Finite Group Databasebeta

← #29590413

Subgroups — #29590413

Order 15616.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#21451695C211yesmaximal, characteristic
2C4×#14519696C211yesmaximal, characteristic
3#21443847C212yesmaximal
4#21443826C212yesmaximal
5C61×#1461C211yesmaximal, characteristic
6C2×#14519769C411yescharacteristic
7C2×#14519696—21no—
8C4×#11758194—21no—
9#16839701C411yescharacteristic
10#16839701C2211yescharacteristic
11#16839700—21no—
12#16839692C411yescharacteristic
13#16839692C2211yescharacteristic
14#16839681—21no—
15#16839646—21no—
16#16839646—21no—
17#16839630C411yescharacteristic
18#16839531C2212yes—
19C2×C4×Q8×C61C2211yescharacteristic
20C61×#431—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23C2×#11758194—22no—
24#14519769—41no—
25#14519769—41no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32#14519696—24no—
33#14519688—41no—
34C4×#92418—41no—
35#14519684—21no—
36#14519684—21no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684C2×C411yescharacteristic
44#14519684C2×C411yescharacteristic
45C22×Q8×C61D411yescharacteristic
46C4×Q8×C61—41no—
47C4×Q8×C61—41no—
48C2×C4⋊C4×C61C2×C411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61C2311yescharacteristic
51C2×C42×C61C2×C411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C4⋊C8×C61—41no—
55C22⋊C8×C61—22no—
56C4×C8×C61—41no—
57C2×Q8×C61—22no—
58C2×Q8×C61—22no—
59C2×Q8×C61—41no—
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22×C411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C22×Dic61—21no—
71C2×C8×C61—42no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C4⋊C4×C61—41no—
75C42×C61—21no—
76C42×C61—21no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C42×C61—21no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758196—42no—
84#11758196—41no—
85#11758196—41no—
86#11758196—42no—
87#11758196—42no—
88#11758194—24no—
89#11758194—42no—
90C2×#92418—42no—
91C23×C61C2×C22⋊C411yescharacteristic
92Q8×C61—44no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—21no—
98C2×C4×C61—21no—
99C2×C4×C61—21no—
100C2×C4×C61—21no—
101C2×C4×C61—21no—
102C2×C4×C61—21no—
103C2×C4×C61—41no—
104C2×C4×C61—41no—
105C2×C4×C61—41no—
106C2×C4×C61—41no—
107C2×C4×C61#9911yescharacteristic
108C2×C4×C61#9911yescharacteristic
109C2×C4×C61#10412yes—
110C2×C4×C61#13512yes—
111C2×Dic61—41no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—42no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—41no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C8×C61—82no—
123#92418—44no—
124#11740—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61C2×#9911yescharacteristic
128C22×C61#41611yescharacteristic
129C22×C61C2×#10411yescharacteristic
130C4×C61—21no—
131C4×C61—21no—
132C4×C61—22no—
133C4×C61—22no—
134C4×C61—41no—
135C4×C61—41no—
136C4×C61—41no—
137C4×C61—41no—
138Dic61—81no—
139Dic61—81no—
140Dic61—81no—
141Dic61—81no—
142#2634—611no—
143C4×#101—611no—
144#1461D6111yescharacteristic
145#1353—612no—
146#1346—612no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61#150111yescharacteristic
150C2×C61#212311yescharacteristic
151C2×C61#213311yescharacteristic
152C2×#125—611no—
153C2×C4×Q8C2×D6111yescharacteristic
154#431—21no—
155C2×#101—1221no—
156C4×M16—1221no—
157#400—611no—
158#400—611no—
159#400—1221no—
160#398—611no—
161#398—611no—
162#395—1221no—
163#387—1221no—
164#387—1221no—
165#383—611no—
166#343—612no—
167#324—21no—
168#324C2×D6112yes—
169C61#1174011yescharacteristic, complemented, Sylow
170C22×Q8D24411yescharacteristic
171C2×M16—1222no—
172#125—2441no—
173#125—2441no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—611no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4C4×D6111yescharacteristic
183C2×C4⋊C4C22⋊D6111yescharacteristic
184C2×C4⋊C4C22×D6111yescharacteristic
185C2×C42C4×D6111yescharacteristic
186C2×C42D24411yescharacteristic
187C2×C42C22⋊D6111yescharacteristic
188C4⋊C8—41no—
189#101—1224no—
190C22⋊C8—22no—
191#97—2441no—
192C4×C8—41no—
193C4×C8—2441no—
194#95—611no—
195#95—611no—
196#95—1221no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203#95—1221no—
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4#1175819811yescharacteristic
212C22×C4#1175819811yescharacteristic
213C22×C4#1175819811yescharacteristic
214C22×C4#1175819811yescharacteristic
215C22×C4C2×C4×D6111yescharacteristic
216C22×C4C2×D24411yescharacteristic
217C22×C4C2×C22⋊D6111yescharacteristic
218M16—1224no—
219M16—2442no—
220C2×C8—42no—
221C2×C8—2442no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—2441no—
226C4⋊C4—2441no—
227C4⋊C4—2442no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C4⋊C4—2442no—
231C4⋊C4—2442no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C23C2×#1175819811yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—2441no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4—2442no—
259C2×C4—2441no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4#1451969111yescharacteristic
266C2×C4#1451969111yescharacteristic
267C2×C4#1451970312yes—
268C2×C4#1451979912yes—
269C8—82no—
270C8—2444no—
271C22—21no—
272C22—21no—
273C22C2×#1451969111yescharacteristic
274C22#1683975911yescharacteristic
275C22C2×#1451970311yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—4881no—
285C4—4881no—
286C4—4881no—
287C4—4881no—
288C2—21no—
289C2—21no—
290C2#2144431111yescharacteristic
291C2#2144747211yescharacteristic
292C2#2144750611yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1461C2
socleC22×C61C2×#99
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1461D61
hypocenterC61#11740
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
169. C61#11740semidirect

Maximal subgroups

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

subgroupindex
#214516952
C4×#145196962
#214438472
#214438262
C61×#14612
#1174061