Finite Group Databasebeta

← #30603826

Subgroups — #30603826

Order 15616.

686 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 686 conjugacy classes of subgroups — too many to draw. Only its 104 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#21461050C212yesmaximal, complemented
2#21460744C214yesmaximal, complemented
3#21448399C211yesmaximal, characteristic
4#16840778—22no—
5#16840607—22no—
6#16840605C2214yes—
7C23×D244C411yescharacteristic
8C2×#14519736C2211yescharacteristic
9#16839664—22no—
10#16839663—22no—
11#16839617C412yes—
12#16839617C2212yes—
13C2×#117×C61C411yescharacteristic
14C4⋊#92420—42no—
15C22⋊#92420—24no—
16C4×#92420—42no—
17C24×D61C2×C412yes—
18C22×D244—21no—
19C22×D244—21no—
20C22×D244—22no—
21C22×D244—42no—
22C22×D244—42no—
23C22×D244C814yescomplemented
24#14519736—42no—
25C2×C4⋊Dic61D412yes—
26C2×C22⋊Dic61C2×C411yescharacteristic
27C2×C22⋊Dic61C2311yescharacteristic
28C2×#11758198—24no—
29C2×#11758198—24no—
30C2×C4×Dic61D412yes—
31C23×C4×C61C2×C411yescharacteristic
32#117×C61—42no—
33C2×C4⋊C4×C61—21no—
34C2×C22⋊C4×C61C2×C412yes—
35C2×C42×C61—21no—
36C24×C61C22×C411yescharacteristic
37C23×D61—22no—
38C23×D61—22no—
39C23×D61—42no—
40C23×D61—42no—
41C23×D61—84no—
42C23×D61C2×C814yes—
43C22×C4×C61—22no—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C22⋊C411yescharacteristic
48C22×C4×C61C2×C812yes—
49C22×C4×C61M1612yes—
50C22×Dic61C22⋊C412yes—
51C22×Dic61C2×D412yes—
52C2×D244—24no—
53C2×D244—24no—
54C2×D244—42no—
55C2×D244—42no—
56C2×D244—48no—
57C2×D244—42no—
58C2×D244—42no—
59C2×D244—48no—
60C2×#92420—44no—
61C4⋊C4×C61—42no—
62C22⋊C4×C61—42no—
63C42×C61—42no—
64C22⋊Dic61—41no—
65C22⋊Dic61—41no—
66#11758198—84no—
67#11758198—84no—
68C4⋊Dic61—42no—
69C4×Dic61—22no—
70C4×Dic61—22no—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—42no—
74C23×C61C2×C22⋊C411yescharacteristic
75C23×C61C22×C811yescharacteristic
76C23×C61C2×M1611yescharacteristic
77C22×D61—24no—
78C22×D61—44no—
79C22×D61—44no—
80C22×D61—44no—
81C22×D61—42no—
82C22×D61—42no—
83C22×D61—44no—
84C22×D61—84no—
85C22×D61—84no—
86C22×D61—88no—
87C22×D61—88no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—24no—
91C2×C4×C61—24no—
92C2×C4×C61—44no—
93C2×C4×C61—42no—
94C2×C4×C61C22⋊C812yes—
95C2×C4×C61C22⋊C812yes—
96C2×C4×C61#9912yes—
97C2×C4×C61#10012yes—
98C2×Dic61—22no—
99C2×Dic61—22no—
100C2×Dic61—42no—
101C2×Dic61—42no—
102D244—48no—
103D244—48no—
104#92420—84no—
105#11427—611nomaximal, Sylow
106C22×C61—22no—
107C22×C61—21no—
108C22×C61—21no—
109C22×C61—41no—
110C22×C61—41no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61C2×C22⋊C811yescharacteristic
114C22×C61C2×#9911yescharacteristic
115C22×C61C2×#10011yescharacteristic
116C2×D61—44no—
117C2×D61—44no—
118C2×D61—44no—
119C2×D61—84no—
120C2×D61—88no—
121C2×D61—84no—
122C2×D61—88no—
123C4×C61—22no—
124C4×C61—82no—
125C4×C61#32314yes—
126Dic61—42no—
127Dic61—42no—
128#2309—611no—
129#1458—612no—
130#1316—614no—
131C2×C61—21no—
132C2×C61—21no—
133C2×C61—41no—
134C2×C61—41no—
135C2×C61C2×#32311yescharacteristic
136C2×C61#212212yes—
137D61—84no—
138C23×D4—611no—
139C2×#117—611no—
140C2×#117#692311yescharacteristic
141#431—1222no—
142#390—1222no—
143#390—1222no—
144#379—612no—
145#379—612no—
146#324—1222no—
147#323—614no—
148C61#1142711yescharacteristic, complemented, Sylow
149C25—612no—
150C22×D4—614no—
151C22×D4—1222no—
152C22×D4—1221no—
153C22×D4—1221no—
154C22×D4—2442no—
155C22×D4—2442no—
156C23×C4C2×#692311yescharacteristic
157#117—42no—
158#117—2442no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—612no—
161C2×C22⋊C4—611no—
162C2×C22⋊C4—611no—
163C2×C22⋊C4—1224no—
164C2×C22⋊C4—1224no—
165C2×C22⋊C4C2×#692312yes—
166C2×C42—21no—
167C2×C42—612no—
168C4⋊C8—2442no—
169C22⋊C8—1224no—
170C4×C8—2442no—
171C24—614no—
172C24—1222no—
173C24—1222no—
174C24—4884no—
175C24—2442no—
176C24—2442no—
177C24C22×#692311yescharacteristic
178C2×D4—1224no—
179C2×D4—1224no—
180C2×D4—2442no—
181C2×D4—2442no—
182C2×D4—2448no—
183C2×D4—2448no—
184C2×D4—2442no—
185C2×D4—2442no—
186C22×C4—22no—
187C22×C4—22no—
188C22×C4—22no—
189C22×C4—612no—
190C22×C4—612no—
191C22×C4D61⋊C812yes—
192C22×C4#1175821312yes—
193C22×C4C22⋊#692311yescharacteristic
194C22×C4C22⋊#692311yescharacteristic
195C2×C8—2444no—
196C4⋊C4—42no—
197C4⋊C4—2442no—
198C22⋊C4—42no—
199C22⋊C4—4884no—
200C22⋊C4—4884no—
201C22⋊C4—2441no—
202C22⋊C4—2441no—
203C42—42no—
204C42—1222no—
205C42—1222no—
206C23—21no—
207C23—21no—
208C23—42no—
209C23—1224no—
210C23—4888no—
211C23—4888no—
212C23—4884no—
213C23—4884no—
214C23—2444no—
215C23—2444no—
216C23—2444no—
217C23—2444no—
218C23—2442no—
219C23—2442no—
220C23C2×C22⋊#692311yescharacteristic
221C23C2×D61⋊C811yescharacteristic
222C23C2×#1175821311yescharacteristic
223D4—2448no—
224D4—2448no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—24no—
228C2×C4—24no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—1222no—
232C2×C4—1222no—
233C2×C4—2442no—
234C2×C4—2442no—
235C2×C4#1451983412yes—
236C2×C4#1451983412yes—
237C2×C4#1451983612yes—
238C2×C4#1451983712yes—
239C8—4884no—
240C22—22no—
241C22—21no—
242C22—21no—
243C22—41no—
244C22—41no—
245C22—42no—
246C22—42no—
247C22—4884no—
248C22—4888no—
249C22—4888no—
250C22—4884no—
251C22—2444no—
252C22—2444no—
253C22—2444no—
254C22C2×#1451983411yescharacteristic
255C22C2×#1451983611yescharacteristic
256C22C2×#1451983711yescharacteristic
257C4—22no—
258C4—82no—
259C4—2442no—
260C4—2442no—
261C4#1684060614yes—
262C2—21no—
263C2—21no—
264C2—41no—
265C2—41no—
266C2—4884no—
267C2C2×#1684060611yescharacteristic
268C2#2146208012yes—
subgroupG/H
centerC22C2×#14519836
commutatorC23×C61C22×C8
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC23×D244C4
cosocleC2×C22⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11427
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21461050C2semidirect
2. #21460744C2semidirect
23. C22×D244C8semidirect
148. C61#11427semidirect

Maximal subgroups

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

subgroupindex
#214610502
#214607442
#214483992
#1142761