Finite Group Databasebeta

← #21455615

Subgroups — #21455615

Order 7808.

440 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 135 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#16840315C211yesmaximal, characteristic, complemented
2C2×#14519739C211yesmaximal, characteristic
3#16840065C212yesmaximal, complemented
4#16840061C212yesmaximal, complemented
5#16840051C212yesmaximal, complemented
6#16840041C212yesmaximal, complemented
7#16839802C211yesmaximal, characteristic, complemented
8#16839785C211yesmaximal, characteristic, complemented
9#16839768C211yesmaximal, characteristic
10#16839766C211yesmaximal, characteristic
11C61×#428C211yesmaximal, characteristic, complemented
12C22×D244C2211yescharacteristic
13C22×C4×D61—21no—
14C2×#11758194C2211yescharacteristic
15#14519776C2211yescharacteristic, complemented
16#14519776C2211yescharacteristic, complemented
17#14519768C2211yescharacteristic, complemented
18#14519768C2211yescharacteristic, complemented
19#14519754—21no—
20#14519754—21no—
21C4×Dic122—21no—
22C4×Dic122—21no—
23#14519739—21no—
24#14519739—21no—
25#14519739C2212yes—
26#14519739C2212yes—
27#14519736C2211yescharacteristic
28C2×#11758198—21no—
29C2×C4×Dic61C2211yescharacteristic
30#14519710C2212yescomplemented
31#14519708C2212yescomplemented
32#14519706C2212yescomplemented
33#14519706C2212yescomplemented
34#14519699C2212yes—
35#14519699C2212yes—
36#14519697C2212yes—
37#14519697C2212yes—
38C2×M16×C61C2211yescharacteristic
39#117×C61C2211yescharacteristic
40C2×C4⋊C4×C61C2211yescharacteristic
41#107×C61C2212yescomplemented
42#106×C61C2212yescomplemented
43C23×D61—21no—
44C22×C4×C61—21no—
45C22×C4×C61C2311yescharacteristic
46C22×Dic61D411yescharacteristic
47C22×Dic61D411yescharacteristic
48C2×D244—21no—
49C2×D244—22no—
50C2×D244Q814yescomplemented
51C2×D244C2312yes—
52C2×C4×D61—22no—
53C2×C4×D61—22no—
54C2×C4×D61—44no—
55C2×Dic122—21no—
56C2×Dic122—21no—
57M16×C61—22no—
58C2×C8×C61C2312yes—
59C4⋊C4×C61—21no—
60C4⋊C4×C61C2311yescharacteristic
61C4⋊C4×C61C2312yes—
62C4⋊C4×C61C2311yescharacteristic
63C22⋊C4×C61—21no—
64C42×C61—21no—
65C22⋊Dic61—21no—
66#11758198—22no—
67#11758198—22no—
68C4⋊Dic61—21no—
69C4⋊Dic61—21no—
70C4⋊Dic61C2311yescharacteristic
71C4⋊Dic61C2311yescharacteristic
72#11758196—21no—
73#11758196—21no—
74#11758196—21no—
75#11758196—21no—
76C4×Dic61—21no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C4×Dic61C2311yescharacteristic
81#11758194—22no—
82C2×#92418C2312yes—
83C23×C61C2×D411yescharacteristic
84C22×D61—24no—
85C22×D61—22no—
86C22×D61—42no—
87C22×D61—42no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—42no—
92C2×C4×C61C2×D411yescharacteristic
93C2×C4×C61C2×Q812yes—
94C2×C4×C61#4112yes—
95C2×C4×C61C2411yescharacteristic
96C2×Dic61—22no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C2×Dic61C2×D411yescharacteristic
103C2×Dic61C2×D411yescharacteristic
104D244—24no—
105D244—22no—
106D244C2×Q814yes—
107C4×D61—44no—
108C4×D61—44no—
109Dic122—42no—
110Dic122—42no—
111C8×C61—22no—
112#92418—22no—
113C22×C61—21no—
114C22×C61—21no—
115C22×C61C22⋊Q812yes—
116C22×C61C22×D411yescharacteristic
117C2×D61—24no—
118C2×D61—48no—
119C2×D61—42no—
120C2×D61—42no—
121C4×C61—41no—
122C4×C61—42no—
123C4×C61—41no—
124C4×C61C22⋊Q812yes—
125C4×C61C22×Q811yescharacteristic
126C4×C61C2×#4111yescharacteristic
127Dic61—21no—
128Dic61—21no—
129Dic61—21no—
130Dic61—41no—
131Dic61—41no—
132Dic61AGL(1,ℤ/8)12yes—
133#3077—611nomaximal, Sylow
134C2×C61—22no—
135C2×C61C2×C22⋊Q811yescharacteristic
136C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C61#57511yescharacteristic
138D61—44no—
139#533—611no—
140C2×C4×D4—611no—
141#478—612no—
142#478—612no—
143#476—612no—
144#474—612no—
145#428—611no—
146#428D6111yescharacteristic, complemented
147#423—611no—
148#418—611no—
149#418—611no—
150C61#307711yescharacteristic, complemented, Sylow
151C22×D4—611no—
152C23×C4—1221no—
153C2×M16—611no—
154C2×M16C2×D6111yescharacteristic
155C4⋊Q8—611no—
156C4⋊Q8—611no—
157#125—611no—
158#125—611no—
159C22⋊Q8—1221no—
160C22⋊Q8—1221no—
161C4×Q8—1221no—
162C4×Q8—1221no—
163C4×D4—612no—
164C4×D4—612no—
165C4×D4—1221no—
166C4×D4—1221no—
167#117—611no—
168#117C2×D6111yescharacteristic
169C2×C4⋊C4C2×D6111yescharacteristic
170C2×C22⋊C4—1221no—
171C2×C42—611no—
172#107—612no—
173#107C2×D6112yescomplemented
174#106—612no—
175#106C2×D6112yescomplemented
176C4⋊C8—612no—
177C4⋊C8—612no—
178#102—612no—
179#102—612no—
180#102—612no—
181#102—612no—
182C24—1221no—
183C2×Q8—1221no—
184C2×Q8—1221no—
185C2×D4—614no—
186C2×D4—612no—
187C2×D4—1222no—
188C2×D4—1221no—
189C22×C4—21no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—1222no—
193C22×C4—1222no—
194C22×C4—2444no—
195C22×C4C22×D6111yescharacteristic
196M16—22no—
197M16—1222no—
198C2×C8—612no—
199C2×C8C22×D6112yes—
200C4⋊C4—21no—
201C4⋊C4—611no—
202C4⋊C4—611no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4—1221no—
206C4⋊C4—1221no—
207C4⋊C4—1221no—
208C4⋊C4—1221no—
209C4⋊C4C22×D6111yescharacteristic
210C4⋊C4C22×D6111yescharacteristic
211C4⋊C4C22×D6112yes—
212C22⋊C4—21no—
213C22⋊C4—1222no—
214C22⋊C4—1222no—
215C22⋊C4—1221no—
216C42—21no—
217C42—611no—
218C42—611no—
219C42—611no—
220C42—611no—
221C42—1221no—
222C23—1222no—
223C23—1224no—
224C23—2442no—
225C23—2442no—
226C23D4×D6111yescharacteristic
227Q8—2442no—
228Q8—2442no—
229D4—614no—
230D4—1222no—
231D4—1224no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—611no—
237C2×C4—611no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1221no—
243C2×C4—2444no—
244C2×C4—2444no—
245C2×C4—2441no—
246C2×C4#1175822212yes—
247C2×C4D4×D6111yescharacteristic
248C2×C4Q8×D6112yes—
249C2×C4C23×D6111yescharacteristic
250C8—22no—
251C8—1222no—
252C22—21no—
253C22—21no—
254C22—1224no—
255C22—2448no—
256C22—2442no—
257C22—2442no—
258C22#1451975512yes—
259C22C2×D4×D6111yescharacteristic
260C4—42no—
261C4—41no—
262C4—41no—
263C4—612no—
264C4—1221no—
265C4—1221no—
266C4—1221no—
267C4—2441no—
268C4—2441no—
269C4#1451975512yes—
270C4C2×Q8×D6111yescharacteristic
271C4C2×#1175822211yescharacteristic
272C2—22no—
273C2—2444no—
274C2C2×#1451975511yescharacteristic
275C2AGL(1,ℤ/8)×D6111yescharacteristic
276C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#428C2
socleC22×C61C22×D4
hypercenter#428D61
hypocenterC61#3077
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #16840315C2semidirect
3. #16840065C2semidirect
4. #16840061C2semidirect
5. #16840051C2semidirect
6. #16840041C2semidirect
7. #16839802C2semidirect
8. #16839785C2semidirect
11. C61×#428C2semidirect
15. #14519776C22semidirect
16. #14519776C22semidirect
17. #14519768C22semidirect
18. #14519768C22semidirect
30. #14519710C22semidirect
31. #14519708C22semidirect
32. #14519706C22semidirect
33. #14519706C22semidirect
41. #107×C61C22semidirect
42. #106×C61C22semidirect
50. C2×D244Q8semidirect
146. #428D61semidirect
150. C61#3077semidirect
173. #107C2×D61semidirect
175. #106C2×D61semidirect