Finite Group Databasebeta

← #21450310

Subgroups — #21450310

Order 7808.

596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14519748C211yesmaximal, characteristic
2C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
3#16839690C214yesmaximal, complemented
4#16839665C211yesmaximal, characteristic, complemented
5#16839638C214yesmaximal, complemented
6#16839628C211yesmaximal, characteristic, complemented
7#16839627C211yesmaximal, characteristic, complemented
8C4×#11758198C211yesmaximal, characteristic, complemented
9C61×#390C211yesmaximal, characteristic, complemented
10C22×C22⋊D61C2212yes—
11C22×C4×D61C2211yescharacteristic
12C22×C4×D61C2212yes—
13#14519748—24no—
14C2×C4⋊Dic61C2211yescharacteristic
15C2×C4⋊Dic61C2211yescharacteristic
16C2×#11758196C2212yes—
17C4⋊C4×D61—24no—
18C2×C22⋊Dic61C2212yes—
19C2×C22⋊Dic61C2214yes—
20C2×#11758198C2212yes—
21C2×C4×Dic61C2211yescharacteristic
22#14519684C2212yes—
23#14519684C2214yes—
24#14519684C2214yes—
25C22×D4×C61C2211yescharacteristic
26C2×C4⋊C4×C61C2211yescharacteristic
27C2×C22⋊C4×C61C2214yes—
28C2×C42×C61C2211yescharacteristic
29C24×C61C2312yes—
30C23×D61C2311yescharacteristic
31C2×D4×C61—22no—
32C2×D4×C61—22no—
33C2×D4×C61—22no—
34C22×C4×C61C2312yes—
35C22×C4×C61C2312yes—
36C22×C4×C61C2311yescharacteristic
37C2×C22⋊D61—24no—
38C2×C22⋊D61—28no—
39C22×Dic61C2312yes—
40C22×Dic61C2312yes—
41C22×Dic61C2312yes—
42C22×Dic61C2311yescharacteristic
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61—24no—
46C2×C4×D61—44no—
47C2×C4×D61D414yes—
48C4⋊C4×C61—22no—
49C22⋊C4×C61—44no—
50C42×C61—22no—
51C22⋊Dic61—24no—
52C22⋊Dic61—44no—
53#11758198—24no—
54C4⋊Dic61—22no—
55C4⋊Dic61—22no—
56#11758196—24no—
57C4×Dic61—22no—
58C23×C61—22no—
59C23×C61—24no—
60C23×C61—22no—
61C23×C61—22no—
62C23×C61—24no—
63C23×C61C2411yescharacteristic
64C22×D61—21no—
65C22×D61—21no—
66C22×D61—22no—
67C22×D61C2×D412yes—
68C22×D61#4114yes—
69D4×C61—44no—
70C2×C4×C61—22no—
71C2×C4×C61—22no—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—24no—
75C2×C4×C61C2×D412yes—
76C2×C4×C61#4112yes—
77C2×C4×C61#4112yes—
78C22⋊D61—48no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—22no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—22no—
85C2×Dic61—24no—
86C2×Dic61—22no—
87C2×Dic61—24no—
88C2×Dic61C2×D412yes—
89C4×D61—28no—
90C4×D61—48no—
91C22×C61—42no—
92C22×C61—42no—
93C22×C61—42no—
94C22×C61—44no—
95C22×C61—44no—
96C22×C61C22×D411yescharacteristic
97C22×C61C2×#4112yes—
98C22×C61C2×#4111yescharacteristic
99C22×C61C2×#4111yescharacteristic
100C22×C61H(5,𝔽2)12yes—
101C2×D61—22no—
102C2×D61—22no—
103C2×D61—24no—
104C2×D61—24no—
105C2×D61#12414yes—
106C4×C61—42no—
107C4×C61—42no—
108C4×C61#12314yes—
109Dic61—22no—
110Dic61—42no—
111Dic61—42no—
112Dic61—42no—
113#2504—611nomaximal, Sylow
114C2×C61—82no—
115C2×C61C2×#12311yescharacteristic
116C2×C61C2×#12411yescharacteristic
117C2×C61#53511yescharacteristic
118C2×C61#55312yes—
119C2×C61#55312yes—
120D61—24no—
121C2×#121—611no—
122C22×C4⋊C4—611no—
123#397—614no—
124#390—611no—
125#390D6111yescharacteristic, complemented
126#386—614no—
127#382—611no—
128#382—611no—
129C4×C22⋊C4—611no—
130C61#250411yescharacteristic, complemented, Sylow
131C22×D4—612no—
132C22×D4C2×D6111yescharacteristic
133C23×C4—611no—
134C23×C4—612no—
135#121—1224no—
136C2×C4⋊C4—611no—
137C2×C4⋊C4—612no—
138C2×C4⋊C4—611no—
139C2×C4⋊C4—1224no—
140C2×C4⋊C4C2×D6111yescharacteristic
141C2×C22⋊C4—612no—
142C2×C22⋊C4—612no—
143C2×C22⋊C4—614no—
144C2×C22⋊C4C2×D6114yes—
145C2×C42—611no—
146C2×C42C2×D6111yescharacteristic
147#95—612no—
148#95—614no—
149#95—614no—
150C24—611no—
151C24C22×D6112yes—
152C2×D4—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—1224no—
156C2×D4—1228no—
157C22×C4—611no—
158C22×C4—614no—
159C22×C4—612no—
160C22×C4—612no—
161C22×C4—612no—
162C22×C4—1224no—
163C22×C4—1222no—
164C22×C4—1222no—
165C22×C4—2444no—
166C22×C4C22×D6112yes—
167C22×C4C22×D6112yes—
168C22×C4C22×D6111yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—1224no—
171C4⋊C4—1222no—
172C4⋊C4—1222no—
173C22⋊C4—44no—
174C22⋊C4—1224no—
175C22⋊C4—1224no—
176C22⋊C4—2444no—
177C42—22no—
178C42—1222no—
179C23—22no—
180C23—24no—
181C23—22no—
182C23—22no—
183C23—24no—
184C23—612no—
185C23—614no—
186C23—1221no—
187C23—1221no—
188C23—1222no—
189C23C23×D6111yescharacteristic
190D4—44no—
191D4—2448no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—24no—
197C2×C4—612no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1228no—
201C2×C4—1222no—
202C2×C4—1222no—
203C2×C4—1222no—
204C2×C4—1224no—
205C2×C4—1222no—
206C2×C4—1222no—
207C2×C4—1224no—
208C2×C4—2448no—
209C2×C4#1175822212yes—
210C2×C4D4×D6112yes—
211C2×C4#1175822412yes—
212C22—44no—
213C22—44no—
214C22—42no—
215C22—42no—
216C22—42no—
217C22—614no—
218C22—1224no—
219C22—1224no—
220C22—1222no—
221C22—1222no—
222C22C2×D4×D6111yescharacteristic
223C22#41×D6112yes—
224C22C2×#1175822411yescharacteristic
225C22C2×#1175822211yescharacteristic
226C22#1451982212yes—
227C4—42no—
228C4—42no—
229C4—1222no—
230C4—2442no—
231C4—2442no—
232C4—2442no—
233C4#1451975914yes—
234C2—82no—
235C2—1224no—
236C2C2×#1451975911yescharacteristic
237C2#124×D6111yescharacteristic
238C2#1684032511yescharacteristic
239C2#1684045912yes—
240C2#1684046212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#390C2
hypercenter#390D61
hypocenterC61#2504
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D61C2semidirect
3. #16839690C2semidirect
4. #16839665C2semidirect
5. #16839638C2semidirect
6. #16839628C2semidirect
7. #16839627C2semidirect
8. C4×#11758198C2semidirect
9. C61×#390C2semidirect
125. #390D61semidirect
130. C61#2504semidirect