Finite Group Databasebeta

← #21444219

Subgroups — #21444219

Order 7808.

260 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 89 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#16840312C211yesmaximal, characteristic
2C2×C4⋊#92418C211yesmaximal, characteristic, complemented
3#16839491C214yesmaximal, complemented
4C61×#431C211yesmaximal, characteristic, complemented
5C2×#11758222—21no—
6C22×#92418—21no—
7#14519777C411yescharacteristic
8#14519774C411yescharacteristic
9#14519765—21no—
10#14519751—21no—
11#14519751C412yes—
12C4×D244—21no—
13C4×D244C2212yes—
14C4⋊#92418—21no—
15C4⋊#92418C2212yes—
16C2×C42×C61C2211yescharacteristic
17C4⋊C8×C61—21no—
18C22⋊C8×C61—21no—
19C4×C8×C61C2212yes—
20C22×C4×C61C2×C411yescharacteristic
21C22×C4×C61D411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C2×C22⋊D61—22no—
24#11758222—42no—
25#11758222—42no—
26C2×D244—21no—
27C2×D244—21no—
28C2×D244C2×C412yes—
29C2×C4×D61—22no—
30C2×Dic122—21no—
31C2×C8×C61—22no—
32C42×C61C2×C411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61D411yescharacteristic
35C42×C61C2311yescharacteristic
36#11758198—22no—
37#11758198—22no—
38C4⋊Dic61—21no—
39C4⋊Dic61C2×C412yes—
40C2×#92418—22no—
41C2×#92418—42no—
42C23×C61C22⋊C411yescharacteristic
43C22×D61—22no—
44C2×C4×C61—22no—
45C2×C4×C61—41no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61D812yes—
50C2×C4×C61SD1612yes—
51C2×C4×C61C22×C411yescharacteristic
52C2×C4×C61C2×D411yescharacteristic
53C2×C4×C61C2×D411yescharacteristic
54C22⋊D61—44no—
55C2×Dic61—22no—
56D244—24no—
57D244—42no—
58D244—42no—
59C4×D61—42no—
60C4×D61—42no—
61Dic122—42no—
62C8×C61—42no—
63#92418—42no—
64C22×C61—21no—
65C22×C61—21no—
66C22×C61#10212yes—
67C22×C61C2×C22⋊C411yescharacteristic
68C2×D61—42no—
69C2×D61—42no—
70C2×D61—42no—
71C4×C61—21no—
72C4×C61—21no—
73C4×C61—21no—
74C4×C61#10212yes—
75C4×C61#13112yes—
76C4×C61C2×D811yescharacteristic
77C4×C61C2×SD1611yescharacteristic
78Dic61—42no—
79#1480—611nomaximal, Sylow
80C2×C61—22no—
81C2×C61#40811yescharacteristic
82C2×C61C2×#10211yescharacteristic
83C2×C61#42111yescharacteristic
84D61—82no—
85#532—611no—
86#431D6111yescharacteristic, complemented
87C2×C4⋊C8—611no—
88D4⋊C8—614no—
89C61#148011yescharacteristic, complemented, Sylow
90C2×#41—1221no—
91C22×C8—1221no—
92C4⋊Q8—611no—
93#127—611no—
94#124—1221no—
95#121—612no—
96#121—1221no—
97C4×D4—612no—
98C4×D4—1221no—
99C2×C42C2×D6111yescharacteristic
100C4⋊C8—21no—
101C4⋊C8—612no—
102C4⋊C8—1221no—
103C22⋊C8—21no—
104C4×C8C2×D6112yes—
105#41—2442no—
106#41—2442no—
107C2×Q8—1221no—
108C2×D4—612no—
109C2×D4—1222no—
110C2×D4—1221no—
111C2×D4—1221no—
112C22×C4—1222no—
113C22×C4C4×D6111yescharacteristic
114C22×C4D24411yescharacteristic
115C22×C4C22⋊D6111yescharacteristic
116C2×C8—22no—
117C2×C8—1222no—
118C2×C8—2442no—
119C4⋊C4—612no—
120C4⋊C4—1221no—
121C22⋊C4—1222no—
122C22⋊C4—1222no—
123C42C4×D6111yescharacteristic
124C42D24411yescharacteristic
125C42C22⋊D6111yescharacteristic
126C42C22×D6111yescharacteristic
127C23—1222no—
128C23#1175819811yescharacteristic
129Q8—2442no—
130D4—1224no—
131D4—2442no—
132D4—2444no—
133D4—2442no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—1222no—
137C2×C4—2442no—
138C2×C4—2442no—
139C2×C4#1175819012yes—
140C2×C4D48812yes—
141C2×C4#1175819811yescharacteristic
142C2×C4#1175819811yescharacteristic
143C2×C4#1175819811yescharacteristic
144C2×C4C2×C4×D6111yescharacteristic
145C2×C4C2×D24411yescharacteristic
146C2×C4C2×C22⋊D6111yescharacteristic
147C8—42no—
148C8—2442no—
149C22—21no—
150C22—21no—
151C22—2442no—
152C22—2442no—
153C22—2442no—
154C22#1451969912yes—
155C22C2×#1175819811yescharacteristic
156C4—21no—
157C4—21no—
158C4—21no—
159C4—2442no—
160C4#1451969912yes—
161C4#1451978512yes—
162C4C2×D48811yescharacteristic
163C4C2×#1175819011yescharacteristic
164C2—22no—
165C2—4882no—
166C2#1683973011yescharacteristic
167C2C2×#1451969911yescharacteristic
168C2#1683978011yescharacteristic
subgroupG/H
centerC2×C4C2×D244
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1480
LCSG ▷ C2×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. C2×C4⋊#92418C2semidirect
3. #16839491C2semidirect
4. C61×#431C2semidirect
86. #431D61semidirect
89. C61#1480semidirect