Finite Group Databasebeta

← #14913825

Subgroups — #14913825

Order 2816.

2446 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66930C211yesmaximal, characteristic
2#13071474C2116yesmaximal, complemented
3#13071230C211yesmaximal, characteristic
4#13071218C214yesmaximal, complemented
5#13071011C214yesmaximal, complemented
6C2×#10622556C212yesmaximal
7#13070969C212yesmaximal
8C11×#2315C211yesmaximal, characteristic
9C24×Dic11C2211yescharacteristic
10C22×C11×C22⋊C4C2212yes—
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C22⋊Dic11C2212yes—
13C22×C22⋊Dic11C2211yescharacteristic
14C22×Dic11⋊C4C2212yes—
15C22×C4×Dic11C2212yes—
16C2×#66930C4116yescomplemented
17C2×#66930C2218yes—
18C11×#385C2218yes—
19C11×#380C2214yes—
20#10622825C2214yes—
21C4×C22⋊Dic11C2218yes—
22C2×C11⋊#95C2218yes—
23#10622591C22116yescomplemented
24#10622590C2218yescomplemented
25C4⋊C4×Dic11C2218yescomplemented
26#10622563C2218yes—
27#10622556C2214yes—
28#10622556C2218yes—
29#10622556C2214yes—
30C22⋊C4×Dic11C2218yes—
31C22⋊C4×Dic11C2218yes—
32#10622268C22116yescomplemented
33#10622264C2218yescomplemented
34#10622261C2218yescomplemented
35C25×C11C2311yescharacteristic
36C23×C4×C11C2314yes—
37C23×C4×C11C2312yes—
38C23×Dic11—24no—
39C23×Dic11—24no—
40C23×Dic11C2×C418yes—
41C23×Dic11C2314yes—
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C23×Dic11C2314yes—
45C23×Dic11C2312yes—
46C2×C11×C4⋊C4C2318yes—
47C2×C11×C22⋊C4—28no—
48C2×C11×C22⋊C4C2×C418yes—
49C2×C11×C22⋊C4C2314yes—
50C2×C11×C22⋊C4C2314yes—
51C2×C11×C22⋊C4C2314yes—
52C2×C22⋊Dic11—28no—
53C2×C22⋊Dic11C2×C418yes—
54C2×C22⋊Dic11C2314yes—
55C2×C22⋊Dic11C2314yes—
56C2×C22⋊Dic11C2314yes—
57C2×C4⋊Dic11C2318yes—
58C2×Dic11⋊C4C2×C4116yescomplemented
59C2×Dic11⋊C4C2318yes—
60C2×C4×Dic11C2×C4116yescomplemented
61C2×C4×Dic11C23116yes—
62C2×C4×Dic11C2314yes—
63C2×C4×Dic11C2314yes—
64#66930C2×C4164yescomplemented
65C11×#95C2318yes—
66C11⋊#95C23116yes—
67C11⋊#95C2318yes—
68C11⋊#95C23116yes—
69C11⋊#95C23116yes—
70#34177—111nomaximal, Sylow
71C24×C11—44no—
72C24×C11C22×C414yes—
73C24×C11#4114yes—
74C24×C11#4114yes—
75C24×C11C2412yes—
76C24×C11C2411yescharacteristic
77C22×C4×C11—28no—
78C22×C4×C11—44no—
79C22×C4×C11—48no—
80C22×C4×C11C22×C418yes—
81C22×C4×C11C2418yes—
82C22×C4×C11C2414yes—
83C22×Dic11—232no—
84C22×Dic11—22no—
85C22×Dic11—22no—
86C22×Dic11—28no—
87C22×Dic11—22no—
88C22×Dic11—22no—
89C22×Dic11—28no—
90C22×Dic11—28no—
91C22×Dic11—44no—
92C22×Dic11—48no—
93C22×Dic11C22×C4116yes—
94C22×Dic11C22×C414yes—
95C22×Dic11C22×C414yes—
96C22×Dic11C22×C418yes—
97C22×Dic11C2418yes—
98C22×Dic11C2412yes—
99C22×Dic11C2412yes—
100C22×Dic11C2414yes—
101C11×C4⋊C4—48no—
102C11×C22⋊C4—28no—
103C11×C22⋊C4—28no—
104C11×C22⋊C4C22×C4116yes—
105C22⋊Dic11—28no—
106C22⋊Dic11—28no—
107C22⋊Dic11C22×C4116yes—
108C4⋊Dic11—48no—
109Dic11⋊C4C22×C4132yes—
110C4×Dic11—416no—
111C4×Dic11C22×C4116yes—
112C4×Dic11C22×C4116yes—
113C22×#117—111no—
114#2343—1116no—
115#2315—111no—
116#2315D1111yescharacteristic
117#2313—114no—
118#2283—114no—
119C2×#381—112no—
120#2273—112no—
121C23×C11—24no—
122C23×C11—28no—
123C23×C11—48no—
124C23×C11—48no—
125C23×C11—48no—
126C23×C11#117116yes—
127C23×C11C23×C414yes—
128C23×C11C23×C412yes—
129C23×C11C2×#4112yes—
130C23×C11C2×#4114yes—
131C23×C11C2×#4112yes—
132C23×C11C2×#4114yes—
133C23×C11C2511yescharacteristic
134C2×C4×C11—28no—
135C2×C4×C11—28no—
136C2×C4×C11—216no—
137C2×C4×C11—48no—
138C2×C4×C11—88no—
139C2×C4×C11C23×C418yes—
140C2×Dic11—232no—
141C2×Dic11—28no—
142C2×Dic11—28no—
143C2×Dic11—22no—
144C2×Dic11—22no—
145C2×Dic11—22no—
146C2×Dic11—22no—
147C2×Dic11—28no—
148C2×Dic11—28no—
149C2×Dic11—216no—
150C2×Dic11—48no—
151C2×Dic11—88no—
152C2×Dic11C23×C414yes—
153C2×Dic11C23×C418yes—
154C2×Dic11C23×C414yes—
155C24×C4—111no—
156C2×#117—118no—
157C2×#117—1116no—
158C22×C4⋊C4—112no—
159C22×C22⋊C4—111no—
160C22×C22⋊C4—112no—
161C22×C22⋊C4C2×D1112yes—
162C22×C22⋊C4C2×D1111yescharacteristic
163C22×C42—112no—
164#387—1116no—
165#387—1116no—
166#385—118no—
167#385C2×D1118yes—
168#383—118no—
169#382—118no—
170#381—114no—
171#381—118no—
172#381—114no—
173#380—114no—
174#380C2×D1114yes—
175C4×C4⋊C4—118no—
176C4×C22⋊C4—118no—
177C4×C22⋊C4—118no—
178C4×C22⋊C4—118no—
179#376—118no—
180C2×#95—118no—
181C22×C11—24no—
182C22×C11—28no—
183C22×C11—28no—
184C22×C11—24no—
185C22×C11—24no—
186C22×C11—28no—
187C22×C11—416no—
188C22×C11C2×#11718yes—
189C22×C11C2×#11714yes—
190C22×C11C24×C411yescharacteristic
191C22×C11C22×#4111yescharacteristic
192C22×C11C22×#4111yescharacteristic
193C22×C11#58514yes—
194C4×C11—28no—
195C4×C11—48no—
196Dic11—24no—
197Dic11—24no—
198Dic11—28no—
199Dic11—48no—
200C25C22×D1111yescharacteristic
201C23×C4—118no—
202C23×C4—111no—
203C23×C4—114no—
204C23×C4—111no—
205C23×C4—112no—
206C23×C4—114no—
207C23×C4—224no—
208C23×C4—224no—
209C23×C4C22×D1114yes—
210C23×C4C22×D1112yes—
211#117—1164no—
212C2×C4⋊C4—1116no—
213C2×C4⋊C4—118no—
214C2×C4⋊C4—118no—
215C2×C4⋊C4C22×D1118yes—
216C2×C22⋊C4—28no—
217C2×C22⋊C4—118no—
218C2×C22⋊C4—114no—
219C2×C22⋊C4—114no—
220C2×C22⋊C4—114no—
221C2×C22⋊C4—228no—
222C2×C22⋊C4C4×D1118yes—
223C2×C22⋊C4C22×D1114yes—
224C2×C22⋊C4C22×D1114yes—
225C2×C22⋊C4C22×D1114yes—
226C2×C42—1116no—
227C2×C42—114no—
228C2×C42—114no—
229C2×C42—1116no—
230#95—1116no—
231#95—1116no—
232#95—118no—
233#95—1116no—
234#95C22×D1118yes—
235C2×C11—24no—
236C2×C11—28no—
237C2×C11C22×#11711yescharacteristic
238C2×C11#342812yes—
239C2×C11#349112yes—
240C2×C11#349112yes—
241C24—44no—
242C24C2×C4×D1114yes—
243C24#434114yes—
244C24#434314yes—
245C24C23×D1112yes—
246C24C23×D1111yescharacteristic
247C22×C4—28no—
248C22×C4—44no—
249C22×C4—48no—
250C22×C4—114no—
251C22×C4—114no—
252C22×C4—1116no—
253C22×C4—112no—
254C22×C4—112no—
255C22×C4—114no—
256C22×C4—118no—
257C22×C4—118no—
258C22×C4—2232no—
259C22×C4—222no—
260C22×C4—222no—
261C22×C4—228no—
262C22×C4—222no—
263C22×C4—222no—
264C22×C4—228no—
265C22×C4—228no—
266C22×C4—444no—
267C22×C4—448no—
268C22×C4C2×C4×D1118yes—
269C22×C4C23×D1118yes—
270C22×C4C23×D1114yes—
271C4⋊C4—48no—
272C4⋊C4—1132no—
273C4⋊C4—448no—
274C22⋊C4—28no—
275C22⋊C4—28no—
276C22⋊C4—1116no—
277C22⋊C4—228no—
278C22⋊C4—228no—
279C22⋊C4C2×C4×D11116yes—
280C42—1116no—
281C42—1116no—
282C42—4416no—
283C11#3417711yescharacteristic, complemented, Sylow
284C23—28no—
285C23—24no—
286C23—48no—
287C23—48no—
288C23—48no—
289C23#66945116yes—
290C23C22×C4×D1114yes—
291C23C22×C4×D1112yes—
292C23C2×#434112yes—
293C23C2×#434114yes—
294C23C2×#434312yes—
295C23C2×#434314yes—
296C23C24×D1111yescharacteristic
297C2×C4—28no—
298C2×C4—28no—
299C2×C4—216no—
300C2×C4—48no—
301C2×C4—88no—
302C2×C4—114no—
303C2×C4—118no—
304C2×C4—114no—
305C2×C4—228no—
306C2×C4—228no—
307C2×C4—2232no—
308C2×C4—222no—
309C2×C4—222no—
310C2×C4—222no—
311C2×C4—222no—
312C2×C4—228no—
313C2×C4—228no—
314C2×C4—2216no—
315C2×C4—448no—
316C2×C4—888no—
317C2×C4C22×C4×D1118yes—
318C22—28no—
319C22—24no—
320C22—28no—
321C22—24no—
322C22—24no—
323C22—28no—
324C22—416no—
325C22C2×#6694518yes—
326C22C2×#6694514yes—
327C22C23×C4×D1111yescharacteristic
328C22C22×#434111yescharacteristic
329C22C22×#434311yescharacteristic
330C22#1062345514yes—
331C4—28no—
332C4—48no—
333C4—224no—
334C4—224no—
335C4—228no—
336C4—448no—
337C2—28no—
338C2—24no—
339C2C22×#6694511yescharacteristic
340C2#1308181412yes—
341C2#1308231312yes—
342C2#1308231512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2315C2
socle, cosocleC23×C11C25
prime radicalC25×C11C23
hypercenter#2315D11
hypocenterC11#34177
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. #13071474C2semidirect
4. #13071218C2semidirect
5. #13071011C2semidirect
16. C2×#66930C4semidirect
23. #10622591C22semidirect
24. #10622590C22semidirect
25. C4⋊C4×Dic11C22semidirect
32. #10622268C22semidirect
33. #10622264C22semidirect
34. #10622261C22semidirect
58. C2×Dic11⋊C4C2×C4semidirect
60. C2×C4×Dic11C2×C4semidirect
64. #66930C2×C4semidirect
283. C11#34177semidirect

Maximal subgroups

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

subgroupindex
C22×#669302
#130714742
#130712302
#130712182
#130710112
C2×#106225562
#130709692
C11×#23152
#3417711