×D61—21no—
35C2×C4×D61—22no—
36C2×Dic122C2311yescharacteristic
37C4⋊C4×C61—24no—
38C4⋊C4×C61—24no—
39C4⋊C4×C61—22no—
40C4⋊C4×C61C2314yes—
41C42×C61D411yescharacteristic
42C42×C61D411yescharacteristic
43C42×C61C2312yes—
44C22⋊Dic61—21no—
45#11758198—22no—
46C4⋊Dic61C2312yes—
47#11758196—22no—
48C4×Dic61—21no—
49C4×Dic61—22no—
50#11758194—24no—
51C2×#92418C2314yes—
52C23×C61C2×D411yescharacteristic
53C22×D61—21no—
54C2×C4×C61—24no—
55C2×C4×C61—42no—
56C2×C4×C61—44no—
57C2×C4×C61C2×D412yes—
58C2×C4×C61C2×D412yes—
59C2×C4×C61C2×D411yescharacteristic
60C2×C4×C61C2×Q812yes—
61C2×C4×C61#4112yes—
62C2×C4×C61C2411yescharacteristic
63C22⋊D61—24no—
64C2×Dic61—21no—
65C2×Dic61—22no—
66D244—21no—
67D244C2×Q812yes—
68C4×D61—24no—
69C4×D61—44no—
70Dic122—21no—
71Dic122C2×Q812yes—
72#92418—24no—
73C22×C61—22no—
74C22×C61C22⋊Q812yes—
75C22×C61C22×D411yescharacteristic
76C2×D61—22no—
77C2×D61—42no—
78C4×C61—22no—
79C4×C61—22no—
80C4×C61—44no—
81C4×C61C22⋊Q812yes—
82C4×C61C22×Q811yescharacteristic
83C4×C61C2×#4111yescharacteristic
84Dic61—22no—
85Dic61—42no—
86#3080—611nomaximal, Sylow
87C2×C61—22no—
88C2×C61C2×C22⋊Q811yescharacteristic
89C2×C61#57512yes—
90D61—42no—
91C2×#125D6111yescharacteristic, complemented
92C4×#41—611no—
93#479—614no—
94#478—614no—
95#428—612no—
96#423—611no—
97#417—612no—
98C61#308011yescharacteristic, complemented, Sylow
99C2×#41—611no—
100C2×M16—612no—
101#125—21no—
102#125—21no—
103#125C2×D6114yes—
104C4×Q8—612no—
105C4×D4—612no—
106C4×D4—1222no—
107#117—611no—
108#117—1221no—
109C2×C4⋊C4—22no—
110C2×C4⋊C4C2×D6112yes—
111C2×C42—1221no—
112C2×C42C2×D6111yescharacteristic
113#107—614no—
114#106—614no—
115C4⋊C8—614no—
116#103—614no—
117#102—614no—
118#41—614no—
119#41—1222no—
120C2×Q8—611no—
121C2×D4—611no—
122C2×D4—1221no—
123C22×C4—22no—
124C22×C4—1221no—
125C22×C4—1222no—
126C22×C4C22⋊D6112yes—
127C22×C4C22×D6111yescharacteristic
128M16—1224no—
129C2×C8—614no—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—612no—
134C4⋊C4—1222no—
135C4⋊C4C22×D6114yes—
136C22⋊C4—1221no—
137C22⋊C4—1222no—
138C42—1221no—
139C42—1222no—
140C42C22⋊D6111yescharacteristic
141C42C22⋊D6111yescharacteristic
142C42C22×D6112yes—
143C23—1221no—
144C23C2×C22⋊D6111yescharacteristic
145Q8—612no—
146Q8—1221no—
147D4—612no—
148D4—1224no—
149D4—1221no—
150C2×C4—24no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—1221no—
154C2×C4—1224no—
155C2×C4—1222no—
156C2×C4—2444no—
157C2×C4Q8×D6112yes—
158C2×C4#1175822612yes—
159C2×C4C2×C22⋊D6112yes—
160C2×C4C2×C22⋊D6112yes—
161C2×C4C2×C22⋊D6111yescharacteristic
162C2×C4C23×D6111yescharacteristic
163C8—1224no—
164C22—22no—
165C22—1222no—
166C22—2442no—
167C22#1451975312yes—
168C22C22×C22⋊D6111yescharacteristic
169C4—22no—
170C4—22no—
171C4—44no—
172C4—1222no—
173C4—2442no—
174C4#1451975312yes—
175C4C2×Q8×D6111yescharacteristic
176C4C2×#1175822611yescharacteristic
177C2—22no—
178C2—2442no—
179C2C2×#1451975311yescharacteristic
180C2#1684056012yes—
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#125×C61C2
socleC22×C61C22×D4
hypercenterC2×#125D61
hypocenterC61#3080
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #16840066C2semidirect
3. #16840059C2semidirect
4. #16839802C2semidirect
5. #16839786C2semidirect
7. C2×#125×C61C2semidirect
91. C2×#125D61semidirect
98. C61#3080semidirect