Finite Group Databasebeta

← #29689488

Subgroups — #29689488

Order 15616.

914 conjugacy classes of subgroups; only the 235 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 235 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
1C2×#16840393C211yesmaximal, characteristic
2#21454454C212yesmaximal
3#21446810C214yesmaximal, complemented
4#21446806C214yesmaximal, complemented
5#21445900C212yesmaximal
6#21445899C211yesmaximal, characteristic
7C61×#1821C211yesmaximal, characteristic
8#16840393—28no—
9C2×#14519776C412yes—
10C2×#14519776C2212yes—
11C2×#14519768C412yes—
12C2×#14519768C2212yes—
13C2×#14519756C414yes—
14C2×#14519736C2211yescharacteristic
15C2×#14519736C2211yescharacteristic
16#16839820—28no—
17#16839785C2214yes—
18#16839726C2212yes—
19M16×Dic61C2214yes—
20#16839531C2214yes—
21#16839530C2214yes—
22#16839530C2214yes—
23C22×C4⋊C4×C61C2211yescharacteristic
24C61×#407C2212yes—
25C61×#343C2214yes—
26C22×Dic122C2×C414yes—
27C2×#11758194C2314yes—
28#14519776—28no—
29#14519776—24no—
30#14519776—24no—
31#14519768—28no—
32#14519768—24no—
33#14519768—24no—
34#14519756—216no—
35#14519736—24no—
36#14519736D418yes—
37C2×C4⋊Dic61C2×C414yes—
38C2×C4⋊Dic61C2×C411yescharacteristic
39C2×C4⋊Dic61C2×C411yescharacteristic
40C2×C4⋊Dic61C2311yescharacteristic
41C2×C4⋊Dic61C2311yescharacteristic
42C2×#11758196C2×C414yes—
43C2×#11758196C2×C414yes—
44C2×C22⋊Dic61C2×C412yes—
45C2×C22⋊Dic61C2×C412yes—
46C2×C4×Dic61C2×C412yes—
47C2×C4×Dic61C2312yes—
48#14519706—28no—
49C22⋊#92418—24no—
50#14519687—24no—
51C8×Dic61—24no—
52C23×C4×C61C2×C412yes—
53C23×C4×C61C2311yescharacteristic
54C2×M16×C61C2314yes—
55C2×C4⋊C4×C61—24no—
56C2×C4⋊C4×C61C2×C412yes—
57C2×C4⋊C4×C61C2312yes—
58C22⋊C8×C61—24no—
59C24×C61C22×C411yescharacteristic
60C22×C4×C61—24no—
61C22×C4×C61—24no—
62C22×C4×C61—82no—
63C22×C4×C61C22×C411yescharacteristic
64C22×C4×C61C22×C414yes—
65C22×C4×C61C2×D414yes—
66C22×C4×C61C2411yescharacteristic
67C22×Dic61C22×C412yes—
68C22×Dic61C22×C412yes—
69C22×Dic61C22×C412yes—
70C22×Dic61C22×C412yes—
71C2×Dic122—28no—
72C2×Dic122—84no—
73M16×C61—28no—
74C2×C8×C61—24no—
75C4⋊C4×C61—24no—
76C4⋊C4×C61—22no—
77C4⋊C4×C61—22no—
78C22⋊Dic61—24no—
79C22⋊Dic61C22⋊C418yes—
80C4⋊Dic61—22no—
81C4⋊Dic61—22no—
82C4⋊Dic61—28no—
83C4⋊Dic61C22⋊C414yes—
84C4⋊Dic61C22⋊C414yes—
85#11758196—28no—
86#11758196—28no—
87C4×Dic61—24no—
88C4×Dic61C2×D414yes—
89C4×Dic61C2×D414yes—
90#11758194—28no—
91C2×#92418—24no—
92C23×C61—22no—
93C23×C61—41no—
94C23×C61—41no—
95C23×C61C2×C22⋊C412yes—
96C23×C61C23×C411yescharacteristic
97C2×C4×C61—22no—
98C2×C4×C61—28no—
99C2×C4×C61—24no—
100C2×C4×C61—44no—
101C2×C4×C61—84no—
102C2×C4×C61C2×C22⋊C412yes—
103C2×C4×C61C22×D412yes—
104C2×C4×C612−1+414yes—
105C2×Dic61—22no—
106C2×Dic61—22no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61C2×C22⋊C414yes—
112C2×Dic61C2×C22⋊C414yes—
113Dic122—88no—
114C8×C61—44no—
115#92418—44no—
116#21832—611nomaximal, Sylow
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—22no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—44no—
123C22×C61C22×C22⋊C411yescharacteristic
124C22×C61#51912yes—
125C4×C61—22no—
126C4×C61—44no—
127C4×C61#53614yes—
128Dic61—24no—
129Dic61—24no—
130Dic61—42no—
131Dic61—42no—
132C2×#544—611no—
133#2921—612no—
134#1998—614no—
135#1997—614no—
136#1822—612no—
137#1821—611no—
138#1821D6111yescharacteristic
139C2×C61—22no—
140C2×C61—42no—
141C2×C61#231011yescharacteristic
142C2×C61#288811yescharacteristic
143C2×C61#288911yescharacteristic
144#544—1228no—
145C2×C4⋊Q8—612no—
146C2×C4⋊Q8—612no—
147C2×#125—612no—
148C2×#125—612no—
149C2×C22⋊Q8—614no—
150C2×#117—611no—
151C2×#117—611no—
152C22×C4⋊C4C2×D6111yescharacteristic
153#433—1228no—
154#423—614no—
155#407—612no—
156#407C2×D6112yes—
157C4×M16—614no—
158#343—614no—
159#343—614no—
160#343—614no—
161#343C2×D6114yes—
162C61#2183211yescharacteristic, complemented, Sylow
163C22×Q8—614no—
164C23×C4C4×D6112yes—
165C23×C4C22×D6111yescharacteristic
166C2×M16—614no—
167C2×M16C22×D6114yes—
168C4⋊Q8—1224no—
169C4⋊Q8—1224no—
170C4⋊Q8—1228no—
171#125—1224no—
172#125—1224no—
173#125—1228no—
174C22⋊Q8—12216no—
175#117—618no—
176#117—1224no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—611no—
179C2×C4⋊C4—611no—
180C2×C4⋊C4—614no—
181C2×C4⋊C4—614no—
182C2×C4⋊C4—614no—
183C2×C4⋊C4—611no—
184C2×C4⋊C4—611no—
185C2×C4⋊C4C4×D6112yes—
186C2×C4⋊C4C22×D6112yes—
187C2×C22⋊C4—612no—
188C2×C22⋊C4—612no—
189C2×C42—612no—
190C2×C42—612no—
191C4⋊C8—1228no—
192C22⋊C8—24no—
193C22⋊C8—1224no—
194#97—1224no—
195C4×C8—1224no—
196C24C2×C4×D6111yescharacteristic
197C2×Q8—1228no—
198C2×Q8—4884no—
199C22×C4—24no—
200C22×C4—24no—
201C22×C4—82no—
202C22×C4—612no—
203C22×C4—612no—
204C22×C4—612no—
205C22×C4—612no—
206C22×C4C2×C4×D6111yescharacteristic
207C22×C4C2×C4×D6114yes—
208C22×C4D4×D6114yes—
209C22×C4C23×D6111yescharacteristic
210M16—28no—
211M16—1228no—
212C2×C8—24no—
213C2×C8—1224no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—24no—
217C4⋊C4—614no—
218C4⋊C4—614no—
219C4⋊C4—1228no—
220C4⋊C4—1228no—
221C4⋊C4—1228no—
222C4⋊C4—1222no—
223C4⋊C4—1222no—
224C22⋊C4—618no—
225C22⋊C4—1224no—
226C42—614no—
227C42—614no—
228C42—1224no—
229C23—22no—
230C23—41no—
231C23—41no—
232C23C22⋊C4×D6112yes—
233C23C22×C4×D6111yescharacteristic
234Q8—4888no—
235C2×C4—22no—
236C2×C4—28no—
237C2×C4—24no—
238C2×C4—44no—
239C2×C4—84no—
240C2×C4—614no—
241C2×C4—614no—
242C2×C4—1222no—
243C2×C4—1222no—
244C2×C4—2442no—
245C2×C4—2442no—
246C2×C4—2442no—
247C2×C4—2442no—
248C2×C4C22⋊C4×D6112yes—
249C2×C4C2×D4×D6112yes—
250C2×C4#1451982414yes—
251C8—44no—
252C8—2444no—
253C22—21no—
254C22—21no—
255C22—22no—
256C22—22no—
257C22—22no—
258C22—44no—
259C22C2×C22⋊C4×D6111yescharacteristic
260C22#1684023912yes—
261C4—22no—
262C4—44no—
263C4—1224no—
264C4—1224no—
265C4—2442no—
266C4—2442no—
267C4#1684033414yes—
268C2—22no—
269C2—42no—
270C2#2144840411yescharacteristic
271C2#2145429511yescharacteristic
272C2#2145429911yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1821C2
socleC22×C61C22×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC22×C4×C61C24
hypercenter#1821D61
hypocenterC61#21832
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1821

Complements

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

NH ≅ G/Ntype
3. #21446810C2semidirect
4. #21446806C2semidirect
162. C61#21832semidirect

Maximal subgroups

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

subgroupindex
C2×#168403932
#214544542
#214468102
#214468062
#214459002
#214458992
C61×#18212
#2183261