Finite Group Databasebeta

← #29580604

Subgroups — #29580604

Order 15616.

632 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×#16840098C212yesmaximal
2#21451933C211yesmaximal, characteristic
3C2×#16839500C212yesmaximal
4#21444088C211yesmaximal, characteristic
5C61×#1280C211yesmaximal, characteristic
6C2×#14519756C2212yes—
7C22×C4⋊Dic61C2211yescharacteristic
8#16840098—24no—
9#16840098—24no—
10C2×#14519711—22no—
11C2×#14519702—22no—
12#16839694—22no—
13#16839683—22no—
14#16839622—22no—
15C2×#14519684—22no—
16C2×#14519684C2211yescharacteristic
17#16839500—24no—
18C2×C22⋊C8×C61C2212yes—
19C2×#95×C61C2211yescharacteristic
20C22×Dic122D412yes—
21C23×Dic61—21no—
22C23×Dic61—21no—
23#14519756—22no—
24#14519756—22no—
25#14519756—22no—
26#14519756—22no—
27C2×C4⋊Dic61—22no—
28C2×C4⋊Dic61—22no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61—22no—
32C2×C4⋊Dic61D412yes—
33C2×C4⋊Dic61D412yes—
34C2×#11758196—22no—
35C2×C22⋊Dic61—22no—
36#14519711—28no—
37#14519702—28no—
38#14519684—24no—
39#14519684—22no—
40#14519684—44no—
41C23×C4×C61D412yes—
42C23×C4×C61C2311yescharacteristic
43C22×C8×C61—22no—
44C22⋊C8×C61—22no—
45C22⋊C8×C61D414yes—
46#95×C61—22no—
47C24×C61C2×D411yescharacteristic
48C22×C4×C61—22no—
49C22×C4×C61—22no—
50C22×C4×C61—42no—
51C22×C4×C61—42no—
52C22×C4×C61—42no—
53C22×C4×C61Q1614yes—
54C22×C4×C61C2×D412yes—
55C22×C4×C61C2×D411yescharacteristic
56C22×C4×C61C2×D412yes—
57C22×C4×C61#4111yescharacteristic
58C22×Dic61—22no—
59C22×Dic61—22no—
60C22×Dic61—22no—
61C22×Dic61—22no—
62C22×Dic61—41no—
63C22×Dic61—42no—
64C22×Dic61—42no—
65C22×Dic61—42no—
66C22×Dic61—41no—
67C22×Dic61—41no—
68C22×Dic61—41no—
69C22×Dic61—42no—
70C2×Dic122—22no—
71C2×Dic122—22no—
72C2×Dic122—44no—
73C2×C8×C61—24no—
74C2×C8×C61—44no—
75C22⋊Dic61—42no—
76C22⋊Dic61—42no—
77C4⋊Dic61—24no—
78C4⋊Dic61—22no—
79C4⋊Dic61—22no—
80C4⋊Dic61—42no—
81C4⋊Dic61—82no—
82C4⋊Dic61—82no—
83#11758196—42no—
84#11758196—42no—
85C23×C61—21no—
86C23×C61—21no—
87C23×C61—22no—
88C23×C61#12011yescharacteristic
89C23×C61#12111yescharacteristic
90C23×C61#12711yescharacteristic
91C23×C61C2×Q1612yes—
92C23×C61#13712yes—
93C2×C4×C61—24no—
94C2×C4×C61—24no—
95C2×C4×C61—41no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61—44no—
101C2×C4×C61—82no—
102C2×C4×C61#12012yes—
103C2×C4×C61#12112yes—
104C2×Dic61—44no—
105C2×Dic61—42no—
106C2×Dic61—44no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—42no—
112C2×Dic61—44no—
113C2×Dic61—82no—
114C2×Dic61—81no—
115C2×Dic61—82no—
116C2×Dic61—81no—
117C2×Dic61—81no—
118C2×Dic61—81no—
119Dic122—44no—
120Dic122—82no—
121C8×C61—44no—
122#9972—611nomaximal, Sylow
123C22×C61—22no—
124C22×C61—22no—
125C22×C61—22no—
126C22×C61—22no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61#39211yescharacteristic
132C22×C61#45112yes—
133C22×C61#45311yescharacteristic
134C22×C61#45411yescharacteristic
135C22×C61#45812yes—
136C22×C61#46212yes—
137C22×C61#49411yescharacteristic
138C22×C61#49711yescharacteristic
139C4×C61—22no—
140C4×C61—22no—
141C4×C61—44no—
142Dic61—82no—
143Dic61—82no—
144Dic61—82no—
145Dic61—82no—
146C2×#484—612no—
147#2659—611no—
148C2×#328—612no—
149#1445—611no—
150#1280D6111yescharacteristic
151C2×C61—21no—
152C2×C61—22no—
153C2×C61—21no—
154C2×C61#161412yes—
155C2×C61#161712yes—
156C2×C61#200611yescharacteristic
157C2×C61#201611yescharacteristic
158C2×C61#202211yescharacteristic
159C2×C22⋊Q8—612no—
160C22×C4⋊C4—611no—
161#484—1224no—
162#484—1224no—
163C2×#107—1222no—
164C2×#103—1222no—
165C2×C22⋊C8C2×D6112yes—
166#398—1222no—
167#395—1222no—
168#380—1222no—
169C2×#95—611no—
170C2×#95—1222no—
171C2×#95C2×D6111yescharacteristic
172#328—1224no—
173C61#997211yescharacteristic, complemented, Sylow
174C22×Q8—612no—
175C23×C4—1221no—
176C23×C4—1221no—
177C23×C4D24412yes—
178C23×C4C22×D6111yescharacteristic
179C22×C8—22no—
180C22⋊Q8—1222no—
181C22⋊Q8—1222no—
182C22⋊Q8—1222no—
183C22⋊Q8—1222no—
184C2×C4⋊C4—612no—
185C2×C4⋊C4—612no—
186C2×C4⋊C4—1222no—
187C2×C4⋊C4—1222no—
188C2×C4⋊C4—1222no—
189C2×C4⋊C4—1222no—
190C2×C4⋊C4—1222no—
191C2×C4⋊C4—1221no—
192C2×C22⋊C4—1222no—
193#107—1228no—
194#103—1228no—
195C22⋊C8—22no—
196C22⋊C8D24414yes—
197#95—22no—
198#95—1224no—
199#95—1222no—
200#95—2444no—
201C24C2×D24411yescharacteristic
202C2×Q8—1222no—
203C2×Q8—1222no—
204C2×Q8—2444no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—1222no—
211C22×C4—1222no—
212C22×C4—1222no—
213C22×C4—1222no—
214C22×C4—2442no—
215C22×C4—2441no—
216C22×C4—2442no—
217C22×C4—2442no—
218C22×C4—2442no—
219C22×C4—2441no—
220C22×C4—2441no—
221C22×C4—2441no—
222C22×C4Dic24414yes—
223C22×C4C2×D24412yes—
224C22×C4D4×D6112yes—
225C22×C4D4×D6111yescharacteristic
226C22×C4#1175822611yescharacteristic
227C2×C8—24no—
228C2×C8—44no—
229C4⋊C4—1224no—
230C4⋊C4—1222no—
231C4⋊C4—1222no—
232C4⋊C4—4882no—
233C4⋊C4—4882no—
234C4⋊C4—2442no—
235C4⋊C4—2442no—
236C4⋊C4—2442no—
237C22⋊C4—2442no—
238C22⋊C4—2442no—
239C23—21no—
240C23—22no—
241C23—21no—
242C23#1451974711yescharacteristic
243C23#1451975211yescharacteristic
244C23#1451977411yescharacteristic
245C23C2×Dic24412yes—
246C23#1451981012yes—
247Q8—4882no—
248Q8—2444no—
249C2×C4—24no—
250C2×C4—24no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—44no—
257C2×C4—82no—
258C2×C4—4881no—
259C2×C4—4882no—
260C2×C4—4882no—
261C2×C4—4881no—
262C2×C4—4881no—
263C2×C4—4881no—
264C2×C4—2442no—
265C2×C4—2444no—
266C2×C4—2444no—
267C2×C4—2442no—
268C2×C4—2444no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4—2442no—
272C2×C4—2442no—
273C2×C4#1451974712yes—
274C2×C4#1451975212yes—
275C8—44no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22—22no—
284C22#1683967211yescharacteristic
285C22#1683992012yes—
286C22#1683993211yescharacteristic
287C22#1683993711yescharacteristic
288C22#1683995312yes—
289C22#1683997312yes—
290C22#1684014211yescharacteristic
291C22#1684015611yescharacteristic
292C4—22no—
293C4—22no—
294C4—44no—
295C4—4882no—
296C4—4882no—
297C4—4882no—
298C4—4882no—
299C2—21no—
300C2—22no—
301C2—21no—
302C2#2144484612yes—
303C2#2144486312yes—
304C2#2144686311yescharacteristic
305C2#2144692111yescharacteristic
306C2#2144695111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#1280D61
hypocenterC61#9972
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
173. C61#9972semidirect

Maximal subgroups

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

subgroupindex
C2×#168400982
#214519332
C2×#168395002
#214440882
C61×#12802
#997261