Finite Group Databasebeta

← #21444522

Subgroups — #21444522

Order 7808.

242 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 73 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
2#16839819C211yesmaximal, characteristic, complemented
3#16839509C212yesmaximal, complemented
4#16839505C212yesmaximal, complemented
5C61×#431C211yesmaximal, characteristic, complemented
6C2×#11758222—21no—
7#14519777C2211yescharacteristic
8#14519774C2211yescharacteristic
9#14519765—21no—
10#14519751—21no—
11#14519751C412yes—
12C4×D244—21no—
13C4×D244C412yes—
14C4⋊#92418C2212yes—
15C22⋊#92418—21no—
16#14519688—21no—
17C2×C42×C61C2211yescharacteristic
18C4⋊C8×C61C2212yes—
19C22⋊C8×C61—21no—
20C4×C8×C61—21no—
21C22×C4×C61C2×C411yescharacteristic
22C22×C4×C61D411yescharacteristic
23C22×C4×C61D411yescharacteristic
24C2×C22⋊D61—22no—
25#11758222—44no—
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—
41C23×C61C22⋊C411yescharacteristic
42C22×D61—22no—
43C2×C4×C61—22no—
44C2×C4×C61—22no—
45C2×C4×C61—41no—
46C2×C4×C61C22⋊C411yescharacteristic
47C2×C4×C61C22⋊C411yescharacteristic
48C2×C4×C61C22⋊C411yescharacteristic
49C2×C4×C61C22×C411yescharacteristic
50C2×C4×C61C2×D411yescharacteristic
51C2×C4×C61C2×D411yescharacteristic
52C22⋊D61—44no—
53C2×Dic61—22no—
54D244—42no—
55D244—42no—
56D244—42no—
57C4×D61—44no—
58Dic122—42no—
59C8×C61—42no—
60#92418—42no—
61C22×C61—21no—
62C22×C61—21no—
63C22×C61—21no—
64C22×C61C2×C22⋊C411yescharacteristic
65C2×D61—42no—
66C2×D61—42no—
67C2×D61—42no—
68C4×C61—21no—
69C4×C61—21no—
70C4×C61—21no—
71C4×C61—21no—
72C4×C61#13512yes—
73C4×C61AGL(1,ℤ/8)12yes—
74Dic61—42no—
75#1553—611nomaximal, Sylow
76C2×C61—41no—
77C2×C61#41311yescharacteristic
78C2×C61#41611yescharacteristic
79C2×C61#41811yescharacteristic
80D61—82no—
81#532—611no—
82#432—611no—
83#431D6111yescharacteristic, complemented
84#332—612no—
85#331—612no—
86C61#155311yescharacteristic, complemented, Sylow
87C2×#41—1221no—
88C4⋊Q8—611no—
89#127—611no—
90#124—1221no—
91#121—612no—
92#121—1221no—
93C4×D4—612no—
94C4×D4—1221no—
95C2×C42C2×D6111yescharacteristic
96C4⋊C8—612no—
97C4⋊C8C2×D6112yes—
98C22⋊C8—21no—
99C22⋊C8—1221no—
100#97—1221no—
101C4×C8—21no—
102#41—2444no—
103C2×Q8—1221no—
104C2×D4—612no—
105C2×D4—1222no—
106C2×D4—1221no—
107C2×D4—1221no—
108C22×C4—1222no—
109C22×C4C4×D6111yescharacteristic
110C22×C4D24411yescharacteristic
111C22×C4C22⋊D6111yescharacteristic
112C2×C8—22no—
113C2×C8—1222no—
114C4⋊C4—612no—
115C4⋊C4—1221no—
116C22⋊C4—1222no—
117C22⋊C4—1222no—
118C42C4×D6111yescharacteristic
119C42D24411yescharacteristic
120C42C22⋊D6111yescharacteristic
121C42C22×D6111yescharacteristic
122C23—1222no—
123C23#1175819811yescharacteristic
124Q8—2442no—
125D4—2442no—
126D4—2444no—
127D4—2442no—
128D4—2442no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—1222no—
133C2×C4—2444no—
134C2×C4#1175819811yescharacteristic
135C2×C4#1175819811yescharacteristic
136C2×C4#1175819811yescharacteristic
137C2×C4C2×C4×D6111yescharacteristic
138C2×C4C2×D24411yescharacteristic
139C2×C4C2×C22⋊D6111yescharacteristic
140C8—42no—
141C8—2442no—
142C22—21no—
143C22—21no—
144C22—21no—
145C22—2442no—
146C22—2442no—
147C22—2442no—
148C22C2×#1175819811yescharacteristic
149C4—21no—
150C4—21no—
151C4—21no—
152C4—21no—
153C4—2442no—
154C4#1451979912yes—
155C4#1451980212yes—
156C2—41no—
157C2—4882no—
158C2#1683974411yescharacteristic
159C2#1683975911yescharacteristic
160C2#1683976611yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC2×C4×C61C22×C4
FrattiniC42C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1553
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839509C2semidirect
4. #16839505C2semidirect
5. C61×#431C2semidirect
83. #431D61semidirect
86. C61#1553semidirect