Finite Group Databasebeta

← #30604092

Subgroups — #30604092

Order 15616.

814 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 88 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#21461067C212yesmaximal, complemented
2#21460747C214yesmaximal, complemented
3C2×#16839665C211yesmaximal, characteristic
4#16840732—22no—
5#16840607—22no—
6#16840607C2214yescomplemented
7C22×C4⋊Dic61C2211yescharacteristic
8C22×C22⋊Dic61—22no—
9C22×C4×Dic61C411yescharacteristic
10#16839665—22no—
11#16839665C412yes—
12#16839665C2212yes—
13C23×D4×C61C411yescharacteristic
14C2×#11758217—42no—
15C22⋊#92420—24no—
16C22⋊#92420—42no—
17C23×Dic61—21no—
18C23×Dic61D412yes—
19C2×C4⋊Dic61—41no—
20C2×C4⋊Dic61—41no—
21C2×C4⋊Dic61C2×C411yescharacteristic
22C2×C4⋊Dic61D412yes—
23C2×C4⋊Dic61C2311yescharacteristic
24C2×C22⋊Dic61—24no—
25C2×C22⋊Dic61—24no—
26C2×C22⋊Dic61—48no—
27C2×C4×Dic61—21no—
28C2×C4×Dic61—42no—
29C2×C4×Dic61C2×C412yes—
30C25×C61—21no—
31C22×D4×C61—24no—
32C22×D4×C61—21no—
33C22×D4×C61—41no—
34C22×D4×C61—41no—
35C22×D4×C61—42no—
36C22×D4×C61C2×C412yes—
37C23×C4×C61C2×C411yescharacteristic
38C24×C61—24no—
39C24×C61—22no—
40C24×C61—42no—
41C24×C61—44no—
42C24×C61—44no—
43C24×C61—41no—
44C24×C61—41no—
45C24×C61C22⋊C411yescharacteristic
46C2×D4×C61—24no—
47C2×D4×C61—22no—
48C2×D4×C61—48no—
49C2×D4×C61—48no—
50C2×D4×C61—42no—
51C2×D4×C61—42no—
52C2×D4×C61—42no—
53C2×D4×C61—42no—
54C2×D4×C61M1614yescomplemented
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—22no—
58C22×C4×C61—22no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22×C411yescharacteristic
61C22×Dic61—24no—
62C22×Dic61—22no—
63C22×Dic61—22no—
64C22×Dic61—22no—
65C22×Dic61—42no—
66C22×Dic61—42no—
67C22×Dic61—44no—
68C22×Dic61C22⋊C412yes—
69C22×Dic61C2×D412yes—
70#11758217—84no—
71C2×#92420—44no—
72C22⋊Dic61—48no—
73C22⋊Dic61—48no—
74C4⋊Dic61—41no—
75C4⋊Dic61—42no—
76C4⋊Dic61—41no—
77C4×Dic61—42no—
78C4×Dic61—42no—
79C23×C61—22no—
80C23×C61—22no—
81C23×C61—21no—
82C23×C61—21no—
83C23×C61—24no—
84C23×C61—44no—
85C23×C61—44no—
86C23×C61—44no—
87C23×C61—416no—
88C23×C61—44no—
89C23×C61—42no—
90C23×C61—42no—
91C23×C61—88no—
92C23×C61—82no—
93C23×C61—82no—
94C23×C61—82no—
95C23×C61—82no—
96C23×C61#9911yescharacteristic
97C23×C61#9911yescharacteristic
98C23×C61C2×C22⋊C411yescharacteristic
99D4×C61—44no—
100D4×C61—48no—
101D4×C61—44no—
102C2×C4×C61—24no—
103C2×C4×C61—24no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61#10012yes—
109C2×C4×C61C2×M1612yes—
110C2×Dic61—24no—
111C2×Dic61—22no—
112C2×Dic61—22no—
113C2×Dic61—48no—
114C2×Dic61—42no—
115C2×Dic61—44no—
116C2×Dic61—42no—
117C2×Dic61—42no—
118C2×Dic61—42no—
119C2×Dic61—82no—
120#92420—84no—
121#11505—611nomaximal, Sylow
122C22×C61—24no—
123C22×C61—24no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—48no—
131C22×C61—44no—
132C22×C61—84no—
133C22×C61—88no—
134C22×C61—88no—
135C22×C61—82no—
136C22×C61—82no—
137C22×C61#35312yes—
138C22×C61#35512yes—
139C22×C61#40711yescharacteristic
140C22×C61C2×#9911yescharacteristic
141C22×C61C2×#10011yescharacteristic
142C4×C61—22no—
143C4×C61—22no—
144Dic61—44no—
145Dic61—42no—
146Dic61—42no—
147C2×#390—611no—
148#1463—612no—
149#1318—614no—
150C2×C61—21no—
151C2×C61—21no—
152C2×C61—22no—
153C2×C61—22no—
154C2×C61—84no—
155C2×C61#146211yescharacteristic
156C2×C61C2×#35311yescharacteristic
157C2×C61C2×#35511yescharacteristic
158C23×D4#692311yescharacteristic
159C22×C4⋊C4—611no—
160C22×C22⋊C4—1222no—
161C22×C42—611no—
162#407—1222no—
163#390—612no—
164#390—612no—
165#390—1222no—
166#324—614no—
167#324—1222no—
168C61#1150511yescharacteristic, complemented, Sylow
169C25—21no—
170C22×D4—24no—
171C22×D4—21no—
172C22×D4—41no—
173C22×D4—41no—
174C22×D4—42no—
175C22×D4C2×#692312yes—
176C23×C4—612no—
177C23×C4—1221no—
178C23×C4C2×#692311yescharacteristic
179C2×M16—2442no—
180C2×C4⋊C4—612no—
181C2×C4⋊C4—611no—
182C2×C4⋊C4—611no—
183C2×C4⋊C4—2441no—
184C2×C4⋊C4—2441no—
185C2×C22⋊C4—1224no—
186C2×C22⋊C4—1224no—
187C2×C22⋊C4—2448no—
188C2×C42—612no—
189C2×C42—1221no—
190C2×C42—2442no—
191C22⋊C8—1224no—
192C22⋊C8—2442no—
193C24—24no—
194C24—22no—
195C24—44no—
196C24—42no—
197C24—44no—
198C24—41no—
199C24—41no—
200C24C22⋊#692311yescharacteristic
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—48no—
206C2×D4—48no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4#1175821714yescomplemented
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—612no—
215C22×C4—612no—
216C22×C4—1222no—
217C22×C4—1224no—
218C22×C4—1222no—
219C22×C4—1222no—
220C22×C4—2444no—
221C22×C4—2442no—
222C22×C4—2442no—
223C22×C4C22⋊#692311yescharacteristic
224C22×C4C22×#692311yescharacteristic
225M16—4884no—
226C2×C8—2444no—
227C4⋊C4—2442no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C22⋊C4—2448no—
231C22⋊C4—2448no—
232C42—2442no—
233C42—2442no—
234C23—21no—
235C23—21no—
236C23—22no—
237C23—22no—
238C23—24no—
239C23—44no—
240C23—44no—
241C23—44no—
242C23—416no—
243C23—44no—
244C23—42no—
245C23—42no—
246C23—88no—
247C23—82no—
248C23—82no—
249C23—82no—
250C23—82no—
251C23#1451983511yescharacteristic
252C23#1451983511yescharacteristic
253C23C2×C22⋊#692311yescharacteristic
254D4—44no—
255D4—48no—
256D4—44no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—1224no—
264C2×C4—1222no—
265C2×C4—1222no—
266C2×C4—4882no—
267C2×C4—2448no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2444no—
271C2×C4—2442no—
272C2×C4—2442no—
273C2×C4#1451983712yes—
274C2×C4C2×#1175821712yes—
275C8—4884no—
276C22—24no—
277C22—24no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—48no—
285C22—44no—
286C22—84no—
287C22—88no—
288C22—88no—
289C22—82no—
290C22—82no—
291C22#1684066612yes—
292C22#1684067012yes—
293C22#1684073211yescharacteristic
294C22C2×#1451983511yescharacteristic
295C22C2×#1451983711yescharacteristic
296C4—22no—
297C4—22no—
298C4—2444no—
299C4—2442no—
300C4—2442no—
301C2—21no—
302C2—21no—
303C2—22no—
304C2—22no—
305C2—84no—
306C2#2146106411yescharacteristic
307C2C2×#1684066611yescharacteristic
308C2C2×#1684067011yescharacteristic
subgroupG/H
centerC22C2×#14519835
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
Fitting, prime radicalC23×D4×C61C4
socleC22×C61C2×#99
cosocleC2×C4⋊Dic61C23
hypercenterC23×D4#6923
hypocenterC61#11505
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. #21461067C2semidirect
2. #21460747C2semidirect
6. #16840607C22semidirect
54. C2×D4×C61M16semidirect
168. C61#11505semidirect
209. C2×D4#11758217semidirect

Maximal subgroups

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

subgroupindex
#214610672
#214607472
C2×#168396652
#1150561