Finite Group Databasebeta

← #30593997

Subgroups — #30593997

Order 15616.

402 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 86 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#21461676C211yesmaximal, characteristic
2#21461676C211yesmaximal, characteristic
3#21445511C211yesmaximal, characteristic
4C2×#14519844—21no—
5C2×#14519844C412yes—
6C2×#14519834—21no—
7C2×#14519834C412yes—
8#16840628—21no—
9#16840628—21no—
10C22×#11758189—21no—
11C2×C42×D61C2211yescharacteristic
12#16839517C411yescharacteristic
13#16839516—21no—
14C61×#336C411yescharacteristic
15C22×#92420—22no—
16C22×#92420—22no—
17#14519844—42no—
18#14519844—42no—
19#14519834—41no—
20#14519834—41no—
21#14519834—42no—
22C22×C4×D61C2×C411yescharacteristic
23C22×C4×D61D411yescharacteristic
24C22×C4×D61Q811yescharacteristic
25C2×#11758189—24no—
26C2×#11758189—42no—
27C2×#11758189—41no—
28C2×#11758189—41no—
29C22×#92418—21no—
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C42×D61—42no—
34C22×C8×C61—21no—
35C2×C42×C61C2×C411yescharacteristic
36C23×D61C4⋊C411yescharacteristic
37C22×C4×C61C4211yescharacteristic
38C22×C4×C61C22⋊C411yescharacteristic
39C22×C4×C61C4⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C22⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—22no—
48C2×C4×D61—41no—
49C2×C4×D61—41no—
50C2×C4×D61—41no—
51C2×C4×D61—41no—
52C2×C4×D61D811yescharacteristic
53C2×C4×D61SD1611yescharacteristic
54C2×C4×D61SD1611yescharacteristic
55C2×C4×D61Q1611yescharacteristic
56C2×#92420—42no—
57C2×#92420—42no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×#92420—42no—
61C2×#92420—42no—
62C2×C8×C61—22no—
63C2×C8×C61—41no—
64C2×C8×C61—41no—
65C42×C61—41no—
66C4×Dic61—22no—
67C4×Dic61—22no—
68C4×Dic61—41no—
69C2×#92418—22no—
70C2×#92418—41no—
71C2×#92418—41no—
72#11758189—44no—
73#11758189—44no—
74C23×C61#9511yescharacteristic
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—21no—
81C22×D61#10611yescharacteristic
82C22×D61#10711yescharacteristic
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61#10211yescharacteristic
92C2×C4×C61#10311yescharacteristic
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61#9912yes—
98C2×Dic61#10011yescharacteristic
99C2×Dic61#10111yescharacteristic
100C2×Dic61#10211yescharacteristic
101C2×Dic61#10311yescharacteristic
102C2×Dic61#10412yes—
103C2×Dic61#10812yes—
104C4×D61—22no—
105C4×D61—22no—
106C4×D61—22no—
107C4×D61—22no—
108C4×D61—44no—
109C4×D61—42no—
110C4×D61—42no—
111#92420—82no—
112#92420—82no—
113C8×C61—42no—
114#92418—42no—
115#7045—611nomaximal, Sylow
116C22×C61#33811yescharacteristic
117C22×C61#33911yescharacteristic
118C22×C61#34011yescharacteristic
119C22×C61#34111yescharacteristic
120C22×C61#34211yescharacteristic
121C22×C61#34311yescharacteristic
122C22×C61#34411yescharacteristic
123C2×D61—21no—
124C2×D61—21no—
125C2×D61—21no—
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—21no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—41no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—41no—
136C4×C61—41no—
137Dic61—22no—
138Dic61—21no—
139Dic61—21no—
140Dic61#32712yes—
141Dic61#32812yes—
142#1797—611no—
143#1797—611no—
144#1728—611no—
145C2×C61#129111yescharacteristic
146C2×C61#129211yescharacteristic
147C2×C61#129311yescharacteristic
148C2×C61#129411yescharacteristic
149C2×C61#129911yescharacteristic
150C2×C61#130111yescharacteristic
151C2×C61#130511yescharacteristic
152D61—41no—
153D61—41no—
154C22×M16—1221no—
155C22×C42—611no—
156C2×C4⋊C8—612no—
157C2×C4⋊C8—1221no—
158C2×C22⋊C8—612no—
159C2×C22⋊C8—1221no—
160#336—611no—
161#336—1221no—
162#336—1221no—
163#336—1221no—
164#336#692311yescharacteristic
165C61#704511yescharacteristic, complemented, Sylow
166C23×C4—611no—
167C23×C4—611no—
168C23×C4—611no—
169C2×M16—1224no—
170C2×M16—2441no—
171C2×M16—2441no—
172C2×M16—2442no—
173C22×C8—21no—
174C22×C8—1221no—
175C22×C8—1222no—
176C22×C8—1222no—
177C2×C42—611no—
178C2×C42—611no—
179C2×C42—611no—
180C2×C42—2442no—
181C2×C42C2×#692311yescharacteristic
182C4⋊C8—2442no—
183C4⋊C8—2442no—
184C22⋊C8—2441no—
185C22⋊C8—2441no—
186C22⋊C8—2442no—
187C24—611no—
188C22×C4—611no—
189C22×C4—611no—
190C22×C4—611no—
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—1222no—
196C22×C4—1222no—
197C22×C4—1221no—
198C22×C4—1222no—
199C22×C4—1221no—
200C22×C4—2441no—
201C22×C4—2441no—
202C22×C4—2441no—
203C22×C4—2441no—
204C22×C4C4×#692311yescharacteristic
205C22×C4C4⋊#692311yescharacteristic
206C22×C4C22⋊#692311yescharacteristic
207M16—2444no—
208M16—2444no—
209C2×C8—22no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—1222no—
213C2×C8—2442no—
214C2×C8—2442no—
215C2×C8—2442no—
216C2×C8—2442no—
217C2×C8—2442no—
218C2×C8—2442no—
219C2×C8—2441no—
220C2×C8—2441no—
221C42—41no—
222C42—1222no—
223C42—1222no—
224C42—2441no—
225C23—611no—
226C23—611no—
227C23—1221no—
228C23—1221no—
229C23—1221no—
230C23—1221no—
231C23—1221no—
232C23—1221no—
233C23(C2×#6923)⋊C411yescharacteristic
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—612no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—612no—
246C2×C4—612no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—1222no—
250C2×C4—1222no—
251C2×C4—1222no—
252C2×C4—1222no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—2444no—
258C2×C4—2442no—
259C2×C4—2442no—
260C2×C4#1451983911yescharacteristic
261C2×C4#1451984011yescharacteristic
262C8—42no—
263C8—4882no—
264C8—4882no—
265C8—2442no—
266C22—1221no—
267C22—1221no—
268C22—1221no—
269C22—1221no—
270C22—1221no—
271C22—1221no—
272C22—2441no—
273C22—2441no—
274C22—2441no—
275C22—2441no—
276C22#1684063111yescharacteristic
277C22#1684063311yescharacteristic
278C22#1684063511yescharacteristic
279C22#1684063711yescharacteristic
280C22#1684063911yescharacteristic
281C22#1684064111yescharacteristic
282C22#1684064411yescharacteristic
283C4—21no—
284C4—21no—
285C4—41no—
286C4—41no—
287C4—612no—
288C4—612no—
289C4—1222no—
290C4—1221no—
291C4—1221no—
292C2—2441no—
293C2—2441no—
294C2#2146068611yescharacteristic
295C2#2146068811yescharacteristic
296C2#2146069011yescharacteristic
297C2#2146069311yescharacteristic
298C2#2146070411yescharacteristic
299C2#2146070911yescharacteristic
300C2#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#7045
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
165. C61#7045semidirect

Maximal subgroups

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

subgroupindex
#214616762
#214455112
#704561