Finite Group Databasebeta

← #29589443

Subgroups — #29589443

Order 15616.

330 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 75 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#21454450C211yesmaximal, characteristic
2#21447631C211yesmaximal, characteristic, complemented
3#21443769C212yesmaximal, complemented
4#21443754C212yesmaximal
5C61×#2165C211yesmaximal, characteristic, complemented
6C2×C42×D61C411yescharacteristic
7#16839817—21no—
8#16839817—21no—
9#16839813—21no—
10#16839813—21no—
11#16839785C411yescharacteristic
12#16839785C2211yescharacteristic
13#16839725C411yescharacteristic
14#16839725C2211yescharacteristic
15C4×#11758194C411yescharacteristic
16#16839583—21no—
17#16839544C2212yes—
18#16839540—21no—
19C4×M16×C61C2211yescharacteristic
20C61×#364—21no—
21C61×#349C2212yes—
22C61×#347—21no—
23C22×C4×D61—21no—
24C22×C4×D61C2×C411yescharacteristic
25C2×#11758194C2×C411yescharacteristic
26C2×#11758194C2×C411yescharacteristic
27C2×C4×Dic61—21no—
28C2×C4×Dic61C2×C411yescharacteristic
29C42×D61—21no—
30C42×D61—21no—
31C42×D61—21no—
32C42×D61—21no—
33#14519717—22no—
34#14519706—21no—
35#14519706—21no—
36#14519706—21no—
37#14519706—21no—
38#14519689—21no—
39#14519689—21no—
40#14519689—21no—
41#14519689—21no—
42#14519688—21no—
43C4×#92418—21no—
44C2×M16×C61C2×C411yescharacteristic
45C2×M16×C61C2311yescharacteristic
46C2×C42×C61C2×C411yescharacteristic
47M32×C61—22no—
48#97×C61D411yescharacteristic
49#97×C61D411yescharacteristic
50C4×C8×C61D411yescharacteristic
51C4×C8×C61D411yescharacteristic
52C23×D61M1611yescharacteristic
53C22×C4×C61—21no—
54C22×C4×C61C22×C411yescharacteristic
55C22×Dic61—21no—
56C22×Dic61M1611yescharacteristic
57C2×C4×D61—21no—
58C2×C4×D61—21no—
59C2×C4×D61—21no—
60C2×C4×D61—21no—
61C2×C4×D61—21no—
62C2×C4×D61—21no—
63C2×C4×D61—44no—
64C2×C4×D61—41no—
65C2×C4×D61—41no—
66M16×C61—41no—
67M16×C61—41no—
68C2×C8×C61C22⋊C411yescharacteristic
69C2×C8×C61C22⋊C411yescharacteristic
70C2×C8×C61C2×D411yescharacteristic
71C2×C8×C61C2×D411yescharacteristic
72C42×C61—21no—
73C42×C61C22⋊C411yescharacteristic
74C42×C61C22⋊C411yescharacteristic
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61M1611yescharacteristic
81C4×Dic61M1611yescharacteristic
82#11758194—41no—
83#11758194—41no—
84C2×#92418—21no—
85C2×#92418—21no—
86C16×C61—42no—
87#11758185—42no—
88C23×C61C2×M1611yescharacteristic
89C22×D61—21no—
90C22×D61—42no—
91C22×D61—41no—
92C2×C4×C61—21no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—42no—
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C2×C4×C61C2×M1611yescharacteristic
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—42no—
103C2×Dic61—41no—
104C4×D61—24no—
105C4×D61—42no—
106C4×D61—42no—
107C4×D61—42no—
108C4×D61—42no—
109C4×D61—41no—
110C4×D61—41no—
111C8×C61—21no—
112C8×C61—21no—
113C8×C61—21no—
114C8×C61—21no—
115#92418—41no—
116#92418—41no—
117#11521—611nomaximal, Sylow
118C22×C61—21no—
119C22×C61—41no—
120C22×C61#40711yescharacteristic
121C2×D61—22no—
122C2×D61—41no—
123C2×D61—42no—
124C2×D61—41no—
125C2×D61—42no—
126C4×C61—22no—
127C4×C61—21no—
128C4×C61—41no—
129C4×C61#41011yescharacteristic
130C4×C61#41311yescharacteristic
131Dic61—22no—
132Dic61—41no—
133Dic61—41no—
134#2920—611no—
135#2165—611no—
136#2165D6111yescharacteristic, complemented
137#1327—612no—
138#1320—612no—
139C2×C61—21no—
140C2×C61—41no—
141C2×C61#146411yescharacteristic
142D61—42no—
143C22×C42—611no—
144#432—1221no—
145#432—1221no—
146#431—1221no—
147#431—1221no—
148#423—611no—
149#423—611no—
150#407—611no—
151#407—611no—
152C4×M16—611no—
153C4×M16C2×D6111yescharacteristic
154#364—21no—
155#364—1221no—
156#349—612no—
157#349C2×D6112yes—
158#347—21no—
159#347—1221no—
160C61#1152111yescharacteristic, complemented, Sylow
161C23×C4—611no—
162C23×C4—1221no—
163C2×M16—611no—
164C2×M16—611no—
165C2×M16C4×D6111yescharacteristic
166C2×M16C22×D6111yescharacteristic
167C2×C42—611no—
168C2×C42—1221no—
169C2×C42—1221no—
170C2×C42—1221no—
171C2×C42—1221no—
172C2×C42—1221no—
173C2×C42C4×D6111yescharacteristic
174M32—22no—
175M32—1222no—
176C4⋊C8—1221no—
177C4⋊C8—1221no—
178C4⋊C8—1221no—
179C4⋊C8—1221no—
180C22⋊C8—1221no—
181C22⋊C8—1221no—
182C22⋊C8—1221no—
183C22⋊C8—1221no—
184#97—1221no—
185#97D24411yescharacteristic
186#97C22⋊D6111yescharacteristic
187C4×C8—1221no—
188C4×C8D24411yescharacteristic
189C4×C8C22⋊D6111yescharacteristic
190C24—611no—
191C22×C4—21no—
192C22×C4—611no—
193C22×C4—1221no—
194C22×C4—1221no—
195C22×C4—1221no—
196C22×C4—1221no—
197C22×C4—1221no—
198C22×C4—1221no—
199C22×C4—1221no—
200C22×C4—2441no—
201C22×C4—2441no—
202C22×C4—2444no—
203C22×C4C2×C4×D6111yescharacteristic
204M16—41no—
205M16—41no—
206M16—2441no—
207M16—2441no—
208C2×C8—1221no—
209C2×C8—1221no—
210C2×C8#1175819811yescharacteristic
211C2×C8#1175819811yescharacteristic
212C2×C8C2×D24411yescharacteristic
213C2×C8C2×C22⋊D6111yescharacteristic
214C42—21no—
215C42—611no—
216C42—611no—
217C42—1221no—
218C42—1221no—
219C42—1221no—
220C42—1221no—
221C42—1221no—
222C42#1175819811yescharacteristic
223C42#1175819811yescharacteristic
224C16—42no—
225C16—2442no—
226C23—1221no—
227C23—2441no—
228C23—2442no—
229C23M16×D6111yescharacteristic
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—1224no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—1221no—
239C2×C4—2442no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2442no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4—2441no—
247C2×C4C2×#1175819811yescharacteristic
248C2×C4M16×D6111yescharacteristic
249C8—21no—
250C8—21no—
251C8—21no—
252C8—21no—
253C8—2441no—
254C8—2441no—
255C22—21no—
256C22—41no—
257C22—1222no—
258C22—2441no—
259C22—2442no—
260C22—2442no—
261C22—2441no—
262C22#1683972511yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—1222no—
267C4—2441no—
268C4—2441no—
269C4#1683973511yescharacteristic
270C4#1683974411yescharacteristic
271C2—21no—
272C2—41no—
273C2—2442no—
274C2#2144415111yescharacteristic
subgroupG/H
centerC4#16839735
commutatorC22×C4×C61C22×C4
FrattiniC2×M16C22×D61
FittingC61×#2165C2
socleC2×C61#1464
prime radicalC23×D61M16
cosocleC2×M16×C61C23
hypercenter#2165D61
hypocenterC61#11521
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C42 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #21447631C2semidirect
3. #21443769C2semidirect
5. C61×#2165C2semidirect
136. #2165D61semidirect
160. C61#11521semidirect

Maximal subgroups

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

subgroupindex
#214544502
#214476312
#214437692
#214437542
C61×#21652
#1152161