Finite Group Databasebeta

← #21451561

Subgroups — #21451561

Order 7808.

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

normal subgroups only

This group has 632 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×#14519760C212yesmaximal, complemented
2C2×#14519751C211yesmaximal, characteristic
3#16839692C212yesmaximal, complemented
4#16839684C214yesmaximal, complemented
5#16839679C212yesmaximal, complemented
6#16839641C212yesmaximal, complemented
7#16839622C211yesmaximal, characteristic, complemented
8C22×C4⋊C4×C61C211yesmaximal, characteristic, complemented
9C22×D244C2211yescharacteristic
10C22×C22⋊D61C2212yes—
11#14519760—28no—
12#14519751—24no—
13C2×C4⋊Dic61C2211yescharacteristic
14C2×C4⋊Dic61C2212yes—
15C2×#11758196C2214yes—
16C2×C22⋊Dic61C2212yes—
17C2×#11758198C2212yes—
18C2×#11758198C2214yes—
19C2×#11758198C2214yes—
20#14519684C2214yes—
21#14519684C2212yes—
22C23×C4×C61C2211yescharacteristic
23C23×C4×C61C2211yescharacteristic
24C23×C4×C61C2211yescharacteristic
25C2×C4⋊C4×C61—24no—
26C2×C4⋊C4×C61C2212yes—
27C2×C4⋊C4×C61C2212yes—
28C24×C61C2311yescharacteristic
29C23×D61C2312yes—
30C22×C4×C61—22no—
31C22×C4×C61—22no—
32C22×C4×C61—22no—
33C22×C4×C61—42no—
34C22×C4×C61—42no—
35C22×C4×C61D414yes—
36C22×C4×C61D414yescomplemented
37C22×C4×C61C2312yes—
38C22×C4×C61C2311yescharacteristic
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C2×C22⋊D61—24no—
42C2×C22⋊D61—24no—
43C2×C22⋊D61—24no—
44C22×Dic61C2312yes—
45C22×Dic61C2314yes—
46C2×D244—22no—
47C2×D244—42no—
48C4⋊C4×C61—24no—
49C4⋊C4×C61—24no—
50C22⋊Dic61—24no—
51#11758198—24no—
52#11758198—28no—
53#11758198—44no—
54C4⋊Dic61—22no—
55C4⋊Dic61—42no—
56#11758196—28no—
57C23×C61—22no—
58C23×C61—22no—
59C23×C61C2×D412yes—
60C23×C61C2×D412yes—
61C23×C61#4112yes—
62C23×C61C2411yescharacteristic
63C22×D61—22no—
64C22×D61—22no—
65C22×D61—22no—
66C22×D61—24no—
67C22×D61—24no—
68C2×C4×C61—28no—
69C2×C4×C61—22no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—24no—
75C2×C4×C61—44no—
76C2×C4×C61—44no—
77C2×C4×C61C2×D414yes—
78C2×C4×C61C2×D412yes—
79C2×C4×C61C2×D412yes—
80C22⋊D61—48no—
81C2×Dic61—22no—
82C2×Dic61—24no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—24no—
86C2×Dic61—24no—
87D244—44no—
88C22×C61—22no—
89C22×C61—22no—
90C22×C61—24no—
91C22×C61—24no—
92C22×C61#12114yes—
93C22×C61C22×D411yescharacteristic
94C22×C61C22×D411yescharacteristic
95C22×C61C2×#4111yescharacteristic
96C22×C61H(5,𝔽2)12yes—
97C22×C612−1+412yes—
98C2×D61—42no—
99C2×D61—42no—
100C2×D61—42no—
101C2×D61—44no—
102C2×D61—44no—
103C4×C61—24no—
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—42no—
107Dic61—42no—
108Dic61—44no—
109#2618—611nomaximal, Sylow
110C2×C61—24no—
111C2×C61C2×#12111yescharacteristic
112C2×C61#53411yescharacteristic
113C2×C61#53611yescharacteristic
114C2×C61#53712yes—
115C2×C61#53912yes—
116D61—82no—
117C2×#123—612no—
118C2×#121—611no—
119C22×C4⋊C4D6111yescharacteristic, complemented
120#398—612no—
121#396—614no—
122#394—612no—
123#386—612no—
124#380—611no—
125C61#261811yescharacteristic, complemented, Sylow
126C22×D4—612no—
127C22×D4—611no—
128C23×C4C2×D6111yescharacteristic
129C23×C4C2×D6111yescharacteristic
130C23×C4C2×D6111yescharacteristic
131#123—1228no—
132#121—1224no—
133C2×C4⋊C4—24no—
134C2×C4⋊C4—611no—
135C2×C4⋊C4—614no—
136C2×C4⋊C4—612no—
137C2×C4⋊C4C2×D6112yes—
138C2×C4⋊C4C2×D6112yes—
139C2×C22⋊C4—612no—
140C2×C22⋊C4—612no—
141C2×C22⋊C4—614no—
142C2×C22⋊C4—614no—
143#95—612no—
144#95—614no—
145C24—612no—
146C24C22×D6111yescharacteristic
147C2×D4—1224no—
148C2×D4—1224no—
149C2×D4—1224no—
150C2×D4—1222no—
151C2×D4—2442no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—614no—
158C22×C4—612no—
159C22×C4D24414yescomplemented
160C22×C4C22⋊D6114yes—
161C22×C4C22×D6112yes—
162C22×C4C22×D6112yes—
163C22×C4C22×D6111yescharacteristic
164C22×C4C22×D6111yescharacteristic
165C4⋊C4—24no—
166C4⋊C4—24no—
167C4⋊C4—1228no—
168C4⋊C4—1222no—
169C4⋊C4—2442no—
170C22⋊C4—1224no—
171C22⋊C4—1228no—
172C22⋊C4—1224no—
173C22⋊C4—2444no—
174C23—22no—
175C23—22no—
176C23—1222no—
177C23—1222no—
178C23—1222no—
179C23—1224no—
180C23—1224no—
181C23C2×D24412yes—
182C23#1175822212yes—
183C23C2×C22⋊D6112yes—
184C23C23×D6111yescharacteristic
185D4—2444no—
186D4—2448no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—24no—
194C2×C4—44no—
195C2×C4—44no—
196C2×C4—1222no—
197C2×C4—1224no—
198C2×C4—1222no—
199C2×C4—1222no—
200C2×C4—1224no—
201C2×C4—1224no—
202C2×C4C2×D24414yes—
203C2×C4C2×C22⋊D6112yes—
204C2×C4C2×C22⋊D6112yes—
205C22—22no—
206C22—22no—
207C22—24no—
208C22—24no—
209C22—2442no—
210C22—2442no—
211C22—2442no—
212C22—2444no—
213C22—2444no—
214C22#1451975114yes—
215C22C22×C22⋊D6111yescharacteristic
216C22C22×D24411yescharacteristic
217C22C2×#1175822211yescharacteristic
218C22#1451982212yes—
219C22#1451982512yes—
220C4—24no—
221C4—22no—
222C4—22no—
223C4—42no—
224C4—2442no—
225C4—2444no—
226C2—24no—
227C2—4882no—
228C2C2×#1451975111yescharacteristic
229C2#1684032111yescharacteristic
230C2#1684033611yescharacteristic
231C2#1684034312yes—
232C2#1684035912yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC22×C4⋊C4×C61C2
hypercenterC22×C4⋊C4D61
hypocenterC61#2618
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#14519760C2semidirect
3. #16839692C2semidirect
4. #16839684C2semidirect
5. #16839679C2semidirect
6. #16839641C2semidirect
7. #16839622C2semidirect
8. C22×C4⋊C4×C61C2semidirect
36. C22×C4×C61D4semidirect
119. C22×C4⋊C4D61semidirect
125. C61#2618semidirect
159. C22×C4D244semidirect