Finite Group Databasebeta

← #21451198

Subgroups — #21451198

Order 7808.

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

normal subgroups only

This group has 544 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×#14519754C211yesmaximal, characteristic
2C22×#11758196C211yesmaximal, characteristic
3#16839696C212yesmaximal, complemented
4#16839682C212yesmaximal, complemented
5#16839659C212yesmaximal, complemented
6#16839658C212yesmaximal, complemented
7#16839637C211yesmaximal, characteristic
8#16839635C211yesmaximal, characteristic
9#16839634C211yesmaximal, characteristic
10C22⋊C4×Dic61C211yesmaximal, characteristic
11C61×#385C211yesmaximal, characteristic
12C22×Dic122C2211yescharacteristic
13C23×Dic61C2211yescharacteristic
14C23×Dic61C2211yescharacteristic
15#14519754—24no—
16C2×C4⋊Dic61C2212yes—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196—24no—
19C2×#11758196C2212yes—
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2212yes—
22C2×#11758196C2212yes—
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2212yes—
25C2×C22⋊Dic61C2211yescharacteristic
26C2×C22⋊Dic61C2211yescharacteristic
27C2×C4×Dic61C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2212yes—
32C23×C4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2212yes—
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2211yescharacteristic
36#95×C61C2212yes—
37C24×C61C2311yescharacteristic
38C22×C4×C61—22no—
39C22×C4×C61—42no—
40C22×C4×C61C2311yescharacteristic
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2312yes—
43C22×C4×C61C2312yes—
44C22×Dic61—22no—
45C22×Dic61—24no—
46C22×Dic61—42no—
47C22×Dic61D414yes—
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2312yes—
53C22×Dic61C2312yes—
54C2×Dic122—22no—
55C2×Dic122—42no—
56C4⋊C4×C61—42no—
57C22⋊C4×C61—22no—
58C22⋊C4×C61Q814yescomplemented
59C22⋊Dic61—22no—
60C22⋊Dic61Q814yescomplemented
61C4⋊Dic61—22no—
62C4⋊Dic61—24no—
63#11758196—24no—
64#11758196—24no—
65#11758196—22no—
66#11758196—22no—
67#11758196—24no—
68#11758196—42no—
69C4×Dic61—42no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61C2×D412yes—
73C23×C61C2×Q812yes—
74C23×C61C2×Q812yes—
75C23×C61C2411yescharacteristic
76C2×C4×C61—22no—
77C2×C4×C61—22no—
78C2×C4×C61—22no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—44no—
86C2×C4×C61C2×Q814yes—
87C2×Dic61—28no—
88C2×Dic61—22no—
89C2×Dic61—22no—
90C2×Dic61—22no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—44no—
99C2×Dic61C2×D412yes—
100C2×Dic61C2×D412yes—
101C2×Dic61C2×Q814yes—
102C2×Dic61#4114yes—
103Dic122—44no—
104C22×C61—22no—
105C22×C61—22no—
106C22×C61—24no—
107C22×C61—24no—
108C22×C61C4⋊Q814yes—
109C22×C61C22×D411yescharacteristic
110C22×C61C22×Q811yescharacteristic
111C22×C61C22×Q811yescharacteristic
112C22×C61C2×#4112yes—
113C22×C61H(5,𝔽2)12yes—
114C4×C61—24no—
115C4×C61—41no—
116C4×C61—41no—
117C4×C61—42no—
118Dic61—24no—
119Dic61—22no—
120Dic61—22no—
121Dic61—24no—
122Dic61—41no—
123Dic61—41no—
124#2583—611nomaximal, Sylow
125C2×C61—24no—
126C2×C61#52511yescharacteristic
127C2×C61C2×C4⋊Q811yescharacteristic
128C2×C61#53411yescharacteristic
129C2×C61#55412yes—
130C2×C61#55412yes—
131C2×C22⋊Q8—611no—
132C22×C4⋊C4—611no—
133#398—612no—
134#395—612no—
135#389—612no—
136#389—612no—
137#385—611no—
138#385—611no—
139#385—611no—
140#385D6111yescharacteristic
141C4×C22⋊C4—611no—
142C61#258311yescharacteristic, complemented, Sylow
143C22×Q8—611no—
144C23×C4—611no—
145C23×C4—611no—
146C23×C4C2×D6111yescharacteristic
147C22⋊Q8—1224no—
148C2×C4⋊C4—612no—
149C2×C4⋊C4—612no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—612no—
154C2×C4⋊C4—612no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—1224no—
157C2×C4⋊C4C2×D6112yes—
158C2×C22⋊C4—611no—
159C2×C22⋊C4—611no—
160C2×C22⋊C4C2×D6111yescharacteristic
161C2×C22⋊C4C2×D6111yescharacteristic
162C2×C42—612no—
163#95—612no—
164#95—612no—
165#95—612no—
166#95—612no—
167#95C2×D6112yes—
168C24C22×D6111yescharacteristic
169C2×Q8—1222no—
170C2×Q8—2442no—
171C22×C4—22no—
172C22×C4—42no—
173C22×C4—612no—
174C22×C4—612no—
175C22×C4—611no—
176C22×C4—611no—
177C22×C4—614no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—1224no—
181C22×C4—1222no—
182C22×C4—2442no—
183C22×C4C22×D6111yescharacteristic
184C22×C4C22×D6112yes—
185C22×C4C22×D6111yescharacteristic
186C22×C4C22×D6112yes—
187C4⋊C4—42no—
188C4⋊C4—1224no—
189C4⋊C4—1224no—
190C4⋊C4—1224no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—1224no—
194C4⋊C4—1222no—
195C4⋊C4—2442no—
196C22⋊C4—22no—
197C22⋊C4—614no—
198C22⋊C4—1222no—
199C22⋊C4Dic12214yescomplemented
200C42—2442no—
201C23—22no—
202C23—22no—
203C23C2×Dic12212yes—
204C23D4×D6112yes—
205C23Q8×D6112yes—
206C23C23×D6111yescharacteristic
207Q8—2444no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—44no—
218C2×C4—612no—
219C2×C4—612no—
220C2×C4—614no—
221C2×C4—614no—
222C2×C4—1228no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1222no—
226C2×C4—1222no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—2444no—
234C2×C4C2×Dic12214yes—
235C22—24no—
236C22—24no—
237C22—22no—
238C22—22no—
239C22#1451977614yes—
240C22C2×D4×D6111yescharacteristic
241C22C2×Q8×D6111yescharacteristic
242C22C22×Dic12211yescharacteristic
243C22#41×D6112yes—
244C22#1451982212yes—
245C4—24no—
246C4—41no—
247C4—42no—
248C4—41no—
249C4—1224no—
250C4—1224no—
251C4—1222no—
252C4—1222no—
253C4—2441no—
254C4—2441no—
255C2—24no—
256C2#1684027011yescharacteristic
257C2C2×#1451977611yescharacteristic
258C2#1684032211yescharacteristic
259C2#1684046612yes—
260C2#1684047112yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#385C2
hypercenter#385D61
hypocenterC61#2583
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
3. #16839696C2semidirect
4. #16839682C2semidirect
5. #16839659C2semidirect
6. #16839658C2semidirect
58. C22⋊C4×C61Q8semidirect
60. C22⋊Dic61Q8semidirect
142. C61#2583semidirect
199. C22⋊C4Dic122semidirect