Finite Group Databasebeta

← #21449430

Subgroups — #21449430

Order 7808.

914 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 161 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, complemented
2C2×#14519762C211yesmaximal, characteristic, complemented
3C2×#14519752C212yesmaximal, complemented
4#16839679C211yesmaximal, characteristic, complemented
5#16839673C211yesmaximal, characteristic, complemented
6#16839672C211yesmaximal, characteristic, complemented
7#16839640C212yesmaximal, complemented
8#16839640C212yesmaximal, complemented
9#16839633C212yesmaximal, complemented
10#95×D61C211yesmaximal, characteristic, complemented
11C61×#395C211yesmaximal, characteristic, complemented
12C2×#11758226—28no—
13C2×#11758226—24no—
14C22×D244C2211yescharacteristic
15C22×D244C2211yescharacteristic
16C22×D244C2212yes—
17C22×D244C2212yes—
18C22×C4×D61C2212yes—
19C22×C4×D61C2212yes—
20C22×C4×D61C2211yescharacteristic
21#14519762—24no—
22#14519752—28no—
23C2×#11758196C2211yescharacteristic
24C2×#11758198C2212yes—
25C2×#11758198C2212yes—
26C2×#11758198C2211yescharacteristic
27C2×#11758198C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2212yes—
30C2×#11758198C2212yes—
31#14519684C2212yes—
32#14519684C2211yescharacteristic
33#14519684C2212yes—
34C22×Q8×C61C2211yescharacteristic
35C2×C4⋊C4×C61C2212yes—
36C2×C4⋊C4×C61C2211yescharacteristic
37#95×C61C2211yescharacteristic
38#95×C61C2212yes—
39C23×D61C2311yescharacteristic
40C23×D61C2312yes—
41C23×D61C2311yescharacteristic
42C2×Q8×C61—24no—
43C2×Q8×C61—22no—
44C22×C4×C61C2311yescharacteristic
45C22×C4×C61C2311yescharacteristic
46C22×C4×C61C2312yes—
47C22×C4×C61C2311yescharacteristic
48C22×C4×C61C2312yes—
49C22×Dic61C2312yes—
50C22×Dic61C2311yescharacteristic
51C22×Dic61C2311yescharacteristic
52#11758226—232no—
53C2×D244—24no—
54C2×D244—24no—
55C2×D244—24no—
56C2×D244—22no—
57C2×D244—24no—
58C2×D244—24no—
59C2×D244—22no—
60C2×D244—24no—
61C2×D244—42no—
62C2×D244D418yescomplemented
63C2×C4×D61—24no—
64C2×C4×D61—24no—
65C2×C4×D61—24no—
66C2×C4×D61—24no—
67C2×C4×D61—24no—
68C2×C4×D61—24no—
69C2×C4×D61—42no—
70C2×C4×D61D414yescomplemented
71C4⋊C4×C61—24no—
72C4⋊C4×C61—22no—
73#11758198—24no—
74#11758198—22no—
75#11758198—24no—
76#11758198—22no—
77#11758198—24no—
78#11758198—22no—
79#11758198—42no—
80#11758196—22no—
81C23×C61C2411yescharacteristic
82C22×D61—22no—
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—22no—
86C22×D61—22no—
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—21no—
92C22×D61—22no—
93C22×D61—22no—
94C22×D61—21no—
95C22×D61—21no—
96C22×D61C2×D414yes—
97C22×D61C2×D412yes—
98C22×D61C2×D414yes—
99Q8×C61—28no—
100C2×C4×C61—22no—
101C2×C4×C61—22no—
102C2×C4×C61—22no—
103C2×C4×C61—22no—
104C2×C4×C61—22no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—22no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61C2×D414yes—
111C2×C4×C61C2×D412yes—
112C2×C4×C61#4114yescomplemented
113C2×Dic61—22no—
114C2×Dic61—21no—
115C2×Dic61—22no—
116C2×Dic61—22no—
117C2×Dic61—22no—
118C2×Dic61—22no—
119C2×Dic61C2×D412yes—
120D244—28no—
121D244—216no—
122D244—48no—
123D244—44no—
124C4×D61—216no—
125C4×D61—28no—
126C4×D61—48no—
127C22×C61C22×D411yescharacteristic
128C22×C61C22×D412yes—
129C22×C61C2×#4112yes—
130C22×C61H(5,𝔽2)11yescharacteristic
131C22×C612−1+411yescharacteristic
132C2×D61—22no—
133C2×D61—22no—
134C2×D61—24no—
135C2×D61—24no—
136C2×D61—24no—
137C2×D61—24no—
138C2×D61—24no—
139C2×D61—42no—
140C2×D61—42no—
141C2×D61—42no—
142C2×D61—42no—
143C2×D61—41no—
144C2×D61—41no—
145C2×D61—41no—
146C2×D61—42no—
147C2×D61—42no—
148C2×D61#12014yes—
149C4×C61—24no—
150C4×C61—22no—
151C4×C61—24no—
152C4×C61—41no—
153C4×C61—41no—
154Dic61—22no—
155Dic61—41no—
156Dic61—42no—
157#2430—611nomaximal, Sylow
158C2×C61C2×#12011yescharacteristic
159C2×C61#53211yescharacteristic
160C2×C61#53711yescharacteristic
161C2×C61#54612yes—
162C2×C61#54712yes—
163D61—24no—
164D61—44no—
165D61—81no—
166C22×#41—611no—
167C2×#123—611no—
168C2×#121—612no—
169#395D6111yescharacteristic, complemented
170#394—611no—
171#393—611no—
172#392—611no—
173#386—612no—
174#386—612no—
175#385—612no—
176C2×#95—611no—
177C61#243011yescharacteristic, complemented, Sylow
178C2×#41—1224no—
179C2×#41—1228no—
180C22×Q8C2×D6111yescharacteristic
181C22×D4—612no—
182C22×D4—611no—
183C22×D4—611no—
184C22×D4—612no—
185C23×C4—611no—
186C23×C4—612no—
187C23×C4—612no—
188#123—1224no—
189#121—1228no—
190C2×C4⋊C4—611no—
191C2×C4⋊C4C2×D6112yes—
192C2×C4⋊C4C2×D6111yescharacteristic
193C2×C22⋊C4—612no—
194C2×C22⋊C4—612no—
195C2×C22⋊C4—611no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—612no—
199C2×C22⋊C4—612no—
200#95—612no—
201#95—611no—
202#95—612no—
203#95C2×D6111yescharacteristic
204#95C2×D6112yes—
205C24—611no—
206C24—612no—
207C24—611no—
208#41—12232no—
209C2×Q8—22no—
210C2×Q8—24no—
211C2×D4—618no—
212C2×D4—1224no—
213C2×D4—1224no—
214C2×D4—1224no—
215C2×D4—1224no—
216C2×D4—1224no—
217C2×D4—1222no—
218C2×D4—1222no—
219C2×D4—1224no—
220C2×D4—2442no—
221C22×C4—611no—
222C22×C4—614no—
223C22×C4—612no—
224C22×C4—611no—
225C22×C4—1224no—
226C22×C4—1224no—
227C22×C4—1224no—
228C22×C4—1224no—
229C22×C4—1224no—
230C22×C4—1224no—
231C22×C4—2442no—
232C22×C4C22×D6111yescharacteristic
233C22×C4C22×D6111yescharacteristic
234C22×C4C22×D6111yescharacteristic
235C22×C4C22×D6112yes—
236C22×C4C22×D6112yes—
237C4⋊C4—24no—
238C4⋊C4—22no—
239C4⋊C4—1222no—
240C22⋊C4—1222no—
241C22⋊C4—1224no—
242C22⋊C4—1222no—
243C22⋊C4—1224no—
244C22⋊C4—1222no—
245C22⋊C4—1224no—
246C22⋊C4—2442no—
247C23—612no—
248C23—614no—
249C23—614no—
250C23—1222no—
251C23—1221no—
252C23—1221no—
253C23—1222no—
254C23—1222no—
255C23—1222no—
256C23—1222no—
257C23—1222no—
258C23—1222no—
259C23—1221no—
260C23—1222no—
261C23—1222no—
262C23—1221no—
263C23—1221no—
264C23C23×D6111yescharacteristic
265Q8—28no—
266D4—12216no—
267D4—1228no—
268D4—2448no—
269D4—2444no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—612no—
281C2×C4—1228no—
282C2×C4—12216no—
283C2×C4—1222no—
284C2×C4—1221no—
285C2×C4—1222no—
286C2×C4—1222no—
287C2×C4—1222no—
288C2×C4—1222no—
289C2×C4—2448no—
290C2×C4D4×D6112yes—
291C2×C4D4×D6114yes—
292C2×C4#1175822614yescomplemented
293C22—614no—
294C22—1222no—
295C22—1222no—
296C22—1224no—
297C22—1224no—
298C22—1224no—
299C22—1224no—
300C22—1224no—
301C22—2441no—
302C22—2441no—
303C22—2441no—
304C22—2442no—
305C22—2442no—
306C22—2442no—
307C22—2442no—
308C22—2442no—
309C22—2442no—
310C22C2×D4×D6111yescharacteristic
311C22C2×D4×D6112yes—
312C22C2×#1175822612yes—
313C22#1451982311yescharacteristic
314C22#1451982511yescharacteristic
315C4—22no—
316C4—24no—
317C4—24no—
318C4—41no—
319C4—41no—
320C4—1222no—
321C4—2441no—
322C4—2442no—
323C2—1224no—
324C2—4881no—
325C2—2444no—
326C2#120×D6111yescharacteristic
327C2#1684031311yescharacteristic
328C2#1684034211yescharacteristic
329C2#1684040312yes—
330C2#1684041512yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#395C2
hypercenter#395D61
hypocenterC61#2430
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
1. C22×#11758226C2semidirect
2. C2×#14519762C2semidirect
3. C2×#14519752C2semidirect
4. #16839679C2semidirect
5. #16839673C2semidirect
6. #16839672C2semidirect
7. #16839640C2semidirect
8. #16839640C2semidirect
9. #16839633C2semidirect
10. #95×D61C2semidirect
11. C61×#395C2semidirect
62. C2×D244D4semidirect
70. C2×C4×D61D4semidirect
112. C2×C4×C61#41semidirect
169. #395D61semidirect
177. C61#2430semidirect
292. C2×C4#11758226semidirect