Finite Group Databasebeta

← #21444186

Subgroups — #21444186

Order 7808.

214 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 69 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×#14519771C211yesmaximal, characteristic
2#16839819C211yesmaximal, characteristic, complemented
3#16839487C212yesmaximal, complemented
4#16839485C212yesmaximal
5C61×#431C211yesmaximal, characteristic, complemented
6#14519771—21no—
7#14519771—21no—
8#14519771—21no—
9#14519771—21no—
10C2×#11758196C411yescharacteristic
11C2×#11758196C411yescharacteristic
12C2×#11758196C2211yescharacteristic
13C2×#11758198C411yescharacteristic
14C2×#11758198C411yescharacteristic
15C2×#11758198C2211yescharacteristic
16C4⋊#92418—21no—
17C22⋊#92418C2212yes—
18#14519688—21no—
19C2×C42×C61C2211yescharacteristic
20C4⋊C8×C61—21no—
21C22⋊C8×C61C2212yes—
22C4×C8×C61—21no—
23C23×D61C2×C411yescharacteristic
24C22×C4×C61C2×C411yescharacteristic
25C22×C4×C61C2×C411yescharacteristic
26C22×C4×C61C2311yescharacteristic
27C22×Dic61C2×C411yescharacteristic
28C22×Dic61C2×C411yescharacteristic
29C22×Dic61C2×C411yescharacteristic
30C2×C8×C61—22no—
31C42×C61D411yescharacteristic
32C42×C61D411yescharacteristic
33C42×C61D411yescharacteristic
34C42×C61D411yescharacteristic
35#11758198—21no—
36#11758198—21no—
37#11758198—21no—
38#11758198—21no—
39#11758198—21no—
40#11758198—21no—
41#11758196—21no—
42#11758196—21no—
43#11758196—21no—
44#11758196—21no—
45#11758196—21no—
46#11758196—21no—
47C2×#92418—22no—
48C23×C61C22×C411yescharacteristic
49C22×D61—21no—
50C22×D61—22no—
51C22×D61—41no—
52C22×D61—41no—
53C2×C4×C61—22no—
54C2×C4×C61—41no—
55C2×C4×C61—41no—
56C2×C4×C61C22⋊C411yescharacteristic
57C2×C4×C61C22⋊C411yescharacteristic
58C2×C4×C61C22⋊C411yescharacteristic
59C2×C4×C61C22⋊C411yescharacteristic
60C2×C4×C61C2×D411yescharacteristic
61C2×C4×C61C2×D411yescharacteristic
62C2×Dic61—21no—
63C2×Dic61—21no—
64C2×Dic61—21no—
65C2×Dic61—22no—
66C2×Dic61—41no—
67C2×Dic61—41no—
68C8×C61—42no—
69#92418—42no—
70C22×C61—21no—
71C22×C61—21no—
72C22×C61C2×C22⋊C411yescharacteristic
73C22×C61#13112yes—
74C2×D61—41no—
75C2×D61—41no—
76C2×D61—41no—
77C2×D61—82no—
78C4×C61—21no—
79C4×C61—21no—
80C4×C61—21no—
81C4×C61—21no—
82C4×C61—21no—
83C4×C61—21no—
84Dic61—41no—
85Dic61—41no—
86Dic61—41no—
87#1473—611nomaximal, Sylow
88C2×C61—22no—
89C2×C61#40811yescharacteristic
90C2×C61#41011yescharacteristic
91C2×C61#41311yescharacteristic
92D61—81no—
93C2×#126—611no—
94#432—611no—
95#431D6111yescharacteristic, complemented
96#324—612no—
97#323—612no—
98C61#147311yescharacteristic, complemented, Sylow
99#126—1221no—
100#126—1221no—
101#126—1221no—
102#126—1221no—
103C2×C4⋊C4—611no—
104C2×C4⋊C4—611no—
105C2×C4⋊C4—611no—
106C2×C22⋊C4—611no—
107C2×C22⋊C4—611no—
108C2×C22⋊C4—611no—
109C2×C42C2×D6111yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—1221no—
112C22⋊C8—612no—
113C22⋊C8C2×D6112yes—
114#97—1221no—
115C4×C8—21no—
116C24—611no—
117C22×C4—611no—
118C22×C4—611no—
119C22×C4—611no—
120C22×C4C4×D6111yescharacteristic
121C22×C4C4×D6111yescharacteristic
122C22×C4C22×D6111yescharacteristic
123C2×C8—22no—
124C2×C8—1222no—
125C4⋊C4—1221no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—1221no—
129C4⋊C4—1221no—
130C4⋊C4—1221no—
131C22⋊C4—1221no—
132C22⋊C4—1221no—
133C22⋊C4—1221no—
134C22⋊C4—1221no—
135C22⋊C4—1221no—
136C22⋊C4—1221no—
137C42D24411yescharacteristic
138C42D24411yescharacteristic
139C42C22⋊D6111yescharacteristic
140C42C22⋊D6111yescharacteristic
141C23—1222no—
142C23—1221no—
143C23—2441no—
144C23—2441no—
145C23C2×C4×D6111yescharacteristic
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—1221no—
150C2×C4—1221no—
151C2×C4—1221no—
152C2×C4—1222no—
153C2×C4—2441no—
154C2×C4—2441no—
155C2×C4#1175819811yescharacteristic
156C2×C4#1175819811yescharacteristic
157C2×C4#1175819811yescharacteristic
158C2×C4#1175819811yescharacteristic
159C2×C4C2×D24411yescharacteristic
160C2×C4C2×C22⋊D6111yescharacteristic
161C8—42no—
162C8—2442no—
163C22—21no—
164C22—21no—
165C22—4882no—
166C22—2441no—
167C22—2441no—
168C22—2441no—
169C22C2×#1175819811yescharacteristic
170C22#1451978312yes—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—2441no—
178C4—2441no—
179C4—2441no—
180C2—22no—
181C2—4881no—
182C2#1683972811yescharacteristic
183C2#1683973511yescharacteristic
184C2#1683974411yescharacteristic
subgroupG/H
centerC22C2×#11758198
commutatorC23×C61C22×C4
FrattiniC22×C4C22×D61
FittingC61×#431C2
socleC22×C61C2×C22⋊C4
hypercenter#431D61
hypocenterC61#1473
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #16839819C2semidirect
3. #16839487C2semidirect
5. C61×#431C2semidirect
95. #431D61semidirect
98. C61#1473semidirect