Finite Group Databasebeta

← #30595408

Subgroups — #30595408

Order 15616.

424 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 106 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#21461747C211yesmaximal, characteristic
2#21461534C211yesmaximal, characteristic
3#21460639C212yesmaximal
4#21460638C212yesmaximal
5#21448294C211yesmaximal, characteristic
6C2×C4×#92420—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628—21no—
10#16840628C2212yes—
11#16840628C2212yes—
12C2×Q8×Dic61C411yescharacteristic
13#16839669C2211yescharacteristic
14#16839660C411yescharacteristic
15#16839658C2211yescharacteristic
16#16839647—21no—
17#16839645—21no—
18C4⋊C4×Dic61C411yescharacteristic
19#16839613—21no—
20#16839607—21no—
21C42×Dic61C2211yescharacteristic
22C61×#391C411yescharacteristic
23C22×#92420—22no—
24C22×#92420—22no—
25C4×#92420—24no—
26Q8×Dic61—22no—
27Q8×Dic61C814yescomplemented
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C4⋊Dic61C2×C411yescharacteristic
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×C4×Dic61—21no—
34C2×C4×Dic61—21no—
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39C2×C4×Dic61D411yescharacteristic
40C2×C4×Dic61C2311yescharacteristic
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46C22×Q8×C61C2×C411yescharacteristic
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C42×C61C2×C411yescharacteristic
49#95×C61—21no—
50#95×C61—21no—
51C2×Q8×C61—21no—
52C2×Q8×C61—41no—
53C2×Q8×C61—41no—
54C2×Q8×C61C2×C812yes—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22×C411yescharacteristic
60C22×Dic61—21no—
61C22×Dic61—21no—
62C22×Dic61C22⋊C411yescharacteristic
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C2×D411yescharacteristic
65C22×Dic61C2×D411yescharacteristic
66C2×#92420—24no—
67C2×#92420—42no—
68C2×#92420—42no—
69C2×#92420—42no—
70C2×#92420—42no—
71C2×#92420—42no—
72C4⋊C4×C61—41no—
73C42×C61—41no—
74C4⋊Dic61—21no—
75C4⋊Dic61—24no—
76C4⋊Dic61—41no—
77C4⋊Dic61C2×C812yes—
78#11758196—42no—
79#11758196—42no—
80C4×Dic61—22no—
81C4×Dic61—24no—
82C4×Dic61—22no—
83C4×Dic61—22no—
84C4×Dic61—41no—
85C4×Dic61—41no—
86C4×Dic61—42no—
87C4×Dic61C2×C812yes—
88C4×Dic61M1612yes—
89C23×C61C2×C22⋊C411yescharacteristic
90Q8×C61—42no—
91Q8×C61—42no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—22no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—41no—
101C2×C4×C61—41no—
102C2×C4×C61—41no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61#10412yes—
106C2×C4×C61C22×C811yescharacteristic
107C2×C4×C61C2×M1611yescharacteristic
108C2×Dic61—21no—
109C2×Dic61—21no—
110C2×Dic61—21no—
111C2×Dic61—21no—
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61—21no—
116C2×Dic61—22no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61C22⋊C812yes—
123C2×Dic61C22⋊C812yes—
124C2×Dic61#13512yes—
125C2×Dic61#13712yes—
126#92420—44no—
127#92420—82no—
128#7581—611nomaximal, Sylow
129C22×C61C2×C22⋊C811yescharacteristic
130C22×C61#41011yescharacteristic
131C22×C61#41311yescharacteristic
132C22×C61#41611yescharacteristic
133C22×C61#41911yescharacteristic
134C22×C61C2×#10411yescharacteristic
135C22×C61#42111yescharacteristic
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—22no—
139C4×C61—41no—
140C4×C61—42no—
141C4×C61—81no—
142Dic61—22no—
143Dic61—22no—
144Dic61—22no—
145Dic61—22no—
146Dic61—42no—
147Dic61—81no—
148#2295—611no—
149#1839—611no—
150#1744—611no—
151#1272—612no—
152#1271—612no—
153C2×C61#145811yescharacteristic
154C2×C61#147611yescharacteristic
155C2×C61#147911yescharacteristic
156C2×C61#150611yescharacteristic
157C2×C61#152111yescharacteristic
158C2×C61#153211yescharacteristic
159C2×C61#155411yescharacteristic
160C2×C4×Q8—611no—
161C2×C4×C8—1221no—
162#391—611no—
163#391#692311yescharacteristic
164#389—611no—
165#389—611no—
166#387—1221no—
167#387—1221no—
168C4×C4⋊C4—611no—
169C4×C4⋊C4—1221no—
170#376—1221no—
171C43—611no—
172#336—612no—
173#336—612no—
174#336—1221no—
175#336—1221no—
176#336—1221no—
177C61#758111yescharacteristic, complemented, Sylow
178C22×Q8C2×#692311yescharacteristic
179C22×C8—1222no—
180C22×C8—1222no—
181C4×Q8—614no—
182C4×Q8—1222no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4—1221no—
186C2×C4⋊C4—1221no—
187C2×C4⋊C4—1221no—
188C2×C4⋊C4C2×#692311yescharacteristic
189C2×C42—611no—
190C2×C42—611no—
191C2×C42—611no—
192C2×C42—611no—
193C2×C42—611no—
194C2×C42—611no—
195C2×C42—1221no—
196C2×C42—1221no—
197C2×C42C2×#692311yescharacteristic
198C4×C8—1224no—
199#95—21no—
200#95—21no—
201#95—1221no—
202#95—1221no—
203#95—1221no—
204#95—1221no—
205#95—1221no—
206C2×Q8—21no—
207C2×Q8—41no—
208C2×Q8—41no—
209C2×Q8D61⋊C812yes—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—611no—
213C22×C4—611no—
214C22×C4—611no—
215C22×C4—611no—
216C22×C4—1221no—
217C22×C4—1221no—
218C22×C4C22⋊#692311yescharacteristic
219C22×C4C22⋊#692311yescharacteristic
220C22×C4C22×#692311yescharacteristic
221C2×C8—1224no—
222C2×C8—2442no—
223C2×C8—2442no—
224C2×C8—2442no—
225C2×C8—2442no—
226C2×C8—2442no—
227C4⋊C4—41no—
228C4⋊C4—612no—
229C4⋊C4—1224no—
230C4⋊C4—1221no—
231C4⋊C4—2441no—
232C4⋊C4—2442no—
233C4⋊C4—2442no—
234C42—41no—
235C42—612no—
236C42—612no—
237C42—1222no—
238C42—1222no—
239C42—1224no—
240C42—1222no—
241C42—2441no—
242C42—2441no—
243C42—2442no—
244C23C2×C22⋊#692311yescharacteristic
245Q8—42no—
246Q8—42no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—612no—
261C2×C4—612no—
262C2×C4—612no—
263C2×C4—612no—
264C2×C4—1221no—
265C2×C4—1221no—
266C2×C4—1221no—
267C2×C4—1221no—
268C2×C4—1221no—
269C2×C4—1221no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—1222no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4#1451984212yes—
279C2×C4C2×D61⋊C811yescharacteristic
280C2×C4D61⋊M1611yescharacteristic
281C8—4882no—
282C8—2444no—
283C22D61⋊(C22⋊C8)11yescharacteristic
284C22#1684074211yescharacteristic
285C22#1684074911yescharacteristic
286C22#1684075211yescharacteristic
287C22#1684075511yescharacteristic
288C22C2×#1451984211yescharacteristic
289C22#1684075911yescharacteristic
290C4—22no—
291C4—21no—
292C4—21no—
293C4—42no—
294C4—41no—
295C4—81no—
296C4—1222no—
297C4—1222no—
298C4—1222no—
299C4—1222no—
300C4—4881no—
301C4—2442no—
302C2#2146105111yescharacteristic
303C2#2146111311yescharacteristic
304C2#2146112211yescharacteristic
305C2#2146121311yescharacteristic
306C2#2146126011yescharacteristic
307C2#2146129711yescharacteristic
308C2#2146134511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#391C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#391#6923
hypocenterC61#7581
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
27. Q8×Dic61C8semidirect
177. C61#7581semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214615342
#214606392
#214606382
#214482942
#758161