Finite Group Databasebeta

← #30595925

Subgroups — #30595925

Order 15616.

494 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 100 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#21461711C211yesmaximal, characteristic
2#21461676C211yesmaximal, characteristic
3#21460640C214yesmaximal, complemented
4#21454172C211yesmaximal, characteristic
5C2×#14519844—21no—
6C2×#14519834—21no—
7C2×#14519834—21no—
8#16840628—21no—
9#16840628C2212yes—
10#16840628C2212yes—
11C2×#14519777C411yescharacteristic
12C2×#14519757C412yes—
13C2×C42×D61C2211yescharacteristic
14#16839667C2212yes—
15#16839661—21no—
16#16839661—21no—
17#16839619—21no—
18#16839619—21no—
19C61×#384C411yescharacteristic
20C22×#92420—22no—
21C22×#92420—22no—
22#14519844—42no—
23#14519834—42no—
24#14519834—42no—
25C22×Dic122C2×C412yes—
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C22×C4×D61D411yescharacteristic
29#14519777—42no—
30#14519757—44no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—22no—
34C2×#11758198—22no—
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61C2311yescharacteristic
38C42×D61—42no—
39#14519684—22no—
40#14519684—22no—
41C2×C4⋊C4×C61—21no—
42C2×C4⋊C4×C61—21no—
43C2×C4⋊C4×C61C2×C412yes—
44C2×C42×C61C2×C411yescharacteristic
45C23×D61C22⋊C411yescharacteristic
46C22×C4×C61—22no—
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—22no—
51C22×Dic61C22⋊C411yescharacteristic
52C22×Dic61C2×D411yescharacteristic
53C22×Dic61C2×D411yescharacteristic
54C2×C4×D61—22no—
55C2×C4×D61—22no—
56C2×C4×D61—22no—
57C2×C4×D61—22no—
58C2×C4×D61—41no—
59C2×C4×D61—41no—
60C2×C4×D61—41no—
61C2×C4×D61—41no—
62C2×C4×D61SD1612yes—
63C2×C4×D61Q1612yes—
64C2×Dic122—24no—
65C2×Dic122—42no—
66C2×Dic122—42no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C2×#92420—42no—
73C4⋊C4×C61—42no—
74C4⋊C4×C61—42no—
75C4⋊C4×C61—42no—
76C42×C61—22no—
77#11758198—44no—
78C4⋊Dic61—42no—
79C4⋊Dic61—42no—
80C4⋊Dic61—44no—
81C4×Dic61—22no—
82C4×Dic61—41no—
83C4×Dic61—41no—
84C23×C61C2×C22⋊C411yescharacteristic
85C22×D61—21no—
86C22×D61—21no—
87C22×D61—21no—
88C22×D61—21no—
89C22×D61—21no—
90C22×D61—21no—
91C22×D61#10312yes—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61—42no—
101C2×C4×C61#9912yes—
102C2×C4×C61#10312yes—
103C2×C4×C61#13112yes—
104C2×Dic61—21no—
105C2×Dic61—21no—
106C2×Dic61—21no—
107C2×Dic61—21no—
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61—42no—
113C2×Dic61#10012yes—
114C2×Dic61C2×SD1611yescharacteristic
115C2×Dic61C2×Q1611yescharacteristic
116C2×Dic61#13712yes—
117C4×D61—42no—
118C4×D61—42no—
119C4×D61—44no—
120C4×D61—44no—
121Dic122—84no—
122#92420—82no—
123#92420—82no—
124#7727—611nomaximal, Sylow
125C22×C61#40811yescharacteristic
126C22×C61C2×#9911yescharacteristic
127C22×C61C2×#10011yescharacteristic
128C22×C61C2×#10311yescharacteristic
129C22×C61#41911yescharacteristic
130C22×C61#42111yescharacteristic
131C22×C61#42111yescharacteristic
132C2×D61—22no—
133C2×D61—22no—
134C2×D61—22no—
135C2×D61—41no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—41no—
139C4×C61—22no—
140C4×C61—22no—
141C4×C61—22no—
142C4×C61—82no—
143Dic61—22no—
144Dic61—22no—
145Dic61—21no—
146Dic61—21no—
147Dic61—82no—
148#2857—611no—
149#1817—611no—
150#1797—611no—
151#1272—614no—
152C2×C61#147111yescharacteristic
153C2×C61#148111yescharacteristic
154C2×C61#149711yescharacteristic
155C2×C61#151111yescharacteristic
156C2×C61#152011yescharacteristic
157C2×C61#153611yescharacteristic
158C2×C61#154811yescharacteristic
159D61—42no—
160C2×C4⋊Q8—611no—
161C2×C22⋊Q8—612no—
162C22×C42—611no—
163C2×C4⋊C8—1221no—
164C2×C22⋊C8—1221no—
165C2×C22⋊C8—1221no—
166#391—612no—
167#389—1221no—
168#389—1221no—
169#384#692311yescharacteristic
170#380—1221no—
171#380—1221no—
172#336—612no—
173#336—612no—
174#336—1221no—
175C61#772711yescharacteristic, complemented, Sylow
176C22×Q8—612no—
177C23×C4—611no—
178C23×C4—611no—
179C23×C4—611no—
180C22×C8—1222no—
181C22×C8—1222no—
182C4⋊Q8—2442no—
183C22⋊Q8—2444no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—1222no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4—1221no—
189C2×C4⋊C4C2×#692312yes—
190C2×C22⋊C4—1222no—
191C2×C42—611no—
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—2442no—
195C2×C42C2×#692311yescharacteristic
196C4⋊C8—2442no—
197C22⋊C8—2442no—
198C22⋊C8—2442no—
199#95—1222no—
200#95—1222no—
201C24—611no—
202C2×Q8—1224no—
203C2×Q8—2442no—
204C2×Q8—2442no—
205C22×C4—22no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—611no—
209C22×C4—612no—
210C22×C4—612no—
211C22×C4—1222no—
212C22×C4—1222no—
213C22×C4—1222no—
214C22×C4—1222no—
215C22×C4—1222no—
216C22×C4—2441no—
217C22×C4—2441no—
218C22×C4—2441no—
219C22×C4—2441no—
220C22×C4C22⋊#692311yescharacteristic
221C22×C4C22⋊#692311yescharacteristic
222C22×C4C22×#692311yescharacteristic
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C2×C8—2442no—
228C2×C8—2442no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C4⋊C4—2442no—
233C4⋊C4—2444no—
234C4⋊C4—2442no—
235C22⋊C4—2444no—
236C42—22no—
237C42—1222no—
238C42—2441no—
239C42—2441no—
240C23—612no—
241C23—1221no—
242C23—1221no—
243C23—1221no—
244C23—1221no—
245C23—1221no—
246C23—1221no—
247C23C2×C22⋊#692311yescharacteristic
248Q8—4884no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—612no—
259C2×C4—611no—
260C2×C4—611no—
261C2×C4—612no—
262C2×C4—1221no—
263C2×C4—1221no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2444no—
271C2×C4—2444no—
272C2×C4—2442no—
273C2×C4—2442no—
274C2×C4—2442no—
275C2×C4#1451983612yes—
276C2×C4#1451984012yes—
277C2×C4#1451986512yes—
278C8—4882no—
279C8—4882no—
280C22—1222no—
281C22—1222no—
282C22—1222no—
283C22—2441no—
284C22—2441no—
285C22—2441no—
286C22—2441no—
287C22#1684073711yescharacteristic
288C22C2×#1451983611yescharacteristic
289C22D61⋊#10011yescharacteristic
290C22C2×#1451984011yescharacteristic
291C22#1684075511yescharacteristic
292C22#1684076011yescharacteristic
293C22#1684076011yescharacteristic
294C4—22no—
295C4—22no—
296C4—22no—
297C4—82no—
298C4—1221no—
299C4—1221no—
300C4—1222no—
301C4—1222no—
302C4—4882no—
303C2—2442no—
304C2#2146109611yescharacteristic
305C2#2146112911yescharacteristic
306C2#2146118311yescharacteristic
307C2#2146122711yescharacteristic
308C2#2146125811yescharacteristic
309C2#2146130811yescharacteristic
310C2#2146133311yescharacteristic
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#7727
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
3. #21460640C2semidirect
175. C61#7727semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214616762
#214606402
#214541722
#772761