Finite Group Databasebeta

← #21446983

Subgroups — #21446983

Order 7808.

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

normal subgroups only

This group has 466 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
1#16840388C211yesmaximal, characteristic, complemented
2#16839618C212yesmaximal
3#16839529C211yesmaximal, characteristic, complemented
4#16839528C212yesmaximal, complemented
5C61×#379C211yesmaximal, characteristic
6#14519756—22no—
7#14519754—24no—
8C2×C22⋊Dic61—24no—
9C2×C22⋊Dic61C2212yes—
10C2×C22⋊Dic61C2212yes—
11C25×C61C2211yescharacteristic
12C2×C22⋊C4×C61—22no—
13C2×C22⋊C4×C61C2211yescharacteristic
14C2×C22⋊C4×C61C2211yescharacteristic
15C24×C61—21no—
16C24×C61—22no—
17C24×C61—21no—
18C24×C61—22no—
19C24×C61—44no—
20C24×C61Q812yescomplemented
21C24×C61C2311yescharacteristic
22C22×C4×C61—21no—
23C22×C4×C61D412yes—
24C22×Dic61—22no—
25C22×Dic61D414yes—
26C2×Dic122—22no—
27C22⋊C4×C61—22no—
28C22⋊C4×C61—22no—
29C22⋊C4×C61—44no—
30C22⋊Dic61—22no—
31C22⋊Dic61—22no—
32C22⋊Dic61—22no—
33C22⋊Dic61—22no—
34C22⋊Dic61—48no—
35C4⋊Dic61—22no—
36#11758196—24no—
37C23×C61—28no—
38C23×C61—24no—
39C23×C61—24no—
40C23×C61—22no—
41C23×C61—44no—
42C23×C61—42no—
43C23×C61—44no—
44C23×C61—42no—
45C23×C61—48no—
46C23×C61—44no—
47C23×C61—41no—
48C23×C61—42no—
49C23×C61—41no—
50C23×C61C2×D412yes—
51C23×C61C2×D411yescharacteristic
52C23×C61C2×Q811yescharacteristic
53C23×C61#4111yescharacteristic
54C23×C61#4112yes—
55C2×C4×C61—22no—
56C2×C4×C61—42no—
57C2×C4×C61—42no—
58C2×C4×C61—41no—
59C2×Dic61—24no—
60C2×Dic61—44no—
61C2×Dic61—44no—
62C2×Dic61—42no—
63Dic122—82no—
64C22×C61—24no—
65C22×C61—22no—
66C22×C61—28no—
67C22×C61—24no—
68C22×C61—41no—
69C22×C61—41no—
70C22×C61—42no—
71C22×C61—48no—
72C22×C61—44no—
73C22×C61—44no—
74C22×C61—42no—
75C22×C61—42no—
76C22×C61—44no—
77C22×C61#12011yescharacteristic
78C22×C61C22⋊Q812yes—
79C22×C61C22⋊Q811yescharacteristic
80C22×C61#12412yes—
81C22×C61#12411yescharacteristic
82C4×C61—42no—
83C4×C61—81no—
84Dic61—44no—
85Dic61—82no—
86#2029—611nomaximal, Sylow
87C2×C61—22no—
88C2×C61—21no—
89C2×C61—22no—
90C2×C61—21no—
91C2×C61—44no—
92C2×C61#39311yescharacteristic
93C2×C61B(4,𝔽2)12yes—
94#543—611no—
95#379—612no—
96#379D6111yescharacteristic
97#342—612no—
98#342—611no—
99C61#202911yescharacteristic, complemented, Sylow
100C25C2×D6111yescharacteristic
101C22⋊Q8—1224no—
102C22⋊Q8—1222no—
103C2×C22⋊C4—22no—
104C2×C22⋊C4—612no—
105C2×C22⋊C4—612no—
106C2×C22⋊C4—1224no—
107C2×C22⋊C4C2×D6111yescharacteristic
108C2×C22⋊C4C2×D6111yescharacteristic
109C24—22no—
110C24—21no—
111C24—21no—
112C24—22no—
113C24—44no—
114C24Dic12212yescomplemented
115C24C22×D6111yescharacteristic
116C2×Q8—1222no—
117C22×C4—21no—
118C22×C4—614no—
119C22×C4—1222no—
120C22×C4C22⋊D6112yes—
121C4⋊C4—1224no—
122C4⋊C4—1222no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—44no—
126C22⋊C4—1222no—
127C22⋊C4—1222no—
128C22⋊C4—1222no—
129C22⋊C4—1222no—
130C22⋊C4—2448no—
131C23—24no—
132C23—28no—
133C23—24no—
134C23—22no—
135C23—44no—
136C23—42no—
137C23—42no—
138C23—44no—
139C23—44no—
140C23—48no—
141C23—41no—
142C23—42no—
143C23—41no—
144C23C2×Dic12211yescharacteristic
145C23#1175822211yescharacteristic
146C23D4×D6112yes—
147C23#1175822412yes—
148C23C2×C22⋊D6111yescharacteristic
149Q8—4882no—
150C2×C4—22no—
151C2×C4—42no—
152C2×C4—42no—
153C2×C4—41no—
154C2×C4—1224no—
155C2×C4—2444no—
156C2×C4—2442no—
157C2×C4—2444no—
158C22—22no—
159C22—24no—
160C22—28no—
161C22—24no—
162C22—41no—
163C22—41no—
164C22—42no—
165C22—44no—
166C22—48no—
167C22—44no—
168C22—42no—
169C22—44no—
170C22—42no—
171C22#1451974511yescharacteristic
172C22#1451975412yes—
173C22#1451975611yescharacteristic
174C22#1451976312yes—
175C22#1451976411yescharacteristic
176C4—42no—
177C4—81no—
178C4—4882no—
179C4—2444no—
180C2—21no—
181C2—22no—
182C2—22no—
183C2—21no—
184C2—44no—
185C2#1683967411yescharacteristic
186C2#1683994812yes—
subgroupG/H
centerC22#14519745
commutatorC24×C61C23
FrattiniC24C22×D61
FittingC61×#379C2
socleC22×C61#120
hypercenter#379D61
hypocenterC61#2029
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #16840388C2semidirect
3. #16839529C2semidirect
4. #16839528C2semidirect
20. C24×C61Q8semidirect
99. C61#2029semidirect
114. C24Dic122semidirect