Finite Group Databasebeta

← #30594557

Subgroups — #30594557

Order 15616.

328 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461678C211yesmaximal, characteristic
2#21461053C211yesmaximal, characteristic
3#21445556C211yesmaximal, characteristic
4#16840779—21no—
5C2×#14519844C411yescharacteristic
6C2×C4⋊#92420C411yescharacteristic
7C2×#14519834—21no—
8#16840628—21no—
9#16840607—21no—
10#16840606C412yes—
11C2×M16×D61—21no—
12C2×#14519735C2211yescharacteristic
13#16839531C411yescharacteristic
14#16839530—21no—
15C61×#343C411yescharacteristic
16C22×#92420—21no—
17C22×#92420—21no—
18#14519844—41no—
19#14519844—41no—
20C4⋊#92420—41no—
21#14519834—41no—
22#14519834—41no—
23C22⋊#92420—22no—
24C4×#92420—41no—
25C22×C4×D61D411yescharacteristic
26C2×#11758194—21no—
27C2×#11758189—41no—
28M16×D61—22no—
29M16×D61—22no—
30M16×D61—41no—
31M16×D61—41no—
32C2×C8×D61—41no—
33#14519735—41no—
34#14519735—41no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758198C2×C411yescharacteristic
37C2×#11758198Q811yescharacteristic
38C2×C4×Dic61C2×C411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×M16×C61—21no—
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C23×D61C4⋊C411yescharacteristic
43C22×C4×C61C4211yescharacteristic
44C22×C4×C61C22⋊C411yescharacteristic
45C22×C4×C61C4⋊C411yescharacteristic
46C22×Dic61C22⋊C411yescharacteristic
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C4⋊C411yescharacteristic
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61D811yescharacteristic
54C2×C4×D61SD1611yescharacteristic
55C2×C4×D61SD1611yescharacteristic
56C2×C4×D61Q1611yescharacteristic
57C2×#92420—42no—
58C2×#92420—41no—
59C2×#92420—41no—
60C2×#92420—41no—
61C2×#92420—41no—
62C2×#92420—41no—
63C2×#92420—41no—
64M16×C61—22no—
65M16×C61—41no—
66C2×C8×C61—41no—
67C4⋊C4×C61—41no—
68#11758198—41no—
69#11758198—41no—
70C4⋊Dic61—41no—
71C4×Dic61—21no—
72C4×Dic61—21no—
73C4×Dic61—21no—
74C4×Dic61—21no—
75#11758194—22no—
76#11758194—41no—
77C2×#92418—41no—
78#11758189—42no—
79#11758189—42no—
80C8×D61—42no—
81C8×D61—42no—
82C23×C61#9511yescharacteristic
83C22×D61—21no—
84C22×D61—21no—
85C22×D61—41no—
86C22×D61—41no—
87C22×D61#10611yescharacteristic
88C22×D61#10711yescharacteristic
89C2×C4×C61—21no—
90C2×C4×C61—21no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—41no—
94C2×C4×C61—41no—
95C2×C4×C61#10211yescharacteristic
96C2×C4×C61#10311yescharacteristic
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—41no—
100C2×Dic61—41no—
101C2×Dic61#9911yescharacteristic
102C2×Dic61#9911yescharacteristic
103C2×Dic61#10211yescharacteristic
104C2×Dic61#10311yescharacteristic
105C2×Dic61#10411yescharacteristic
106C2×Dic61#10411yescharacteristic
107C4×D61—21no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—21no—
111C4×D61—21no—
112C4×D61—21no—
113C4×D61—21no—
114C4×D61—21no—
115#92420—82no—
116#92420—81no—
117#92420—81no—
118C8×C61—42no—
119#92418—42no—
120#7253—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61#33911yescharacteristic
124C22×C61#34011yescharacteristic
125C22×C61#34211yescharacteristic
126C2×D61—21no—
127C2×D61—21no—
128C2×D61—41no—
129C2×D61—41no—
130C2×D61—41no—
131C2×D61—41no—
132C2×D61—81no—
133C4×C61—21no—
134C4×C61—21no—
135C4×C61—41no—
136C4×C61—41no—
137Dic61—41no—
138Dic61—41no—
139Dic61#32711yescharacteristic
140Dic61#32711yescharacteristic
141Dic61#32811yescharacteristic
142Dic61#32811yescharacteristic
143#1798—611no—
144#1742—611no—
145#1458—611no—
146C2×C61—21no—
147C2×C61—21no—
148C2×C61#129411yescharacteristic
149C2×C61#139211yescharacteristic
150C2×C61#139511yescharacteristic
151D61—41no—
152D61—41no—
153C22×M16—1221no—
154C2×#117—611no—
155#431—1221no—
156C2×C4⋊C8—611no—
157C2×C4⋊C8—611no—
158C2×C22⋊C8—1221no—
159#343—611no—
160#343—1221no—
161#343#692311yescharacteristic
162#336—1221no—
163#324—1221no—
164#323—612no—
165C61#725311yescharacteristic, complemented, Sylow
166C23×C4—611no—
167C2×M16—21no—
168C2×M16—1222no—
169C2×M16—1222no—
170C2×M16—1221no—
171C2×M16—2441no—
172C2×M16—2441no—
173C2×M16—2441no—
174C22×C8—1221no—
175C22×C8—1221no—
176C22×C8—2441no—
177#117—2441no—
178#117—2441no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4C2×#692311yescharacteristic
181C2×C22⋊C4—611no—
182C2×C22⋊C4—611no—
183C2×C42—611no—
184C2×C42—611no—
185C4⋊C8—2441no—
186C4⋊C8—2441no—
187C4⋊C8—2441no—
188C22⋊C8—1222no—
189C22⋊C8—2441no—
190C22⋊C8—2441no—
191C4×C8—2441no—
192C24—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—611no—
200C22×C4—1221no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4—1221no—
204C22×C4C4×#692311yescharacteristic
205C22×C4C4⋊#692311yescharacteristic
206C22×C4C22⋊#692311yescharacteristic
207M16—22no—
208M16—41no—
209M16—1222no—
210M16—2442no—
211M16—2442no—
212M16—2441no—
213C2×C8—41no—
214C2×C8—2442no—
215C2×C8—2442no—
216C2×C8—2441no—
217C2×C8—2441no—
218C2×C8—2441no—
219C2×C8—2441no—
220C2×C8—2441no—
221C2×C8—2441no—
222C2×C8—2442no—
223C2×C8—2441no—
224C4⋊C4—41no—
225C4⋊C4—2441no—
226C22⋊C4—2441no—
227C22⋊C4—2441no—
228C42—1221no—
229C42—1221no—
230C42—1221no—
231C42—1221no—
232C23—611no—
233C23—611no—
234C23—1221no—
235C23—1221no—
236C23—2441no—
237C23—2441no—
238C23(C2×#6923)⋊C411yescharacteristic
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—611no—
248C2×C4—611no—
249C2×C4—611no—
250C2×C4—611no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4#1451983911yescharacteristic
264C2×C4#1451984011yescharacteristic
265C8—42no—
266C8—4881no—
267C8—4881no—
268C8—4882no—
269C8—2442no—
270C22—21no—
271C22—21no—
272C22—1221no—
273C22—1221no—
274C22—4881no—
275C22—2441no—
276C22—2441no—
277C22—2441no—
278C22—2441no—
279C22#1684063311yescharacteristic
280C22#1684063511yescharacteristic
281C22#1684063911yescharacteristic
282C4—21no—
283C4—21no—
284C4—41no—
285C4—41no—
286C4—611no—
287C4—611no—
288C4—611no—
289C4—611no—
290C4—2441no—
291C4—2441no—
292C2—21no—
293C2—21no—
294C2—2441no—
295C2—2441no—
296C2#2146069311yescharacteristic
297C2#2146090911yescharacteristic
298C2#2146092111yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#343C4
socleC22×C61#342
prime radicalC23×D61C4⋊C4
cosocleC2×#14519735C22
hypercenter#343#6923
hypocenterC61#7253
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
165. C61#7253semidirect

Maximal subgroups

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

subgroupindex
#214616782
#214610532
#214455562
#725361