Finite Group Databasebeta

← #21455602

Subgroups — #21455602

Order 7808.

388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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×#11758226C211yesmaximal, characteristic
3#16840067C212yesmaximal, complemented
4#16840061C212yesmaximal, complemented
5#16840057C211yesmaximal, characteristic, complemented
6#16840053C211yesmaximal, characteristic, complemented
7#16840039C211yesmaximal, characteristic, complemented
8#16839797C212yesmaximal, complemented
9C4⋊C8×D61C211yesmaximal, characteristic, complemented
10#16839757C212yesmaximal
11C61×#475C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×C8×D61C2212yes—
14#14519777C2211yescharacteristic
15#14519768C2212yes—
16#14519757—21no—
17#14519753—21no—
18Q8×Dic61—21no—
19Q8×Dic61C2211yescharacteristic
20#14519742—21no—
21C4×D244—21no—
22C4×D244C2211yescharacteristic
23#14519739—21no—
24#14519739C2211yescharacteristic
25#14519735—21no—
26#14519735C2211yescharacteristic
27#14519735C2212yes—
28C42×D61—21no—
29C42×D61C2211yescharacteristic
30#14519710C2212yes—
31#14519710C2212yes—
32#14519709C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519701C2212yes—
36#14519699C2212yes—
37#14519697C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×Q8×C61C2211yescharacteristic
40#106×C61C2212yes—
41C4⋊C8×C61C2211yescharacteristic
42#103×C61C2212yes—
43C2×Q8×C61—21no—
44C2×Q8×C61C2311yescharacteristic
45#11758226—22no—
46#11758226Q814yescomplemented
47C2×D244—21no—
48C2×D244C2311yescharacteristic
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61D411yescharacteristic
53C2×C4×D61D411yescharacteristic
54C2×C4×D61C2311yescharacteristic
55C2×Dic122—21no—
56C2×C8×C61C2312yes—
57C4⋊C4×C61—21no—
58C4⋊C4×C61—21no—
59C4⋊C4×C61C2312yes—
60C4⋊C4×C61C2311yescharacteristic
61C42×C61—21no—
62C42×C61C2311yescharacteristic
63#11758198—21no—
64#11758198—22no—
65#11758198—21no—
66#11758198—21no—
67C4⋊Dic61—21no—
68C4⋊Dic61—21no—
69C4⋊Dic61—22no—
70C4⋊Dic61C2312yes—
71C4⋊Dic61C2311yescharacteristic
72#11758196—22no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—22no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80C8×D61—24no—
81C22×D61—21no—
82C22×D61C2×D411yescharacteristic
83Q8×C61—21no—
84Q8×C61—42no—
85Q8×C61C2×Q812yes—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—21no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C2×Dic61—21no—
93C2×Dic61—22no—
94C2×Dic61C2×D411yescharacteristic
95C2×Dic61C2×D411yescharacteristic
96C2×Dic61C2×D411yescharacteristic
97D244—24no—
98D244—21no—
99D244C2×Q812yes—
100C4×D61—22no—
101C4×D61—24no—
102C4×D61—41no—
103C4×D61—42no—
104C4×D61—42no—
105C4×D61C2×Q812yes—
106C4×D61#4112yes—
107Dic122—42no—
108C8×C61—22no—
109#92418—22no—
110C22×C61C22×D411yescharacteristic
111C2×D61—21no—
112C2×D61—21no—
113C2×D61—22no—
114C2×D61—41no—
115C2×D61—41no—
116C2×D61C22⋊Q812yes—
117C4×C61—22no—
118C4×C61—21no—
119C4×C61—42no—
120C4×C61—41no—
121C4×C61#13512yes—
122C4×C61C22×Q811yescharacteristic
123C4×C61C2×#4111yescharacteristic
124Dic61—21no—
125Dic61—21no—
126Dic61—41no—
127Dic61—42no—
128Dic61C22⋊Q812yes—
129#3076—611nomaximal, Sylow
130C2×C61C2×C22⋊Q811yescharacteristic
131C2×C61C2×#13511yescharacteristic
132C2×C61#57511yescharacteristic
133D61—22no—
134D61—42no—
135#533—611no—
136C4×#41—611no—
137#479—612no—
138#478—612no—
139#477—611no—
140#476—611no—
141#475D6111yescharacteristic, complemented
142#474—611no—
143#427—612no—
144C2×C4⋊C8—611no—
145#416—612no—
146C61#307611yescharacteristic, complemented, Sylow
147C2×#41—611no—
148C22×C8—612no—
149C4⋊Q8—611no—
150C4⋊Q8C2×D6111yescharacteristic
151#125—612no—
152C22⋊Q8—1221no—
153C22⋊Q8—1221no—
154C4×Q8—611no—
155C4×Q8—1221no—
156C4×Q8—1221no—
157C4×Q8C2×D6111yescharacteristic
158C4×D4—611no—
159C4×D4—611no—
160C4×D4—1221no—
161C4×D4—1221no—
162#117—611no—
163#117—612no—
164#117—1221no—
165C2×C42—611no—
166C2×C42—1221no—
167#107—612no—
168#107—612no—
169#106—612no—
170#106C2×D6112yes—
171C4⋊C8—612no—
172C4⋊C8—611no—
173C4⋊C8C2×D6111yescharacteristic
174#103—612no—
175#103C2×D6112yes—
176#102—612no—
177#102—612no—
178#41—614no—
179#41—1222no—
180C2×Q8—21no—
181C2×Q8—1221no—
182C2×Q8C22×D6111yescharacteristic
183C2×D4—611no—
184C2×D4—1221no—
185C22×C4—611no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—1221no—
189C22×C4—1221no—
190C22×C4—1221no—
191C2×C8—612no—
192C2×C8—1224no—
193C2×C8C22×D6112yes—
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—612no—
197C4⋊C4—611no—
198C4⋊C4—1222no—
199C4⋊C4—1221no—
200C4⋊C4—1222no—
201C4⋊C4—1221no—
202C4⋊C4C22×D6112yes—
203C4⋊C4C22×D6111yescharacteristic
204C22⋊C4—1221no—
205C22⋊C4—1221no—
206C22⋊C4—1222no—
207C22⋊C4—1221no—
208C42—21no—
209C42—611no—
210C42—611no—
211C42—611no—
212C42—1221no—
213C42—1221no—
214C42—1222no—
215C42C22×D6111yescharacteristic
216C23—611no—
217C23—1221no—
218Q8—21no—
219Q8—42no—
220Q8—2442no—
221Q8Q8×D6112yes—
222D4—612no—
223D4—1224no—
224D4—1221no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—611no—
229C2×C4—612no—
230C2×C4—612no—
231C2×C4—611no—
232C2×C4—611no—
233C2×C4—1224no—
234C2×C4—1222no—
235C2×C4—1221no—
236C2×C4—1222no—
237C2×C4—2441no—
238C2×C4—2442no—
239C2×C4—2442no—
240C2×C4D4×D6111yescharacteristic
241C2×C4D4×D6111yescharacteristic
242C2×C4C23×D6111yescharacteristic
243C8—22no—
244C8—1222no—
245C22—612no—
246C22—1221no—
247C22—1221no—
248C22—1222no—
249C22—2441no—
250C22—2441no—
251C22C2×D4×D6111yescharacteristic
252C4—22no—
253C4—21no—
254C4—42no—
255C4—41no—
256C4—612no—
257C4—1221no—
258C4—1221no—
259C4—2441no—
260C4—2442no—
261C4#1451979812yes—
262C4C2×Q8×D6111yescharacteristic
263C4#41×D6111yescharacteristic
264C2—1222no—
265C2—2442no—
266C2C22⋊Q8×D6111yescharacteristic
267C2C2×#1451979811yescharacteristic
268C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#475C2
socleC22×C61C22×D4
hypercenter#475D61
hypocenterC61#3076
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840067C2semidirect
4. #16840061C2semidirect
5. #16840057C2semidirect
6. #16840053C2semidirect
7. #16840039C2semidirect
8. #16839797C2semidirect
9. C4⋊C8×D61C2semidirect
11. C61×#475C2semidirect
46. #11758226Q8semidirect
141. #475D61semidirect
146. C61#3076semidirect