Finite Group Databasebeta

← #21451750

Subgroups — #21451750

Order 7808.

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

normal subgroups only

This group has 576 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×#14519755C211yesmaximal, characteristic, complemented
2C2×#14519748C211yesmaximal, characteristic
3#16839702C211yesmaximal, characteristic, complemented
4#16839701C211yesmaximal, characteristic, complemented
5#16839690C212yesmaximal, complemented
6#16839676C211yesmaximal, characteristic, complemented
7#16839674C212yesmaximal, complemented
8#16839638C212yesmaximal, complemented
9#16839638C212yesmaximal, complemented
10#95×D61C211yesmaximal, characteristic, complemented
11C61×#394C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C22×C4×D61C2212yes—
15C22×C4×D61C2211yescharacteristic
16#14519755—24no—
17#14519748—24no—
18C2×C4⋊Dic61C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2211yescharacteristic
26#14519684C2212yes—
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2211yescharacteristic
30#14519684C2212yes—
31#14519684C2212yes—
32C22×D4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2312yes—
38C23×D61C2311yescharacteristic
39C2×D4×C61—22no—
40C2×D4×C61—42no—
41C22×C4×C61C2312yes—
42C22×C4×C61C2311yescharacteristic
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2311yescharacteristic
45C2×C22⋊D61—24no—
46C2×C22⋊D61—24no—
47C2×C22⋊D61—24no—
48C22×Dic61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52C22×Dic61C2311yescharacteristic
53C2×C4×D61—24no—
54C2×C4×D61—42no—
55C2×C4×D61—42no—
56C2×C4×D61—42no—
57C2×C4×D61D414yes—
58C2×Dic122—22no—
59C2×Dic122—42no—
60C4⋊C4×C61—22no—
61C22⋊C4×C61—42no—
62C22⋊C4×C61—42no—
63C22⋊Dic61—24no—
64C22⋊Dic61—42no—
65C22⋊Dic61—42no—
66#11758198—22no—
67#11758198—22no—
68C4⋊Dic61—22no—
69#11758196—22no—
70#11758196—22no—
71C23×C61—22no—
72C23×C61—22no—
73C23×C61—22no—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61C2411yescharacteristic
79C22×D61—22no—
80C22×D61—21no—
81C22×D61—21no—
82C22×D61C2×D412yes—
83C22×D61#4114yes—
84D4×C61—44no—
85C2×C4×C61—22no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—22no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61C2×D412yes—
95C22⋊D61—48no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—22no—
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—22no—
103C2×Dic61—21no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—21no—
108C2×Dic61C2×D412yes—
109C4×D61—44no—
110C4×D61—48no—
111Dic122—44no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—42no—
115C22×C61—42no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61C22×D411yescharacteristic
120C22×C61C2×#4112yes—
121C22×C61H(5,𝔽2)12yes—
122C22×C61H(5,𝔽2)11yescharacteristic
123C22×C612−1+411yescharacteristic
124C2×D61—22no—
125C2×D61—22no—
126C2×D61—24no—
127C2×D61—24no—
128C2×D61#12414yes—
129C4×C61—22no—
130C4×C61—41no—
131C4×C61—41no—
132C4×C61—42no—
133Dic61—22no—
134Dic61—42no—
135Dic61—41no—
136Dic61—41no—
137Dic61—42no—
138#2639—611nomaximal, Sylow
139C2×C61—82no—
140C2×C61C2×#12411yescharacteristic
141C2×C61#53411yescharacteristic
142C2×C61#53711yescharacteristic
143C2×C61#53812yes—
144C2×C61#53912yes—
145D61—24no—
146C2×C22⋊Q8—611no—
147C2×#121—611no—
148#400—611no—
149#400—611no—
150#397—612no—
151#394—611no—
152#394D6111yescharacteristic, complemented
153#393—612no—
154#386—612no—
155#386—612no—
156C2×#95—611no—
157C61#263911yescharacteristic, complemented, Sylow
158C22×Q8—611no—
159C22×D4—612no—
160C22×D4C2×D6111yescharacteristic
161C23×C4—611no—
162C23×C4—612no—
163C22⋊Q8—1224no—
164#121—1224no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4—611no—
167C2×C4⋊C4—611no—
168C2×C4⋊C4C2×D6111yescharacteristic
169C2×C22⋊C4—612no—
170C2×C22⋊C4—611no—
171C2×C22⋊C4—611no—
172C2×C22⋊C4—612no—
173C2×C22⋊C4—612no—
174C2×C22⋊C4C2×D6112yes—
175C2×C22⋊C4C2×D6112yes—
176#95—612no—
177#95—611no—
178#95—612no—
179#95—612no—
180#95—612no—
181#95—612no—
182#95C2×D6111yescharacteristic
183C24—611no—
184C24C22×D6112yes—
185C2×Q8—1222no—
186C2×Q8—2442no—
187C2×D4—22no—
188C2×D4—42no—
189C2×D4—1224no—
190C2×D4—1224no—
191C2×D4—1224no—
192C22×C4—611no—
193C22×C4—614no—
194C22×C4—612no—
195C22×C4—612no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—1224no—
199C22×C4—2442no—
200C22×C4—2442no—
201C22×C4—2442no—
202C22×C4C22×D6112yes—
203C22×C4C22×D6111yescharacteristic
204C22×C4C22×D6111yescharacteristic
205C22×C4C22×D6111yescharacteristic
206C4⋊C4—22no—
207C4⋊C4—1222no—
208C4⋊C4—1222no—
209C4⋊C4—1222no—
210C22⋊C4—42no—
211C22⋊C4—42no—
212C22⋊C4—1222no—
213C22⋊C4—1222no—
214C22⋊C4—1224no—
215C22⋊C4—2442no—
216C22⋊C4—2442no—
217C23—22no—
218C23—22no—
219C23—22no—
220C23—22no—
221C23—22no—
222C23—22no—
223C23—22no—
224C23—612no—
225C23—614no—
226C23—1222no—
227C23—1221no—
228C23—1221no—
229C23C23×D6111yescharacteristic
230Q8—2444no—
231D4—44no—
232D4—2448no—
233C2×C4—22no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—21no—
242C2×C4—612no—
243C2×C4—1222no—
244C2×C4—1221no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—1222no—
248C2×C4—1222no—
249C2×C4—1222no—
250C2×C4—1221no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1222no—
254C2×C4—1221no—
255C2×C4—2444no—
256C2×C4—2448no—
257C2×C4D4×D6112yes—
258C22—42no—
259C22—42no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—614no—
266C22—1222no—
267C22—1222no—
268C22—1224no—
269C22—1224no—
270C22C2×D4×D6111yescharacteristic
271C22#41×D6112yes—
272C22#1451982212yes—
273C22#1451982211yescharacteristic
274C22#1451982411yescharacteristic
275C4—22no—
276C4—41no—
277C4—41no—
278C4—42no—
279C4—1222no—
280C4—2442no—
281C4—2441no—
282C4—2441no—
283C4—2442no—
284C2—82no—
285C2—1224no—
286C2#124×D6111yescharacteristic
287C2#1684032211yescharacteristic
288C2#1684034111yescharacteristic
289C2#1684034412yes—
290C2#1684035512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2639
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14519755C2semidirect
3. #16839702C2semidirect
4. #16839701C2semidirect
5. #16839690C2semidirect
6. #16839676C2semidirect
7. #16839674C2semidirect
8. #16839638C2semidirect
9. #16839638C2semidirect
10. #95×D61C2semidirect
11. C61×#394C2semidirect
152. #394D61semidirect
157. C61#2639semidirect