Finite Group Databasebeta

← #21451547

Subgroups — #21451547

Order 7808.

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

normal subgroups only

This group has 816 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
1C22×#11758224C211yesmaximal, characteristic
2C2×#14519755C211yesmaximal, characteristic, complemented
3C2×#14519754C212yesmaximal, complemented
4#16839683C211yesmaximal, characteristic, complemented
5#16839682C211yesmaximal, characteristic, complemented
6#16839678C212yesmaximal, complemented
7#16839677C212yesmaximal, complemented
8#16839676C211yesmaximal, characteristic, complemented
9#16839621C211yesmaximal, characteristic, complemented
10#16839620C212yesmaximal, complemented
11C61×#394C211yesmaximal, characteristic, complemented
12C2×#11758224—28no—
13C2×#11758224—24no—
14C22×Dic122C2211yescharacteristic
15C22×Dic122C2211yescharacteristic
16C22×C22⋊D61C2212yes—
17C23×Dic61C2212yes—
18C22×C4×D61C2211yescharacteristic
19#14519755—24no—
20#14519754—28no—
21C2×C4⋊Dic61C2212yes—
22C2×#11758196C2212yes—
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2212yes—
25C2×#11758196C2211yescharacteristic
26C2×C22⋊Dic61C2212yes—
27C2×C22⋊Dic61C2212yes—
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2212yes—
31#14519684C2212yes—
32#14519684C2211yescharacteristic
33#14519684C2212yes—
34C22×D4×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2211yescharacteristic
36C2×C22⋊C4×C61C2212yes—
37C2×C22⋊C4×C61C2212yes—
38#95×C61C2211yescharacteristic
39C24×C61C2312yes—
40C23×D61C2311yescharacteristic
41C2×D4×C61—24no—
42C2×D4×C61—22no—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2311yescharacteristic
47C2×C22⋊D61—24no—
48C2×C22⋊D61—24no—
49C2×C22⋊D61—24no—
50C22×Dic61—24no—
51C22×Dic61—24no—
52C22×Dic61D418yes—
53C22×Dic61C2311yescharacteristic
54C22×Dic61C2311yescharacteristic
55C22×Dic61C2312yes—
56C22×Dic61C2312yes—
57C22×Dic61C2311yescharacteristic
58#11758224—232no—
59C2×C4×D61—24no—
60C2×C4×D61D414yes—
61C2×Dic122—22no—
62C2×Dic122—24no—
63C2×Dic122—24no—
64C2×Dic122—22no—
65C4⋊C4×C61—22no—
66C22⋊C4×C61—24no—
67C22⋊C4×C61—42no—
68C22⋊Dic61—24no—
69C22⋊Dic61—42no—
70#11758198—22no—
71#11758198—22no—
72#11758198—42no—
73C4⋊Dic61—24no—
74#11758196—22no—
75#11758196—24no—
76#11758196—24no—
77#11758196—22no—
78C23×C61—22no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—22no—
82C23×C61—22no—
83C23×C61—22no—
84C23×C61C2×D414yes—
85C23×C61C2411yescharacteristic
86C22×D61—22no—
87C22×D61—21no—
88C22×D61—22no—
89C22×D61—21no—
90C22×D61C2×D412yes—
91D4×C61—28no—
92C2×C4×C61—22no—
93C2×C4×C61—22no—
94C2×C4×C61—21no—
95C2×C4×C61—22no—
96C2×C4×C61—21no—
97C2×C4×C61—22no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—21no—
101C2×C4×C61C2×D412yes—
102C22⋊D61—216no—
103C2×Dic61—22no—
104C2×Dic61—22no—
105C2×Dic61—216no—
106C2×Dic61—21no—
107C2×Dic61—22no—
108C2×Dic61—21no—
109C2×Dic61—22no—
110C2×Dic61—22no—
111C2×Dic61—21no—
112C2×Dic61—22no—
113C2×Dic61—21no—
114C2×Dic61C2×D414yes—
115C2×Dic61C2×D414yes—
116C2×Dic61C2×D412yes—
117C4×D61—28no—
118Dic122—28no—
119Dic122—44no—
120C22×C61—24no—
121C22×C61—24no—
122C22×C61—24no—
123C22×C61—42no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—42no—
127C22×C61C22×D411yescharacteristic
128C22×C61C22×D412yes—
129C22×C61H(5,𝔽2)11yescharacteristic
130C22×C612−1+412yes—
131C22×C612−1+411yescharacteristic
132C2×D61—22no—
133C2×D61—22no—
134C2×D61—22no—
135C2×D61—42no—
136C2×D61—42no—
137C4×C61—22no—
138C4×C61—41no—
139C4×C61—42no—
140C4×C61—41no—
141Dic61—24no—
142Dic61—41no—
143Dic61—42no—
144Dic61—41no—
145Dic61#12014yes—
146#2616—611nomaximal, Sylow
147C2×C61—44no—
148C2×C61C2×#12011yescharacteristic
149C2×C61#53611yescharacteristic
150C2×C61#53612yes—
151C2×C61#53712yes—
152C2×C61#53711yescharacteristic
153D61—42no—
154C22×#41—611no—
155C2×C22⋊Q8—611no—
156C2×C22⋊Q8—612no—
157#395—611no—
158#395—611no—
159#394—611no—
160#394—612no—
161#394—612no—
162#394D6111yescharacteristic, complemented
163#380—612no—
164#380—611no—
165C61#261611yescharacteristic, complemented, Sylow
166C2×#41—1228no—
167C2×#41—1224no—
168C22×Q8—611no—
169C22×Q8—611no—
170C22×D4—612no—
171C22×D4C2×D6111yescharacteristic
172C23×C4—612no—
173C23×C4—611no—
174C22⋊Q8—1228no—
175C22⋊Q8—1224no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—612no—
178C2×C4⋊C4—612no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—612no—
181C2×C4⋊C4C2×D6111yescharacteristic
182C2×C22⋊C4—612no—
183C2×C22⋊C4—611no—
184C2×C22⋊C4—611no—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—612no—
187C2×C22⋊C4C2×D6112yes—
188C2×C22⋊C4C2×D6112yes—
189#95—612no—
190#95—612no—
191#95—611no—
192#95C2×D6111yescharacteristic
193C24—611no—
194C24C22×D6112yes—
195#41—12232no—
196C2×Q8—1224no—
197C2×Q8—1224no—
198C2×Q8—1222no—
199C2×Q8—1222no—
200C2×D4—24no—
201C2×D4—22no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—1224no—
205C22×C4—611no—
206C22×C4—618no—
207C22×C4—612no—
208C22×C4—614no—
209C22×C4—612no—
210C22×C4—611no—
211C22×C4—611no—
212C22×C4—1224no—
213C22×C4—1224no—
214C22×C4—1224no—
215C22×C4C22×D6111yescharacteristic
216C22×C4C22×D6112yes—
217C22×C4C22×D6111yescharacteristic
218C22×C4C22×D6111yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—1224no—
221C4⋊C4—1224no—
222C4⋊C4—1222no—
223C4⋊C4—1224no—
224C4⋊C4—1222no—
225C22⋊C4—24no—
226C22⋊C4—42no—
227C22⋊C4—1222no—
228C22⋊C4—1222no—
229C22⋊C4—1224no—
230C22⋊C4—2442no—
231C22⋊C4—2442no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—612no—
239C23—1222no—
240C23—1221no—
241C23—1222no—
242C23—1221no—
243C23D4×D6114yes—
244C23C23×D6111yescharacteristic
245Q8—1228no—
246Q8—2444no—
247D4—28no—
248D4—12216no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—612no—
259C2×C4—614no—
260C2×C4—614no—
261C2×C4—1228no—
262C2×C4—12216no—
263C2×C4—1222no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1222no—
269C2×C4—1222no—
270C2×C4—1221no—
271C2×C4—1222no—
272C2×C4—1221no—
273C2×C4D4×D6112yes—
274C22—24no—
275C22—24no—
276C22—24no—
277C22—42no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—1222no—
282C22—1222no—
283C22—1222no—
284C22—2442no—
285C22—2442no—
286C22C2×D4×D6111yescharacteristic
287C22C2×D4×D6112yes—
288C22#1451982211yescharacteristic
289C22#1451982412yes—
290C22#1451982411yescharacteristic
291C4—22no—
292C4—41no—
293C4—42no—
294C4—41no—
295C4—614no—
296C4—1224no—
297C4—2441no—
298C4—2442no—
299C4—2441no—
300C2—44no—
301C2—2442no—
302C2#120×D6111yescharacteristic
303C2#1684033211yescharacteristic
304C2#1684033412yes—
305C2#1684033912yes—
306C2#1684034111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2616
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#14519755C2semidirect
3. C2×#14519754C2semidirect
4. #16839683C2semidirect
5. #16839682C2semidirect
6. #16839678C2semidirect
7. #16839677C2semidirect
8. #16839676C2semidirect
9. #16839621C2semidirect
10. #16839620C2semidirect
11. C61×#394C2semidirect
162. #394D61semidirect
165. C61#2616semidirect