Finite Group Databasebeta

← #21450257

Subgroups — #21450257

Order 7808.

546 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 153 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×#14519760C211yesmaximal, characteristic
2#16839700C211yesmaximal, characteristic, complemented
3#16839697C211yesmaximal, characteristic, complemented
4#16839693C211yesmaximal, characteristic, complemented
5#16839688C211yesmaximal, characteristic, complemented
6#16839653C212yesmaximal, complemented
7#16839646C212yesmaximal, complemented
8#16839639C212yesmaximal
9#16839620C212yesmaximal, complemented
10C2×#14519684C211yesmaximal, characteristic, complemented
11C2×#117×C61C211yesmaximal, characteristic, complemented
12C22×C22⋊D61C2211yescharacteristic
13C23×Dic61C2212yes—
14#14519760—24no—
15C2×#11758196C2211yescharacteristic
16C2×#11758196C2212yes—
17C2×#11758196C2211yescharacteristic
18C2×#11758196C2212yes—
19C2×C22⋊Dic61C2211yescharacteristic
20C2×#11758198C2211yescharacteristic
21C2×#11758198C2212yes—
22C2×#11758198C2211yescharacteristic
23C2×#11758198C2212yes—
24#14519684C2211yescharacteristic
25#14519684C2212yes—
26#14519684C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31C23×C4×C61C2211yescharacteristic
32#117×C61—24no—
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C4⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36C2×C42×C61C2212yes—
37C24×C61C2311yescharacteristic
38C23×D61C2311yescharacteristic
39C22×C4×C61—24no—
40C22×C4×C61D414yes—
41C22×C4×C61C2312yes—
42C22×C4×C61C2312yes—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—22no—
46C2×C22⋊D61—24no—
47C22×Dic61—24no—
48C22×Dic61—24no—
49C22×Dic61—42no—
50C22×Dic61C2312yes—
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2312yes—
55C4⋊C4×C61—22no—
56C4⋊C4×C61—22no—
57C22⋊C4×C61—24no—
58C42×C61—24no—
59C22⋊Dic61—22no—
60#11758198—22no—
61#11758198—22no—
62#11758198—24no—
63#11758198—42no—
64#11758196—22no—
65#11758196—22no—
66#11758196—24no—
67#11758196—42no—
68C23×C61—22no—
69C23×C61—21no—
70C23×C61—21no—
71C23×C61C2×D412yes—
72C23×C61#4114yes—
73C23×C61C2411yescharacteristic
74C22×D61—21no—
75C22×D61—22no—
76C22×D61—22no—
77C22×D61—21no—
78C22×D61—21no—
79C2×C4×C61—28no—
80C2×C4×C61—22no—
81C2×C4×C61—22no—
82C2×C4×C61—22no—
83C2×C4×C61—22no—
84C2×C4×C61—22no—
85C2×C4×C61—22no—
86C2×C4×C61—22no—
87C2×C4×C61—22no—
88C2×C4×C61C2×D412yes—
89C2×C4×C61C2×D412yes—
90C22⋊D61—44no—
91C2×Dic61—22no—
92C2×Dic61—22no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—22no—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—21no—
101C2×Dic61—22no—
102C2×Dic61—21no—
103C2×Dic61—48no—
104C2×Dic61#4114yes—
105C22×C61—22no—
106C22×C61—22no—
107C22×C61—24no—
108C22×C61—24no—
109C22×C61#12314yes—
110C22×C61C22×D411yescharacteristic
111C22×C61C2×#4112yes—
112C22×C61C2×#4112yes—
113C22×C61H(5,𝔽2)11yescharacteristic
114C22×C612−1+411yescharacteristic
115C2×D61—41no—
116C2×D61—41no—
117C2×D61—41no—
118C2×D61—42no—
119C2×D61—42no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—42no—
123C4×C61—42no—
124Dic61—24no—
125Dic61—41no—
126Dic61—41no—
127Dic61—41no—
128Dic61—42no—
129#2498—611nomaximal, Sylow
130C2×C61—24no—
131C2×C61C2×#12311yescharacteristic
132C2×C61#53211yescharacteristic
133C2×C61#53711yescharacteristic
134C2×C61#55112yes—
135C2×C61#55212yes—
136D61—81no—
137C2×#123—611no—
138C2×#117D6111yescharacteristic, complemented
139#400—611no—
140#399—611no—
141#398—611no—
142#397—611no—
143#388—612no—
144#387—612no—
145#386—612no—
146#380—612no—
147C2×#95—611no—
148C61#249811yescharacteristic, complemented, Sylow
149C22×D4—611no—
150C23×C4—612no—
151C23×C4C2×D6111yescharacteristic
152#123—1224no—
153#117—24no—
154C2×C4⋊C4—611no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—612no—
157C2×C4⋊C4—612no—
158C2×C4⋊C4C2×D6111yescharacteristic
159C2×C4⋊C4C2×D6111yescharacteristic
160C2×C22⋊C4—611no—
161C2×C22⋊C4—611no—
162C2×C22⋊C4—611no—
163C2×C22⋊C4—612no—
164C2×C22⋊C4—612no—
165C2×C22⋊C4C2×D6112yes—
166C2×C42C2×D6112yes—
167#95—612no—
168#95—611no—
169#95—611no—
170#95—612no—
171#95—612no—
172#95—612no—
173#95—612no—
174C24—611no—
175C24C22×D6111yescharacteristic
176C2×D4—1224no—
177C2×D4—1222no—
178C22×C4—24no—
179C22×C4—612no—
180C22×C4—612no—
181C22×C4—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—1224no—
185C22×C4—1224no—
186C22×C4—2442no—
187C22×C4C22⋊D6114yes—
188C22×C4C22×D6112yes—
189C22×C4C22×D6112yes—
190C22×C4C22×D6111yescharacteristic
191C22×C4C22×D6111yescharacteristic
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—1224no—
195C4⋊C4—1222no—
196C4⋊C4—1222no—
197C4⋊C4—2442no—
198C22⋊C4—24no—
199C22⋊C4—1224no—
200C22⋊C4—1222no—
201C22⋊C4—1222no—
202C22⋊C4—1222no—
203C22⋊C4—2442no—
204C42—24no—
205C23—22no—
206C23—21no—
207C23—21no—
208C23—1221no—
209C23—1222no—
210C23—1222no—
211C23—1221no—
212C23—1221no—
213C23#1175822214yes—
214C23C2×C22⋊D6112yes—
215C23C23×D6111yescharacteristic
216D4—2444no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—28no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—614no—
227C2×C4—1222no—
228C2×C4—1222no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—1222no—
233C2×C4—1222no—
234C2×C4—1222no—
235C2×C4—1222no—
236C2×C4—1222no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—2448no—
240C2×C4C2×C22⋊D6112yes—
241C2×C4C2×C22⋊D6112yes—
242C22—22no—
243C22—22no—
244C22—24no—
245C22—24no—
246C22—2441no—
247C22—2441no—
248C22—2441no—
249C22—2442no—
250C22—2442no—
251C22#1451976014yes—
252C22C22×C22⋊D6111yescharacteristic
253C22#41×D6112yes—
254C22C2×#1175822212yes—
255C22#1451982311yescharacteristic
256C22#1451982411yescharacteristic
257C4—22no—
258C4—22no—
259C4—42no—
260C4—42no—
261C4—1224no—
262C4—2441no—
263C4—2441no—
264C4—2441no—
265C4—2442no—
266C2—24no—
267C2—4881no—
268C2C2×#1451976011yescharacteristic
269C2#1684030811yescharacteristic
270C2#1684034011yescharacteristic
271C2#1684043612yes—
272C2#1684044512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#117×C61C2
hypercenterC2×#117D61
hypocenterC61#2498
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #16839700C2semidirect
3. #16839697C2semidirect
4. #16839693C2semidirect
5. #16839688C2semidirect
6. #16839653C2semidirect
7. #16839646C2semidirect
9. #16839620C2semidirect
10. C2×#14519684C2semidirect
11. C2×#117×C61C2semidirect
138. C2×#117D61semidirect
148. C61#2498semidirect