Finite Group Databasebeta

← #21451686

Subgroups — #21451686

Order 7808.

512 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14519767C211yesmaximal, characteristic, complemented
2C2×D4×Dic61C211yesmaximal, characteristic
3#16839698C212yesmaximal, complemented
4#16839694C211yesmaximal, characteristic, complemented
5#16839692C211yesmaximal, characteristic, complemented
6#16839690C212yesmaximal, complemented
7#16839676C211yesmaximal, characteristic
8#16839637C212yesmaximal, complemented
9#16839634C212yesmaximal, complemented
10#16839629C211yesmaximal, characteristic, complemented
11C61×#394C211yesmaximal, characteristic
12C23×Dic61C2212yes—
13#14519767—24no—
14D4×Dic61—24no—
15C2×C4⋊Dic61C2211yescharacteristic
16C2×C4⋊Dic61C2211yescharacteristic
17C2×C4⋊Dic61C2212yes—
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×#11758196C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×C22⋊Dic61C2212yes—
25C2×C22⋊Dic61C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C22×D4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2312yes—
38C2×D4×C61—24no—
39C2×D4×C61—22no—
40C22×C4×C61C2312yes—
41C22×C4×C61C2311yescharacteristic
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×Dic61—24no—
45C22×Dic61—42no—
46C22×Dic61—42no—
47C22×Dic61C2312yes—
48C22×Dic61C2312yes—
49C22×Dic61C2311yescharacteristic
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C4⋊C4×C61—22no—
54C22⋊C4×C61—24no—
55C22⋊C4×C61—42no—
56C22⋊Dic61—24no—
57C22⋊Dic61—24no—
58C22⋊Dic61—42no—
59C4⋊Dic61—22no—
60C4⋊Dic61—22no—
61C4⋊Dic61—42no—
62#11758196—22no—
63#11758196—22no—
64#11758196—22no—
65#11758196—22no—
66#11758196—42no—
67C4×Dic61D414yes—
68C23×C61—22no—
69C23×C61—22no—
70C23×C61—22no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61#4114yes—
75C23×C61C2411yescharacteristic
76D4×C61—28no—
77C2×C4×C61—22no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—21no—
83C2×C4×C61—22no—
84C2×C4×C61—21no—
85C2×C4×C61—22no—
86C2×C4×C61C2×D412yes—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—22no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—22no—
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—22no—
99C2×Dic61—21no—
100C2×Dic61—22no—
101C2×Dic61—48no—
102C2×Dic61C2×D412yes—
103C2×Dic61C2×D412yes—
104C22×C61—24no—
105C22×C61—24no—
106C22×C61—24no—
107C22×C61—42no—
108C22×C61—42no—
109C22×C61—42no—
110C22×C61—42no—
111C22×C61C22×D411yescharacteristic
112C22×C61C2×#4112yes—
113C22×C61H(5,𝔽2)11yescharacteristic
114C22×C61H(5,𝔽2)11yescharacteristic
115C22×C612−1+412yes—
116C4×C61—22no—
117C4×C61—41no—
118C4×C61—41no—
119C4×C61—42no—
120Dic61—22no—
121Dic61—22no—
122Dic61—41no—
123Dic61—41no—
124Dic61—42no—
125Dic61—42no—
126#2633—611nomaximal, Sylow
127C2×C61—44no—
128C2×C61#52511yescharacteristic
129C2×C61#53511yescharacteristic
130C2×C61#53611yescharacteristic
131C2×C61#53912yes—
132C2×C61#53912yes—
133C2×#125—611no—
134C2×C4×D4—611no—
135#399—612no—
136#398—611no—
137#398—611no—
138#397—612no—
139#394—611no—
140#394D6111yescharacteristic
141#385—612no—
142#385—612no—
143#383—611no—
144C61#263311yescharacteristic, complemented, Sylow
145C22×D4C2×D6111yescharacteristic
146C23×C4—612no—
147#125—1224no—
148C4×D4—1224no—
149C2×C4⋊C4—611no—
150C2×C4⋊C4—611no—
151C2×C4⋊C4—611no—
152C2×C4⋊C4—611no—
153C2×C4⋊C4—611no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—612no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4C2×D6111yescharacteristic
158C2×C22⋊C4—612no—
159C2×C22⋊C4—612no—
160C2×C22⋊C4—612no—
161C2×C22⋊C4C2×D6112yes—
162C2×C22⋊C4C2×D6112yes—
163C2×C42—611no—
164#95—612no—
165#95—611no—
166#95—612no—
167#95—612no—
168#95—612no—
169#95C2×D6111yescharacteristic
170C24C22×D6112yes—
171C2×D4—24no—
172C2×D4—22no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—612no—
176C22×C4—611no—
177C22×C4—612no—
178C22×C4—611no—
179C22×C4—1224no—
180C22×C4—2442no—
181C22×C4—2442no—
182C22×C4C22×D6112yes—
183C22×C4C22×D6111yescharacteristic
184C22×C4C22×D6111yescharacteristic
185C22×C4C22×D6111yescharacteristic
186C4⋊C4—22no—
187C4⋊C4—1222no—
188C4⋊C4—1222no—
189C4⋊C4—1222no—
190C4⋊C4—1222no—
191C4⋊C4—1222no—
192C4⋊C4—1222no—
193C4⋊C4—2442no—
194C4⋊C4—2442no—
195C22⋊C4—24no—
196C22⋊C4—42no—
197C22⋊C4—1224no—
198C22⋊C4—1224no—
199C22⋊C4—2442no—
200C42—614no—
201C23—22no—
202C23—22no—
203C23—22no—
204C23—22no—
205C23—22no—
206C23—22no—
207C23#1175822414yes—
208C23C23×D6111yescharacteristic
209D4—28no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—612no—
220C2×C4—612no—
221C2×C4—1221no—
222C2×C4—1221no—
223C2×C4—1222no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1221no—
230C2×C4—1222no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—2448no—
236C2×C4D4×D6112yes—
237C22—24no—
238C22—24no—
239C22—24no—
240C22—42no—
241C22—42no—
242C22—42no—
243C22—42no—
244C22C2×D4×D6111yescharacteristic
245C22C2×#1175822412yes—
246C22#1451982211yescharacteristic
247C22#1451982311yescharacteristic
248C22#1451982412yes—
249C4—22no—
250C4—41no—
251C4—41no—
252C4—42no—
253C4—1222no—
254C4—1222no—
255C4—2441no—
256C4—2441no—
257C4—2442no—
258C4—2442no—
259C2—44no—
260C2#1684026811yescharacteristic
261C2#1684032811yescharacteristic
262C2#1684033211yescharacteristic
263C2#1684035612yes—
264C2#1684035712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2633
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14519767C2semidirect
3. #16839698C2semidirect
4. #16839694C2semidirect
5. #16839692C2semidirect
6. #16839690C2semidirect
8. #16839637C2semidirect
9. #16839634C2semidirect
10. #16839629C2semidirect
144. C61#2633semidirect