Finite Group Databasebeta

← #21444243

Subgroups — #21444243

Order 7808.

312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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×#423C211yesmaximal, 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×M16×C61—21no—
17C2×C42×C61C2211yescharacteristic
18C4⋊C8×C61—21no—
19C4⋊C8×C61C2212yescomplemented
20C23×D61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C22×Dic61—21no—
25C2×D244—21no—
26C2×D244—24no—
27C2×D244C2×C412yes—
28C2×C4×D61—22no—
29C2×C4×D61—22no—
30C2×C4×D61—42no—
31C2×C4×D61—42no—
32M16×C61—42no—
33C2×C8×C61—22no—
34C42×C61C2×C411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61D411yescharacteristic
37C42×C61C2311yescharacteristic
38#11758198—22no—
39#11758198—22no—
40C4⋊Dic61—21no—
41C4⋊Dic61C2×C412yes—
42C2×#92418—22no—
43C23×C61C22⋊C411yescharacteristic
44C22×D61—24no—
45C22×D61—22no—
46C22×D61—42no—
47C22×D61—42no—
48C2×C4×C61—22no—
49C2×C4×C61—41no—
50C2×C4×C61C22⋊C411yescharacteristic
51C2×C4×C61C22⋊C411yescharacteristic
52C2×C4×C61C22⋊C411yescharacteristic
53C2×C4×C61D812yes—
54C2×C4×C61SD1612yes—
55C2×C4×C61C22×C411yescharacteristic
56C2×C4×C61C2×D411yescharacteristic
57C2×C4×C61C2×D411yescharacteristic
58C2×Dic61—22no—
59C2×Dic61—42no—
60D244—24no—
61D244—22no—
62D244M1614yescomplemented
63C4×D61—44no—
64C4×D61—42no—
65C4×D61—42no—
66C8×C61—42no—
67#92418—42no—
68C22×C61—21no—
69C22×C61—21no—
70C22×C61#10212yes—
71C22×C61C2×C22⋊C411yescharacteristic
72C2×D61—24no—
73C2×D61—48no—
74C2×D61—42no—
75C2×D61—42no—
76C4×C61—21no—
77C4×C61—21no—
78C4×C61—21no—
79C4×C61#10212yes—
80C4×C61C2×M1612yes—
81C4×C61C2×D811yescharacteristic
82C4×C61C2×SD1611yescharacteristic
83Dic61—42no—
84#1486—611nomaximal, Sylow
85C2×C61—22no—
86C2×C61#40711yescharacteristic
87C2×C61C2×#10211yescharacteristic
88C2×C61#42111yescharacteristic
89D61—44no—
90C2×C4×D4—611no—
91#431—611no—
92#423D6111yescharacteristic, complemented
93D4⋊C8—614no—
94C61#148611yescharacteristic, complemented, Sylow
95C22×D4—611no—
96C23×C4—1221no—
97C2×M16—21no—
98C4×D4—612no—
99C4×D4—612no—
100C4×D4—1221no—
101C4×D4—1221no—
102C2×C4⋊C4—611no—
103C2×C22⋊C4—1221no—
104C2×C42C2×D6111yescharacteristic
105C4⋊C8—21no—
106C4⋊C8—1221no—
107C4⋊C8C2×D6112yescomplemented
108C22⋊C8—1221no—
109C4×C8—612no—
110C24—1221no—
111C2×D4—612no—
112C2×D4—1224no—
113C2×D4—1221no—
114C22×C4—1221no—
115C22×C4—1222no—
116C22×C4—1222no—
117C22×C4—2442no—
118C22×C4—2442no—
119C22×C4C4×D6111yescharacteristic
120C22×C4D24411yescharacteristic
121C22×C4C22⋊D6111yescharacteristic
122M16—42no—
123C2×C8—22no—
124C2×C8—1222no—
125C4⋊C4—612no—
126C4⋊C4—1221no—
127C22⋊C4—1222no—
128C22⋊C4—1222no—
129C42C4×D6111yescharacteristic
130C42D24411yescharacteristic
131C42C22⋊D6111yescharacteristic
132C42C22×D6111yescharacteristic
133C23—1224no—
134C23—1222no—
135C23—2442no—
136C23—2442no—
137C23#1175819811yescharacteristic
138D4—614no—
139D4—1224no—
140D4—1222no—
141C2×C4—22no—
142C2×C4—41no—
143C2×C4—1222no—
144C2×C4—2442no—
145C2×C4—2444no—
146C2×C4—2442no—
147C2×C4—2442no—
148C2×C4#1175819811yescharacteristic
149C2×C4#1175819811yescharacteristic
150C2×C4#1175819811yescharacteristic
151C2×C4#1175819912yes—
152C2×C4#1175820112yes—
153C2×C4C2×C4×D6111yescharacteristic
154C2×C4C2×D24411yescharacteristic
155C2×C4C2×C22⋊D6111yescharacteristic
156C8—42no—
157C8—2442no—
158C22—21no—
159C22—21no—
160C22—1224no—
161C22—2448no—
162C22—2442no—
163C22—2442no—
164C22#1451969712yes—
165C22C2×#1175819811yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—2442no—
170C4#1451969712yes—
171C4M16×D6112yes—
172C4C2×#1175819911yescharacteristic
173C4C2×#1175820111yescharacteristic
174C2—22no—
175C2—2444no—
176C2#1683972511yescharacteristic
177C2C2×#1451969711yescharacteristic
178C2#1683977811yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D61
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#423C2
socleC22×C61C2×C22⋊C4
hypercenter#423D61
hypocenterC61#1486
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #423

Complements

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

NH ≅ G/Ntype
2. #16839815C2semidirect
3. #16839489C2semidirect
4. C61×#423C2semidirect
15. C4×#92418C22semidirect
19. C4⋊C8×C61C22semidirect
62. D244M16semidirect
92. #423D61semidirect
94. C61#1486semidirect
107. C4⋊C8C2×D61semidirect