Finite Group Databasebeta

← #21451021

Subgroups — #21451021

Order 7808.

548 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 165 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×#14519768C211yesmaximal, characteristic, complemented
2C2×D4×Dic61C211yesmaximal, characteristic
3#16839685C214yesmaximal, complemented
4#16839665C211yesmaximal, characteristic
5#16839637C214yesmaximal, complemented
6#16839632C211yesmaximal, characteristic, complemented
7#16839627C211yesmaximal, characteristic, complemented
8C4×#11758196C211yesmaximal, characteristic, complemented
9C61×#390C211yesmaximal, characteristic
10C23×Dic61C2212yes—
11#14519768—24no—
12D4×Dic61—24no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2212yes—
16C2×C4⋊Dic61C2214yes—
17C2×#11758196C2212yes—
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2212yes—
20C2×C22⋊Dic61C2214yes—
21C2×C4×Dic61C2211yescharacteristic
22C2×C4×Dic61C2211yescharacteristic
23#14519684C2214yes—
24#14519684C2212yes—
25C22×D4×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2214yes—
28C2×C42×C61C2211yescharacteristic
29C24×C61C2312yes—
30C2×D4×C61—22no—
31C2×D4×C61—22no—
32C2×D4×C61Q814yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61—24no—
37C22×Dic61—44no—
38C22×Dic61C2312yes—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2311yescharacteristic
42C22×Dic61C2311yescharacteristic
43C4⋊C4×C61—22no—
44C22⋊C4×C61—28no—
45C42×C61—22no—
46C22⋊Dic61—24no—
47C22⋊Dic61—44no—
48C4⋊Dic61—22no—
49C4⋊Dic61—22no—
50C4⋊Dic61—24no—
51C4⋊Dic61—44no—
52#11758196—24no—
53#11758196—24no—
54C4×Dic61—22no—
55C4×Dic61D414yes—
56C23×C61—22no—
57C23×C61—24no—
58C23×C61—22no—
59C23×C61—24no—
60C23×C61C2×Q814yes—
61C23×C61C2411yescharacteristic
62D4×C61—28no—
63C2×C4×C61—22no—
64C2×C4×C61—22no—
65C2×C4×C61—22no—
66C2×C4×C61—24no—
67C2×C4×C61C2×D412yes—
68C2×C4×C61C2×Q812yes—
69C2×C4×C61#4114yes—
70C2×C4×C61#4112yes—
71C2×Dic61—22no—
72C2×Dic61—22no—
73C2×Dic61—22no—
74C2×Dic61—22no—
75C2×Dic61—22no—
76C2×Dic61—22no—
77C2×Dic61—24no—
78C2×Dic61—24no—
79C2×Dic61—22no—
80C2×Dic61—48no—
81C2×Dic61C2×D412yes—
82C2×Dic61C2×D412yes—
83C22×C61—24no—
84C22×C61—28no—
85C22×C61—42no—
86C22×C61—42no—
87C22×C61—44no—
88C22×C61C22×D411yescharacteristic
89C22×C61C22×Q811yescharacteristic
90C22×C61C2×#4111yescharacteristic
91C22×C61C2×#4112yes—
92C22×C61H(5,𝔽2)12yes—
93C4×C61—24no—
94C4×C61—42no—
95C4×C61C22⋊Q814yes—
96Dic61—22no—
97Dic61—22no—
98Dic61—42no—
99Dic61—42no—
100Dic61—42no—
101#2566—611nomaximal, Sylow
102C2×C61—44no—
103C2×C61C2×C22⋊Q811yescharacteristic
104C2×C61#53211yescharacteristic
105C2×C61#53511yescharacteristic
106C2×C61#55312yes—
107C2×C61#55412yes—
108C2×#125—611no—
109C2×C4×D4—611no—
110#396—614no—
111#390—611no—
112#390D6111yescharacteristic
113#385—614no—
114#384—611no—
115#382—611no—
116C4×C4⋊C4—611no—
117C61#256611yescharacteristic, complemented, Sylow
118C22×D4C2×D6111yescharacteristic
119C23×C4—612no—
120#125—1224no—
121C4×D4—1224no—
122C2×C4⋊C4—611no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4—612no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—612no—
127C2×C4⋊C4—614no—
128C2×C4⋊C4C2×D6111yescharacteristic
129C2×C22⋊C4—612no—
130C2×C22⋊C4—614no—
131C2×C22⋊C4C2×D6114yes—
132C2×C42—611no—
133C2×C42—611no—
134C2×C42C2×D6111yescharacteristic
135#95—612no—
136#95—614no—
137C24C22×D6112yes—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4Dic12214yes—
141C22×C4—611no—
142C22×C4—611no—
143C22×C4—612no—
144C22×C4—612no—
145C22×C4—612no—
146C22×C4—1224no—
147C22×C4—2444no—
148C22×C4C22×D6112yes—
149C22×C4C22×D6112yes—
150C22×C4C22×D6111yescharacteristic
151C4⋊C4—22no—
152C4⋊C4—1224no—
153C4⋊C4—1224no—
154C4⋊C4—1222no—
155C4⋊C4—1222no—
156C4⋊C4—1224no—
157C4⋊C4—2444no—
158C22⋊C4—28no—
159C22⋊C4—1224no—
160C22⋊C4—2444no—
161C42—22no—
162C42—614no—
163C42—1222no—
164C23—22no—
165C23—24no—
166C23—22no—
167C23—24no—
168C23C2×Dic12214yes—
169C23C23×D6111yescharacteristic
170D4—28no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—24no—
175C2×C4—612no—
176C2×C4—612no—
177C2×C4—1222no—
178C2×C4—1222no—
179C2×C4—1222no—
180C2×C4—1222no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—1222no—
184C2×C4—1224no—
185C2×C4—1224no—
186C2×C4—2448no—
187C2×C4C2×Dic12212yes—
188C2×C4D4×D6112yes—
189C2×C4#1175822414yes—
190C2×C4#1175822412yes—
191C22—28no—
192C22—24no—
193C22—44no—
194C22—42no—
195C22—42no—
196C22C2×D4×D6111yescharacteristic
197C22C22×Dic12211yescharacteristic
198C22C2×#1175822411yescharacteristic
199C22C2×#1175822412yes—
200C22#1451982312yes—
201C4—24no—
202C4—42no—
203C4—1222no—
204C4—1222no—
205C4—2442no—
206C4—2442no—
207C4—2442no—
208C4#1451975414yes—
209C2—44no—
210C2C2×#1451975411yescharacteristic
211C2#1684031011yescharacteristic
212C2#1684033011yescharacteristic
213C2#1684046412yes—
214C2#1684046912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2566
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#14519768C2semidirect
3. #16839685C2semidirect
5. #16839637C2semidirect
6. #16839632C2semidirect
7. #16839627C2semidirect
8. C4×#11758196C2semidirect
117. C61#2566semidirect