Finite Group Databasebeta

← #21444209

Subgroups — #21444209

Order 7808.

312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×C4×D244C211yesmaximal, characteristic
2#16839815C211yesmaximal, characteristic, complemented
3#16839489C214yesmaximal, complemented
4C61×#431C211yesmaximal, characteristic, complemented
5C22×D244C411yescharacteristic
6C22×C4×D61—21no—
7C4×D244—21no—
8C4×D244—21no—
9C4×D244C412yes—
10C4×D244C2212yes—
11C2×C4⋊Dic61C411yescharacteristic
12C2×#11758198—21no—
13C4⋊#92418—21no—
14C22⋊#92418—21no—
15C4×#92418C2212yescomplemented
16C2×C42×C61C2211yescharacteristic
17C4⋊C8×C61C2212yescomplemented
18C22⋊C8×C61—21no—
19C4×C8×C61—21no—
20C23×D61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C22×Dic61—21no—
25C2×D244—21no—
26C2×D244—22no—
27C2×D244C814yescomplemented
28C2×D244C2×C412yes—
29C2×C4×D61—22no—
30C2×C4×D61—22no—
31C2×C4×D61—44no—
32C2×C8×C61—22no—
33C42×C61C2×C411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61C2311yescharacteristic
37#11758198—22no—
38#11758198—22no—
39C4⋊Dic61—21no—
40C4⋊Dic61C2×C412yes—
41C2×#92418—22no—
42C23×C61C22⋊C411yescharacteristic
43C22×D61—24no—
44C22×D61—22no—
45C22×D61—42no—
46C22×D61—42no—
47C2×C4×C61—22no—
48C2×C4×C61—41no—
49C2×C4×C61C22⋊C411yescharacteristic
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C2×C812yes—
53C2×C4×C61M1612yes—
54C2×C4×C61C22×C411yescharacteristic
55C2×C4×C61C2×D411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×Dic61—22no—
58C2×Dic61—42no—
59D244—24no—
60D244—22no—
61D244C2×C814yes—
62C4×D61—44no—
63C4×D61—44no—
64C8×C61—42no—
65#92418—42no—
66C22×C61—21no—
67C22×C61—21no—
68C22×C61C22⋊C812yes—
69C22×C61C2×C22⋊C411yescharacteristic
70C2×D61—24no—
71C2×D61—48no—
72C2×D61—42no—
73C2×D61—42no—
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—21no—
77C4×C61C22⋊C812yes—
78C4×C61C22×C811yescharacteristic
79C4×C61C2×M1611yescharacteristic
80C4×C61AGL(1,ℤ/8)12yes—
81Dic61—42no—
82#1478—611nomaximal, Sylow
83C2×C61—22no—
84C2×C61C2×C22⋊C811yescharacteristic
85C2×C61#41811yescharacteristic
86C2×C61#42111yescharacteristic
87D61—44no—
88C2×C4×D4—611no—
89#431—611no—
90#431D6111yescharacteristic, complemented
91D4⋊C8—614no—
92C61#147811yescharacteristic, complemented, Sylow
93C22×D4—611no—
94C23×C4—1221no—
95C4×D4—612no—
96C4×D4—612no—
97C4×D4—1221no—
98C4×D4—1221no—
99C2×C4⋊C4—611no—
100C2×C22⋊C4—1221no—
101C2×C42C2×D6111yescharacteristic
102C4⋊C8—1221no—
103C4⋊C8C2×D6112yescomplemented
104C22⋊C8—21no—
105C22⋊C8—1221no—
106C4×C8—21no—
107C4×C8—612no—
108C24—1221no—
109C2×D4—614no—
110C2×D4—612no—
111C2×D4—1222no—
112C2×D4—1221no—
113C22×C4—1221no—
114C22×C4—1222no—
115C22×C4—1222no—
116C22×C4—2444no—
117C22×C4C4×D6111yescharacteristic
118C22×C4D24411yescharacteristic
119C22×C4C22⋊D6111yescharacteristic
120C2×C8—22no—
121C2×C8—1222no—
122C4⋊C4—612no—
123C4⋊C4—1221no—
124C22⋊C4—1222no—
125C22⋊C4—1222no—
126C42C4×D6111yescharacteristic
127C42D24411yescharacteristic
128C42C22⋊D6111yescharacteristic
129C42C22×D6111yescharacteristic
130C23—1224no—
131C23—1222no—
132C23—2442no—
133C23—2442no—
134C23#1175819811yescharacteristic
135D4—614no—
136D4—1224no—
137D4—1222no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—1222no—
141C2×C4—2444no—
142C2×C4—2442no—
143C2×C4—2444no—
144C2×C4C8×D6112yes—
145C2×C4#1175818912yes—
146C2×C4#1175819811yescharacteristic
147C2×C4#1175819811yescharacteristic
148C2×C4#1175819811yescharacteristic
149C2×C4C2×C4×D6111yescharacteristic
150C2×C4C2×D24411yescharacteristic
151C2×C4C2×C22⋊D6111yescharacteristic
152C8—42no—
153C8—2442no—
154C22—21no—
155C22—21no—
156C22—1224no—
157C22—2448no—
158C22—2442no—
159C22—2442no—
160C22#1451968912yes—
161C22C2×#1175819811yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—2442no—
166C4#1451968912yes—
167C4C2×C8×D6111yescharacteristic
168C4C2×#1175818911yescharacteristic
169C4#1451980212yes—
170C2—22no—
171C2—2444no—
172C2C2×#1451968911yescharacteristic
173C2#1683976611yescharacteristic
174C2#1683977811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC4×C61C22×C8
FrattiniC42C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1478
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #16839815C2semidirect
3. #16839489C2semidirect
4. C61×#431C2semidirect
15. C4×#92418C22semidirect
17. C4⋊C8×C61C22semidirect
27. C2×D244C8semidirect
90. #431D61semidirect
92. C61#1478semidirect
103. C4⋊C8C2×D61semidirect