Finite Group Databasebeta

← #21449155

Subgroups — #21449155

Order 7808.

864 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 159 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×#11758226C211yesmaximal, characteristic
2C2×#14519762C212yesmaximal, complemented
3C2×C4⋊C4×D61C211yesmaximal, characteristic, complemented
4#16839681C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839679C211yesmaximal, characteristic, complemented
7#16839640C212yesmaximal, complemented
8#16839636C212yesmaximal, complemented
9#16839633C212yesmaximal, complemented
10#16839624C211yesmaximal, characteristic, complemented
11C61×#395C211yesmaximal, characteristic, complemented
12C2×#11758226—28no—
13C2×#11758226—24no—
14C22×D244C2211yescharacteristic
15C22×D244C2212yes—
16C22×C4×D61C2211yescharacteristic
17C22×C4×D61C2211yescharacteristic
18C22×C4×D61C2212yes—
19C22×C4×D61C2211yescharacteristic
20#14519762—28no—
21C2×C4⋊Dic61C2211yescharacteristic
22C2×#11758196C2211yescharacteristic
23C2×#11758196C2212yes—
24C2×#11758196C2211yescharacteristic
25C4⋊C4×D61—24no—
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2212yes—
29C2×#11758198C2212yes—
30C2×#11758198C2212yes—
31#14519684C2211yescharacteristic
32#14519684C2212yes—
33#14519684C2212yes—
34C22×Q8×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2211yescharacteristic
36C2×C4⋊C4×C61C2212yes—
37#95×C61C2211yescharacteristic
38#95×C61C2212yes—
39C23×D61C2312yes—
40C23×D61C2311yescharacteristic
41C2×Q8×C61—24no—
42C2×Q8×C61—22no—
43C22×C4×C61C2311yescharacteristic
44C22×C4×C61C2312yes—
45C22×C4×C61C2312yes—
46C22×C4×C61C2311yescharacteristic
47C22×C4×C61C2311yescharacteristic
48C22×Dic61C2311yescharacteristic
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52#11758226—232no—
53C2×D244—24no—
54C2×D244—24no—
55C2×D244—24no—
56C2×D244—22no—
57C2×D244D418yes—
58C2×C4×D61—24no—
59C2×C4×D61—24no—
60C2×C4×D61—22no—
61C2×C4×D61—24no—
62C2×C4×D61—22no—
63C2×C4×D61—24no—
64C2×C4×D61—22no—
65C2×C4×D61—22no—
66C2×C4×D61—24no—
67C2×C4×D61D414yes—
68C4⋊C4×C61—22no—
69C4⋊C4×C61—24no—
70#11758198—24no—
71#11758198—24no—
72#11758198—24no—
73#11758198—24no—
74#11758198—24no—
75C4⋊Dic61—22no—
76#11758196—22no—
77#11758196—24no—
78#11758196—22no—
79C23×C61C2411yescharacteristic
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—22no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61C2×D414yes—
90C22×D61C2×D414yes—
91C22×D61C2×D412yes—
92Q8×C61—28no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—22no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—22no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61C2×D414yes—
104C2×C4×C61C2×D412yes—
105C2×C4×C61#4112yescomplemented
106C2×Dic61—21no—
107C2×Dic61—22no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—22no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—22no—
114C2×Dic61C2×D412yes—
115C2×Dic61#4112yescomplemented
116D244—28no—
117D244—216no—
118C4×D61—28no—
119C4×D61—216no—
120C4×D61—28no—
121C4×D61—44no—
122C22×C61C22×D411yescharacteristic
123C22×C61C22×D412yes—
124C22×C61C2×#4111yescharacteristic
125C22×C61C2×#4111yescharacteristic
126C22×C612−1+412yes—
127C2×D61—22no—
128C2×D61—22no—
129C2×D61—24no—
130C2×D61—24no—
131C2×D61—24no—
132C2×D61—24no—
133C2×D61—24no—
134C2×D61—42no—
135C2×D61—42no—
136C2×D61—42no—
137C2×D61—42no—
138C2×D61#12014yes—
139C4×C61—24no—
140C4×C61—22no—
141C4×C61—22no—
142C4×C61—41no—
143C4×C61—42no—
144Dic61—22no—
145Dic61—22no—
146Dic61—41no—
147Dic61—42no—
148#2406—611nomaximal, Sylow
149C2×C61C2×#12011yescharacteristic
150C2×C61#52511yescharacteristic
151C2×C61#53611yescharacteristic
152C2×C61#54712yes—
153C2×C61#54712yes—
154D61—24no—
155D61—44no—
156C22×#41—611no—
157C2×#123—612no—
158C22×C4⋊C4—611no—
159#395—611no—
160#395D6111yescharacteristic, complemented
161#394—611no—
162#394—611no—
163#386—612no—
164#385—612no—
165#385—612no—
166#381—611no—
167C61#240611yescharacteristic, complemented, Sylow
168C2×#41—1224no—
169C2×#41—1228no—
170C22×Q8C2×D6111yescharacteristic
171C22×D4—612no—
172C22×D4—611no—
173C23×C4—611no—
174C23×C4—611no—
175C23×C4—611no—
176C23×C4—612no—
177#123—1228no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—611no—
181C2×C4⋊C4—612no—
182C2×C4⋊C4—1224no—
183C2×C4⋊C4C2×D6111yescharacteristic
184C2×C4⋊C4C2×D6112yes—
185C2×C22⋊C4—612no—
186C2×C22⋊C4—612no—
187C2×C22⋊C4—612no—
188C2×C22⋊C4—612no—
189C2×C22⋊C4—612no—
190#95—612no—
191#95—611no—
192#95—612no—
193#95C2×D6111yescharacteristic
194#95C2×D6112yes—
195C24—611no—
196C24—612no—
197#41—12232no—
198C2×Q8—22no—
199C2×Q8—24no—
200C2×D4—618no—
201C2×D4—1224no—
202C2×D4—1224no—
203C2×D4—1224no—
204C2×D4—1222no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—614no—
208C22×C4—612no—
209C22×C4—611no—
210C22×C4—1222no—
211C22×C4—1224no—
212C22×C4—1222no—
213C22×C4—1224no—
214C22×C4—1224no—
215C22×C4—1222no—
216C22×C4—1224no—
217C22×C4—1224no—
218C22×C4—1222no—
219C22×C4C22×D6112yes—
220C22×C4C22×D6111yescharacteristic
221C22×C4C22×D6111yescharacteristic
222C22×C4C22×D6112yes—
223C22×C4C22×D6111yescharacteristic
224C4⋊C4—22no—
225C4⋊C4—24no—
226C4⋊C4—1222no—
227C4⋊C4—1222no—
228C4⋊C4—1222no—
229C4⋊C4—1224no—
230C22⋊C4—1224no—
231C22⋊C4—1224no—
232C22⋊C4—1224no—
233C22⋊C4—1224no—
234C22⋊C4—1224no—
235C23—614no—
236C23—612no—
237C23—614no—
238C23—1221no—
239C23—1221no—
240C23—1222no—
241C23—1222no—
242C23—1222no—
243C23—1222no—
244C23—1222no—
245C23—1222no—
246C23—1222no—
247C23C23×D6111yescharacteristic
248Q8—28no—
249D4—12216no—
250D4—1228no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—612no—
262C2×C4—612no—
263C2×C4—1228no—
264C2×C4—1228no—
265C2×C4—12216no—
266C2×C4—1221no—
267C2×C4—1222no—
268C2×C4—1221no—
269C2×C4—1222no—
270C2×C4—1222no—
271C2×C4—1221no—
272C2×C4—1222no—
273C2×C4—1222no—
274C2×C4—2444no—
275C2×C4D4×D6112yes—
276C2×C4D4×D6114yes—
277C2×C4#1175822612yescomplemented
278C22—614no—
279C22—1222no—
280C22—1222no—
281C22—1224no—
282C22—1224no—
283C22—1224no—
284C22—1224no—
285C22—1224no—
286C22—2442no—
287C22—2442no—
288C22—2442no—
289C22—2442no—
290C22C2×D4×D6111yescharacteristic
291C22C2×D4×D6112yes—
292C22#41×D6111yescharacteristic
293C22C2×#1175822611yescharacteristic
294C22#1451982512yes—
295C4—22no—
296C4—24no—
297C4—22no—
298C4—41no—
299C4—42no—
300C4—1222no—
301C4—1222no—
302C4—2441no—
303C4—2442no—
304C2—1224no—
305C2—2444no—
306C2#120×D6111yescharacteristic
307C2#1684027511yescharacteristic
308C2#1684033711yescharacteristic
309C2#1684041412yes—
310C2#1684041512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2406
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#14519762C2semidirect
3. C2×C4⋊C4×D61C2semidirect
4. #16839681C2semidirect
5. #16839680C2semidirect
6. #16839679C2semidirect
7. #16839640C2semidirect
8. #16839636C2semidirect
9. #16839633C2semidirect
10. #16839624C2semidirect
11. C61×#395C2semidirect
105. C2×C4×C61#41semidirect
115. C2×Dic61#41semidirect
160. #395D61semidirect
167. C61#2406semidirect
277. C2×C4#11758226semidirect