Finite Group Databasebeta

← #21458055

Subgroups — #21458055

Order 7808.

460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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
1D4×D244C211yesmaximal, characteristic, complemented
2#16840110C211yesmaximal, characteristic, complemented
3#16840086C212yesmaximal, complemented
4#16840049C211yesmaximal, characteristic, complemented
5#16840013C212yesmaximal, complemented
6#16839957C211yesmaximal, characteristic, complemented
7#16839895C212yesmaximal, complemented
8C4×#11758199C211yesmaximal, characteristic, complemented
9#16839840C211yesmaximal, characteristic, complemented
10#16839766C212yesmaximal, complemented
11C61×#555C211yesmaximal, characteristic, complemented
12C22×D244C2212yes—
13C2×D4×D61—21no—
14C2×#11758199C2211yescharacteristic
15C2×#11758199C2212yescomplemented
16C2×#11758194C2212yescomplemented
17#14519774C2211yescharacteristic
18#14519752—21no—
19#14519751C2212yes—
20#14519747—22no—
21C4×D244C2211yescharacteristic
22#14519710C2211yescharacteristic, complemented
23#14519708C2212yescomplemented
24C4⋊#92418C2211yescharacteristic, complemented
25#14519698C2211yescharacteristic, complemented
26#14519697C2211yescharacteristic
27#14519697C2212yes—
28#14519697C2212yescomplemented
29#14519697C2212yescomplemented
30#14519697C2212yescomplemented
31C22⋊#92418C2212yescomplemented
32C4×#92418C2211yescharacteristic, complemented
33C4⋊Q8×C61C2211yescharacteristic, complemented
34#124×C61—22no—
35#121×C61—21no—
36#121×C61C2212yescomplemented
37C4×D4×C61C2211yescharacteristic
38C4×D4×C61C2211yescharacteristic, complemented
39#117×C61—21no—
40#117×C61C2212yescomplemented
41C23×D61—22no—
42C2×Q8×C61—21no—
43C2×D4×C61—22no—
44C2×D4×C61D411yescharacteristic
45C2×D4×C61C2311yescharacteristic
46C22×C4×C61—21no—
47C22×C4×C61C2312yes—
48C2×C22⋊D61—22no—
49D4×D61—44no—
50C2×D244—24no—
51C2×D244—21no—
52C2×D244—22no—
53C2×D244—21no—
54C2×D244—42no—
55C2×D244C2312yes—
56C2×D244C2311yescharacteristic
57C2×C4×D61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61D411yescharacteristic
60C4⋊C4×C61C2311yescharacteristic
61C4⋊C4×C61C2312yes—
62C22⋊C4×C61—22no—
63C22⋊C4×C61—22no—
64C22⋊C4×C61—21no—
65C22⋊C4×C61D412yes—
66C42×C61—22no—
67C42×C61C2311yescharacteristic
68#11758199—22no—
69#11758199—42no—
70#11758198—21no—
71#11758198—22no—
72C4⋊Dic61C2311yescharacteristic
73#11758194—42no—
74C2×#92418C2311yescharacteristic
75C2×#92418C2311yescharacteristic
76C2×#92418C2312yes—
77C23×C61—21no—
78C23×C61C2×D412yes—
79C22×D61—21no—
80C22×D61—22no—
81C22×D61—44no—
82C22×D61—44no—
83C22×D61—82no—
84Q8×C61—81no—
85D4×C61—22no—
86D4×C61—21no—
87D4×C61—21no—
88D4×C61—82no—
89C2×C4×C61—22no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—22no—
93C2×C4×C61—42no—
94C2×C4×C61C2×D412yes—
95C2×C4×C61C2×D411yescharacteristic
96C2×C4×C61C2×D411yescharacteristic
97C2×C4×C61C2411yescharacteristic
98C22⋊D61—44no—
99C2×Dic61—21no—
100D244—22no—
101D244—21no—
102D244—22no—
103D244—44no—
104D244—42no—
105D244—81no—
106D244#4112yes—
107C4×D61—42no—
108#92418—21no—
109#92418—21no—
110#92418—22no—
111C22×C61—22no—
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61C22×D411yescharacteristic
118C2×D61—22no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—42no—
122C2×D61—42no—
123C2×D61—42no—
124C2×D61—88no—
125C4×C61—22no—
126C4×C61—21no—
127C4×C61—41no—
128C4×C61—42no—
129C4×C61AGL(1,ℤ/8)12yes—
130C4×C61C2×#4111yescharacteristic
131C4×C61H(5,𝔽2)11yescharacteristic
132Dic61—41no—
133#3325—611nomaximal, Sylow
134C2×C61—42no—
135C2×C61—81no—
136C2×C61#54611yescharacteristic
137C2×C61C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C61#57611yescharacteristic
139D61—42no—
140D61—82no—
141#555D6111yescharacteristic, complemented
142D42—611no—
143#486—611no—
144#482—612no—
145#476—611no—
146#469—612no—
147#459—611no—
148#447—612no—
149C4×D8—611no—
150#436—611no—
151#418—612no—
152C61#332511yescharacteristic, complemented, Sylow
153C22×D4—612no—
154C22×D4—1221no—
155C2×D8—611no—
156C2×D8—612no—
157C2×M16—612no—
158C4⋊Q8C2×D6111yescharacteristic, complemented
159#127—611no—
160#124—22no—
161#121—21no—
162#121—612no—
163#121—1221no—
164#121C2×D6112yescomplemented
165#120—1222no—
166C4×D4—611no—
167C4×D4C2×D6111yescharacteristic
168C4×D4C2×D6111yescharacteristic, complemented
169#117—21no—
170#117C2×D6112yescomplemented
171#107—611no—
172#106—612no—
173C4⋊C8—611no—
174#102—611no—
175#102—611no—
176#102—612no—
177#102—612no—
178#102—612no—
179#102—612no—
180C22⋊C8—612no—
181C4×C8—611no—
182C24—1222no—
183C2×Q8—21no—
184C2×D4—22no—
185C2×D4—611no—
186C2×D4—612no—
187C2×D4—1224no—
188C2×D4—1222no—
189C2×D4—1221no—
190C2×D4—1222no—
191C2×D4—1221no—
192C2×D4—2442no—
193C2×D4—2444no—
194C2×D4C22⋊D6111yescharacteristic
195C2×D4C22×D6111yescharacteristic
196C22×C4—21no—
197C22×C4—1221no—
198C22×C4C22×D6112yes—
199D8—1222no—
200D8—2442no—
201M16—2442no—
202C2×C8—611no—
203C2×C8—611no—
204C2×C8—612no—
205C4⋊C4—21no—
206C4⋊C4—611no—
207C4⋊C4C22⋊D6111yescharacteristic
208C4⋊C4C22×D6112yes—
209C4⋊C4C22×D6111yescharacteristic
210C22⋊C4—22no—
211C22⋊C4—22no—
212C22⋊C4—21no—
213C22⋊C4—1221no—
214C22⋊C4—1222no—
215C22⋊C4C22⋊D6112yes—
216C42—22no—
217C42C22×D6111yescharacteristic
218C23—21no—
219C23—1221no—
220C23—1222no—
221C23—4882no—
222C23—2444no—
223C23—2444no—
224C23C2×C22⋊D6112yes—
225Q8—81no—
226D4—21no—
227D4—21no—
228D4—22no—
229D4—82no—
230D4—612no—
231D4—1222no—
232D4—1221no—
233D4—1222no—
234D4—4881no—
235D4—2444no—
236D4—2444no—
237D4—2442no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—1221no—
244C2×C4—2442no—
245C2×C4C2×C22⋊D6112yes—
246C2×C4C2×C22⋊D6111yescharacteristic
247C2×C4C2×C22⋊D6111yescharacteristic
248C2×C4C23×D6111yescharacteristic
249C8—1221no—
250C8—1221no—
251C8—1222no—
252C22—22no—
253C22—22no—
254C22—22no—
255C22—41no—
256C22—41no—
257C22—41no—
258C22—1222no—
259C22—4888no—
260C22—2442no—
261C22—2442no—
262C22—2442no—
263C22—2441no—
264C22—2441no—
265C22C22×C22⋊D6111yescharacteristic
266C4—21no—
267C4—22no—
268C4—41no—
269C4—42no—
270C4—2441no—
271C4#1451980212yes—
272C4#41×D6111yescharacteristic
273C4#1451982311yescharacteristic
274C2—42no—
275C2—81no—
276C2—4882no—
277C2—2442no—
278C2#1684040011yescharacteristic
279C2C2×#1451980211yescharacteristic
280C2#1684056511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#555C2
socleC22×C61C22×D4
hypercenter#555D61
hypocenterC61#3325
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #555

Complements

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

NH ≅ G/Ntype
1. D4×D244C2semidirect
2. #16840110C2semidirect
3. #16840086C2semidirect
4. #16840049C2semidirect
5. #16840013C2semidirect
6. #16839957C2semidirect
7. #16839895C2semidirect
8. C4×#11758199C2semidirect
9. #16839840C2semidirect
10. #16839766C2semidirect
11. C61×#555C2semidirect
15. C2×#11758199C22semidirect
16. C2×#11758194C22semidirect
22. #14519710C22semidirect
23. #14519708C22semidirect
24. C4⋊#92418C22semidirect
25. #14519698C22semidirect
28. #14519697C22semidirect
29. #14519697C22semidirect
30. #14519697C22semidirect
31. C22⋊#92418C22semidirect
32. C4×#92418C22semidirect
33. C4⋊Q8×C61C22semidirect
36. #121×C61C22semidirect
38. C4×D4×C61C22semidirect
40. #117×C61C22semidirect
141. #555D61semidirect
152. C61#3325semidirect
158. C4⋊Q8C2×D61semidirect
164. #121C2×D61semidirect
168. C4×D4C2×D61semidirect
170. #117C2×D61semidirect