Finite Group Databasebeta

← #21444532

Subgroups — #21444532

Order 7808.

332 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 77 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×#14519774C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic, complemented
3#16839505C214yesmaximal, complemented
4C61×#432C211yesmaximal, characteristic, complemented
5C22×D244—21no—
6C22×D244—21no—
7C22×D244C412yes—
8#14519774—21no—
9#14519774—21no—
10#14519774C412yes—
11#14519774C2212yes—
12C4⋊#92418C2212yescomplemented
13C22⋊#92418—21no—
14#14519688—21no—
15C2×C42×C61C2211yescharacteristic
16C4⋊C8×C61C2212yescomplemented
17C22⋊C8×C61—21no—
18#97×C61—21no—
19C23×D61—22no—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C2×D244—22no—
24C2×D244—22no—
25C2×D244—22no—
26C2×D244—22no—
27C2×D244—22no—
28C2×D244—44no—
29C2×D244—44no—
30C2×D244—44no—
31C2×D244C2×C414yes—
32C2×C8×C61—22no—
33C42×C61C2×C411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61D411yescharacteristic
36C42×C61C2311yescharacteristic
37C2×#92418—22no—
38C23×C61C22⋊C411yescharacteristic
39C22×D61—24no—
40C22×D61—44no—
41C22×D61—44no—
42C22×D61—44no—
43C2×C4×C61—22no—
44C2×C4×C61—22no—
45C2×C4×C61—22no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22×C411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52D244—44no—
53D244—44no—
54D244—44no—
55D244—44no—
56D244—44no—
57D244—44no—
58C8×C61—42no—
59#92418—42no—
60C22×C61—21no—
61C22×C61—21no—
62C22×C61#10012yes—
63C22×C61C2×C22⋊C411yescharacteristic
64C2×D61—44no—
65C2×D61—44no—
66C2×D61—44no—
67C2×D61—88no—
68C4×C61—21no—
69C4×C61—21no—
70C4×C61—21no—
71C4×C61—21no—
72C4×C61AGL(1,ℤ/8)12yes—
73C4×C61AGL(1,ℤ/8)12yes—
74#1555—611nomaximal, Sylow
75C2×C61—22no—
76C2×C61C2×#10011yescharacteristic
77C2×C61#41811yescharacteristic
78C2×C61#41811yescharacteristic
79D61—84no—
80C2×#127—611no—
81#432—611no—
82#432D6111yescharacteristic, complemented
83#331—614no—
84C61#155511yescharacteristic, complemented, Sylow
85C22×D4—612no—
86C22×D4—1221no—
87C22×D4—1221no—
88#127—612no—
89#127—612no—
90#127—1221no—
91#127—1221no—
92C2×C42C2×D6111yescharacteristic
93C4⋊C8—612no—
94C4⋊C8C2×D6112yescomplemented
95C22⋊C8—21no—
96C22⋊C8—1221no—
97#97—21no—
98#97—1221no—
99C24—1222no—
100C2×D4—614no—
101C2×D4—1222no—
102C2×D4—1222no—
103C2×D4—1222no—
104C2×D4—1222no—
105C2×D4—1222no—
106C2×D4—2444no—
107C2×D4—2444no—
108C2×D4—2444no—
109C22×C4C4×D6111yescharacteristic
110C22×C4D24411yescharacteristic
111C22×C4C22⋊D6111yescharacteristic
112C2×C8—22no—
113C2×C8—1222no—
114C42C4×D6111yescharacteristic
115C42D24411yescharacteristic
116C42C22⋊D6111yescharacteristic
117C42C22×D6111yescharacteristic
118C23—1224no—
119C23—2444no—
120C23—2444no—
121C23—2444no—
122C23#1175819811yescharacteristic
123D4—2444no—
124D4—2444no—
125D4—2444no—
126D4—2444no—
127D4—2444no—
128D4—2444no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4#1175819811yescharacteristic
133C2×C4#1175819811yescharacteristic
134C2×C4#1175819811yescharacteristic
135C2×C4C2×C4×D6111yescharacteristic
136C2×C4C2×D24411yescharacteristic
137C2×C4C2×C22⋊D6111yescharacteristic
138C8—42no—
139C8—2442no—
140C22—21no—
141C22—21no—
142C22—4888no—
143C22—2444no—
144C22—2444no—
145C22—2444no—
146C22#1451969312yes—
147C22C2×#1175819811yescharacteristic
148C4—21no—
149C4—21no—
150C4—21no—
151C4—21no—
152C4#1451980212yes—
153C4#1451980512yes—
154C2—22no—
155C2—4884no—
156C2C2×#1451969311yescharacteristic
157C2#1683976611yescharacteristic
158C2#1683976811yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#432C2
socleC22×C61C2×C22⋊C4
hypercenter#432D61
hypocenterC61#1555
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839505C2semidirect
4. C61×#432C2semidirect
12. C4⋊#92418C22semidirect
16. C4⋊C8×C61C22semidirect
82. #432D61semidirect
84. C61#1555semidirect
94. C4⋊C8C2×D61semidirect