Finite Group Databasebeta

← #30607251

Subgroups — #30607251

Order 15616.

786 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461647C212yesmaximal
2#21460913C214yesmaximal, complemented
3#21448399C211yesmaximal, characteristic
4C2×#14519836—22no—
5C2×#14519836C2214yes—
6#16840703—22no—
7C23×D244C2211yescharacteristic
8C2×#14519736C411yescharacteristic, complemented
9#16839664C412yescomplemented
10#16839664C2212yes—
11#16839663—22no—
12#16839617—22no—
13C2×#117×C61C411yescharacteristic, complemented
14C2×C22⋊#6923—24no—
15C2×C22⋊#6923—44no—
16#14519836—28no—
17#14519836—44no—
18C24×D61D412yes—
19C22×D244—24no—
20C22×D244—42no—
21C22×D244—42no—
22C22×D244C2×C411yescharacteristic
23C22×D244D412yes—
24C22×D244C2311yescharacteristic
25#14519736—42no—
26C2×C4⋊Dic61C2×C412yes—
27C2×C22⋊Dic61—21no—
28C2×#11758198—24no—
29C2×#11758198—24no—
30C2×C4×Dic61—21no—
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—24no—
38C23×D61—24no—
39C23×D61—42no—
40C23×D61—84no—
41C23×D61C22⋊C412yes—
42C23×D61C2×D412yes—
43C22×#6923—44no—
44C22×C4×C61—22no—
45C22×C4×C61—22no—
46C22×C4×C61—22no—
47C22×C4×C61—22no—
48C22×C4×C61C22⋊C411yescharacteristic
49C22×C4×C61C22×C411yescharacteristic
50C22×Dic61—22no—
51C2×D244—24no—
52C2×D244—24no—
53C2×D244—22no—
54C2×D244—41no—
55C2×D244—41no—
56C2×D244—42no—
57C2×D244—41no—
58C2×D244—41no—
59C2×D244—416no—
60C2×D244#4114yes—
61C22⋊#6923—44no—
62C22⋊#6923—44no—
63C22⋊#6923—88no—
64C4⋊C4×C61—42no—
65C22⋊C4×C61—42no—
66C42×C61—42no—
67C22⋊Dic61—42no—
68#11758198—84no—
69#11758198—84no—
70C4⋊Dic61—42no—
71C4×Dic61—42no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—42no—
75C23×C61#9912yes—
76C23×C61C2×C22⋊C411yescharacteristic
77C22×D61—22no—
78C22×D61—22no—
79C22×D61—22no—
80C22×D61—22no—
81C22×D61—22no—
82C22×D61—48no—
83C22×D61—44no—
84C22×D61—44no—
85C22×D61—48no—
86C22×D61—84no—
87C22×D61—88no—
88C22×D61—88no—
89C22×D61#12314yes—
90C2×#6923—84no—
91C2×#6923—88no—
92C2×C4×C61—28no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—21no—
96C2×C4×C61—21no—
97C2×C4×C61—42no—
98C2×C4×C61—42no—
99C2×C4×C61—42no—
100C2×C4×C61#9912yes—
101C2×C4×C61#11712yes—
102C2×Dic61—44no—
103C2×Dic61—42no—
104D244—44no—
105D244—48no—
106D244—44no—
107#12858—611nomaximal, Sylow
108C22×C61—22no—
109C22×C61—22no—
110C22×C61—24no—
111C22×C61—42no—
112C22×C61—42no—
113C22×C61#38111yescharacteristic
114C22×C61C2×#9911yescharacteristic
115C22×C61C2×#9911yescharacteristic
116C2×D61—24no—
117C2×D61—44no—
118C2×D61—44no—
119C2×D61—44no—
120C2×D61—42no—
121C2×D61—44no—
122C2×D61—82no—
123C2×D61—816no—
124C2×D61—82no—
125#6923—164no—
126C4×C61—22no—
127C4×C61—22no—
128C4×C61—82no—
129Dic61—82no—
130#2309—611no—
131#1781—612no—
132#1393—614no—
133C2×C61—21no—
134C2×C61—21no—
135C2×C61—42no—
136C2×C61#181911yescharacteristic
137C2×C61#212712yes—
138D61—44no—
139D61—82no—
140C23×D4—611no—
141C2×#117—611no—
142C2×#117#692311yescharacteristic, complemented
143C2×#99—614no—
144C2×#99—1222no—
145#390—612no—
146#390—612no—
147#390—1222no—
148#379—1222no—
149#379—1222no—
150C61#1285811yescharacteristic, complemented, Sylow
151C25—612no—
152C22×D4—612no—
153C22×D4—611no—
154C22×D4—611no—
155C22×D4—1224no—
156C22×D4—2442no—
157C22×D4—2442no—
158C23×C4C2×#692311yescharacteristic
159#117—42no—
160#117—2442no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—612no—
163C2×C22⋊C4—21no—
164C2×C22⋊C4—1224no—
165C2×C22⋊C4—1224no—
166C2×C22⋊C4—1221no—
167C2×C22⋊C4—1224no—
168C2×C22⋊C4—2444no—
169C2×C42—1221no—
170C2×C42C2×#692312yes—
171#99—1228no—
172#99—2444no—
173C24—612no—
174C24—612no—
175C24—1224no—
176C24—1224no—
177C24—4884no—
178C24—2442no—
179C24C22⋊#692311yescharacteristic
180C2×D4—614no—
181C2×D4—1224no—
182C2×D4—1224no—
183C2×D4—1222no—
184C2×D4—2441no—
185C2×D4—2441no—
186C2×D4—2442no—
187C2×D4—2441no—
188C2×D4—2441no—
189C2×D4—24416no—
190C22×C4—22no—
191C22×C4—22no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—1222no—
195C22×C4—2444no—
196C22×C4C22⋊#692311yescharacteristic
197C22×C4C22×#692311yescharacteristic
198C4⋊C4—42no—
199C4⋊C4—2442no—
200C22⋊C4—42no—
201C22⋊C4—4884no—
202C22⋊C4—4884no—
203C22⋊C4—4888no—
204C22⋊C4—2444no—
205C22⋊C4—2444no—
206C22⋊C4—2442no—
207C42—42no—
208C42—2442no—
209C23—21no—
210C23—21no—
211C23—42no—
212C23—614no—
213C23—1222no—
214C23—1222no—
215C23—1222no—
216C23—1222no—
217C23—1222no—
218C23—4884no—
219C23—4888no—
220C23—4888no—
221C23—2448no—
222C23—2448no—
223C23—2444no—
224C23—2444no—
225C23#1451983612yes—
226C23C2×C22⋊#692311yescharacteristic
227D4—2444no—
228D4—2448no—
229D4—2444no—
230C2×C4—28no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4—4884no—
239C2×C4—4888no—
240C2×C4—2444no—
241C2×C4—2442no—
242C2×C4#1451983512yes—
243C2×C4#1451985612yes—
244C22—22no—
245C22—24no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—1224no—
250C22—4882no—
251C22—4882no—
252C22—48816no—
253C22—2444no—
254C22—2444no—
255C22—2444no—
256C22—2442no—
257C22—2444no—
258C22#1684070511yescharacteristic
259C22C2×#1451983511yescharacteristic
260C22C2×#1451983611yescharacteristic
261C4—22no—
262C4—22no—
263C4—82no—
264C4—9764no—
265C4—4882no—
266C2—21no—
267C2—21no—
268C2—42no—
269C2—4882no—
270C2—2444no—
271C2#2146171411yescharacteristic
272C2#2146209612yes—
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC23×D244C22
cosocleC22×D244C23
hypercenterC2×#117#6923
hypocenterC61#12858
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460913C2semidirect
8. C2×#14519736C4semidirect
9. #16839664C4semidirect
13. C2×#117×C61C4semidirect
142. C2×#117#6923semidirect
150. C61#12858semidirect

Maximal subgroups

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

subgroupindex
#214616472
#214609132
#214483992
#1285861