Finite Group Databasebeta

← #21451761

Subgroups — #21451761

Order 7808.

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

normal subgroups only

This group has 584 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×#14519773C211yesmaximal, characteristic
2C2×#14519767C211yesmaximal, characteristic, complemented
3#16839680C211yesmaximal, characteristic, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839678C212yesmaximal, complemented
6#16839677C212yesmaximal, complemented
7#16839676C211yesmaximal, characteristic, complemented
8#16839662C212yesmaximal, complemented
9#16839662C212yesmaximal, complemented
10#16839607C211yesmaximal, characteristic, complemented
11C61×#394C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C22⋊D61C2212yes—
14C22×C22⋊D61C2212yes—
15#14519773—24no—
16#14519767—24no—
17C2×C4⋊Dic61C2211yescharacteristic
18C2×#11758196C2211yescharacteristic
19C2×#11758196C2211yescharacteristic
20C2×#11758196C2211yescharacteristic
21C2×#11758196C2211yescharacteristic
22C2×C22⋊Dic61C2212yes—
23C2×C22⋊Dic61C2212yes—
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×C4×Dic61C2212yes—
29C2×C4×Dic61C2211yescharacteristic
30#14519684C2211yescharacteristic
31#14519684C2212yes—
32C22×D4×C61C2211yescharacteristic
33C2×C4⋊C4×C61C2211yescharacteristic
34C2×C22⋊C4×C61C2212yes—
35C2×C22⋊C4×C61C2212yes—
36#95×C61C2211yescharacteristic
37C24×C61C2312yes—
38C23×D61C2312yes—
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—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—42no—
50C2×C22⋊D61—42no—
51C22×Dic61C2312yes—
52C22×Dic61C2311yescharacteristic
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2311yescharacteristic
56C2×D244—22no—
57C2×D244—42no—
58C4⋊C4×C61—22no—
59C22⋊C4×C61—42no—
60C22⋊C4×C61—42no—
61C22⋊Dic61—42no—
62C22⋊Dic61—42no—
63#11758198—42no—
64#11758198—42no—
65#11758198—42no—
66#11758198—42no—
67C4⋊Dic61—22no—
68#11758196—22no—
69#11758196—22no—
70#11758196—22no—
71#11758196—22no—
72C4×Dic61—24no—
73C4×Dic61D414yes—
74C23×C61—22no—
75C23×C61—22no—
76C23×C61—22no—
77C23×C61—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61C2411yescharacteristic
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89D4×C61—44no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61C2×D412yes—
100C22⋊D61—48no—
101C22⋊D61—48no—
102C2×Dic61—21no—
103C2×Dic61—21no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—22no—
107C2×Dic61—21no—
108C2×Dic61—22no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61C2×D412yes—
113C2×Dic61C2×D412yes—
114C2×Dic61#4114yes—
115D244—44no—
116C22×C61—42no—
117C22×C61—42no—
118C22×C61—42no—
119C22×C61—42no—
120C22×C61—42no—
121C22×C61—42no—
122C22×C61—42no—
123C22×C61C22×D411yescharacteristic
124C22×C61C2×#4112yes—
125C22×C61H(5,𝔽2)12yes—
126C22×C61H(5,𝔽2)11yescharacteristic
127C22×C61H(5,𝔽2)11yescharacteristic
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—42no—
131C2×D61—42no—
132C2×D61—42no—
133C2×D61—42no—
134C2×D61—42no—
135C4×C61—22no—
136C4×C61—41no—
137C4×C61—41no—
138C4×C61—42no—
139Dic61—22no—
140Dic61—41no—
141Dic61—41no—
142Dic61—42no—
143Dic61#12414yes—
144#2641—611nomaximal, Sylow
145C2×C61—82no—
146C2×C61C2×#12411yescharacteristic
147C2×C61#53511yescharacteristic
148C2×C61#53511yescharacteristic
149C2×C61#54012yes—
150C2×C61#54012yes—
151D61—82no—
152C2×#127—611no—
153C2×#125—611no—
154#394—611no—
155#394—611no—
156#394—612no—
157#394—612no—
158#394—611no—
159#394D6111yescharacteristic, complemented
160#390—612no—
161#390—612no—
162#376—611no—
163C61#264111yescharacteristic, complemented, Sylow
164C22×D4—612no—
165C22×D4—612no—
166C22×D4—611no—
167C22×D4C2×D6111yescharacteristic
168#127—1224no—
169#125—1224no—
170C2×C4⋊C4—611no—
171C2×C4⋊C4—611no—
172C2×C4⋊C4—611no—
173C2×C4⋊C4—611no—
174C2×C4⋊C4—611no—
175C2×C4⋊C4C2×D6111yescharacteristic
176C2×C22⋊C4—612no—
177C2×C22⋊C4—612no—
178C2×C22⋊C4—612no—
179C2×C22⋊C4—612no—
180C2×C22⋊C4—612no—
181C2×C22⋊C4—612no—
182C2×C22⋊C4C2×D6112yes—
183C2×C22⋊C4C2×D6112yes—
184C2×C42—611no—
185C2×C42—612no—
186#95—612no—
187#95—611no—
188#95C2×D6111yescharacteristic
189C24—612no—
190C24C22×D6112yes—
191C2×D4—22no—
192C2×D4—42no—
193C2×D4—1224no—
194C2×D4—1224no—
195C2×D4—1224no—
196C2×D4—1224no—
197C2×D4—1222no—
198C2×D4—2442no—
199C2×D4—2442no—
200C2×D4—2442no—
201C22×C4—611no—
202C22×C4—611no—
203C22×C4—612no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4C22×D6112yes—
207C22×C4C22×D6111yescharacteristic
208C22×C4C22×D6111yescharacteristic
209C22×C4C22×D6111yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—1222no—
212C4⋊C4—1222no—
213C4⋊C4—1222no—
214C4⋊C4—1222no—
215C4⋊C4—1222no—
216C22⋊C4—42no—
217C22⋊C4—42no—
218C22⋊C4—2442no—
219C22⋊C4—2442no—
220C22⋊C4—2442no—
221C22⋊C4—2442no—
222C22⋊C4—2442no—
223C22⋊C4—2442no—
224C42—614no—
225C42—1224no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—22no—
233C23—1222no—
234C23—1222no—
235C23—1222no—
236C23—1222no—
237C23—1222no—
238C23—1222no—
239C23—1222no—
240C23C23×D6111yescharacteristic
241D4—44no—
242D4—2444no—
243D4—2448no—
244D4—2448no—
245C2×C4—22no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—612no—
255C2×C4—614no—
256C2×C4—612no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1222no—
262C2×C4—1222no—
263C2×C4—1221no—
264C2×C4—1222no—
265C2×C4—1221no—
266C2×C4—1222no—
267C2×C4D4×D6112yes—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—42no—
274C22—42no—
275C22—2442no—
276C22—2442no—
277C22—2442no—
278C22—2442no—
279C22—2442no—
280C22—2442no—
281C22—2442no—
282C22C2×D4×D6111yescharacteristic
283C22#41×D6112yes—
284C22#1451982212yes—
285C22#1451982211yescharacteristic
286C22#1451982311yescharacteristic
287C4—22no—
288C4—41no—
289C4—41no—
290C4—42no—
291C4—614no—
292C4—1222no—
293C4—2441no—
294C4—2441no—
295C4—2442no—
296C2—82no—
297C2—4882no—
298C2#124×D6111yescharacteristic
299C2#1684032711yescharacteristic
300C2#1684032811yescharacteristic
301C2#1684036212yes—
302C2#1684036412yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2641
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14519767C2semidirect
3. #16839680C2semidirect
4. #16839679C2semidirect
5. #16839678C2semidirect
6. #16839677C2semidirect
7. #16839676C2semidirect
8. #16839662C2semidirect
9. #16839662C2semidirect
10. #16839607C2semidirect
11. C61×#394C2semidirect
159. #394D61semidirect
163. C61#2641semidirect