Finite Group Databasebeta

← #30599238

Subgroups — #30599238

Order 15616.

540 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 126 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
2C4×#14519834C211yesmaximal, characteristic
3#21460655C214yesmaximal, complemented
4#21448224C211yesmaximal, characteristic
5C2×C4⋊#92420C2212yes—
6C2×#14519834—21no—
7C2×#14519834—21no—
8C2×C4×#92420C2212yes—
9#16840628—21no—
10#16840628—21no—
11C2×#14519735—21no—
12C2×C42×D61C2211yescharacteristic
13#16839632C411yescharacteristic
14#16839627—21no—
15#16839619—21no—
16#16839619C412yes—
17C4⋊C4×Dic61—21no—
18C4⋊C4×Dic61C2212yes—
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22C4⋊#92420—24no—
23#14519834—24no—
24#14519834—42no—
25C4×#92420—24no—
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29#14519735—42no—
30#14519735—42no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61C2×C412yes—
34C2×#11758198—22no—
35C2×C4×Dic61—22no—
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61C2311yescharacteristic
39C42×D61—24no—
40#14519684—22no—
41#14519684—22no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61—21no—
44C2×C4⋊C4×C61C2×C412yes—
45C2×C42×C61C2×C411yescharacteristic
46C23×D61C22⋊C411yescharacteristic
47C22×C4×C61—22no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22⋊C411yescharacteristic
50C22×C4×C61C22×C411yescharacteristic
51C22×Dic61—22no—
52C22×Dic61C22⋊C411yescharacteristic
53C22×Dic61C2×D411yescharacteristic
54C22×Dic61C2×D411yescharacteristic
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—22no—
59C2×C4×D61—22no—
60C2×C4×D61—22no—
61C2×C4×D61—22no—
62C2×C4×D61—41no—
63C2×C4×D61D812yes—
64C2×C4×D61SD1612yes—
65C2×#92420—24no—
66C2×#92420—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C4⋊C4×C61—24no—
72C4⋊C4×C61—42no—
73C4⋊C4×C61—42no—
74C42×C61—22no—
75#11758198—44no—
76C4⋊Dic61—24no—
77C4⋊Dic61—42no—
78C4⋊Dic61—42no—
79C4×Dic61—22no—
80C4×Dic61—22no—
81C4×Dic61—42no—
82C4×Dic61—42no—
83C4×Dic61#4114yes—
84C23×C61C2×C22⋊C411yescharacteristic
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61#10212yes—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—42no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61#10212yes—
100C2×C4×C61#10412yes—
101C2×C4×C61#11712yes—
102C2×C4×C61#13112yes—
103C2×C4×C61#13112yes—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61#12312yes—
113C2×Dic61#12312yes—
114C2×Dic61C2×D811yescharacteristic
115C2×Dic61C2×SD1611yescharacteristic
116C2×Dic61#13712yes—
117C4×D61—24no—
118C4×D61—24no—
119C4×D61—44no—
120C4×D61—44no—
121#92420—44no—
122#92420—82no—
123#8709—611nomaximal, Sylow
124C22×C61#38111yescharacteristic
125C22×C61#40811yescharacteristic
126C22×C61#40811yescharacteristic
127C22×C61C2×#10211yescharacteristic
128C22×C61#41911yescharacteristic
129C22×C61C2×#10411yescharacteristic
130C22×C61#42111yescharacteristic
131C2×D61—22no—
132C2×D61—22no—
133C2×D61—22no—
134C2×D61—41no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—41no—
138C4×C61—22no—
139C4×C61—22no—
140C4×C61—82no—
141C4×C61#43314yes—
142Dic61—22no—
143Dic61—41no—
144Dic61—82no—
145Dic61#48012yes—
146Dic61#48312yes—
147#2285—611no—
148#1797—611no—
149C4×C22⋊C8—611no—
150#1279—614no—
151C2×C61#148011yescharacteristic
152C2×C61#148511yescharacteristic
153C2×C61#149211yescharacteristic
154C2×C61#149711yescharacteristic
155C2×C61#181811yescharacteristic
156C2×C61#182311yescharacteristic
157C2×C61#182611yescharacteristic
158D61—42no—
159C2×#117—1221no—
160C22×C42—611no—
161C2×C4⋊C8—612no—
162C2×C22⋊C8—1221no—
163C2×C22⋊C8—1221no—
164C2×C4×C8—612no—
165#384—611no—
166#384#692311yescharacteristic
167#382—1221no—
168#380—612no—
169#380—1221no—
170C4×C4⋊C4—612no—
171C4×C4⋊C4—1221no—
172#336—1221no—
173#336—1221no—
174C61#870911yescharacteristic, complemented, Sylow
175C23×C4—611no—
176C23×C4—611no—
177C23×C4—611no—
178C22×C8—1222no—
179C22×C8—1222no—
180#117—2442no—
181#117—2442no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—612no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4C2×#692312yes—
188C2×C22⋊C4—1222no—
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—1224no—
193C2×C42—1222no—
194C2×C42C2×#692311yescharacteristic
195C4⋊C8—1224no—
196C22⋊C8—1224no—
197C22⋊C8—2442no—
198C4×C8—1224no—
199#95—1222no—
200#95—1222no—
201C24—611no—
202C22×C4—22no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—612no—
206C22×C4—612no—
207C22×C4—611no—
208C22×C4—1222no—
209C22×C4—1222no—
210C22×C4—1222no—
211C22×C4—1222no—
212C22×C4—1222no—
213C22×C4—1222no—
214C22×C4—1222no—
215C22×C4—1222no—
216C22×C4—2441no—
217C22×C4C22⋊#692311yescharacteristic
218C22×C4C22⋊#692311yescharacteristic
219C22×C4C22×#692311yescharacteristic
220C2×C8—1224no—
221C2×C8—2442no—
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C4⋊C4—24no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—1224no—
230C4⋊C4—2442no—
231C4⋊C4—2442no—
232C22⋊C4—2444no—
233C42—22no—
234C42—614no—
235C42—1222no—
236C42—1222no—
237C42—2442no—
238C42—2442no—
239C23—612no—
240C23—1221no—
241C23—1221no—
242C23—1221no—
243C23—1221no—
244C23—1221no—
245C23—1221no—
246C23C2×C22⋊#692311yescharacteristic
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—612no—
255C2×C4—611no—
256C2×C4—611no—
257C2×C4—612no—
258C2×C4—612no—
259C2×C4—1224no—
260C2×C4—1224no—
261C2×C4—1221no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—2444no—
267C2×C4—2442no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2444no—
271C2×C4#1451983912yes—
272C2×C4#1451984212yes—
273C2×C4#1451985612yes—
274C2×C4#1451986412yes—
275C2×C4#1451986512yes—
276C8—4882no—
277C8—2444no—
278C22—1222no—
279C22—1222no—
280C22—1222no—
281C22—2441no—
282C22—2441no—
283C22—2441no—
284C22—2441no—
285C22#1684070511yescharacteristic
286C22#1684073611yescharacteristic
287C22#1684073711yescharacteristic
288C22C2×#1451983911yescharacteristic
289C22#1684075511yescharacteristic
290C22C2×#1451984211yescharacteristic
291C22#1684076011yescharacteristic
292C4—22no—
293C4—22no—
294C4—82no—
295C4—612no—
296C4—612no—
297C4—1222no—
298C4—4882no—
299C4—2441no—
300C4#1684078714yes—
301C2—2442no—
302C2#2146112511yescharacteristic
303C2#2146114211yescharacteristic
304C2#2146116611yescharacteristic
305C2#2146118311yescharacteristic
306C2#2146171311yescharacteristic
307C2#2146172211yescharacteristic
308C2#2146172611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socleC23×C61C2×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#8709
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #21460655C2semidirect
174. C61#8709semidirect

Maximal subgroups

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

subgroupindex
#214616742
C4×#145198342
#214606552
#214482242
#870961