Finite Group Databasebeta

← #29577715

Subgroups — #29577715

Order 15616.

432 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 103 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#21454904C211yesmaximal, characteristic
2#21451031C211yesmaximal, characteristic
3#21444535C212yesmaximal
4#21443674C212yesmaximal
5C61×#1467C211yesmaximal, characteristic
6C2×#14519777C2211yescharacteristic
7#16839893—24no—
8#16839819—21no—
9#16839819C2212yes—
10#16839815—21no—
11#16839701—21no—
12#16839701—21no—
13#16839669C412yes—
14#16839668—21no—
15#16839668—21no—
16#16839627C412yes—
17C4×C4⋊Dic61C2211yescharacteristic
18#16839507—24no—
19C2×C4×Q8×C61C2211yescharacteristic
20C61×#432C2212yes—
21C61×#324—21no—
22C61×#324—21no—
23C22×Dic122—21no—
24#14519777—22no—
25#14519777—22no—
26C2×C4⋊Dic61—21no—
27C2×C4⋊Dic61—21no—
28C2×C4⋊Dic61C2×C412yes—
29C2×C4×Dic61C2×C412yes—
30C4⋊#92418—22no—
31C4⋊#92418—22no—
32C4⋊#92418D414yes—
33C22⋊#92418—22no—
34#14519688—22no—
35#14519688—22no—
36C4×#92418—22no—
37#14519684—22no—
38#14519684—22no—
39#14519684—22no—
40#14519684—22no—
41#14519684—21no—
42C22×Q8×C61C2×C411yescharacteristic
43C4×Q8×C61—22no—
44C4×Q8×C61—22no—
45C2×C4⋊C4×C61C2×C411yescharacteristic
46C2×C4⋊C4×C61D411yescharacteristic
47C2×C4⋊C4×C61D411yescharacteristic
48C2×C42×C61D411yescharacteristic
49C2×C42×C61D411yescharacteristic
50C2×C42×C61C2311yescharacteristic
51C4⋊C8×C61—22no—
52C22⋊C8×C61—22no—
53#97×C61—22no—
54C2×Q8×C61—22no—
55C2×Q8×C61—22no—
56C2×Q8×C61—41no—
57C22×C4×C61C22⋊C411yescharacteristic
58C22×C4×C61C22⋊C411yescharacteristic
59C22×C4×C61C22⋊C411yescharacteristic
60C22×C4×C61C22⋊C411yescharacteristic
61C22×C4×C61C22×C411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×Dic61—22no—
65C22×Dic61—22no—
66C2×Dic122—44no—
67C2×Dic122—41no—
68C2×Dic122—41no—
69C2×C8×C61—42no—
70C4⋊C4×C61—22no—
71C4⋊C4×C61—22no—
72C4⋊C4×C61—22no—
73C42×C61—21no—
74C42×C61—21no—
75C42×C61—21no—
76C42×C61—21no—
77C42×C61C2×D412yes—
78C42×C61#4112yes—
79C4⋊Dic61—24no—
80C4⋊Dic61—42no—
81C4⋊Dic61—42no—
82C4×Dic61—42no—
83C2×#92418—24no—
84C23×C61C2×C22⋊C411yescharacteristic
85Q8×C61—44no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—22no—
91C2×C4×C61—21no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—41no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61#10112yes—
100C2×C4×C61C4×D412yes—
101C2×C4×C61#12011yescharacteristic
102C2×C4×C61#12112yes—
103C2×C4×C61#12311yescharacteristic
104C2×Dic61—42no—
105C2×Dic61—44no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109Dic122—82no—
110Dic122—82no—
111C8×C61—82no—
112#92418—44no—
113#9456—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61#38611yescharacteristic
117C22×C61C2×#10111yescharacteristic
118C22×C61#41311yescharacteristic
119C4×C61—21no—
120C4×C61—22no—
121C4×C61—22no—
122C4×C61—22no—
123C4×C61—41no—
124C4×C61—41no—
125C4×C61—41no—
126C4×C61#45412yes—
127Dic61—82no—
128Dic61—82no—
129#2983—611no—
130#2568—611no—
131#1556—612no—
132#1467D6111yescharacteristic
133#1285—612no—
134C2×C61—21no—
135C2×C61—21no—
136C2×C61#188811yescharacteristic
137C2×C61#190111yescharacteristic
138C2×C61#190911yescharacteristic
139C2×C4⋊Q8—611no—
140C2×C4×Q8C2×D6111yescharacteristic
141#446—1224no—
142#432—612no—
143#432—1221no—
144#432C2×D6112yes—
145#431—1221no—
146#400—1221no—
147#400—1221no—
148#391—612no—
149#391—1221no—
150#391—1221no—
151#382—612no—
152C4×C4⋊C4—611no—
153#332—1224no—
154#324—21no—
155#324—21no—
156C61#945611yescharacteristic, complemented, Sylow
157C22×Q8—1221no—
158C22×Q8C4×D6111yescharacteristic
159C4⋊Q8—1222no—
160C4⋊Q8—1222no—
161C4×Q8—22no—
162C4×Q8—22no—
163C2×C4⋊C4—612no—
164C2×C4⋊C4—1221no—
165C2×C4⋊C4—1221no—
166C2×C4⋊C4C4×D6111yescharacteristic
167C2×C4⋊C4C22⋊D6111yescharacteristic
168C2×C4⋊C4C22⋊D6111yescharacteristic
169C2×C42—612no—
170C2×C42D24411yescharacteristic
171C2×C42D24411yescharacteristic
172C2×C42C22×D6111yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—614no—
175C4⋊C8—1222no—
176C4⋊C8—1222no—
177C22⋊C8—22no—
178C22⋊C8—1222no—
179#97—22no—
180#97—1222no—
181#97—1222no—
182C4×C8—1222no—
183#95—1222no—
184#95—1222no—
185#95—1222no—
186#95—1222no—
187#95—1221no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—2444no—
192C2×Q8—2441no—
193C2×Q8—2441no—
194C22×C4—1222no—
195C22×C4—1222no—
196C22×C4#1175819811yescharacteristic
197C22×C4#1175819811yescharacteristic
198C22×C4#1175819811yescharacteristic
199C22×C4#1175819811yescharacteristic
200C22×C4C2×C4×D6111yescharacteristic
201C22×C4C2×D24411yescharacteristic
202C22×C4C2×C22⋊D6111yescharacteristic
203C2×C8—42no—
204C2×C8—1224no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—1224no—
209C4⋊C4—2442no—
210C4⋊C4—2442no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—2442no—
216C42D4×D6112yes—
217C42#1175822412yes—
218C23C2×#1175819811yescharacteristic
219Q8—44no—
220Q8—4882no—
221Q8—4882no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—2442no—
236C2×C4—2442no—
237C2×C4—2444no—
238C2×C4—2442no—
239C2×C4—2442no—
240C2×C4#1451969512yes—
241C2×C4#1451973712yes—
242C2×C4#1451974711yescharacteristic
243C2×C4#1451974912yes—
244C2×C4#1451976111yescharacteristic
245C8—82no—
246C8—2444no—
247C22—21no—
248C22—21no—
249C22#1683963911yescharacteristic
250C22C2×#1451969511yescharacteristic
251C22#1683974411yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—4882no—
260C4—4882no—
261C4#1683993712yes—
262C2—21no—
263C2—21no—
264C2#2144622011yescharacteristic
265C2#2144628511yescharacteristic
266C2#2144633911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1467C2
socleC22×C61#386
prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1467D61
hypocenterC61#9456
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
156. C61#9456semidirect

Maximal subgroups

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

subgroupindex
#214549042
#214510312
#214445352
#214436742
C61×#14672
#945661