Finite Group Databasebeta

← #30593979

Subgroups — #30593979

Order 15616.

358 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 76 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#21461674C211yesmaximal, characteristic
2#21461546C211yesmaximal, characteristic
3#21445886C211yesmaximal, characteristic
4C2×C4⋊#92420—21no—
5C2×#14519834—21no—
6C2×#14519834C412yes—
7C2×#14519832C412yes—
8#16840628—21no—
9#16840628—21no—
10C2×C42×D61C2211yescharacteristic
11C2×#14519689—21no—
12#16839517C411yescharacteristic
13#16839516—21no—
14C61×#336C411yescharacteristic
15C22×#92420—22no—
16C22×#92420—22no—
17C4⋊#92420—42no—
18#14519834—22no—
19#14519834—22no—
20#14519834—42no—
21#14519832—42no—
22C22×C4×D61C2×C411yescharacteristic
23C22×C4×D61D411yescharacteristic
24C22×C4×D61Q811yescharacteristic
25C22×#92418—21no—
26C2×C4×Dic61C2×C411yescharacteristic
27C2×C4×Dic61D411yescharacteristic
28C2×C4×Dic61D411yescharacteristic
29C42×D61—42no—
30#14519689—42no—
31C22×C8×C61—21no—
32C2×C42×C61C2×C411yescharacteristic
33C23×D61C4⋊C411yescharacteristic
34C22×C4×C61C4211yescharacteristic
35C22×C4×C61C22⋊C411yescharacteristic
36C22×C4×C61C4⋊C411yescharacteristic
37C22×Dic61C22⋊C411yescharacteristic
38C22×Dic61C22⋊C411yescharacteristic
39C22×Dic61C4⋊C411yescharacteristic
40C2×C4×D61—22no—
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×C4×D61—21no—
44C2×C4×D61—21no—
45C2×C4×D61—22no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—41no—
49C2×C4×D61—41no—
50C2×C4×D61—41no—
51C2×C4×D61—41no—
52C2×#92420—24no—
53C2×#92420—42no—
54C2×#92420—42no—
55C2×#92420—42no—
56C2×#92420—42no—
57C2×#92420—42no—
58C2×C8×C61—41no—
59C2×C8×C61—41no—
60C2×C8×C61—41no—
61C42×C61—41no—
62C4×Dic61—22no—
63C4×Dic61—22no—
64C4×Dic61—41no—
65C2×#92418—41no—
66C2×#92418—41no—
67C2×#92418—41no—
68C23×C61#9511yescharacteristic
69C22×D61—21no—
70C22×D61—21no—
71C22×D61—21no—
72C22×D61—21no—
73C22×D61—21no—
74C22×D61—21no—
75C22×D61#10812yes—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61#10411yescharacteristic
84C2×C4×C61#10411yescharacteristic
85C2×C4×C61#10811yescharacteristic
86C2×C4×C61#10811yescharacteristic
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61#9912yes—
95C2×Dic61#10011yescharacteristic
96C2×Dic61#10111yescharacteristic
97C4×D61—42no—
98C4×D61—42no—
99C4×D61—42no—
100C4×D61—42no—
101C4×D61—42no—
102C4×D61—42no—
103#92420—44no—
104#92420—82no—
105C8×C61—81no—
106#92418—81no—
107#7038—611nomaximal, Sylow
108C22×C61H(3,ℤ/4)11yescharacteristic
109C22×C61#33911yescharacteristic
110C22×C61#34111yescharacteristic
111C22×C61#34111yescharacteristic
112C22×C61#34211yescharacteristic
113C22×C61#34311yescharacteristic
114C22×C61#34411yescharacteristic
115C2×D61—22no—
116C2×D61—22no—
117C2×D61—22no—
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—41no—
121C2×D61—41no—
122C4×C61—21no—
123C4×C61—21no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—41no—
127Dic61—22no—
128Dic61—21no—
129Dic61—21no—
130Dic61—41no—
131#1817—611no—
132#1797—611no—
133#1749—611no—
134C2×C61#128411yescharacteristic
135C2×C61#128711yescharacteristic
136C2×C61#129011yescharacteristic
137C2×C61#129811yescharacteristic
138C2×C61#129911yescharacteristic
139C2×C61#130211yescharacteristic
140C2×C61#130511yescharacteristic
141D61—42no—
142C22×C42—611no—
143C2×C4⋊C8—1221no—
144C2×C22⋊C8—612no—
145C2×C22⋊C8—1221no—
146C2×C22⋊C8—1221no—
147C2×#97—612no—
148#336—611no—
149#336—1221no—
150#336—1221no—
151#336—1221no—
152#336#692311yescharacteristic
153C61#703811yescharacteristic, complemented, Sylow
154C23×C4—611no—
155C23×C4—611no—
156C23×C4—611no—
157C22×C8—21no—
158C22×C8—1222no—
159C22×C8—1222no—
160C22×C8—1221no—
161C2×C42—611no—
162C2×C42—611no—
163C2×C42—611no—
164C2×C42—2442no—
165C2×C42C2×#692311yescharacteristic
166C4⋊C8—2442no—
167C22⋊C8—1222no—
168C22⋊C8—1222no—
169C22⋊C8—2442no—
170C22⋊C8—2442no—
171#97—2442no—
172C24—611no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—611no—
176C22×C4—1221no—
177C22×C4—1222no—
178C22×C4—1221no—
179C22×C4—1222no—
180C22×C4—1221no—
181C22×C4—1221no—
182C22×C4—1221no—
183C22×C4—1221no—
184C22×C4—2441no—
185C22×C4—2441no—
186C22×C4—2441no—
187C22×C4—2441no—
188C22×C4C4×#692311yescharacteristic
189C22×C4C4⋊#692311yescharacteristic
190C22×C4C22⋊#692311yescharacteristic
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—1224no—
195C2×C8—2441no—
196C2×C8—2441no—
197C2×C8—2442no—
198C2×C8—2442no—
199C2×C8—2442no—
200C2×C8—2441no—
201C2×C8—2442no—
202C2×C8—2442no—
203C42—41no—
204C42—1222no—
205C42—1222no—
206C42—2441no—
207C23—612no—
208C23—1221no—
209C23—1221no—
210C23—1221no—
211C23—1221no—
212C23—1221no—
213C23—1221no—
214C23(C2×#6923)⋊C411yescharacteristic
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—612no—
223C2×C4—611no—
224C2×C4—611no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—1221no—
232C2×C4—2442no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4—2442no—
238C2×C4#1451984111yescharacteristic
239C2×C4#1451984211yescharacteristic
240C2×C4#1451984711yescharacteristic
241C2×C4#1451984811yescharacteristic
242C8—81no—
243C8—4881no—
244C8—4882no—
245C8—2444no—
246C22—1222no—
247C22—1222no—
248C22—1222no—
249C22—2441no—
250C22—2441no—
251C22—2441no—
252C22—2441no—
253C22#1684062911yescharacteristic
254C22#1684063211yescharacteristic
255C22#1684063711yescharacteristic
256C22#1684063811yescharacteristic
257C22#1684063911yescharacteristic
258C22#1684064111yescharacteristic
259C22#1684064411yescharacteristic
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—41no—
265C4—1222no—
266C4—1221no—
267C4—1221no—
268C4—2441no—
269C2—2442no—
270C2#2146066611yescharacteristic
271C2#2146067611yescharacteristic
272C2#2146068311yescharacteristic
273C2#2146070211yescharacteristic
274C2#2146070511yescharacteristic
275C2#2146071211yescharacteristic
276C2#2146072111yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#336C4
socleC23×C61#95
prime radicalC23×D61C4⋊C4
cosocleC2×C42×D61C22
hypercenter#336#6923
hypocenterC61#7038
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
153. C61#7038semidirect

Maximal subgroups

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

subgroupindex
#214616742
#214615462
#214458862
#703861