Finite Group Databasebeta

← #21449429

Subgroups — #21449429

Order 7808.

914 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11758222C211yesmaximal, characteristic, complemented
2C2×#14519760C211yesmaximal, characteristic, complemented
3C2×#14519751C212yesmaximal, complemented
4#16839683C211yesmaximal, characteristic, complemented
5#16839680C211yesmaximal, characteristic, complemented
6#16839675C211yesmaximal, characteristic, complemented
7#16839672C211yesmaximal, characteristic, complemented
8#16839641C212yesmaximal, complemented
9#16839640C212yesmaximal, complemented
10#16839636C212yesmaximal, complemented
11C2×#95×C61C211yesmaximal, characteristic, complemented
12C2×#11758222—24no—
13C2×#11758222—28no—
14C22×Dic122C2211yescharacteristic
15C22×D244C2211yescharacteristic
16C22×D244C2212yes—
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2212yes—
19C22×C4×D61C2212yes—
20#14519760—24no—
21#14519751—28no—
22C2×C4⋊Dic61C2212yes—
23C2×#11758196C2211yescharacteristic
24C2×#11758196C2211yescharacteristic
25C2×C22⋊Dic61C2211yescharacteristic
26C2×#11758198C2212yes—
27C2×#11758198C2212yes—
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2212yes—
31C2×#11758198C2212yes—
32#14519684C2212yes—
33#14519684C2212yes—
34C23×C4×C61C2212yes—
35C23×C4×C61C2211yescharacteristic
36#95×C61C2211yescharacteristic
37#95×C61C2211yescharacteristic
38#95×C61C2212yes—
39C24×C61C2311yescharacteristic
40C23×D61C2311yescharacteristic
41C23×D61C2312yes—
42C22×C4×C61—24no—
43C22×C4×C61—24no—
44C22×C4×C61—24no—
45C22×C4×C61—42no—
46C22×C4×C61D414yescomplemented
47C22×C4×C61C2312yes—
48C22×C4×C61C2311yescharacteristic
49C22×C4×C61C2311yescharacteristic
50C22×C4×C61C2312yes—
51C2×C22⋊D61—24no—
52C2×C22⋊D61—24no—
53C2×C22⋊D61—24no—
54C2×C22⋊D61—22no—
55C2×C22⋊D61D418yescomplemented
56C22×Dic61C2311yescharacteristic
57C22×Dic61C2311yescharacteristic
58C22×Dic61C2311yescharacteristic
59C22×Dic61C2312yes—
60#11758222—232no—
61C2×D244—24no—
62C2×D244—22no—
63C2×D244—24no—
64C2×D244—24no—
65C2×D244—42no—
66C2×C4×D61—24no—
67C2×C4×D61—24no—
68C2×C4×D61—24no—
69C2×Dic122—22no—
70C2×Dic122—24no—
71C22⋊Dic61—22no—
72#11758198—24no—
73#11758198—22no—
74#11758198—22no—
75#11758198—24no—
76#11758198—24no—
77#11758198—42no—
78C4⋊Dic61—24no—
79#11758196—22no—
80#11758196—22no—
81C23×C61—22no—
82C23×C61—21no—
83C23×C61—21no—
84C23×C61C2×D412yes—
85C23×C61C2×D414yes—
86C23×C61C2411yescharacteristic
87C22×D61—22no—
88C22×D61—22no—
89C22×D61—22no—
90C22×D61—22no—
91C22×D61—22no—
92C22×D61—22no—
93C22×D61—21no—
94C22×D61—22no—
95C22×D61—22no—
96C22×D61—21no—
97C22×D61—21no—
98C22×D61C2×D414yes—
99C2×C4×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—22no—
106C2×C4×C61—22no—
107C2×C4×C61—48no—
108C2×C4×C61C2×D412yes—
109C2×C4×C61C2×D412yes—
110C2×C4×C61#4114yescomplemented
111C22⋊D61—216no—
112C22⋊D61—44no—
113C2×Dic61—22no—
114C2×Dic61—22no—
115C2×Dic61—21no—
116C2×Dic61—21no—
117C2×Dic61—21no—
118C2×Dic61—22no—
119C2×Dic61—22no—
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61C2×D414yes—
123D244—28no—
124D244—48no—
125C4×D61—216no—
126Dic122—28no—
127C22×C61—22no—
128C22×C61—22no—
129C22×C61—24no—
130C22×C61—24no—
131C22×C61#12014yes—
132C22×C61C22×D412yes—
133C22×C61C22×D411yescharacteristic
134C22×C61C2×#4112yes—
135C22×C61H(5,𝔽2)11yescharacteristic
136C22×C612−1+411yescharacteristic
137C2×D61—24no—
138C2×D61—24no—
139C2×D61—24no—
140C2×D61—42no—
141C2×D61—42no—
142C2×D61—42no—
143C2×D61—42no—
144C2×D61—41no—
145C2×D61—41no—
146C2×D61—41no—
147C2×D61—42no—
148C2×D61—42no—
149C4×C61—22no—
150C4×C61—22no—
151C4×C61—24no—
152C4×C61—42no—
153Dic61—24no—
154Dic61—41no—
155Dic61—41no—
156Dic61—41no—
157#2430—611nomaximal, Sylow
158C2×C61—24no—
159C2×C61C2×#12011yescharacteristic
160C2×C61#53211yescharacteristic
161C2×C61#53711yescharacteristic
162C2×C61#54612yes—
163C2×C61#54712yes—
164D61—44no—
165D61—81no—
166C22×#41—611no—
167C2×#123—611no—
168C2×#121—612no—
169#395—611no—
170#394—611no—
171#393—611no—
172#392—611no—
173#386—612no—
174#386—612no—
175#385—612no—
176C2×#95D6111yescharacteristic, complemented
177C61#243011yescharacteristic, complemented, Sylow
178C2×#41—1228no—
179C2×#41—1224no—
180C22×Q8—611no—
181C22×D4—612no—
182C22×D4—611no—
183C22×D4—611no—
184C22×D4—612no—
185C23×C4—612no—
186C23×C4C2×D6112yes—
187C23×C4C2×D6111yescharacteristic
188#123—1224no—
189#121—1228no—
190C2×C4⋊C4—612no—
191C2×C4⋊C4—611no—
192C2×C4⋊C4—611no—
193C2×C22⋊C4—611no—
194C2×C22⋊C4—612no—
195C2×C22⋊C4—612no—
196C2×C22⋊C4—611no—
197C2×C22⋊C4—611no—
198C2×C22⋊C4—612no—
199C2×C22⋊C4—612no—
200#95—612no—
201#95—612no—
202#95C2×D6112yes—
203#95C2×D6111yescharacteristic
204#95C2×D6111yescharacteristic
205C24—612no—
206C24—611no—
207C24C22×D6111yescharacteristic
208#41—12232no—
209C2×Q8—1224no—
210C2×Q8—1222no—
211C2×D4—618no—
212C2×D4—1224no—
213C2×D4—1224no—
214C2×D4—1224no—
215C2×D4—1224no—
216C2×D4—1222no—
217C2×D4—1224no—
218C2×D4—1222no—
219C2×D4—1224no—
220C2×D4—2442no—
221C22×C4—24no—
222C22×C4—24no—
223C22×C4—24no—
224C22×C4—42no—
225C22×C4—612no—
226C22×C4—611no—
227C22×C4—611no—
228C22×C4—611no—
229C22×C4—1224no—
230C22×C4—1224no—
231C22×C4—1224no—
232C22×C4D24414yescomplemented
233C22×C4C22×D6112yes—
234C22×C4C22×D6111yescharacteristic
235C22×C4C22×D6111yescharacteristic
236C22×C4C22×D6112yes—
237C4⋊C4—1224no—
238C4⋊C4—1222no—
239C4⋊C4—1222no—
240C22⋊C4—1224no—
241C22⋊C4—1224no—
242C22⋊C4—1222no—
243C22⋊C4—1222no—
244C22⋊C4—1222no—
245C22⋊C4—1224no—
246C22⋊C4—2442no—
247C23—22no—
248C23—21no—
249C23—21no—
250C23—614no—
251C23—1222no—
252C23—1222no—
253C23—1222no—
254C23—1222no—
255C23—1222no—
256C23—1222no—
257C23—1222no—
258C23—1221no—
259C23—1222no—
260C23—1221no—
261C23—1221no—
262C23C2×D24412yes—
263C23D4×D6114yes—
264C23C23×D6111yescharacteristic
265Q8—1228no—
266D4—1228no—
267D4—12216no—
268D4—2448no—
269D4—2444no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—28no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—48no—
279C2×C4—614no—
280C2×C4—12216no—
281C2×C4—1222no—
282C2×C4—1222no—
283C2×C4—1222no—
284C2×C4—1221no—
285C2×C4—1221no—
286C2×C4—1221no—
287C2×C4—1222no—
288C2×C4—1221no—
289C2×C4—1221no—
290C2×C4C2×D24412yes—
291C2×C4C2×D24412yes—
292C2×C4#1175822214yescomplemented
293C22—22no—
294C22—22no—
295C22—24no—
296C22—24no—
297C22—1224no—
298C22—1224no—
299C22—1224no—
300C22—2441no—
301C22—2441no—
302C22—2441no—
303C22—2442no—
304C22—2442no—
305C22—2442no—
306C22—2442no—
307C22—2442no—
308C22—2442no—
309C22#1451974714yes—
310C22C2×D4×D6112yes—
311C22C22×D24411yescharacteristic
312C22C2×#1175822212yes—
313C22#1451982211yescharacteristic
314C22#1451982511yescharacteristic
315C4—22no—
316C4—22no—
317C4—24no—
318C4—42no—
319C4—1224no—
320C4—2441no—
321C4—2441no—
322C4—2441no—
323C2—24no—
324C2—4881no—
325C2—2444no—
326C2C2×#1451974711yescharacteristic
327C2#1684031211yescharacteristic
328C2#1684034311yescharacteristic
329C2#1684040212yes—
330C2#1684041312yes—
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC2×#95×C61C2
hypercenterC2×#95D61
hypocenterC61#2430
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. C22×#11758222C2semidirect
2. C2×#14519760C2semidirect
3. C2×#14519751C2semidirect
4. #16839683C2semidirect
5. #16839680C2semidirect
6. #16839675C2semidirect
7. #16839672C2semidirect
8. #16839641C2semidirect
9. #16839640C2semidirect
10. #16839636C2semidirect
11. C2×#95×C61C2semidirect
46. C22×C4×C61D4semidirect
55. C2×C22⋊D61D4semidirect
110. C2×C4×C61#41semidirect
176. C2×#95D61semidirect
177. C61#2430semidirect
232. C22×C4D244semidirect
292. C2×C4#11758222semidirect