Finite Group Databasebeta

← #29589667

Subgroups — #29589667

Order 15616.

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

normal subgroups only

This group has 350 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#21451006C211yesmaximal, characteristic
2#21444163C211yesmaximal, characteristic
3#21443764C212yesmaximal
4#21443762C212yesmaximal
5C61×#1461C211yesmaximal, characteristic
6C2×#14519769C411yescharacteristic
7#16839819—21no—
8#16839695—21no—
9#16839695—21no—
10#16839669C411yescharacteristic
11#16839669C411yescharacteristic
12#16839646—21no—
13#16839646—21no—
14#16839631C2211yescharacteristic
15#16839627C2211yescharacteristic
16C4×C4⋊Dic61C411yescharacteristic
17#16839488—21no—
18#16839488C2212yes—
19C2×C4×Q8×C61C2211yescharacteristic
20C61×#431—21no—
21C61×#324—21no—
22C61×#324C2212yes—
23#14519769—41no—
24#14519769—41no—
25C2×C4⋊Dic61—21no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×#11758196—21no—
29C2×#11758196—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×C4×Dic61C2×C411yescharacteristic
33C2×C4×Dic61C2×C411yescharacteristic
34C4⋊#92418—41no—
35C22⋊#92418—22no—
36#14519688—41no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44C22×Q8×C61C2×C411yescharacteristic
45C4×Q8×C61—41no—
46C4×Q8×C61—41no—
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61C2311yescharacteristic
50C2×C42×C61C2×C411yescharacteristic
51C2×C42×C61D411yescharacteristic
52C2×C42×C61D411yescharacteristic
53C4⋊C8×C61—41no—
54C22⋊C8×C61—22no—
55C4×C8×C61—41no—
56C2×Q8×C61—22no—
57C2×Q8×C61—22no—
58C2×Q8×C61—41no—
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22⋊C411yescharacteristic
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—21no—
70C2×C8×C61—42no—
71C4⋊C4×C61—41no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—21no—
77C42×C61—21no—
78C42×C61—21no—
79C42×C61—21no—
80C4⋊Dic61—42no—
81C4⋊Dic61—41no—
82C4⋊Dic61—41no—
83#11758196—42no—
84#11758196—42no—
85#11758196—42no—
86#11758196—41no—
87#11758196—41no—
88C4×Dic61—22no—
89C4×Dic61—22no—
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#10112yes—
110C2×C4×C61#13112yes—
111C2×Dic61—22no—
112C2×Dic61—41no—
113C2×Dic61—41no—
114C2×Dic61—41no—
115C2×Dic61—41no—
116C2×Dic61—41no—
117C2×Dic61—41no—
118C2×Dic61—42no—
119C2×Dic61—41no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C8×C61—82no—
123#92418—82no—
124#11571—611nomaximal, Sylow
125C22×C61—21no—
126C22×C61—21no—
127C22×C61#40811yescharacteristic
128C22×C61C2×#9911yescharacteristic
129C22×C61C2×#10111yescharacteristic
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—42no—
139Dic61—81no—
140Dic61—81no—
141Dic61—81no—
142#2565—611no—
143#1467—611no—
144#1461D6111yescharacteristic
145#1325—612no—
146#1324—612no—
147C2×C61—21no—
148C2×C61—21no—
149C2×C61#147211yescharacteristic
150C2×C61#212611yescharacteristic
151C2×C61#213311yescharacteristic
152C2×#125—611no—
153C2×C4×Q8C2×D6111yescharacteristic
154#432—1221no—
155#431—21no—
156#398—1221no—
157#398—1221no—
158#391—611no—
159#391—611no—
160#387—1221no—
161#387—1221no—
162#384—611no—
163#382—611no—
164C4×C4⋊C4—611no—
165#324—21no—
166#324—612no—
167#324—1221no—
168#324C2×D6112yes—
169C61#1157111yescharacteristic, complemented, Sylow
170C22×Q8C4×D6111yescharacteristic
171#125—2441no—
172#125—2441no—
173C4×Q8—41no—
174C4×Q8—41no—
175C2×C4⋊C4—611no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—1221no—
178C2×C4⋊C4—1221no—
179C2×C4⋊C4—1221no—
180C2×C4⋊C4—1221no—
181C2×C4⋊C4—1221no—
182C2×C4⋊C4D24411yescharacteristic
183C2×C4⋊C4C22⋊D6111yescharacteristic
184C2×C4⋊C4C22×D6111yescharacteristic
185C2×C42—611no—
186C2×C42—611no—
187C2×C42C4×D6111yescharacteristic
188C2×C42D24411yescharacteristic
189C2×C42C22⋊D6111yescharacteristic
190C4⋊C8—41no—
191C4⋊C8—2441no—
192C22⋊C8—22no—
193C22⋊C8—1222no—
194#97—2441no—
195C4×C8—41no—
196#95—1221no—
197#95—1221no—
198#95—1221no—
199#95—1221no—
200#95—1221no—
201#95—1221no—
202#95—1221no—
203C2×Q8—22no—
204C2×Q8—22no—
205C2×Q8—41no—
206C22×C4—1221no—
207C22×C4—1221no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4#1175819811yescharacteristic
211C22×C4#1175819811yescharacteristic
212C22×C4#1175819811yescharacteristic
213C22×C4#1175819811yescharacteristic
214C22×C4C2×C4×D6111yescharacteristic
215C22×C4C2×D24411yescharacteristic
216C22×C4C2×C22⋊D6111yescharacteristic
217C2×C8—42no—
218C2×C8—2442no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—2441no—
223C4⋊C4—2441no—
224C4⋊C4—2442no—
225C4⋊C4—2442no—
226C4⋊C4—2442no—
227C4⋊C4—2442no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C42—21no—
231C42—21no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—1222no—
237C42—1222no—
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—1222no—
255C2×C4—2441no—
256C2×C4—2441no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4—2442no—
260C2×C4—2441no—
261C2×C4—2441no—
262C2×C4—2441no—
263C2×C4—2441no—
264C2×C4—2441no—
265C2×C4#1451969111yescharacteristic
266C2×C4#1451969111yescharacteristic
267C2×C4#1451969512yes—
268C2×C4#1451978312yes—
269C8—82no—
270C8—4882no—
271C22—21no—
272C22—21no—
273C22#1683972811yescharacteristic
274C22C2×#1451969111yescharacteristic
275C22C2×#1451969511yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—4881no—
285C4—4881no—
286C4—4881no—
287C4—2442no—
288C2—21no—
289C2—21no—
290C2#2144418211yescharacteristic
291C2#2144748211yescharacteristic
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#11571
LCSG ▷ C22×C4×C61 ▷ C22×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#11571semidirect

Maximal subgroups

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

subgroupindex
#214510062
#214441632
#214437642
#214437622
C61×#14612
#1157161