Finite Group Databasebeta

← #21455762

Subgroups — #21455762

Order 7808.

410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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⋊Q8×D61C211yesmaximal, characteristic
2C2×#14519735C211yesmaximal, characteristic
3#16840106C212yesmaximal, complemented
4#16840102C212yesmaximal, complemented
5#16840098C211yesmaximal, characteristic, complemented
6#16840095C211yesmaximal, characteristic, complemented
7#16840092C211yesmaximal, characteristic, complemented
8#16839801C212yesmaximal, complemented
9#16839769C212yesmaximal, complemented
10#16839724C211yesmaximal, characteristic
11C61×#483C211yesmaximal, characteristic, complemented
12C2×Q8×D61C2211yescharacteristic
13C22×C4×D61C2211yescharacteristic
14C2×#11758189C2212yes—
15#14519757C2211yescharacteristic
16#14519756C2211yescharacteristic
17#14519755—21no—
18#14519754—21no—
19#14519753C2211yescharacteristic
20#14519735—21no—
21#14519735—21no—
22#14519735C2212yes—
23#14519735C2212yes—
24C2×C4⋊Dic61C2211yescharacteristic
25C4⋊C4×D61—21no—
26C4⋊C4×D61C2211yescharacteristic
27C2×#11758198—21no—
28C22⋊C4×D61—21no—
29C2×C4×Dic61—21no—
30#14519711C2212yescomplemented
31#14519710C2212yescomplemented
32#14519708C2212yescomplemented
33#14519702C2212yescomplemented
34#14519701C2212yescomplemented
35#14519700C2212yescomplemented
36C22⋊#92418C2211yescharacteristic
37#14519689C2212yes—
38C22⋊Q8×C61C2211yescharacteristic
39C2×C4⋊C4×C61C2211yescharacteristic
40#106×C61C2212yescomplemented
41#103×C61C2212yescomplemented
42C22⋊C8×C61C2211yescharacteristic
43C23×D61D411yescharacteristic
44C2×Q8×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C22×C4×C61C2311yescharacteristic
47C22×Dic61—21no—
48C22×Dic61D411yescharacteristic
49Q8×D61—24no—
50C2×C4×D61—24no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61D411yescharacteristic
54C2×C4×D61D411yescharacteristic
55C2×C4×D61C2311yescharacteristic
56C2×C4×D61C2311yescharacteristic
57C2×Dic122—21no—
58C2×Dic122C2311yescharacteristic
59C2×C8×C61C2312yes—
60C4⋊C4×C61—21no—
61C4⋊C4×C61—21no—
62C4⋊C4×C61C2312yes—
63C4⋊C4×C61C2311yescharacteristic
64C22⋊C4×C61—21no—
65C22⋊Dic61—21no—
66#11758198—21no—
67#11758198—21no—
68#11758198—22no—
69#11758198—22no—
70C4⋊Dic61—21no—
71C4⋊Dic61—21no—
72C4⋊Dic61C2312yes—
73C4⋊Dic61C2311yescharacteristic
74#11758196—21no—
75#11758196—21no—
76#11758196—21no—
77C4×Dic61—22no—
78C4×Dic61—22no—
79C2×#92418C2312yes—
80#11758189—24no—
81C23×C61C2×D411yescharacteristic
82C22×D61—22no—
83C22×D61—22no—
84C22×D61—41no—
85C22×D61C2×D411yescharacteristic
86C22×D61C2×D411yescharacteristic
87Q8×C61—22no—
88C2×C4×C61—22no—
89C2×C4×C61—22no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—42no—
93C2×C4×C61C2×D411yescharacteristic
94C2×C4×C61C2411yescharacteristic
95C2×Dic61—22no—
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—42no—
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C4×D61—22no—
103C4×D61—22no—
104C4×D61—22no—
105C4×D61—42no—
106C4×D61—42no—
107C4×D61#4114yes—
108Dic122—22no—
109Dic122—42no—
110C8×C61—22no—
111#92418—22no—
112C22×C61—21no—
113C22×C61—21no—
114C22×C61#13712yes—
115C22×C61C22×D411yescharacteristic
116C2×D61—21no—
117C2×D61—21no—
118C2×D61—21no—
119C2×D61—21no—
120C2×D61—21no—
121C2×D61—44no—
122C2×D61#12312yes—
123C4×C61—21no—
124C4×C61—41no—
125C4×C61—42no—
126C4×C61—41no—
127C4×C61C2×#4112yes—
128Dic61—21no—
129Dic61—41no—
130Dic61—41no—
131Dic61—42no—
132Dic61#12312yes—
133#3095—611nomaximal, Sylow
134C2×C61—22no—
135C2×C61C2×#12311yescharacteristic
136C2×C61C2×#13711yescharacteristic
137C2×C61#57511yescharacteristic
138D61—22no—
139D61—41no—
140C2×C22⋊Q8—611no—
141C2×#117—611no—
142#485—612no—
143#485—612no—
144#484—611no—
145#484—611no—
146#483—611no—
147#483D6111yescharacteristic, complemented
148#428—612no—
149#419—612no—
150#407—611no—
151C61#309511yescharacteristic, complemented, Sylow
152C22×Q8—611no—
153C23×C4—611no—
154C2×M16—612no—
155C22⋊Q8—611no—
156C22⋊Q8—611no—
157C22⋊Q8—611no—
158C22⋊Q8—1221no—
159C22⋊Q8—1221no—
160C22⋊Q8C2×D6111yescharacteristic
161#117—612no—
162#117—612no—
163#117—1221no—
164#117—1221no—
165C2×C4⋊C4—611no—
166C2×C4⋊C4—611no—
167C2×C4⋊C4—1221no—
168C2×C4⋊C4C2×D6111yescharacteristic
169C2×C22⋊C4—1221no—
170C2×C22⋊C4—1221no—
171C2×C42—1221no—
172#107—612no—
173#107—612no—
174#106—612no—
175#106C2×D6112yescomplemented
176#103—612no—
177#103—612no—
178#103—612no—
179#103C2×D6112yescomplemented
180C22⋊C8—611no—
181C22⋊C8—612no—
182C22⋊C8C2×D6111yescharacteristic
183C24—611no—
184C2×Q8—611no—
185C2×Q8—1221no—
186C2×Q8—1224no—
187C2×Q8C22×D6111yescharacteristic
188C22×C4—21no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—1224no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4C22×D6111yescharacteristic
199M16—1224no—
200C2×C8—612no—
201C2×C8C22×D6112yes—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—612no—
205C4⋊C4—611no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4—1221no—
210C4⋊C4—1221no—
211C4⋊C4C22×D6112yes—
212C4⋊C4C22×D6111yescharacteristic
213C22⋊C4—21no—
214C22⋊C4—1222no—
215C22⋊C4—1222no—
216C22⋊C4—1221no—
217C22⋊C4—1221no—
218C22⋊C4—1221no—
219C42—1222no—
220C42—1222no—
221C23—611no—
222C23—611no—
223C23—1222no—
224C23—1222no—
225C23—2441no—
226C23D4×D6111yescharacteristic
227Q8—22no—
228Q8—1222no—
229Q8—2442no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—611no—
236C2×C4—614no—
237C2×C4—611no—
238C2×C4—1222no—
239C2×C4—1222no—
240C2×C4—1222no—
241C2×C4—1222no—
242C2×C4—1222no—
243C2×C4—1221no—
244C2×C4—1221no—
245C2×C4—2442no—
246C2×C4—2442no—
247C2×C4—2442no—
248C2×C4D4×D6111yescharacteristic
249C2×C4C23×D6111yescharacteristic
250C8—22no—
251C8—1222no—
252C22—21no—
253C22—21no—
254C22—612no—
255C22—1221no—
256C22—1221no—
257C22—1221no—
258C22—1221no—
259C22—1221no—
260C22—2444no—
261C22#1451980612yes—
262C22C2×D4×D6111yescharacteristic
263C4—21no—
264C4—41no—
265C4—42no—
266C4—41no—
267C4—612no—
268C4—1221no—
269C4—2441no—
270C4—2441no—
271C4—2442no—
272C4#41×D6112yes—
273C2—22no—
274C2—1222no—
275C2—2441no—
276C2#123×D6111yescharacteristic
277C2C2×#1451980611yescharacteristic
278C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#483C2
socleC22×C61C22×D4
hypercenter#483D61
hypocenterC61#3095
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #16840106C2semidirect
4. #16840102C2semidirect
5. #16840098C2semidirect
6. #16840095C2semidirect
7. #16840092C2semidirect
8. #16839801C2semidirect
9. #16839769C2semidirect
11. C61×#483C2semidirect
30. #14519711C22semidirect
31. #14519710C22semidirect
32. #14519708C22semidirect
33. #14519702C22semidirect
34. #14519701C22semidirect
35. #14519700C22semidirect
40. #106×C61C22semidirect
41. #103×C61C22semidirect
147. #483D61semidirect
151. C61#3095semidirect
175. #106C2×D61semidirect
179. #103C2×D61semidirect