Finite Group Databasebeta

← #14920644

Subgroups — #14920644

Order 2816.

1698 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074795C218yesmaximal, complemented
2#13074730C212yesmaximal
3#13074586C212yesmaximal
4#13074429C214yesmaximal
5#13071924C214yesmaximal, complemented
6#13071910C214yesmaximal, complemented
7C4×#66977C214yesmaximal
8#13071014C212yesmaximal
9C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2212yes—
11C22×C42×C11C2212yes—
12C22×C42×C11C2211yescharacteristic
13C2×#66977C2214yes—
14C2×C4×Dic22C2214yes—
15C4×C11×C4⋊C4C2214yes—
16C4×C11×C4⋊C4C2214yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11×#95C2211yescharacteristic
19#10622825C2214yes—
20#10622825C2214yes—
21#10622824C2214yes—
22#10622823C2218yes—
23C4×C22⋊Dic11C2214yes—
24#10622599C2218yes—
25#10622597C2218yes—
26#10622597C2218yes—
27#10622592C2218yes—
28#10622550C2214yes—
29#10622549C2214yes—
30C4×C4⋊Dic11C2212yes—
31C4×C4⋊Dic11C2214yes—
32C4×C4⋊Dic11C2212yes—
33#10622546C2218yes—
34#10622545C2214yes—
35C4×Dic11⋊C4C2218yes—
36#10622542C2214yes—
37#10622541C2214yes—
38#10622274C2218yes—
39#10622273C2218yes—
40#10622270C2218yes—
41#10622269C2218yes—
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2312yes—
47C22×Dic22C2314yes—
48C2×C11×C4⋊C4—28no—
49C2×C11×C4⋊C4C2318yes—
50C2×C42×C11—44no—
51C2×C42×C11Q818yescomplemented
52C2×C42×C11C2314yes—
53C2×C42×C11C2314yes—
54C2×C42×C11C2312yes—
55C2×C42×C11C2312yes—
56C2×C22⋊Dic11C2318yes—
57C2×C4⋊Dic11C2314yes—
58C2×C4⋊Dic11C2314yes—
59C2×C4⋊Dic11C2314yes—
60C2×C4⋊Dic11C2314yes—
61C2×C4⋊Dic11C2314yes—
62#66977—216no—
63C2×Dic11⋊C4C2318yes—
64C2×Dic11⋊C4C2318yes—
65C2×Dic11⋊C4C2318yes—
66C2×C4×Dic11C2314yes—
67C2×C4×Dic11C2314yes—
68C4×Dic22—48no—
69C11×#95C2314yes—
70C11×#95C2314yes—
71C11⋊#95C2318yes—
72C11⋊#95C2318yes—
73C11⋊#95C2318yes—
74C11⋊#95C2318yes—
75C11⋊#95C2318yes—
76C11⋊#95C2318yes—
77C11⋊#95C2314yes—
78C11⋊#95C2314yes—
79#34595—111nomaximal, Sylow
80C24×C11C2411yescharacteristic
81C22×C4×C11—24no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—24no—
85C22×C4×C11—42no—
86C22×C4×C11—42no—
87C22×C4×C11—42no—
88C22×C4×C11—42no—
89C22×C4×C11—42no—
90C22×C4×C11C2×Q814yes—
91C22×C4×C11C2×Q814yes—
92C22×C4×C11C2×Q814yes—
93C22×C4×C11#4118yes—
94C22×C4×C11C2414yes—
95C22×C4×C11C2411yescharacteristic
96C22×C4×C11C2412yes—
97C22×C4×C11C2412yes—
98C22×C4×C11C2414yes—
99C22×C4×C11C2411yescharacteristic
100C22×Dic11C2418yes—
101C22×Dic11C2418yes—
102C2×Dic22—28no—
103C2×Dic22—44no—
104C2×Dic22—44no—
105C11×C4⋊C4—216no—
106C42×C11—28no—
107C42×C11—44no—
108C42×C11C2×Q818yes—
109C42×C11C2×Q818yes—
110C22⋊Dic11—216no—
111C4⋊Dic11—28no—
112C4⋊Dic11—44no—
113C4⋊Dic11—44no—
114C4⋊Dic11—44no—
115C4⋊Dic11—44no—
116Dic11⋊C4—216no—
117Dic11⋊C4—48no—
118Dic11⋊C4—48no—
119C4×Dic11—28no—
120C4×Dic11—28no—
121#2666—118no—
122#2659—112no—
123#2646—112no—
124#2627—114no—
125#2402—114no—
126#2399—114no—
127C4×C22⋊Q8—114no—
128#2283—112no—
129C2×C4×C4⋊C4D1111yescharacteristic
130C23×C11—21no—
131C23×C11—21no—
132C23×C11—22no—
133C23×C11C22×Q812yes—
134C23×C11C2×#4114yes—
135C23×C11C2511yescharacteristic
136C2×C4×C11—28no—
137C2×C4×C11—24no—
138C2×C4×C11—24no—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—24no—
142C2×C4×C11—24no—
143C2×C4×C11—28no—
144C2×C4×C11—24no—
145C2×C4×C11—24no—
146C2×C4×C11—24no—
147C2×C4×C11—44no—
148C2×C4×C11—48no—
149C2×C4×C11—48no—
150C2×C4×C11C22×Q814yes—
151C2×C4×C11C22×Q812yes—
152C2×C4×C11C22×Q814yes—
153C2×C4×C11C22×Q812yes—
154C2×C4×C11C2×#4118yes—
155C2×C4×C11H(5,𝔽2)12yes—
156C2×C4×C112−1+412yes—
157C2×Dic11—28no—
158C2×Dic11—28no—
159C2×Dic11—28no—
160C2×Dic11—28no—
161C2×Dic11—28no—
162C2×Dic11—28no—
163Dic22—416no—
164C2×C22⋊Q8—114no—
165C2×C4×Q8—114no—
166C22×C4⋊C4C2×D1112yes—
167C22×C42C2×D1112yes—
168C22×C42C2×D1111yescharacteristic
169#400—118no—
170#400—118no—
171#398—118no—
172#398—118no—
173#398—118no—
174#398—118no—
175#395—118no—
176#395—118no—
177#391—114no—
178#389—114no—
179#387—118no—
180#385—118no—
181#383—114no—
182#382—114no—
183#381—114no—
184#380—114no—
185#380—114no—
186C4×C4⋊C4—118no—
187C4×C4⋊C4—112no—
188C4×C4⋊C4—112no—
189C4×C4⋊C4—114no—
190C4×C4⋊C4C2×D1114yes—
191C4×C4⋊C4C2×D1114yes—
192C4×C22⋊C4—114no—
193#376—114no—
194C2×#95C2×D1111yescharacteristic
195C2×#95C2×D1111yescharacteristic
196C22×C11—22no—
197C22×C11—22no—
198C22×C11—24no—
199C22×C11—24no—
200C22×C11#53314yes—
201C22×C11C23×Q811yescharacteristic
202C22×C11C22×#4112yes—
203C22×C11C2×H(5,𝔽2)11yescharacteristic
204C22×C11C2×2−1+411yescharacteristic
205C22×C11#58512yes—
206C4×C11—24no—
207C4×C11—22no—
208C4×C11—24no—
209C4×C11—28no—
210C4×C11—44no—
211C4×C11#54414yes—
212Dic11—48no—
213Dic11—48no—
214C22×Q8—114no—
215C23×C4C22×D1111yescharacteristic
216C23×C4C22×D1111yescharacteristic
217C23×C4C22×D1112yes—
218C23×C4C22×D1111yescharacteristic
219C23×C4C22×D1112yes—
220C22⋊Q8—2216no—
221C4×Q8—448no—
222C2×C4⋊C4—28no—
223C2×C4⋊C4—118no—
224C2×C4⋊C4—114no—
225C2×C4⋊C4—114no—
226C2×C4⋊C4—118no—
227C2×C4⋊C4—114no—
228C2×C4⋊C4—114no—
229C2×C4⋊C4—114no—
230C2×C4⋊C4—118no—
231C2×C4⋊C4C22×D1118yes—
232C2×C22⋊C4—118no—
233C2×C42—44no—
234C2×C42—114no—
235C2×C42—114no—
236C2×C42Dic2218yescomplemented
237C2×C42C22×D1114yes—
238C2×C42C22×D1114yes—
239C2×C42C22×D1112yes—
240C2×C42C22×D1112yes—
241#95—118no—
242#95—118no—
243#95—118no—
244#95—118no—
245#95—114no—
246#95—114no—
247#95—118no—
248#95—118no—
249#95C22×D1114yes—
250#95C22×D1114yes—
251C2×C11—24no—
252C2×C11C2×#53311yescharacteristic
253C2×C11C2×#54411yescharacteristic
254C2×C11#345811yescharacteristic
255C2×C11#345912yes—
256C2×C11#346112yes—
257C24C23×D1111yescharacteristic
258C2×Q8—228no—
259C2×Q8—444no—
260C2×Q8—444no—
261C22×C4—24no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—24no—
265C22×C4—42no—
266C22×C4—42no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4—118no—
271C22×C4—118no—
272C22×C4C2×Dic2214yes—
273C22×C4C2×Dic2214yes—
274C22×C4C2×Dic2214yes—
275C22×C4#433918yes—
276C22×C4C23×D1114yes—
277C22×C4C23×D1111yescharacteristic
278C22×C4C23×D1112yes—
279C22×C4C23×D1112yes—
280C22×C4C23×D1114yes—
281C22×C4C23×D1111yescharacteristic
282C4⋊C4—216no—
283C4⋊C4—2216no—
284C4⋊C4—228no—
285C4⋊C4—448no—
286C4⋊C4—444no—
287C4⋊C4—448no—
288C4⋊C4—444no—
289C4⋊C4—444no—
290C4⋊C4—444no—
291C22⋊C4—2216no—
292C42—28no—
293C42—44no—
294C42—228no—
295C42—228no—
296C42C2×Dic2218yes—
297C42C2×Dic2218yes—
298C11#3459511yescharacteristic, complemented, Sylow
299C23—21no—
300C23—21no—
301C23—22no—
302C23C22×Dic2212yes—
303C23C2×#433914yes—
304C23C24×D1111yescharacteristic
305Q8—4416no—
306C2×C4—28no—
307C2×C4—24no—
308C2×C4—24no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—28no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—24no—
317C2×C4—44no—
318C2×C4—48no—
319C2×C4—48no—
320C2×C4—228no—
321C2×C4—228no—
322C2×C4—228no—
323C2×C4—228no—
324C2×C4—228no—
325C2×C4—228no—
326C2×C4C22×Dic2214yes—
327C2×C4C22×Dic2212yes—
328C2×C4C22×Dic2214yes—
329C2×C4C22×Dic2212yes—
330C2×C4C2×#433918yes—
331C2×C4#6703712yes—
332C2×C4#6704012yes—
333C22—22no—
334C22—22no—
335C22—24no—
336C22—24no—
337C22#1062300114yes—
338C22C23×Dic2211yescharacteristic
339C22C22×#433912yes—
340C22C2×#6703711yescharacteristic
341C22C2×#6704011yescharacteristic
342C22#1062345312yes—
343C4—24no—
344C4—22no—
345C4—24no—
346C4—28no—
347C4—44no—
348C4—448no—
349C4—448no—
350C4#1062303114yes—
351C2—24no—
352C2C2×#1062300111yescharacteristic
353C2C2×#1062303111yescharacteristic
354C2#1308202111yescharacteristic
355C2#1308202512yes—
356C2#1308204912yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C4⋊C4C2
prime radicalC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#34595
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #13074795C2semidirect
5. #13071924C2semidirect
6. #13071910C2semidirect
51. C2×C42×C11Q8semidirect
236. C2×C42Dic22semidirect
298. C11#34595semidirect

Maximal subgroups

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

subgroupindex
#130747952
#130747302
#130745862
#130744292
#130719242
#130719102
C4×#669772
#130710142
C2×C4×C11×C4⋊C42
#3459511