Finite Group Databasebeta

← #30594109

Subgroups — #30594109

Order 15616.

692 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 76 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#21460657C212yesmaximal, complemented
2#21444059C211yesmaximal, characteristic
3C2×C22⋊#92420—22no—
4C23×D244C411yescharacteristic
5C22×#11758198—22no—
6C2×#14519684C2211yescharacteristic
7C2×#95×C61C411yescharacteristic
8C22×#92420—42no—
9C22⋊#92420—24no—
10C22⋊#92420—42no—
11C24×D61—21no—
12C22×D244—21no—
13C22×D244—41no—
14C22×D244—41no—
15C22×D244—44no—
16C22×D244C812yescomplemented
17C23×Dic61D412yes—
18C2×#11758198—44no—
19C2×#11758198—44no—
20C2×#11758198—42no—
21C2×#11758198—42no—
22#14519684—41no—
23C23×C4×C61—21no—
24C23×C4×C61C2×C411yescharacteristic
25#95×C61—41no—
26C24×C61C22⋊C411yescharacteristic
27C23×D61—24no—
28C23×D61—22no—
29C23×D61—42no—
30C23×D61—42no—
31C23×D61—42no—
32C23×D61—41no—
33C23×D61—41no—
34C23×D61—42no—
35C23×D61—42no—
36C22×C4×C61—21no—
37C22×C4×C61—21no—
38C22×C4×C61—22no—
39C22×C4×C61—42no—
40C22×C4×C61—41no—
41C22×C4×C61—42no—
42C22×C4×C61—41no—
43C22×C4×C61—42no—
44C22×C4×C61C2×C811yescharacteristic
45C22×C4×C61M1611yescharacteristic
46C22×Dic61—22no—
47C22×Dic61—22no—
48C22×Dic61—42no—
49C22×Dic61—42no—
50C22×Dic61D812yes—
51C22×Dic61SD1612yes—
52C2×D244—42no—
53C2×D244—42no—
54C2×D244—44no—
55C2×D244—48no—
56C2×D244—44no—
57C2×D244—44no—
58C2×D244—44no—
59C2×#92420—44no—
60C2×#92420—82no—
61C2×#92420—82no—
62#11758198—48no—
63#11758198—48no—
64C23×C61—22no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61C22⋊C811yescharacteristic
68C23×C61#9911yescharacteristic
69C23×C61#10011yescharacteristic
70C23×C61#10212yes—
71C23×C61#10412yes—
72C22×D61—24no—
73C22×D61—44no—
74C22×D61—44no—
75C22×D61—42no—
76C22×D61—44no—
77C22×D61—44no—
78C22×D61—44no—
79C22×D61—44no—
80C22×D61—42no—
81C22×D61—44no—
82C22×D61—44no—
83C22×D61—82no—
84C22×D61—82no—
85C22×D61—82no—
86C22×D61—82no—
87C22×D61—82no—
88C22×D61—82no—
89C22×D61—81no—
90C22×D61—81no—
91C22×D61—81no—
92C22×D61—81no—
93C2×C4×C61—21no—
94C2×C4×C61—21no—
95C2×C4×C61—42no—
96C2×C4×C61—42no—
97C2×C4×C61—41no—
98C2×C4×C61—41no—
99C2×C4×C61—44no—
100C2×C4×C61—42no—
101C2×C4×C61—81no—
102C2×C4×C61—82no—
103C2×C4×C61—81no—
104C2×Dic61—22no—
105C2×Dic61—22no—
106C2×Dic61—42no—
107C2×Dic61—42no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—82no—
111D244—44no—
112D244—48no—
113D244—44no—
114#92420—84no—
115#7103—611nomaximal, Sylow
116C22×C61—21no—
117C22×C61—21no—
118C22×C61—21no—
119C22×C61—21no—
120C22×C61—22no—
121C22×C61—22no—
122C22×C61—22no—
123C22×C61—22no—
124C22×C61#32311yescharacteristic
125C22×C61D4⋊C812yes—
126C22×C61#32712yes—
127C22×C61#32911yescharacteristic
128C22×C61#33111yescharacteristic
129C22×C61AΣL(1,𝔽16)12yes—
130C22×C61#35311yescharacteristic
131C22×C61#35511yescharacteristic
132C2×D61—48no—
133C2×D61—44no—
134C2×D61—84no—
135C2×D61—84no—
136C2×D61—84no—
137C2×D61—82no—
138C2×D61—84no—
139C2×D61—84no—
140C2×D61—82no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—82no—
144Dic61—42no—
145Dic61—42no—
146#1438—611no—
147#1280—612no—
148C2×C61—21no—
149C2×C61—22no—
150C2×C61—21no—
151C2×C61#127011yescharacteristic
152C2×C61#131611yescharacteristic
153C2×C61#131811yescharacteristic
154C2×C61#134312yes—
155C2×C61#134512yes—
156D61—84no—
157C23×D4—611no—
158C22×C22⋊C4—1222no—
159C2×C22⋊C8—1222no—
160C2×#95—611no—
161C2×#95#692311yescharacteristic
162C61#710311yescharacteristic, complemented, Sylow
163C25—1221no—
164C22×D4—612no—
165C22×D4—1221no—
166C22×D4—2441no—
167C22×D4—2441no—
168C22×D4—2444no—
169C23×C4—21no—
170C23×C4—612no—
171C23×C4C2×#692311yescharacteristic
172C22×C8—2442no—
173C2×C22⋊C4—2444no—
174C2×C22⋊C4—2442no—
175C2×C22⋊C4—2442no—
176C2×C22⋊C4—2444no—
177C22⋊C8—1224no—
178C22⋊C8—2442no—
179#95—41no—
180#95—2441no—
181C24—1224no—
182C24—1222no—
183C24—2442no—
184C24—2442no—
185C24—2442no—
186C24—2441no—
187C24—2441no—
188C24—2442no—
189C24—2442no—
190C24C22⋊#692311yescharacteristic
191C2×D4—2442no—
192C2×D4—2442no—
193C2×D4—2444no—
194C2×D4—2444no—
195C2×D4—2448no—
196C2×D4—2444no—
197C2×D4—2444no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—22no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—42no—
206C22×C4—612no—
207C22×C4—612no—
208C22×C4—1222no—
209C22×C4—1222no—
210C22×C4—2442no—
211C22×C4—2442no—
212C22×C4D61⋊C811yescharacteristic
213C22×C4#1175821311yescharacteristic
214C2×C8—4882no—
215C2×C8—4882no—
216C2×C8—2444no—
217C22⋊C4—2448no—
218C22⋊C4—2448no—
219C23—22no—
220C23—21no—
221C23—21no—
222C23—1224no—
223C23—4882no—
224C23—4882no—
225C23—4882no—
226C23—4882no—
227C23—4882no—
228C23—4882no—
229C23—4881no—
230C23—4881no—
231C23—4881no—
232C23—4881no—
233C23—2444no—
234C23—2444no—
235C23—2442no—
236C23—2444no—
237C23—2444no—
238C23—2444no—
239C23—2444no—
240C23—2442no—
241C23—2444no—
242C23—2444no—
243C23#1451983411yescharacteristic
244C23#1451983611yescharacteristic
245C23#1451983711yescharacteristic
246C23#1451983912yes—
247C23#1451984212yes—
248D4—2444no—
249D4—2444no—
250D4—2448no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—81no—
260C2×C4—82no—
261C2×C4—81no—
262C2×C4—1222no—
263C2×C4—1222no—
264C2×C4—4882no—
265C2×C4—2442no—
266C2×C4—2442no—
267C2×C4—2442no—
268C2×C4—2442no—
269C8—4884no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—22no—
275C22—22no—
276C22—22no—
277C22—22no—
278C22—4884no—
279C22—4884no—
280C22—4884no—
281C22—4882no—
282C22—4884no—
283C22—4884no—
284C22—4882no—
285C22—2448no—
286C22—2444no—
287C22#1684060611yescharacteristic
288C22#1684061012yes—
289C22#1684061412yes—
290C22#1684061811yescharacteristic
291C22#1684062011yescharacteristic
292C22#1684066312yes—
293C22#1684066711yescharacteristic
294C22#1684067111yescharacteristic
295C4—41no—
296C4—41no—
297C4—82no—
298C4—2442no—
299C4—2442no—
300C2—21no—
301C2—21no—
302C2—22no—
303C2—4884no—
304C2#2146063611yescharacteristic
305C2#2146074411yescharacteristic
306C2#2146074811yescharacteristic
307C2#2146079812yes—
308C2#2146080212yes—
subgroupG/H
centerC23#14519836
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC2×#95×C61C4
socleC23×C61#99
prime radicalC23×D244C4
cosocleC2×#14519684C22
hypercenterC2×#95#6923
hypocenterC61#7103
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
1. #21460657C2semidirect
16. C22×D244C8semidirect
162. C61#7103semidirect

Maximal subgroups

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

subgroupindex
#214606572
#214440592
#710361