Finite Group Databasebeta

← #21450287

Subgroups — #21450287

Order 7808.

708 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 169 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×#14519762C214yesmaximal, complemented
2C2×#14519752C211yesmaximal, characteristic
3C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839697C214yesmaximal, complemented
5#16839664C211yesmaximal, characteristic, complemented
6#16839663C211yesmaximal, characteristic, complemented
7#16839631C211yesmaximal, characteristic, complemented
8C4×#11758198C211yesmaximal, characteristic, complemented
9C61×#384C211yesmaximal, characteristic, complemented
10C22×D244C2212yes—
11C22×D244C2211yescharacteristic
12C22×C4×D61C2212yes—
13C22×C4×D61C2211yescharacteristic
14#14519762—216no—
15#14519752—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2212yes—
18C2×#11758196C2214yes—
19C4⋊C4×D61—24no—
20C2×#11758198C2212yes—
21C2×#11758198C2214yes—
22C2×#11758198C2214yes—
23C2×#11758198C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25#14519684C2212yes—
26C2×C4⋊C4×C61C2214yes—
27C2×C4⋊C4×C61C2211yescharacteristic
28C2×C4⋊C4×C61C2211yescharacteristic
29C2×C42×C61C2211yescharacteristic
30C23×D61C2312yes—
31C23×D61C2311yescharacteristic
32C22×C4×C61C2312yes—
33C22×C4×C61C2312yes—
34C22×C4×C61C2312yes—
35C22×C4×C61C2311yescharacteristic
36C22×Dic61C2312yes—
37C22×Dic61C2311yescharacteristic
38C22×Dic61C2312yes—
39C2×D244—24no—
40C2×D244—28no—
41C2×D244—22no—
42C2×D244—22no—
43C2×D244—22no—
44C2×C4×D61—22no—
45C2×C4×D61—22no—
46C2×C4×D61—24no—
47C2×C4×D61—28no—
48C2×C4×D61D414yes—
49C4⋊C4×C61—22no—
50C4⋊C4×C61—22no—
51C4⋊C4×C61—28no—
52C42×C61—22no—
53#11758198—28no—
54#11758198—24no—
55#11758198—28no—
56#11758198D418yescomplemented
57C4⋊Dic61—22no—
58#11758196—24no—
59#11758196—28no—
60C4×Dic61—22no—
61C23×C61C2411yescharacteristic
62C22×D61—21no—
63C22×D61—21no—
64C22×D61—22no—
65C22×D61—24no—
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—22no—
69C22×D61—24no—
70C22×D61C2×D414yes—
71C22×D61C2×D412yes—
72C2×C4×C61—22no—
73C2×C4×C61—22no—
74C2×C4×C61—22no—
75C2×C4×C61—24no—
76C2×C4×C61—24no—
77C2×C4×C61—22no—
78C2×C4×C61C2×D414yes—
79C2×C4×C61C2×D412yes—
80C2×C4×C61#4112yes—
81C2×C4×C61#4112yes—
82C2×Dic61—22no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—22no—
86C2×Dic61—22no—
87C2×Dic61—24no—
88C2×Dic61C2×D414yes—
89C2×Dic61C2×D412yes—
90D244—48no—
91D244—44no—
92C4×D61—28no—
93C4×D61—48no—
94C22×C61C22×D411yescharacteristic
95C22×C61C22×D412yes—
96C22×C61C2×#4111yescharacteristic
97C22×C61C2×#4111yescharacteristic
98C22×C612−1+412yes—
99C2×D61—22no—
100C2×D61—22no—
101C2×D61—24no—
102C2×D61—24no—
103C2×D61—42no—
104C2×D61—42no—
105C2×D61—42no—
106C2×D61—44no—
107C2×D61—44no—
108C2×D61#12714yes—
109C4×C61—24no—
110C4×C61—42no—
111C4×C61—42no—
112C4×C61#12314yescomplemented
113Dic61—22no—
114Dic61—24no—
115Dic61—42no—
116#2501—611nomaximal, Sylow
117C2×C61C2×#12311yescharacteristic
118C2×C61C2×#12711yescharacteristic
119C2×C61#53611yescharacteristic
120C2×C61#54712yes—
121C2×C61#54712yes—
122D61—24no—
123D61—82no—
124C2×#123—614no—
125C2×#121—611no—
126C22×C4⋊C4—611no—
127#399—614no—
128#390—611no—
129#390—611no—
130#384—611no—
131#384D6111yescharacteristic, complemented
132C4×C22⋊C4—611no—
133C61#250111yescharacteristic, complemented, Sylow
134C22×D4—612no—
135C22×D4—611no—
136C23×C4—611no—
137C23×C4—612no—
138#123—12216no—
139#121—1224no—
140C2×C4⋊C4—611no—
141C2×C4⋊C4—612no—
142C2×C4⋊C4—614no—
143C2×C4⋊C4—1224no—
144C2×C4⋊C4C2×D6111yescharacteristic
145C2×C4⋊C4C2×D6111yescharacteristic
146C2×C4⋊C4C2×D6114yes—
147C2×C22⋊C4—612no—
148C2×C22⋊C4—612no—
149C2×C22⋊C4—614no—
150C2×C22⋊C4—614no—
151C2×C42—611no—
152C2×C42C2×D6111yescharacteristic
153#95—612no—
154C24—611no—
155C24—612no—
156C2×D4—1224no—
157C2×D4—1228no—
158C2×D4—1222no—
159C2×D4—1222no—
160C2×D4—1222no—
161C22×C4—611no—
162C22×C4—612no—
163C22×C4—614no—
164C22×C4—612no—
165C22×C4—1224no—
166C22×C4—1228no—
167C22×C4—1222no—
168C22×C4—1222no—
169C22×C4C22×D6112yes—
170C22×C4C22×D6112yes—
171C22×C4C22×D6112yes—
172C22×C4C22×D6111yescharacteristic
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—28no—
176C4⋊C4—1224no—
177C4⋊C4—1228no—
178C4⋊C4—1222no—
179C22⋊C4—618no—
180C22⋊C4—1224no—
181C22⋊C4—1228no—
182C22⋊C4—1228no—
183C42—22no—
184C42—1222no—
185C23—614no—
186C23—612no—
187C23—1221no—
188C23—1221no—
189C23—1222no—
190C23—1224no—
191C23—1222no—
192C23—1222no—
193C23—1222no—
194C23—1224no—
195C23C23×D6111yescharacteristic
196D4—2448no—
197D4—2444no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—22no—
203C2×C4—24no—
204C2×C4—614no—
205C2×C4—612no—
206C2×C4—1221no—
207C2×C4—1222no—
208C2×C4—1221no—
209C2×C4—1222no—
210C2×C4—1228no—
211C2×C4—1224no—
212C2×C4—1222no—
213C2×C4—2448no—
214C2×C4#1175822212yes—
215C2×C4D4×D6114yes—
216C2×C4D4×D6112yes—
217C2×C4#1175822612yes—
218C22—614no—
219C22—1222no—
220C22—1222no—
221C22—1224no—
222C22—1224no—
223C22—2442no—
224C22—2442no—
225C22—2442no—
226C22—2444no—
227C22—2444no—
228C22C2×D4×D6111yescharacteristic
229C22C2×D4×D6112yes—
230C22C2×#1175822211yescharacteristic
231C22C2×#1175822611yescharacteristic
232C22#1451982512yes—
233C4—24no—
234C4—42no—
235C4—42no—
236C4—1222no—
237C4—1224no—
238C4—2442no—
239C4#1451976214yescomplemented
240C2—1224no—
241C2—4882no—
242C2C2×#1451976211yescharacteristic
243C2#127×D6111yescharacteristic
244C2#1684033711yescharacteristic
245C2#1684041312yes—
246C2#1684041512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#384C2
hypercenter#384D61
hypocenterC61#2501
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
1. C2×#14519762C2semidirect
3. C2×C4⋊C4×D61C2semidirect
4. #16839697C2semidirect
5. #16839664C2semidirect
6. #16839663C2semidirect
7. #16839631C2semidirect
8. C4×#11758198C2semidirect
9. C61×#384C2semidirect
56. #11758198D4semidirect
112. C4×C61#123semidirect
131. #384D61semidirect
133. C61#2501semidirect
239. C4#14519762semidirect