Finite Group Databasebeta

← #21455892

Subgroups — #21455892

Order 7808.

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

normal subgroups only

This group has 390 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
1#16840317C211yesmaximal, characteristic, complemented
2C4×#11758224C211yesmaximal, characteristic
3#16840105C212yesmaximal, complemented
4#16840044C211yesmaximal, characteristic, complemented
5#16839973C211yesmaximal, characteristic, complemented
6#16839967C211yesmaximal, characteristic, complemented
7#16839925C212yesmaximal
8#16839856C212yesmaximal, complemented
9#16839853C212yesmaximal, complemented
10#16839814C211yesmaximal, characteristic, complemented
11C61×#474C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C2×Dic244C2212yes—
14C2×#11758200C2212yes—
15#14519777C2211yescharacteristic
16#14519768—21no—
17#14519757C2212yes—
18#14519753—21no—
19Q8×Dic61—21no—
20C4×Dic122C2211yescharacteristic
21#14519742C2211yescharacteristic
22#14519742C2212yes—
23D4×Dic61C2211yescharacteristic
24C4×C22⋊D61—21no—
25#14519737—21no—
26#14519735—21no—
27#14519735C2211yescharacteristic
28#14519733—21no—
29C2×C4×Dic61—21no—
30C42×D61C2211yescharacteristic
31#14519708C2212yes—
32C4⋊#92418C2211yescharacteristic
33#14519702C2212yes—
34#14519700C2212yes—
35#14519700C2212yes—
36#14519689C2212yes—
37C8×Dic61C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×D4×C61C2211yescharacteristic
40#107×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#102×C61C2212yes—
43C2×Q8×C61—21no—
44C2×D4×C61C2311yescharacteristic
45C22×C4×C61—21no—
46C2×C22⋊D61—21no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49#11758224—22no—
50#11758224—22no—
51C2×C4×D61D411yescharacteristic
52C2×C4×D61D411yescharacteristic
53C2×C4×D61C2311yescharacteristic
54C2×Dic122C2312yes—
55C2×Dic122C2311yescharacteristic
56C2×C8×C61C2312yes—
57C4⋊C4×C61—21no—
58C4⋊C4×C61C2312yes—
59C4⋊C4×C61C2311yescharacteristic
60C22⋊C4×C61—21no—
61C42×C61C2311yescharacteristic
62C22⋊Dic61—21no—
63#11758200—24no—
64#11758198—22no—
65#11758198—21no—
66C4⋊Dic61—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—22no—
69C4⋊Dic61C2311yescharacteristic
70#11758196—21no—
71#11758196—21no—
72#11758196—22no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—21no—
76C4×Dic61—22no—
77C4×Dic61D411yescharacteristic
78C4×Dic61D411yescharacteristic
79C4×Dic61C2311yescharacteristic
80C2×#92418C2312yes—
81Dic244—24no—
82C23×C61—21no—
83C22×D61C2×D411yescharacteristic
84Q8×C61—42no—
85D4×C61—21no—
86D4×C61#4112yes—
87C2×C4×C61—21no—
88C2×C4×C61—22no—
89C2×C4×C61—42no—
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2×D411yescharacteristic
92C2×C4×C61C2411yescharacteristic
93C22⋊D61—24no—
94C2×Dic61—24no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—22no—
98C2×Dic61—42no—
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C2×Dic61C2×D411yescharacteristic
102C4×D61—22no—
103C4×D61—21no—
104C4×D61—21no—
105C4×D61—22no—
106Dic122—21no—
107Dic122—22no—
108Dic122—22no—
109Dic122#4112yes—
110C8×C61—22no—
111#92418—22no—
112C22×C61—22no—
113C22×C61—41no—
114C22×C61—41no—
115C22×C61C22×D411yescharacteristic
116C2×D61—21no—
117C2×D61—21no—
118C2×D61—21no—
119C4×C61—21no—
120C4×C61—41no—
121C4×C61—42no—
122C4×C61#13512yes—
123C4×C61C2×#4111yescharacteristic
124C4×C61C2×#4111yescharacteristic
125Dic61—22no—
126Dic61—21no—
127Dic61—21no—
128Dic61—42no—
129Dic61—41no—
130Dic61#13712yes—
131#3107—611nomaximal, Sylow
132C2×C61—42no—
133C2×C61#52511yescharacteristic
134C2×C61C2×#13511yescharacteristic
135C2×C61C2×#13711yescharacteristic
136D61—41no—
137#533—611no—
138C4×#41—611no—
139#485—612no—
140#475—611no—
141#474D6111yescharacteristic, complemented
142#462—611no—
143#461—611no—
144#452—612no—
145C4×Q16—612no—
146C4×SD16—612no—
147#431—611no—
148C61#310711yescharacteristic, complemented, Sylow
149C2×#41—611no—
150C2×Q16—612no—
151C2×SD16—612no—
152C4⋊Q8—611no—
153C4⋊Q8C2×D6111yescharacteristic
154#125—1221no—
155C22⋊Q8—612no—
156C22⋊Q8—1221no—
157C4×Q8—611no—
158C4×Q8—612no—
159C4×Q8—611no—
160C4×Q8—1221no—
161C4×D4—611no—
162C4×D4—1221no—
163C4×D4—1221no—
164C4×D4C2×D6111yescharacteristic
165#117—611no—
166#117—1221no—
167#117—1221no—
168C2×C42—611no—
169C2×C42—1221no—
170#107C2×D6112yes—
171#106—612no—
172C4⋊C8—611no—
173C4⋊C8C2×D6111yescharacteristic
174#103—612no—
175#103—612no—
176#103—612no—
177#102C2×D6112yes—
178C22⋊C8—612no—
179C4×C8—612no—
180#41—1222no—
181#41—1222no—
182C2×Q8—21no—
183C2×Q8—611no—
184C2×Q8—612no—
185C2×D4—1221no—
186C2×D4C22×D6111yescharacteristic
187C22×C4—21no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—1221no—
192C22×C4—1221no—
193Q16—1224no—
194SD16—1224no—
195C2×C8—612no—
196C2×C8C22×D6112yes—
197C4⋊C4—21no—
198C4⋊C4—611no—
199C4⋊C4—1221no—
200C4⋊C4—1222no—
201C4⋊C4—1222no—
202C4⋊C4—1221no—
203C4⋊C4—1221no—
204C4⋊C4—1221no—
205C4⋊C4C22×D6112yes—
206C4⋊C4C22×D6111yescharacteristic
207C22⋊C4—21no—
208C22⋊C4—1221no—
209C22⋊C4—1222no—
210C22⋊C4—1221no—
211C42—611no—
212C42—611no—
213C42—611no—
214C42—1221no—
215C42—1221no—
216C42—1222no—
217C42—1221no—
218C42C22×D6111yescharacteristic
219C23—21no—
220C23—611no—
221Q8—42no—
222Q8—612no—
223Q8—1221no—
224Q8—1222no—
225Q8—1222no—
226D4—21no—
227D4—1224no—
228D4#1175822612yes—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—42no—
232C2×C4—611no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—1222no—
236C2×C4—1224no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—1221no—
240C2×C4—1222no—
241C2×C4—1221no—
242C2×C4—1222no—
243C2×C4—2442no—
244C2×C4D4×D6111yescharacteristic
245C2×C4D4×D6111yescharacteristic
246C2×C4C23×D6111yescharacteristic
247C8—22no—
248C8—1222no—
249C22—22no—
250C22—41no—
251C22—41no—
252C22—1221no—
253C22—1221no—
254C22—1221no—
255C22C2×D4×D6111yescharacteristic
256C4—21no—
257C4—41no—
258C4—42no—
259C4—612no—
260C4—1221no—
261C4—1222no—
262C4—1221no—
263C4—2442no—
264C4—2441no—
265C4#1451979612yes—
266C4#41×D6111yescharacteristic
267C4C2×#1175822611yescharacteristic
268C2—42no—
269C2—2441no—
270C2#1684027511yescharacteristic
271C2C2×#1451979611yescharacteristic
272C2#137×D6111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#474C2
socleC22×C61C22×D4
hypercenter#474D61
hypocenterC61#3107
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840105C2semidirect
4. #16840044C2semidirect
5. #16839973C2semidirect
6. #16839967C2semidirect
8. #16839856C2semidirect
9. #16839853C2semidirect
10. #16839814C2semidirect
11. C61×#474C2semidirect
141. #474D61semidirect
148. C61#3107semidirect