Finite Group Databasebeta

← #30601932

Subgroups — #30601932

Order 15616.

374 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 78 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#21461537C211yesmaximal, characteristic
2#21461382C211yesmaximal, characteristic
3#21461292C212yesmaximal
4#21461211C212yesmaximal
5#21456403C211yesmaximal, characteristic
6#16840784C2212yes—
7#16840721C2211yescharacteristic
8#16840698C2211yescharacteristic
9(C2×#6923)⋊C8—21no—
10(C2×#6923)⋊C8—21no—
11#16840626—21no—
12#16840624—21no—
13#16840619—24no—
14#16840615—24no—
15#16840317C2212yes—
16#16840167C411yescharacteristic, complemented
17#16840112C412yescomplemented
18#16840000—21no—
19#16840000—21no—
20Q16×Dic61—21no—
21Q16×Dic61—21no—
22C4×C8×D61C2211yescharacteristic
23C61×#494C411yescharacteristic, complemented
24C2×D61⋊C8—21no—
25C2×C4×#6923—21no—
26C4⋊#92420—22no—
27#14519834—22no—
28#14519832—22no—
29#14519832—21no—
30#14519832D412yes—
31(C2×#6923)⋊C4—21no—
32(C2×#6923)⋊C4D412yes—
33C2×C8×D61D411yescharacteristic
34C2×C8×D61D411yescharacteristic
35#14519777C2×C412yes—
36#14519768—22no—
37#14519757—22no—
38#14519753—22no—
39Q8×Dic61—22no—
40#14519742—22no—
41#14519735—22no—
42C42×D61C2311yescharacteristic
43#14519711—21no—
44#14519711—21no—
45#14519701—22no—
46#14519701—22no—
47C4×#92418C2×C411yescharacteristic
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C2×Q16×C61—21no—
51C2×Q16×C61—21no—
52C4⋊Q8×C61C2×C412yes—
53C4×C8×C61C2×C411yescharacteristic
54C22×#6923—22no—
55C2×Q8×C61—22no—
56C2×C4×D61C2×D411yescharacteristic
57C2×C4×D61C2×D411yescharacteristic
58C2×C4×D61#4111yescharacteristic
59C2×Dic122—22no—
60C2×#92420—22no—
61C2×#92420—42no—
62C4×#6923—41no—
63C4×#6923—41no—
64D61⋊C8—41no—
65D61⋊C8—41no—
66Q16×C61—42no—
67Q16×C61—42no—
68C2×C8×C61C22⋊C411yescharacteristic
69C2×C8×C61C22⋊C411yescharacteristic
70C4⋊C4×C61—22no—
71C4⋊C4×C61—22no—
72C42×C61C22×C411yescharacteristic
73#11758198—42no—
74C4⋊Dic61—22no—
75C4⋊Dic61—22no—
76C4⋊Dic61—42no—
77#11758196—42no—
78C4×Dic61—42no—
79C4×Dic61C2×D411yescharacteristic
80C4×Dic61C2×D411yescharacteristic
81C4×Dic61#4111yescharacteristic
82C2×#92418C22⋊C411yescharacteristic
83C2×#92418C22⋊C411yescharacteristic
84C8×D61—41no—
85C8×D61—41no—
86C22×D61#12111yescharacteristic
87C2×#6923—42no—
88C2×#6923—42no—
89C2×#6923—42no—
90Q8×C61—42no—
91Q8×C61—42no—
92C2×C4×C61—42no—
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61C4×D411yescharacteristic
95C2×C4×C61C4×D411yescharacteristic
96C2×Dic61—42no—
97C2×Dic61#12111yescharacteristic
98C2×Dic61#12411yescharacteristic
99C2×Dic61#12711yescharacteristic
100C4×D61—22no—
101C4×D61—21no—
102C4×D61—21no—
103C4×D61—41no—
104Dic122—82no—
105#92420—42no—
106#92420—82no—
107C8×C61—21no—
108C8×C61—21no—
109#92418—21no—
110#92418—21no—
111#9765—611nomaximal, Sylow
112C22×C61#39011yescharacteristic
113C2×D61—21no—
114C2×D61—21no—
115C2×D61#47312yes—
116#6923—82no—
117C4×C61—21no—
118C4×C61—21no—
119C4×C61—82no—
120C4×C61#42111yescharacteristic
121C4×C61#42111yescharacteristic
122Dic61—21no—
123Dic61—21no—
124Dic61—21no—
125Dic61—82no—
126#3170—611no—
127#1746—611no—
128#1568—611no—
129#1531—612no—
130#1506—612no—
131C2×C61#196311yescharacteristic
132C2×C61#197611yescharacteristic
133C2×C61#197911yescharacteristic
134D61—22no—
135#533—612no—
136#500—611no—
137#494#692311yescharacteristic, complemented
138#487—612no—
139#467—1221no—
140#467—1221no—
141C4×Q16—1221no—
142C4×Q16—1221no—
143#432—612no—
144C2×#97—611no—
145C2×C4×C8—611no—
146#376—611no—
147#336—1221no—
148#336—1221no—
149#335—1221no—
150#334—1221no—
151#330—1224no—
152#328—1224no—
153C61#976511yescharacteristic, complemented, Sylow
154C2×Q16—21no—
155C2×Q16—21no—
156C22×C8—611no—
157C22×C8—611no—
158C22×C8—1221no—
159C4⋊Q8—612no—
160C4⋊Q8C2×#692312yes—
161#125—1222no—
162C22⋊Q8—1222no—
163C22⋊Q8—1222no—
164C4×Q8—1222no—
165C4×Q8—1222no—
166#117—1222no—
167C2×C42—611no—
168C2×C42—1221no—
169#107—1221no—
170#107—1221no—
171C4⋊C8—1222no—
172#103—1222no—
173#103—1222no—
174C22⋊C8—1222no—
175#97—612no—
176#97—1221no—
177#97—1222no—
178C4×C8—611no—
179C4×C8—611no—
180C4×C8—611no—
181C4×C8C2×#692311yescharacteristic
182#95—612no—
183#95—1221no—
184C2×Q8—22no—
185C2×Q8—1222no—
186C22×C4—611no—
187C22×C4—611no—
188C22×C4—611no—
189C22×C4—1222no—
190Q16—42no—
191Q16—42no—
192C2×C8—611no—
193C2×C8—611no—
194C2×C8—1222no—
195C2×C8—2441no—
196C2×C8—2441no—
197C2×C8—2442no—
198C2×C8—2441no—
199C2×C8—2441no—
200C2×C8C22⋊#692311yescharacteristic
201C2×C8C22⋊#692311yescharacteristic
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—1222no—
205C4⋊C4—1222no—
206C4⋊C4—2442no—
207C4⋊C4—2442no—
208C22⋊C4—2442no—
209C42—611no—
210C42—611no—
211C42—611no—
212C42—2442no—
213C42—2441no—
214C42—2441no—
215C42C22×#692311yescharacteristic
216C23—611no—
217Q8—42no—
218Q8—42no—
219Q8—4882no—
220C2×C4—42no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—611no—
224C2×C4—1222no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—2441no—
228C2×C4—2442no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4C2×C22⋊#692311yescharacteristic
233C2×C4D4×#692311yescharacteristic
234C2×C4D4×#692311yescharacteristic
235C8—21no—
236C8—21no—
237C8—1221no—
238C8—1221no—
239C8—4882no—
240C8—2442no—
241C22—612no—
242C22—1221no—
243C22—1221no—
244C22#1684071411yescharacteristic
245C4—21no—
246C4—21no—
247C4—82no—
248C4—1221no—
249C4—1221no—
250C4—1221no—
251C4—4882no—
252C4—4882no—
253C4#1684076011yescharacteristic
254C4#1684076011yescharacteristic
255C2—1222no—
256C2#2146195711yescharacteristic
257C2#2146197811yescharacteristic
258C2#2146198111yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#494C4
socleC22×C61#390
prime radicalC22×D61#121
cosocleC42×D61C23
hypercenter#494#6923
hypocenterC61#9765
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
16. #16840167C4semidirect
17. #16840112C4semidirect
23. C61×#494C4semidirect
137. #494#6923semidirect
153. C61#9765semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214615372
#214613822
#214612922
#214612112
#214564032
#976561