Finite Group Databasebeta

← #21451645

Subgroups — #21451645

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×#14519733C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic, complemented
4#16839700C211yesmaximal, characteristic, complemented
5#16839698C211yesmaximal, characteristic
6#16839682C212yesmaximal, complemented
7#16839674C212yesmaximal
8#16839657C212yesmaximal, complemented
9#16839626C211yesmaximal, characteristic, complemented
10#16839620C212yesmaximal
11C61×#399C211yesmaximal, characteristic
12C22×Dic122C2212yes—
13C23×Dic61C2211yescharacteristic
14#14519776—24no—
15#14519733—24no—
16C2×C4⋊Dic61C2211yescharacteristic
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2212yes—
20C2×#11758196C2212yes—
21C2×#11758196C2212yes—
22C2×C22⋊Dic61C2211yescharacteristic
23C2×C22⋊Dic61C2212yes—
24C2×C4×Dic61C2211yescharacteristic
25C2×C4×Dic61C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32C2×C4⋊C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2212yes—
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2311yescharacteristic
38C22×C4×C61C2312yes—
39C22×C4×C61C2312yes—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×Dic61—22no—
43C22×Dic61—22no—
44C22×Dic61Q814yescomplemented
45C22×Dic61C2312yes—
46C22×Dic61C2311yescharacteristic
47C22×Dic61C2312yes—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2311yescharacteristic
51C2×Dic122—24no—
52C2×Dic122—42no—
53C2×Dic122—42no—
54C4⋊C4×C61—22no—
55C4⋊C4×C61—42no—
56C22⋊C4×C61—22no—
57C22⋊C4×C61—42no—
58C22⋊Dic61—22no—
59C22⋊Dic61—42no—
60C4⋊Dic61—22no—
61#11758196—22no—
62#11758196—22no—
63#11758196—24no—
64#11758196—24no—
65#11758196—42no—
66C4×Dic61—22no—
67C4×Dic61D414yes—
68C23×C61—21no—
69C23×C61—21no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61C2×Q812yes—
73C23×C61C2411yescharacteristic
74C2×C4×C61—22no—
75C2×C4×C61—21no—
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—22no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61C2×D412yes—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—22no—
87C2×Dic61—28no—
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×Dic61C2×Q812yes—
100C2×Dic61#4112yes—
101Dic122—48no—
102C22×C61—22no—
103C22×C61—24no—
104C22×C61—41no—
105C22×C61—41no—
106C22×C61—42no—
107C22×C61C22×D411yescharacteristic
108C22×C61C22×Q811yescharacteristic
109C22×C61C2×#4111yescharacteristic
110C22×C61H(5,𝔽2)12yes—
111C22×C612−1+412yes—
112C4×C61—22no—
113C4×C61—42no—
114C4×C61—41no—
115C4×C61—42no—
116Dic61—22no—
117Dic61—22no—
118Dic61—42no—
119Dic61—41no—
120Dic61—42no—
121Dic61C22⋊Q814yes—
122#2628—611nomaximal, Sylow
123C2×C61—42no—
124C2×C61C2×C22⋊Q811yescharacteristic
125C2×C61#53511yescharacteristic
126C2×C61#53611yescharacteristic
127C2×C61#54212yes—
128C2×C61#54412yes—
129C2×C4⋊Q8—611no—
130C2×#117—611no—
131#400—611no—
132#400—611no—
133#399—611no—
134#399D6111yescharacteristic
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—611no—
147C2×C4⋊C4—612no—
148C2×C4⋊C4—611no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—612no—
151C2×C4⋊C4C2×D6111yescharacteristic
152C2×C4⋊C4C2×D6112yes—
153C2×C22⋊C4—611no—
154C2×C22⋊C4—612no—
155C2×C22⋊C4C2×D6111yescharacteristic
156C2×C22⋊C4C2×D6112yes—
157C2×C42—611no—
158C2×C42—611no—
159#95—612no—
160#95—612no—
161#95—612no—
162#95—611no—
163#95—612no—
164#95—612no—
165#95C2×D6111yescharacteristic
166C24C22×D6111yescharacteristic
167C2×Q8—1224no—
168C2×Q8—2442no—
169C2×Q8—2442no—
170C22×C4—611no—
171C22×C4—614no—
172C22×C4—611no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—612no—
176C22×C4—612no—
177C22×C4—1222no—
178C22×C4—1222no—
179C22×C4C22×D6112yes—
180C22×C4C22×D6112yes—
181C22×C4C22×D6111yescharacteristic
182C22×C4C22×D6111yescharacteristic
183C4⋊C4—22no—
184C4⋊C4—42no—
185C4⋊C4—1224no—
186C4⋊C4—1222no—
187C4⋊C4—1224no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4—2442no—
191C22⋊C4—22no—
192C22⋊C4—42no—
193C22⋊C4—1222no—
194C22⋊C4—2442no—
195C42—614no—
196C42—1222no—
197C23—21no—
198C23—21no—
199C23—22no—
200C23—22no—
201C23Q8×D6112yes—
202C23C23×D6111yescharacteristic
203Q8—2448no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—612no—
214C2×C4—612no—
215C2×C4—612no—
216C2×C4—612no—
217C2×C4—612no—
218C2×C4—1228no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1222no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1222no—
230C2×C4D4×D6112yes—
231C22—22no—
232C22—24no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22C2×D4×D6111yescharacteristic
237C22C2×Q8×D6111yescharacteristic
238C22#41×D6111yescharacteristic
239C22#1451982212yes—
240C22#1451982412yes—
241C4—22no—
242C4—41no—
243C4—42no—
244C4—42no—
245C4—614no—
246C4—1222no—
247C4—1222no—
248C4—2442no—
249C4—2441no—
250C4—2442no—
251C2—42no—
252C2C22⋊Q8×D6111yescharacteristic
253C2#1684032511yescharacteristic
254C2#1684033411yescharacteristic
255C2#1684038012yes—
256C2#1684039112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#399C2
hypercenter#399D61
hypocenterC61#2628
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
1. C2×#14519776C2semidirect
3. #16839702C2semidirect
4. #16839700C2semidirect
6. #16839682C2semidirect
8. #16839657C2semidirect
9. #16839626C2semidirect
44. C22×Dic61Q8semidirect
140. C61#2628semidirect