Finite Group Databasebeta

← #30594147

Subgroups — #30594147

Order 15616.

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

normal subgroups only

This group has 368 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#21460657C211yesmaximal, characteristic
2#21460657C211yesmaximal, characteristic
3#21444078C211yesmaximal, characteristic
4C2×C22⋊#92420—21no—
5C2×C22⋊#92420—21no—
6C2×#14519684—21no—
7C2×#14519684—21no—
8C2×#14519684C411yescharacteristic
9C2×#14519684C2211yescharacteristic
10C22×C4⋊C4×C61C411yescharacteristic
11C22×#92420—41no—
12C22×#92420—41no—
13C22⋊#92420—22no—
14C22⋊#92420—22no—
15C22⋊#92420—41no—
16C22⋊#92420—41no—
17C23×Dic61—21no—
18C23×Dic61D411yescharacteristic
19C23×Dic61D411yescharacteristic
20#14519684—21no—
21#14519684—41no—
22#14519684—42no—
23#14519684—41no—
24#14519684—41no—
25#14519684C812yescomplemented
26C23×C4×C61—21no—
27C23×C4×C61C2×C411yescharacteristic
28C2×C4⋊C4×C61—41no—
29C2×C4⋊C4×C61—42no—
30C24×C61C22⋊C411yescharacteristic
31C22×C4×C61—21no—
32C22×C4×C61—21no—
33C22×C4×C61—22no—
34C22×C4×C61—41no—
35C22×C4×C61—41no—
36C22×C4×C61—41no—
37C22×C4×C61—41no—
38C22×C4×C61—41no—
39C22×C4×C61—41no—
40C22×C4×C61—41no—
41C22×C4×C61—41no—
42C22×C4×C61C2×C811yescharacteristic
43C22×C4×C61M1611yescharacteristic
44C22×Dic61—21no—
45C22×Dic61—21no—
46C22×Dic61—21no—
47C22×Dic61—21no—
48C22×Dic61—22no—
49C22×Dic61—41no—
50C22×Dic61—41no—
51C22×Dic61—41no—
52C22×Dic61—41no—
53C22×Dic61—41no—
54C22×Dic61—41no—
55C22×Dic61—41no—
56C22×Dic61—41no—
57C22×Dic61—41no—
58C22×Dic61—41no—
59C22×Dic61D811yescharacteristic
60C22×Dic61SD1611yescharacteristic
61C22×Dic61SD1611yescharacteristic
62C22×Dic61Q1611yescharacteristic
63C2×#92420—42no—
64C2×#92420—42no—
65C2×#92420—81no—
66C2×#92420—81no—
67C2×#92420—81no—
68C2×#92420—81no—
69C4⋊C4×C61—42no—
70C4⋊C4×C61—42no—
71C23×C61—21no—
72C23×C61—21no—
73C23×C61—21no—
74C23×C61—21no—
75C23×C61C22⋊C811yescharacteristic
76C23×C61#9911yescharacteristic
77C23×C61#10111yescharacteristic
78C23×C61#10211yescharacteristic
79C23×C61#10311yescharacteristic
80C23×C61#10411yescharacteristic
81C23×C61#10411yescharacteristic
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—42no—
85C2×C4×C61—41no—
86C2×C4×C61—41no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C2×C4×C61—42no—
90C2×C4×C61—42no—
91C2×C4×C61—42no—
92C2×C4×C61—81no—
93C2×C4×C61—81no—
94C2×C4×C61—81no—
95C2×C4×C61—81no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—41no—
101C2×Dic61—41no—
102C2×Dic61—41no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61—41no—
106C2×Dic61—41no—
107C2×Dic61—41no—
108C2×Dic61—42no—
109C2×Dic61—42no—
110C2×Dic61—42no—
111C2×Dic61—81no—
112C2×Dic61—81no—
113C2×Dic61—81no—
114C2×Dic61—81no—
115C2×Dic61—81no—
116C2×Dic61—81no—
117#92420—82no—
118#92420—82no—
119#7122—611nomaximal, Sylow
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—21no—
124C22×C61—21no—
125C22×C61—21no—
126C22×C61—21no—
127C22×C61—21no—
128C22×C61—21no—
129C22×C61—21no—
130C22×C61—21no—
131C22×C61—21no—
132C22×C61#32411yescharacteristic
133C22×C61D4⋊C811yescharacteristic
134C22×C61Q8⋊C811yescharacteristic
135C22×C61#32711yescharacteristic
136C22×C61#32811yescharacteristic
137C22×C61#33011yescharacteristic
138C22×C61#33211yescharacteristic
139C22×C61AΣL(1,𝔽16)11yescharacteristic
140C22×C61#35211yescharacteristic
141C22×C61#35411yescharacteristic
142C22×C61#35511yescharacteristic
143C4×C61—41no—
144C4×C61—41no—
145C4×C61—82no—
146Dic61—41no—
147Dic61—41no—
148Dic61—41no—
149Dic61—41no—
150Dic61—82no—
151#1442—611no—
152#1280—611no—
153#1280—611no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61—21no—
157C2×C61—21no—
158C2×C61#127111yescharacteristic
159C2×C61#132411yescharacteristic
160C2×C61#132611yescharacteristic
161C2×C61#134411yescharacteristic
162C2×C61#134511yescharacteristic
163C2×C61#135111yescharacteristic
164C2×C61#135311yescharacteristic
165C22×C4⋊C4#692311yescharacteristic
166C2×C22⋊C8—1221no—
167C2×C22⋊C8—1221no—
168C2×#95—611no—
169C2×#95—611no—
170C2×#95—1221no—
171C2×#95—1221no—
172C61#712211yescharacteristic, complemented, Sylow
173C23×C4—21no—
174C23×C4—611no—
175C23×C4—611no—
176C23×C4—1221no—
177C23×C4C2×#692311yescharacteristic
178C22×C8—2441no—
179C22×C8—2441no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4—42no—
182C22⋊C8—1222no—
183C22⋊C8—1222no—
184C22⋊C8—2441no—
185C22⋊C8—2441no—
186#95—612no—
187#95—1221no—
188#95—2441no—
189#95—2442no—
190#95—2441no—
191#95—2441no—
192C24C22⋊#692311yescharacteristic
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—611no—
205C22×C4—611no—
206C22×C4—611no—
207C22×C4—611no—
208C22×C4—1221no—
209C22×C4—1221no—
210C22×C4—1221no—
211C22×C4—1221no—
212C22×C4—1222no—
213C22×C4—2441no—
214C22×C4—2441no—
215C22×C4—2441no—
216C22×C4—2441no—
217C22×C4—2441no—
218C22×C4—2441no—
219C22×C4—2441no—
220C22×C4—2441no—
221C22×C4—2441no—
222C22×C4—2441no—
223C22×C4D61⋊C811yescharacteristic
224C22×C4#1175821311yescharacteristic
225C2×C8—4881no—
226C2×C8—4881no—
227C2×C8—4881no—
228C2×C8—4881no—
229C2×C8—2442no—
230C2×C8—2442no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C23—21no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23#1451983411yescharacteristic
238C23#1451983511yescharacteristic
239C23#1451983811yescharacteristic
240C23#1451983911yescharacteristic
241C23#1451984011yescharacteristic
242C23#1451984111yescharacteristic
243C23#1451984211yescharacteristic
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—1221no—
259C2×C4—1221no—
260C2×C4—1221no—
261C2×C4—1221no—
262C2×C4—4881no—
263C2×C4—4881no—
264C2×C4—4881no—
265C2×C4—4881no—
266C2×C4—4881no—
267C2×C4—4881no—
268C2×C4—2442no—
269C2×C4—2442no—
270C2×C4—2442no—
271C2×C4—2441no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4—2441no—
279C8—4882no—
280C8—4882no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22#1684060811yescharacteristic
294C22#1684061011yescharacteristic
295C22#1684061211yescharacteristic
296C22#1684061311yescharacteristic
297C22#1684061611yescharacteristic
298C22#1684061911yescharacteristic
299C22#1684062111yescharacteristic
300C22#1684066211yescharacteristic
301C22#1684066411yescharacteristic
302C22#1684066811yescharacteristic
303C22#1684067011yescharacteristic
304C4—41no—
305C4—41no—
306C4—82no—
307C4—4882no—
308C4—2441no—
309C4—2441no—
310C4—2441no—
311C4—2441no—
312C2—21no—
313C2—21no—
314C2—21no—
315C2—21no—
316C2#2146063811yescharacteristic
317C2#2146076011yescharacteristic
318C2#2146076411yescharacteristic
319C2#2146079911yescharacteristic
320C2#2146080111yescharacteristic
321C2#2146081411yescharacteristic
322C2#2146081811yescharacteristic
subgroupG/H
centerC23#14519835
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC22×C4⋊C4×C61C4
socleC23×C61#99
prime radicalC24×C61C22⋊C4
cosocleC2×#14519684C22
hypercenterC22×C4⋊C4#6923
hypocenterC61#7122
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
25. #14519684C8semidirect
172. C61#7122semidirect

Maximal subgroups

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

subgroupindex
#214606572
#214440782
#712261