Finite Group Databasebeta

← #21455816

Subgroups — #21455816

Order 7808.

492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#16840307C211yesmaximal, characteristic, complemented
2C2×#14519739C211yesmaximal, characteristic, complemented
3#16840075C211yesmaximal, characteristic, complemented
4#16840041C212yesmaximal, complemented
5#16839956C212yesmaximal, complemented
6#16839898C211yesmaximal, characteristic, complemented
7#16839895C211yesmaximal, characteristic, complemented
8#16839844C212yesmaximal, complemented
9#16839842C212yesmaximal, complemented
10#16839812C211yesmaximal, characteristic, complemented
11C61×#480C211yesmaximal, characteristic, complemented
12C2×#11758224—21no—
13C22×D244C2211yescharacteristic
14C22×C4×D61—21no—
15C2×D488C2212yes—
16C2×#11758199C2212yes—
17#14519776C2211yescharacteristic, complemented
18#14519773C2211yescharacteristic, complemented
19#14519763—21no—
20#14519751C2211yescharacteristic
21#14519749—21no—
22D4×Dic61C2211yescharacteristic, complemented
23#14519739—21no—
24#14519739—21no—
25#14519739C2212yes—
26#14519739C2212yes—
27#14519739C2211yescharacteristic, complemented
28#14519737—21no—
29C2×#11758198—21no—
30C2×C4×Dic61C2211yescharacteristic
31#14519710C2212yescomplemented
32#14519706C2212yescomplemented
33#14519699C2212yes—
34#14519697C2212yes—
35#14519697C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37C8×Dic61C2212yescomplemented
38#121×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#107×C61C2212yescomplemented
41#102×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61—21no—
44C2×D4×C61—21no—
45C2×D4×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C2311yescharacteristic
48C2×C22⋊D61—21no—
49C2×C22⋊D61—21no—
50C2×C22⋊D61—21no—
51C22×Dic61—21no—
52C22×Dic61D411yescharacteristic
53C22×Dic61D411yescharacteristic
54#11758224—44no—
55C2×D244—21no—
56C2×D244—24no—
57C2×D244C2311yescharacteristic
58C2×D244C2312yes—
59C2×C4×D61—22no—
60C2×C4×D61—22no—
61C2×C4×D61—21no—
62C2×C4×D61—44no—
63C2×Dic122—21no—
64C2×C8×C61C2312yes—
65C4⋊C4×C61—21no—
66C4⋊C4×C61C2312yes—
67C4⋊C4×C61C2311yescharacteristic
68C22⋊C4×C61—21no—
69C22⋊Dic61—21no—
70#11758199—24no—
71#11758198—21no—
72#11758198—22no—
73#11758198—22no—
74#11758198—21no—
75C4⋊Dic61C2311yescharacteristic
76#11758196—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C4×Dic61C2311yescharacteristic
81C2×#92418C2312yes—
82D488—24no—
83C23×C61—21no—
84C23×C61C2×D411yescharacteristic
85C22×D61—24no—
86C22×D61—22no—
87C22×D61—21no—
88C22×D61—42no—
89C22×D61—42no—
90D4×C61—22no—
91D4×C61—42no—
92C2×C4×C61—22no—
93C2×C4×C61—21no—
94C2×C4×C61—22no—
95C2×C4×C61—42no—
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2411yescharacteristic
98C22⋊D61—42no—
99C22⋊D61—42no—
100C22⋊D61—42no—
101C2×Dic61—21no—
102C2×Dic61—41no—
103C2×Dic61—42no—
104C2×Dic61D814yescomplemented
105C2×Dic61C2×D411yescharacteristic
106C2×Dic61C2×D411yescharacteristic
107C2×Dic61C2×D411yescharacteristic
108C2×Dic61C2×D411yescharacteristic
109D244—24no—
110D244—22no—
111D244—22no—
112D244#4114yescomplemented
113C4×D61—44no—
114C4×D61—44no—
115C4×D61—42no—
116Dic122—42no—
117C8×C61—22no—
118#92418—22no—
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61—41no—
124C22×C61C2×D812yes—
125C22×C61C22×D411yescharacteristic
126C2×D61—24no—
127C2×D61—48no—
128C2×D61—42no—
129C2×D61—42no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C4×C61—21no—
134C4×C61—41no—
135C4×C61—42no—
136C4×C61C2×#4112yes—
137Dic61—21no—
138Dic61—21no—
139Dic61—41no—
140Dic61C2×D812yes—
141Dic61C2×D812yes—
142#3100—611nomaximal, Sylow
143C2×C61—22no—
144C2×C61—81no—
145C2×C61#52511yescharacteristic
146C2×C61C22×D811yescharacteristic
147C2×C61#57511yescharacteristic
148D61—44no—
149D61—81no—
150#532—611no—
151C2×C4×D4—611no—
152#480—611no—
153#480D6111yescharacteristic, complemented
154#474—612no—
155#459—612no—
156#447—611no—
157#447—611no—
158C4×D8—612no—
159C4×D8—612no—
160#431—611no—
161C61#310011yescharacteristic, complemented, Sylow
162C2×#41—1221no—
163C22×D4—611no—
164C23×C4—1221no—
165C2×D8—612no—
166C2×D8—612no—
167C4⋊Q8—611no—
168#127—611no—
169#124—1221no—
170#121—611no—
171#121—1221no—
172#121C2×D6111yescharacteristic
173C4×D4—611no—
174C4×D4—612no—
175C4×D4—612no—
176C4×D4—611no—
177C4×D4—1221no—
178C4×D4—1221no—
179C4×D4—1221no—
180C2×C4⋊C4C2×D6111yescharacteristic
181C2×C22⋊C4—1221no—
182C2×C42—611no—
183#107—612no—
184#107C2×D6112yescomplemented
185C4⋊C8—612no—
186#102—612no—
187#102—612no—
188#102—612no—
189#102C2×D6112yescomplemented
190C22⋊C8—611no—
191C22⋊C8C2×D6111yescharacteristic
192C4×C8—612no—
193C24—1221no—
194#41—2444no—
195C2×Q8—1221no—
196C2×D4—21no—
197C2×D4—612no—
198C2×D4—611no—
199C2×D4—1224no—
200C2×D4—1221no—
201C2×D4—1221no—
202C2×D4—1221no—
203C2×D4—1221no—
204C2×D4C22×D6111yescharacteristic
205C22×C4—21no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1222no—
209C22×C4—1222no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—2444no—
213C22×C4C22×D6111yescharacteristic
214D8—1224no—
215D8—1224no—
216C2×C8—612no—
217C2×C8C22×D6112yes—
218C4⋊C4—21no—
219C4⋊C4—611no—
220C4⋊C4—1221no—
221C4⋊C4C22×D6111yescharacteristic
222C4⋊C4C22×D6112yes—
223C22⋊C4—21no—
224C22⋊C4—1222no—
225C22⋊C4—1222no—
226C22⋊C4—1221no—
227C22⋊C4—1221no—
228C22⋊C4—1221no—
229C42—611no—
230C42—611no—
231C42—611no—
232C42—611no—
233C23—21no—
234C23—1224no—
235C23—1222no—
236C23—1221no—
237C23—2442no—
238C23—2442no—
239C23D4×D6111yescharacteristic
240Q8—2442no—
241D4—22no—
242D4—42no—
243D4—614no—
244D4—1224no—
245D4—1222no—
246D4—1222no—
247D4—2442no—
248D4—2442no—
249D4—2442no—
250C2×C4—22no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—42no—
254C2×C4—611no—
255C2×C4—611no—
256C2×C4—614no—
257C2×C4—611no—
258C2×C4—611no—
259C2×C4—1221no—
260C2×C4—2444no—
261C2×C4—2444no—
262C2×C4—2442no—
263C2×C4—2442no—
264C2×C4—2441no—
265C2×C4D4×D6111yescharacteristic
266C2×C4C23×D6111yescharacteristic
267C8—22no—
268C8—1222no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—1224no—
275C22—2448no—
276C22—2441no—
277C22—2441no—
278C22—2441no—
279C22—2442no—
280C22—2442no—
281C22D8×D6112yes—
282C22C2×D4×D6111yescharacteristic
283C4—21no—
284C4—42no—
285C4—41no—
286C4—612no—
287C4—612no—
288C4—1221no—
289C4—1221no—
290C4—2441no—
291C4#41×D6112yes—
292C2—22no—
293C2—81no—
294C2—4881no—
295C2—2444no—
296C2#1684027011yescharacteristic
297C2C2×D8×D6111yescharacteristic
298C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#480C2
socleC22×C61C22×D4
hypercenter#480D61
hypocenterC61#3100
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #16840307C2semidirect
2. C2×#14519739C2semidirect
3. #16840075C2semidirect
4. #16840041C2semidirect
5. #16839956C2semidirect
6. #16839898C2semidirect
7. #16839895C2semidirect
8. #16839844C2semidirect
9. #16839842C2semidirect
10. #16839812C2semidirect
11. C61×#480C2semidirect
17. #14519776C22semidirect
18. #14519773C22semidirect
22. D4×Dic61C22semidirect
27. #14519739C22semidirect
31. #14519710C22semidirect
32. #14519706C22semidirect
35. #14519697C22semidirect
37. C8×Dic61C22semidirect
40. #107×C61C22semidirect
41. #102×C61C22semidirect
104. C2×Dic61D8semidirect
112. D244#41semidirect
153. #480D61semidirect
161. C61#3100semidirect
184. #107C2×D61semidirect
189. #102C2×D61semidirect