Finite Group Databasebeta

← #21451676

Subgroups — #21451676

Order 7808.

628 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 131 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×#14519764C211yesmaximal, characteristic, complemented
2C2×#14519737C211yesmaximal, characteristic, complemented
3#16839690C212yesmaximal, complemented
4#16839675C211yesmaximal, characteristic, complemented
5#16839674C211yesmaximal, characteristic, complemented
6#16839670C212yesmaximal, complemented
7#16839670C211yesmaximal, characteristic, complemented
8#16839642C212yesmaximal, complemented
9#16839638C212yesmaximal, complemented
10#16839629C211yesmaximal, characteristic, complemented
11C61×#392C211yesmaximal, characteristic, complemented
12C22×Dic122C2211yescharacteristic
13C22×C22⋊D61C2211yescharacteristic
14C22×C22⋊D61C2212yes—
15C23×Dic61C2211yescharacteristic
16C22×C4×D61C2211yescharacteristic
17#14519764—24no—
18#14519737—24no—
19C2×#11758196C2211yescharacteristic
20C2×C22⋊Dic61C2212yes—
21C2×C22⋊Dic61C2212yes—
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2211yescharacteristic
25C2×#11758198C2212yes—
26C2×C4×Dic61C2211yescharacteristic
27#14519684C2212yes—
28#14519684C2212yes—
29#14519684C2212yes—
30#14519684C2212yes—
31#14519684C2211yescharacteristic
32C22×D4×C61C2211yescharacteristic
33C22×D4×C61C2212yes—
34C2×C22⋊C4×C61C2211yescharacteristic
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2312yes—
38C24×C61C2311yescharacteristic
39C23×D61C2311yescharacteristic
40C2×D4×C61—24no—
41C2×D4×C61—22no—
42C2×D4×C61—42no—
43C2×D4×C61—42no—
44C2×D4×C61—42no—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—22no—
49C2×C22⋊D61—22no—
50C2×C22⋊D61—24no—
51C2×C22⋊D61—22no—
52C2×C22⋊D61—42no—
53C2×C22⋊D61—42no—
54C22×Dic61—22no—
55C22×Dic61—42no—
56C22×Dic61C2311yescharacteristic
57C22×Dic61C2312yes—
58C22×Dic61C2312yes—
59C22×Dic61C2311yescharacteristic
60C22×Dic61C2311yescharacteristic
61C2×C4×D61—22no—
62C2×C4×D61—42no—
63C2×Dic122—22no—
64C2×Dic122—42no—
65C22⋊C4×C61—22no—
66C22⋊C4×C61—42no—
67C22⋊Dic61—24no—
68C22⋊Dic61—24no—
69C22⋊Dic61—42no—
70C22⋊Dic61—42no—
71#11758198—22no—
72#11758198—42no—
73#11758196—22no—
74C4×Dic61D414yescomplemented
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61—22no—
85C23×C61—22no—
86C23×C61#4112yes—
87C23×C61C2411yescharacteristic
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—22no—
91C22×D61—22no—
92C22×D61#4112yes—
93D4×C61—44no—
94D4×C61—48no—
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—22no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61C2×D412yes—
102C22⋊D61—28no—
103C22⋊D61—48no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61—22no—
115C2×Dic61—44no—
116C2×Dic61C2×D412yes—
117C2×Dic61C2×D412yes—
118C4×D61—44no—
119Dic122—44no—
120C22×C61—22no—
121C22×C61—24no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61—42no—
128C22×C61—42no—
129C22×C61—42no—
130C22×C61—42no—
131C22×C61—42no—
132C22×C61C22×D411yescharacteristic
133C22×C61C2×#4111yescharacteristic
134C22×C61C2×#4111yescharacteristic
135C22×C61H(5,𝔽2)12yes—
136C22×C61H(5,𝔽2)12yes—
137C2×D61—22no—
138C2×D61—24no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—42no—
142C4×C61—22no—
143C4×C61—41no—
144C4×C61—42no—
145Dic61—22no—
146Dic61—22no—
147Dic61—42no—
148Dic61—41no—
149Dic61—42no—
150#2631—611nomaximal, Sylow
151C2×C61—42no—
152C2×C61—82no—
153C2×C61#52511yescharacteristic
154C2×C61#53511yescharacteristic
155C2×C61#53511yescharacteristic
156C2×C61#53812yes—
157C2×C61#53812yes—
158D61—42no—
159C2×#124—611no—
160C2×C4×D4—611no—
161#397—612no—
162#393—611no—
163#393—611no—
164#392—611no—
165#392—612no—
166#392D6111yescharacteristic, complemented
167#386—612no—
168#386—612no—
169#383—611no—
170C61#263111yescharacteristic, complemented, Sylow
171C22×Q8—611no—
172C22×D4—611no—
173C22×D4—612no—
174C22×D4C2×D6111yescharacteristic
175C22×D4C2×D6112yes—
176C23×C4—611no—
177C23×C4—611no—
178#124—1224no—
179C4×D4—1224no—
180C2×C4⋊C4—611no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4—612no—
183C2×C22⋊C4—611no—
184C2×C22⋊C4—612no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—612no—
187C2×C22⋊C4C2×D6111yescharacteristic
188C2×C22⋊C4C2×D6112yes—
189C2×C42—611no—
190#95—612no—
191#95—611no—
192#95—612no—
193#95—612no—
194#95—612no—
195#95C2×D6111yescharacteristic
196C24—611no—
197C24C22×D6112yes—
198C24C22×D6111yescharacteristic
199C2×Q8—1222no—
200C2×Q8—2442no—
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—1222no—
207C2×D4—1222no—
208C2×D4—1222no—
209C2×D4—1224no—
210C2×D4—2442no—
211C2×D4—2442no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—612no—
215C22×C4—612no—
216C22×C4—611no—
217C22×C4—1222no—
218C22×C4—1222no—
219C22×C4—2442no—
220C22×C4—2442no—
221C22×C4C22×D6112yes—
222C22×C4C22×D6111yescharacteristic
223C22×C4C22×D6111yescharacteristic
224C4⋊C4—1222no—
225C22⋊C4—22no—
226C22⋊C4—42no—
227C22⋊C4—1224no—
228C22⋊C4—1224no—
229C22⋊C4—1222no—
230C22⋊C4—2442no—
231C22⋊C4—2442no—
232C22⋊C4—2442no—
233C42—614no—
234C23—21no—
235C23—21no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—22no—
243C23—22no—
244C23—22no—
245C23—612no—
246C23—1221no—
247C23—1221no—
248C23—1222no—
249C23—1222no—
250C23#1175822412yes—
251C23C23×D6111yescharacteristic
252Q8—2444no—
253D4—44no—
254D4—48no—
255D4—1228no—
256D4—2448no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—612no—
264C2×C4—612no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1222no—
269C2×C4—1221no—
270C2×C4—1222no—
271C2×C4—1222no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—1222no—
275C2×C4—1222no—
276C2×C4—2444no—
277C2×C4—2444no—
278C2×C4D4×D6112yes—
279C22—22no—
280C22—24no—
281C22—41no—
282C22—41no—
283C22—42no—
284C22—42no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—1222no—
292C22—1224no—
293C22—2441no—
294C22—2441no—
295C22—2442no—
296C22C2×D4×D6111yescharacteristic
297C22#41×D6111yescharacteristic
298C22C2×#1175822411yescharacteristic
299C22#1451982212yes—
300C22#1451982212yes—
301C4—22no—
302C4—41no—
303C4—42no—
304C4—1222no—
305C4—1222no—
306C4—2441no—
307C4—2442no—
308C4—2442no—
309C2—42no—
310C2—82no—
311C2—2442no—
312C2#1684027211yescharacteristic
313C2#1684032511yescharacteristic
314C2#1684032711yescharacteristic
315C2#1684034412yes—
316C2#1684034712yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#392C2
hypercenter#392D61
hypocenterC61#2631
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#14519764C2semidirect
2. C2×#14519737C2semidirect
3. #16839690C2semidirect
4. #16839675C2semidirect
5. #16839674C2semidirect
6. #16839670C2semidirect
7. #16839670C2semidirect
8. #16839642C2semidirect
9. #16839638C2semidirect
10. #16839629C2semidirect
11. C61×#392C2semidirect
74. C4×Dic61D4semidirect
166. #392D61semidirect
170. C61#2631semidirect