Finite Group Databasebeta

← #21446984

Subgroups — #21446984

Order 7808.

466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 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#16840388C211yesmaximal, characteristic, complemented
2#16839617C212yesmaximal
3#16839617C211yesmaximal, characteristic
4#16839528C212yesmaximal, complemented
5C61×#342C211yesmaximal, characteristic, complemented
6C24×D61C2211yescharacteristic
7#14519756—22no—
8#14519754—24no—
9C2×C22⋊Dic61C2211yescharacteristic
10C2×C22⋊Dic61C2212yes—
11C2×#11758198—22no—
12C2×#11758198—24no—
13C2×C22⋊C4×C61C2212yes—
14C2×C22⋊C4×C61C2211yescharacteristic
15C24×C61C2311yescharacteristic
16C23×D61—21no—
17C23×D61—22no—
18C23×D61—22no—
19C23×D61—21no—
20C23×D61—44no—
21C23×D61Q812yescomplemented
22C22×C4×C61—22no—
23C22×C4×C61D412yes—
24C22×Dic61—21no—
25C22×Dic61D414yes—
26C2×Dic122—22no—
27C22⋊C4×C61—22no—
28C22⋊C4×C61—22no—
29C22⋊C4×C61—22no—
30C22⋊Dic61—22no—
31C22⋊Dic61—22no—
32C22⋊Dic61—22no—
33#11758198—48no—
34#11758198—44no—
35C4⋊Dic61—22no—
36#11758196—24no—
37C23×C61—42no—
38C23×C61C2×D411yescharacteristic
39C23×C61C2×D412yes—
40C23×C61C2×Q811yescharacteristic
41C23×C61#4112yes—
42C23×C61#4111yescharacteristic
43C22×D61—24no—
44C22×D61—28no—
45C22×D61—24no—
46C22×D61—22no—
47C22×D61—44no—
48C22×D61—48no—
49C22×D61—44no—
50C22×D61—42no—
51C22×D61—44no—
52C22×D61—41no—
53C22×D61—42no—
54C22×D61—41no—
55C2×C4×C61—22no—
56C2×C4×C61—42no—
57C2×C4×C61—44no—
58C2×C4×C61—42no—
59C2×Dic61—24no—
60C2×Dic61—44no—
61C2×Dic61—42no—
62C2×Dic61—41no—
63Dic122—82no—
64C22×C61—22no—
65C22×C61—24no—
66C22×C61—41no—
67C22×C61—42no—
68C22×C61—41no—
69C22×C61#12011yescharacteristic
70C22×C61C22⋊Q812yes—
71C22×C61C22⋊Q811yescharacteristic
72C22×C61#12412yes—
73C22×C61#12411yescharacteristic
74C2×D61—28no—
75C2×D61—24no—
76C2×D61—44no—
77C2×D61—48no—
78C2×D61—44no—
79C2×D61—42no—
80C2×D61—42no—
81C2×D61—44no—
82C4×C61—42no—
83C4×C61—82no—
84Dic61—44no—
85Dic61—81no—
86#2029—611nomaximal, Sylow
87C2×C61—21no—
88C2×C61—22no—
89C2×C61—22no—
90C2×C61—21no—
91C2×C61#39311yescharacteristic
92C2×C61B(4,𝔽2)12yes—
93D61—44no—
94#543—611no—
95#379—612no—
96#379—611no—
97#342—612no—
98#342D6111yescharacteristic, complemented
99C61#202911yescharacteristic, complemented, Sylow
100C25—611no—
101C22⋊Q8—1224no—
102C22⋊Q8—1222no—
103C2×C22⋊C4—612no—
104C2×C22⋊C4—611no—
105C2×C22⋊C4—1224no—
106C2×C22⋊C4—1222no—
107C2×C22⋊C4C2×D6112yes—
108C2×C22⋊C4C2×D6111yescharacteristic
109C24—612no—
110C24—1221no—
111C24—1222no—
112C24—1222no—
113C24—1221no—
114C24—2444no—
115C24C22×D6111yescharacteristic
116C2×Q8—1222no—
117C22×C4—22no—
118C22×C4—614no—
119C22×C4—1221no—
120C22×C4D24412yes—
121C4⋊C4—1224no—
122C4⋊C4—1222no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—22no—
126C22⋊C4—1222no—
127C22⋊C4—1222no—
128C22⋊C4—1222no—
129C22⋊C4—2444no—
130C22⋊C4—2448no—
131C23—42no—
132C23—1224no—
133C23—1228no—
134C23—1224no—
135C23—1222no—
136C23—2442no—
137C23—2444no—
138C23—2444no—
139C23—2448no—
140C23—2444no—
141C23—2441no—
142C23—2442no—
143C23—2441no—
144C23C2×D24411yescharacteristic
145C23#1175822212yes—
146C23D4×D6112yes—
147C23#1175822411yescharacteristic
148C23Q8×D6111yescharacteristic
149Q8—4882no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—42no—
154C2×C4—1224no—
155C2×C4—2442no—
156C2×C4—2441no—
157C2×C4—2444no—
158C22—22no—
159C22—24no—
160C22—42no—
161C22—41no—
162C22—41no—
163C22—1228no—
164C22—1224no—
165C22—2448no—
166C22—2444no—
167C22—2444no—
168C22—2442no—
169C22—2444no—
170C22—2442no—
171C22#1451974711yescharacteristic
172C22#1451975512yes—
173C22#1451975711yescharacteristic
174C22#1451976312yes—
175C22#1451976511yescharacteristic
176C4—42no—
177C4—82no—
178C4—4881no—
179C4—2444no—
180C2—22no—
181C2—21no—
182C2—22no—
183C2—21no—
184C2—2444no—
185C2#1683967511yescharacteristic
186C2#1683995012yes—
subgroupG/H
centerC22#14519747
commutatorC24×C61C23
FrattiniC24C22×D61
FittingC61×#342C2
socleC22×C61#120
hypercenter#342D61
hypocenterC61#2029
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #16840388C2semidirect
4. #16839528C2semidirect
5. C61×#342C2semidirect
21. C23×D61Q8semidirect
98. #342D61semidirect
99. C61#2029semidirect