Finite Group Databasebeta

← #21451647

Subgroups — #21451647

Order 7808.

488 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 143 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×#14519776C211yesmaximal, characteristic, complemented
2C2×#14519735C211yesmaximal, characteristic
3#16839701C211yesmaximal, characteristic, complemented
4#16839699C211yesmaximal, characteristic
5#16839697C211yesmaximal, characteristic
6#16839683C212yesmaximal, complemented
7#16839675C212yesmaximal
8#16839659C212yesmaximal, complemented
9#16839626C211yesmaximal, characteristic, complemented
10#16839621C212yesmaximal
11C61×#400C211yesmaximal, characteristic, complemented
12C22×Dic122C2212yes—
13C22×C4×D61C2211yescharacteristic
14#14519776—24no—
15#14519735—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2211yescharacteristic
18C2×C4⋊Dic61C2212yes—
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27C2×C4×Dic61C2211yescharacteristic
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34#95×C61C2212yes—
35#95×C61C2211yescharacteristic
36#95×C61C2212yes—
37C23×D61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×Dic61C2312yes—
44C22×Dic61C2312yes—
45C22×Dic61C2311yescharacteristic
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2311yescharacteristic
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61Q814yescomplemented
51C2×Dic122—24no—
52C2×Dic122—42no—
53C2×Dic122—42no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—22no—
56#11758198—22no—
57#11758198—22no—
58#11758198—42no—
59#11758198—42no—
60C4⋊Dic61—22no—
61C4⋊Dic61—22no—
62C4⋊Dic61—42no—
63#11758196—24no—
64#11758196—24no—
65#11758196—42no—
66C4×Dic61—22no—
67C4×Dic61D414yes—
68C23×C61C2411yescharacteristic
69C22×D61—21no—
70C22×D61—21no—
71C22×D61—22no—
72C22×D61—22no—
73C22×D61C2×Q812yes—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—21no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61C2×D412yes—
86C2×C4×C61C2×Q812yes—
87C2×Dic61—22no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61C2×D412yes—
97C2×Dic61C2×D412yes—
98C2×Dic61C2×Q812yes—
99C2×Dic61#4112yes—
100C4×D61—28no—
101Dic122—48no—
102C22×C61C22×D411yescharacteristic
103C22×C61C22×Q811yescharacteristic
104C22×C61C2×#4111yescharacteristic
105C22×C61H(5,𝔽2)12yes—
106C22×C612−1+412yes—
107C2×D61—22no—
108C2×D61—24no—
109C2×D61—41no—
110C2×D61—41no—
111C2×D61—42no—
112C4×C61—22no—
113C4×C61—22no—
114C4×C61—42no—
115C4×C61—41no—
116C4×C61—42no—
117Dic61—22no—
118Dic61—42no—
119Dic61—41no—
120Dic61—42no—
121Dic61C22⋊Q814yes—
122#2628—611nomaximal, Sylow
123C2×C61C2×C22⋊Q811yescharacteristic
124C2×C61#53511yescharacteristic
125C2×C61#53611yescharacteristic
126C2×C61#54212yes—
127C2×C61#54412yes—
128D61—42no—
129C2×C4⋊Q8—611no—
130C2×#117—611no—
131#400—611no—
132#400D6111yescharacteristic, complemented
133#399—611no—
134#399—611no—
135#395—612no—
136#393—612no—
137#389—612no—
138#382—611no—
139#380—612no—
140C61#262811yescharacteristic, complemented, Sylow
141C22×Q8—612no—
142C23×C4—611no—
143C4⋊Q8—1224no—
144#117—1224no—
145C2×C4⋊C4—611no—
146C2×C4⋊C4—612no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4—612no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C4⋊C4C2×D6111yescharacteristic
153C2×C22⋊C4—611no—
154C2×C22⋊C4—611no—
155C2×C22⋊C4—612no—
156C2×C22⋊C4—612no—
157C2×C42—611no—
158C2×C42—611no—
159#95—612no—
160#95—612no—
161#95—611no—
162#95—612no—
163#95C2×D6112yes—
164#95C2×D6111yescharacteristic
165#95C2×D6112yes—
166C24—611no—
167C2×Q8—1224no—
168C2×Q8—2442no—
169C2×Q8—2442no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—614no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—611no—
176C22×C4—1222no—
177C22×C4—1222no—
178C22×C4C22×D6111yescharacteristic
179C22×C4C22×D6112yes—
180C22×C4C22×D6112yes—
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6111yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—1224no—
186C4⋊C4—1224no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—2442no—
190C4⋊C4—2442no—
191C22⋊C4—1222no—
192C22⋊C4—1222no—
193C22⋊C4—2442no—
194C22⋊C4—2442no—
195C42—614no—
196C42—1222no—
197C23—612no—
198C23—1221no—
199C23—1221no—
200C23—1222no—
201C23—1222no—
202C23C23×D6111yescharacteristic
203Q8—2448no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—612no—
216C2×C4—612no—
217C2×C4—612no—
218C2×C4—612no—
219C2×C4—1228no—
220C2×C4—1222no—
221C2×C4—1221no—
222C2×C4—1222no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4D4×D6112yes—
230C2×C4Q8×D6112yes—
231C22—1222no—
232C22—1224no—
233C22—2441no—
234C22—2441no—
235C22—2442no—
236C22C2×D4×D6111yescharacteristic
237C22C2×Q8×D6111yescharacteristic
238C22#41×D6111yescharacteristic
239C22#1451982312yes—
240C22#1451982412yes—
241C4—22no—
242C4—22no—
243C4—42no—
244C4—41no—
245C4—42no—
246C4—614no—
247C4—1222no—
248C4—2441no—
249C4—2442no—
250C4—2442no—
251C2—2442no—
252C2C22⋊Q8×D6111yescharacteristic
253C2#1684033011yescharacteristic
254C2#1684033411yescharacteristic
255C2#1684037812yes—
256C2#1684039212yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#400C2
hypercenter#400D61
hypocenterC61#2628
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
3. #16839701C2semidirect
6. #16839683C2semidirect
8. #16839659C2semidirect
9. #16839626C2semidirect
11. C61×#400C2semidirect
50. C2×C4×D61Q8semidirect
132. #400D61semidirect
140. C61#2628semidirect