Finite Group Databasebeta

← #30599028

Subgroups — #30599028

Order 15616.

450 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 94 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#21461381C212yesmaximal, complemented
2#21461078C212yesmaximal
3#21460684C212yesmaximal, complemented
4C2×#16839825C211yesmaximal, characteristic
5#16840783C2214yes—
6#16840625—22no—
7#16840624—22no—
8#16840606—22no—
9#16840605—22no—
10C23×#92418C411yescharacteristic
11C22×C8×D61C411yescharacteristic
12C2×C4×C22⋊D61C2211yescharacteristic
13#16839825—22no—
14#16839825—22no—
15C2×#14519706C2211yescharacteristic
16C2×#14519689C411yescharacteristic
17C2×C8×Dic61C2211yescharacteristic
18C2×C22⋊C8×C61C411yescharacteristic
19C4⋊#92420—24no—
20C22⋊#92420—24no—
21#14519832—24no—
22C22×C22⋊D61Q811yescharacteristic
23C22×C4×D61C2×C411yescharacteristic
24C22×#92418—21no—
25C22×#92418—21no—
26C22×#92418—42no—
27C22×#92418C2×C411yescharacteristic
28C22×#92418C2×C411yescharacteristic
29C2×C8×D61—21no—
30C2×C8×D61—21no—
31C2×C8×D61—42no—
32C4×C22⋊D61—22no—
33C4×C22⋊D61—22no—
34C2×#11758196Q811yescharacteristic
35C2×C22⋊Dic61D411yescharacteristic
36C2×#11758198D411yescharacteristic
37C2×C4×Dic61C2311yescharacteristic
38#14519706—22no—
39#14519689—22no—
40C8×Dic61D412yes—
41C8×Dic61D412yes—
42C23×C4×C61C2×C411yescharacteristic
43C22×C8×C61C2×C411yescharacteristic
44C22×C8×C61C2×C411yescharacteristic
45C22⋊C8×C61—22no—
46C24×C61C4⋊C411yescharacteristic
47C23×D61C4⋊C411yescharacteristic
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—41no—
51C22×C4×C61—41no—
52C22×C4×C61C4⋊C411yescharacteristic
53C22×C4×C61C22×C411yescharacteristic
54C2×C22⋊D61—22no—
55C2×C22⋊D61—22no—
56C2×C22⋊D61—22no—
57C22×Dic61C4⋊C411yescharacteristic
58C22×Dic61C2×D411yescharacteristic
59C22×Dic61C2×Q811yescharacteristic
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—41no—
63C2×C4×D61—41no—
64C2×#92420—44no—
65C2×C8×C61—21no—
66C2×C8×C61—41no—
67C2×C8×C61—41no—
68C2×C8×C61C22⋊C412yes—
69C22⋊Dic61—22no—
70#11758198—22no—
71#11758196—22no—
72C4×Dic61C2×D412yes—
73C4×Dic61#4112yes—
74C2×#92418—22no—
75C2×#92418—21no—
76C2×#92418—42no—
77C2×#92418—42no—
78C2×#92418—41no—
79C2×#92418C22⋊C411yescharacteristic
80C2×#92418C22⋊C411yescharacteristic
81C8×D61—42no—
82C8×D61—42no—
83C23×C61—21no—
84C23×C61—21no—
85C23×C61—41no—
86C23×C61—41no—
87C23×C61#10812yes—
88C23×C61C2×C4⋊C411yescharacteristic
89C22×D61—21no—
90C22×D61—21no—
91C22×D61—41no—
92C22×D61—41no—
93C22×D61#10812yes—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—42no—
98C2×C4×C61—41no—
99C2×C4×C61—41no—
100C2×C4×C61—41no—
101C2×C4×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61#11711yescharacteristic
103C22⋊D61—28no—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—41no—
108C2×Dic61—41no—
109C2×Dic61#12112yes—
110C2×Dic61C22⋊Q812yes—
111C4×D61—42no—
112C4×D61—41no—
113C4×D61—41no—
114#92420—84no—
115C8×C61—22no—
116C8×C61—41no—
117#92418—21no—
118#92418—41no—
119#92418#10012yes—
120#8620—611nomaximal, Sylow
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—22no—
124C22×C61—42no—
125C22×C61—42no—
126C22×C61—41no—
127C22×C61—41no—
128C22×C61#38011yescharacteristic
129C22×C61C2×#10811yescharacteristic
130C22×C61C2×#10811yescharacteristic
131C2×D61—22no—
132C2×D61—42no—
133C2×D61—41no—
134C2×D61—41no—
135C2×D61—42no—
136C4×C61—21no—
137C4×C61—41no—
138C4×C61C2×#10011yescharacteristic
139C4×C61#41311yescharacteristic
140Dic61—22no—
141Dic61—22no—
142Dic61—41no—
143C2×C8×D4—611no—
144#1568—612no—
145#1466—612no—
146#1290—612no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61—42no—
150C2×C61#180011yescharacteristic
151C2×C61#181011yescharacteristic
152C2×C61#181211yescharacteristic
153D61—42no—
154C23×C8—611no—
155C23×C8—611no—
156C2×C4×D4—611no—
157C8×D4—1222no—
158C8×D4—1222no—
159#432—614no—
160C2×C4⋊C8—611no—
161C2×C22⋊C8—611no—
162C2×C22⋊C8#692311yescharacteristic
163C2×C4×C8—611no—
164#335—1222no—
165#334—1222no—
166#323—1222no—
167#323—1222no—
168C61#862011yescharacteristic, complemented, Sylow
169C22×D4—611no—
170C23×C4—611no—
171C23×C4C2×#692311yescharacteristic
172C22×C8—611no—
173C22×C8—611no—
174C22×C8—1221no—
175C22×C8—1221no—
176C22×C8—1221no—
177C22×C8—1221no—
178C22×C8—2442no—
179C22×C8—2442no—
180C22×C8C2×#692311yescharacteristic
181C22×C8C2×#692311yescharacteristic
182C4×D4—1222no—
183C4×D4—1222no—
184C2×C4⋊C4—611no—
185C2×C22⋊C4—611no—
186C2×C22⋊C4—611no—
187C2×C42—611no—
188C4⋊C8—1222no—
189C4⋊C8—1224no—
190C22⋊C8—22no—
191C22⋊C8—1222no—
192C22⋊C8—1224no—
193#97—1224no—
194C4×C8—612no—
195C4×C8—612no—
196C24—611no—
197C24C4⋊#692311yescharacteristic
198C2×D4—1222no—
199C2×D4—1222no—
200C2×D4—1222no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4—2441no—
211C22×C4—2441no—
212C22×C4C4⋊#692311yescharacteristic
213C22×C4C22×#692311yescharacteristic
214C2×C8—21no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—611no—
218C2×C8—611no—
219C2×C8—1222no—
220C2×C8—1221no—
221C2×C8—2442no—
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2444no—
226C2×C8—2441no—
227C2×C8C22⋊#692312yes—
228C4⋊C4—1222no—
229C22⋊C4—1222no—
230C22⋊C4—1222no—
231C42—612no—
232C42—612no—
233C23—21no—
234C23—21no—
235C23—41no—
236C23—41no—
237C23—612no—
238C23—1221no—
239C23—1221no—
240C23—2441no—
241C23—2441no—
242C23#1451984812yes—
243C23C2×C4⋊#692311yescharacteristic
244D4—1228no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—612no—
253C2×C4—612no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—2442no—
258C2×C4—2441no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4C2×C22⋊#692311yescharacteristic
263C2×C4#1451985611yescharacteristic
264C8—22no—
265C8—41no—
266C8—612no—
267C8—1221no—
268C8—4884no—
269C8—2441no—
270C22—21no—
271C22—21no—
272C22—22no—
273C22—42no—
274C22—42no—
275C22—41no—
276C22—41no—
277C22—1222no—
278C22—2442no—
279C22—2442no—
280C22—2441no—
281C22—2441no—
282C22#1684070411yescharacteristic
283C22D61⋊#10811yescharacteristic
284C22C2×#1451984811yescharacteristic
285C4—21no—
286C4—41no—
287C4—1222no—
288C4—1222no—
289C4—2441no—
290C4D61⋊#10011yescharacteristic
291C4#1684074911yescharacteristic
292C2—21no—
293C2—21no—
294C2—42no—
295C2—2442no—
296C2#2146168411yescharacteristic
297C2#2146169911yescharacteristic
298C2#2146170211yescharacteristic
subgroupG/H
centerC22#16840704
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#380
prime radicalC22×C22⋊D61Q8
cosocleC2×C4×Dic61C23
hypercenterC2×C22⋊C8#6923
hypocenterC61#8620
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #21461381C2semidirect
3. #21460684C2semidirect
168. C61#8620semidirect

Maximal subgroups

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

subgroupindex
#214613812
#214610782
#214606842
C2×#168398252
#862061