Finite Group Databasebeta

← #30603846

Subgroups — #30603846

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#21460748C214yesmaximal, complemented
3#21448399C211yesmaximal, characteristic
4#16840778—22no—
5#16840607C2214yescomplemented
6#16840605—22no—
7C23×D244C411yescharacteristic
8C2×#14519736C2211yescharacteristic
9#16839664C412yes—
10#16839664C2212yes—
11#16839663—22no—
12#16839617—22no—
13C2×#117×C61C411yescharacteristic
14C4⋊#92420—42no—
15C22⋊#92420—24no—
16C4×#92420—42no—
17C24×D61—21no—
18C22×D244—21no—
19C22×D244—22no—
20C22×D244—42no—
21C22×D244—42no—
22C22×D244C814yescomplemented
23C22×D244C2×C412yes—
24#14519736—42no—
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C4⋊Dic61C2311yescharacteristic
27C2×C22⋊Dic61D412yes—
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×C61—21no—
35C2×C42×C61C2×C412yes—
36C24×C61C22⋊C411yescharacteristic
37C23×D61—22no—
38C23×D61—24no—
39C23×D61—42no—
40C23×D61—42no—
41C23×D61—82no—
42C23×D61—82no—
43C22×C4×C61—22no—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61C22⋊C411yescharacteristic
47C22×C4×C61C2×C812yes—
48C22×C4×C61M1612yes—
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61C22⋊C412yes—
51C22×Dic61C2×D412yes—
52C2×D244—24no—
53C2×D244—22no—
54C2×D244—48no—
55C2×D244—42no—
56C2×D244—42no—
57C2×D244—42no—
58C2×D244—42no—
59C2×D244—48no—
60C2×D244C2×C814yes—
61C2×#92420—44no—
62C4⋊C4×C61—42no—
63C22⋊C4×C61—42no—
64C42×C61—42no—
65C22⋊Dic61—42no—
66#11758198—84no—
67#11758198—84no—
68C4⋊Dic61—41no—
69C4⋊Dic61—41no—
70C4×Dic61—22no—
71C4×Dic61—22no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—41no—
75C23×C61—41no—
76C23×C61C22⋊C812yes—
77C23×C61C2×C22⋊C411yescharacteristic
78C22×D61—24no—
79C22×D61—44no—
80C22×D61—44no—
81C22×D61—48no—
82C22×D61—42no—
83C22×D61—42no—
84C22×D61—88no—
85C22×D61—88no—
86C22×D61—84no—
87C22×D61—84no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—24no—
91C2×C4×C61—24no—
92C2×C4×C61—42no—
93C2×C4×C61—42no—
94C2×C4×C61—42no—
95C2×C4×C61C22⋊C812yes—
96C2×C4×C61#9912yes—
97C2×C4×C61#10012yes—
98C2×C4×C61C22×C811yescharacteristic
99C2×C4×C61C2×M1611yescharacteristic
100C2×Dic61—22no—
101C2×Dic61—22no—
102C2×Dic61—42no—
103C2×Dic61—42no—
104D244—44no—
105D244—44no—
106D244—48no—
107#92420—84no—
108#11433—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—21no—
111C22×C61—22no—
112C22×C61—42no—
113C22×C61—42no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61C2×C22⋊C811yescharacteristic
117C22×C61C2×#9911yescharacteristic
118C22×C61C2×#10011yescharacteristic
119C2×D61—48no—
120C2×D61—44no—
121C2×D61—84no—
122C2×D61—816no—
123C2×D61—82no—
124C2×D61—82no—
125C4×C61—21no—
126C4×C61—21no—
127C4×C61—82no—
128C4×C61#32314yes—
129Dic61—42no—
130Dic61—42no—
131#2309—611no—
132#1458—612no—
133#1318—614no—
134C2×C61—21no—
135C2×C61—21no—
136C2×C61—42no—
137C2×C61C2×#32311yescharacteristic
138C2×C61#212811yescharacteristic
139C2×C61#213411yescharacteristic
140D61—84no—
141C23×D4—611no—
142C2×#117—611no—
143C2×#117#692311yescharacteristic
144#431—1222no—
145#390—612no—
146#390—612no—
147#390—1222no—
148#379—1222no—
149#324—614no—
150#323—1222no—
151C61#1143311yescharacteristic, complemented, Sylow
152C25—1221no—
153C22×D4—614no—
154C22×D4—612no—
155C22×D4—1222no—
156C22×D4—1221no—
157C22×D4—2442no—
158C22×D4—2442no—
159C23×C4C2×#692311yescharacteristic
160#117—42no—
161#117—2442no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—611no—
164C2×C4⋊C4—611no—
165C2×C22⋊C4—21no—
166C2×C22⋊C4—612no—
167C2×C22⋊C4—1224no—
168C2×C22⋊C4—1224no—
169C2×C42—612no—
170C2×C42C2×#692312yes—
171C4⋊C8—2442no—
172C22⋊C8—1224no—
173C4×C8—2442no—
174C24—1224no—
175C24—1222no—
176C24—4882no—
177C24—4882no—
178C24—2442no—
179C24—2442no—
180C24C22⋊#692311yescharacteristic
181C2×D4—614no—
182C2×D4—1224no—
183C2×D4—1222no—
184C2×D4—2442no—
185C2×D4—2442no—
186C2×D4—2448no—
187C2×D4—2448no—
188C2×D4—2442no—
189C2×D4—2442no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—612no—
194C22×C4—612no—
195C22×C4D61⋊C812yes—
196C22×C4#1175821312yes—
197C22×C4C22⋊#692311yescharacteristic
198C22×C4C22×#692311yescharacteristic
199C2×C8—2444no—
200C4⋊C4—42no—
201C4⋊C4—2441no—
202C4⋊C4—2441no—
203C22⋊C4—42no—
204C22⋊C4—4884no—
205C22⋊C4—4884no—
206C22⋊C4—2442no—
207C42—42no—
208C42—1222no—
209C42—1222no—
210C23—21no—
211C23—21no—
212C23—41no—
213C23—41no—
214C23—1224no—
215C23—4888no—
216C23—4884no—
217C23—4884no—
218C23—4888no—
219C23—2444no—
220C23—2444no—
221C23—2448no—
222C23—2442no—
223C23—2442no—
224C23#1451983412yes—
225C23C2×C22⋊#692311yescharacteristic
226D4—2444no—
227D4—2444no—
228D4—2448no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—24no—
232C2×C4—24no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—1222no—
237C2×C4—1222no—
238C2×C4—2442no—
239C2×C4—2442no—
240C2×C4#1451983412yes—
241C2×C4#1451983612yes—
242C2×C4#1451983712yes—
243C2×C4C2×D61⋊C811yescharacteristic
244C2×C4C2×#1175821311yescharacteristic
245C8—4884no—
246C22—21no—
247C22—21no—
248C22—22no—
249C22—42no—
250C22—42no—
251C22—41no—
252C22—41no—
253C22—4884no—
254C22—48816no—
255C22—4882no—
256C22—4882no—
257C22—2448no—
258C22—2444no—
259C22C2×#1451983411yescharacteristic
260C22C2×#1451983611yescharacteristic
261C22C2×#1451983711yescharacteristic
262C4—21no—
263C4—21no—
264C4—82no—
265C4—2442no—
266C4—2442no—
267C4#1684060614yes—
268C2—21no—
269C2—21no—
270C2—42no—
271C2—4884no—
272C2C2×#1684060611yescharacteristic
273C2#2146210011yescharacteristic
274C2#2146212011yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC23×D244C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11433
LCSG ▷ C2×C4×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. #21460748C2semidirect
5. #16840607C22semidirect
22. C22×D244C8semidirect
151. C61#11433semidirect

Maximal subgroups

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

subgroupindex
#214610502
#214607482
#214483992
#1143361