Finite Group Databasebeta

← #21455608

Subgroups — #21455608

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×#11758224C211yesmaximal, characteristic
3#16840072C212yesmaximal, complemented
4#16840064C212yesmaximal, complemented
5#16840054C211yesmaximal, characteristic, complemented
6#16840048C211yesmaximal, characteristic, complemented
7#16840042C211yesmaximal, characteristic, complemented
8#16839797C212yesmaximal, complemented
9C4⋊C8×D61C211yesmaximal, characteristic, complemented
10#16839755C212yesmaximal
11C61×#476C211yesmaximal, characteristic, complemented
12C2×#11758224C2211yescharacteristic
13C2×C8×D61C2212yes—
14#14519777C2211yescharacteristic
15#14519768C2212yes—
16#14519757—21no—
17#14519753—21no—
18Q8×Dic61—21no—
19C4×Dic122C2211yescharacteristic
20#14519742—21no—
21#14519742C2211yescharacteristic
22D4×Dic61C2211yescharacteristic
23C4×C22⋊D61—21no—
24#14519737—21no—
25#14519735C2211yescharacteristic
26#14519735C2212yes—
27#14519733—21no—
28C2×C4×Dic61—21no—
29C42×D61C2211yescharacteristic
30#14519710C2212yes—
31#14519710C2212yes—
32#14519709C2212yes—
33C4⋊#92418C2211yescharacteristic
34#14519706C2212yes—
35#14519702C2212yes—
36#14519700C2212yes—
37#14519698C2212yes—
38C4⋊Q8×C61C2211yescharacteristic
39C4×D4×C61C2211yescharacteristic
40#106×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#11758224Q814yescomplemented
51C2×C4×D61D411yescharacteristic
52C2×C4×D61D411yescharacteristic
53C2×C4×D61C2311yescharacteristic
54C2×Dic122—21no—
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#11758198—21no—
64#11758198—22no—
65C4⋊Dic61—21no—
66C4⋊Dic61—22no—
67C4⋊Dic61C2312yes—
68C4⋊Dic61C2311yescharacteristic
69#11758196—21no—
70#11758196—21no—
71#11758196—22no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75C4×Dic61—22no—
76C4×Dic61D411yescharacteristic
77C4×Dic61D411yescharacteristic
78C4×Dic61C2311yescharacteristic
79C2×#92418C2312yes—
80C8×D61—24no—
81C23×C61—21no—
82C22×D61C2×D411yescharacteristic
83Q8×C61—42no—
84D4×C61—21no—
85D4×C61C2×Q812yes—
86C2×C4×C61—21no—
87C2×C4×C61—22no—
88C2×C4×C61—42no—
89C2×C4×C61C2×D411yescharacteristic
90C2×C4×C61C2×D411yescharacteristic
91C2×C4×C61C2411yescharacteristic
92C22⋊D61—24no—
93C2×Dic61—21no—
94C2×Dic61—24no—
95C2×Dic61—21no—
96C2×Dic61—22no—
97C2×Dic61—42no—
98C2×Dic61C2×D411yescharacteristic
99C2×Dic61C2×D411yescharacteristic
100C2×Dic61C2×D411yescharacteristic
101C4×D61—22no—
102C4×D61—41no—
103C4×D61C2×Q812yes—
104C4×D61#4112yes—
105Dic122—21no—
106Dic122—42no—
107Dic122C2×Q812yes—
108C8×C61—22no—
109#92418—22no—
110C22×C61—22no—
111C22×C61—41no—
112C22×C61—41no—
113C22×C61C22×D411yescharacteristic
114C2×D61—21no—
115C2×D61—21no—
116C2×D61C22⋊Q812yes—
117C4×C61—21no—
118C4×C61—41no—
119C4×C61—42no—
120C4×C61#13512yes—
121C4×C61C22×Q811yescharacteristic
122C4×C61C2×#4111yescharacteristic
123Dic61—22no—
124Dic61—21no—
125Dic61—21no—
126Dic61—42no—
127Dic61—41no—
128Dic61C22⋊Q812yes—
129#3076—611nomaximal, Sylow
130C2×C61—42no—
131C2×C61C2×C22⋊Q811yescharacteristic
132C2×C61C2×#13511yescharacteristic
133C2×C61#57511yescharacteristic
134D61—22no—
135#533—611no—
136C4×#41—611no—
137#479—612no—
138#478—612no—
139#477—611no—
140#476D6111yescharacteristic, complemented
141#475—611no—
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—611no—
156C4×Q8—1221no—
157C4×Q8—1221no—
158C4×D4—611no—
159C4×D4—1221no—
160C4×D4—1221no—
161C4×D4C2×D6111yescharacteristic
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#103—612no—
176#102—612no—
177#102C2×D6112yes—
178#41—614no—
179#41—1222no—
180C2×Q8—21no—
181C2×Q8—611no—
182C2×Q8—1221no—
183C2×D4—1221no—
184C2×D4C22×D6111yescharacteristic
185C22×C4—21no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—1221no—
190C22×C4—1221no—
191C2×C8—612no—
192C2×C8—1224no—
193C2×C8C22×D6112yes—
194C4⋊C4—21no—
195C4⋊C4—612no—
196C4⋊C4—611no—
197C4⋊C4—1221no—
198C4⋊C4—1222no—
199C4⋊C4—1222no—
200C4⋊C4—1221no—
201C4⋊C4—1221no—
202C4⋊C4C22×D6112yes—
203C4⋊C4C22×D6111yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—1221no—
206C22⋊C4—1222no—
207C22⋊C4—1221no—
208C42—611no—
209C42—611no—
210C42—611no—
211C42—1221no—
212C42—1221no—
213C42—1222no—
214C42—1221no—
215C42C22×D6111yescharacteristic
216C23—21no—
217C23—611no—
218Q8—42no—
219Q8—612no—
220Q8—1221no—
221Q8—2442no—
222D4—21no—
223D4—1224no—
224D4Q8×D6112yes—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—611no—
229C2×C4—612no—
230C2×C4—612no—
231C2×C4—611no—
232C2×C4—611no—
233C2×C4—1224no—
234C2×C4—1221no—
235C2×C4—1222no—
236C2×C4—1221no—
237C2×C4—1222no—
238C2×C4—2441no—
239C2×C4—2442no—
240C2×C4D4×D6111yescharacteristic
241C2×C4D4×D6111yescharacteristic
242C2×C4C23×D6111yescharacteristic
243C8—22no—
244C8—1222no—
245C22—22no—
246C22—41no—
247C22—41no—
248C22—612no—
249C22—1221no—
250C22—1221no—
251C22C2×D4×D6111yescharacteristic
252C4—21no—
253C4—41no—
254C4—42no—
255C4—612no—
256C4—1222no—
257C4—1221no—
258C4—1221no—
259C4—2442no—
260C4—2441no—
261C4#1451979812yes—
262C4C2×Q8×D6111yescharacteristic
263C4#41×D6111yescharacteristic
264C2—42no—
265C2—1222no—
266C2C22⋊Q8×D6111yescharacteristic
267C2C2×#1451979811yescharacteristic
268C2#1684055811yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC61×#476C2
socleC22×C61C22×D4
hypercenter#476D61
hypocenterC61#3076
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #16840317C2semidirect
3. #16840072C2semidirect
4. #16840064C2semidirect
5. #16840054C2semidirect
6. #16840048C2semidirect
7. #16840042C2semidirect
8. #16839797C2semidirect
9. C4⋊C8×D61C2semidirect
11. C61×#476C2semidirect
50. #11758224Q8semidirect
140. #476D61semidirect
146. C61#3076semidirect