Finite Group Databasebeta

← #14913897

Subgroups — #14913897

Order 2816.

2858 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2#13071585C218yesmaximal, complemented
3#13071561C218yesmaximal, complemented
4#13071211C214yesmaximal, complemented
5#13071196C212yesmaximal
6#13071019C212yesmaximal, complemented
7#13070997C214yesmaximal, complemented
8#13070973C211yesmaximal, characteristic, complemented
9C11×#2274C211yesmaximal, characteristic, complemented
10C23×D44C2211yescharacteristic
11C23×C4×D11C2212yes—
12C2×C11×#117C2212yes—
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×(C2×D11)⋊C4C2212yes—
15C2×#66979C2212yes—
16C22×C4×Dic11C2211yescharacteristic
17C2×#66946C4116yescomplemented
18C2×#66946C2214yes—
19C2×#66946C2214yes—
20C2×#66925C2218yescomplemented
21C4×C11×C4⋊C4C2218yescomplemented
22C4×C11×C22⋊C4C2214yes—
23C4×C22⋊Dic11C2214yes—
24#10622601C2218yes—
25#10622590C2214yescomplemented
26#10622589C2214yescomplemented
27C4⋊C4×Dic11C2218yescomplemented
28#10622568C2218yes—
29#10622555C2214yes—
30#10622555C2214yes—
31#10622553C22116yescomplemented
32#10622552C2218yes—
33C4×(C2×D11)⋊C4C2218yescomplemented
34C4×Dic11⋊C4C2214yescomplemented
35C4×Dic11⋊C4C2214yescomplemented
36#10622282C22116yescomplemented
37#10622280C2218yescomplemented
38#10622277C2218yescomplemented
39C24×D11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2311yescharacteristic
43C23×Dic11C2311yescharacteristic
44C22×D44—28no—
45C22×D44C2×C418yes—
46C22×D44C2314yes—
47C22×C4×D11—48no—
48C22×C4×D11C2×C4116yes—
49C22×C4×D11C2314yes—
50C22×C4×D11C2314yes—
51C11×#117—28no—
52C2×C11×C4⋊C4C2×C418yes—
53C2×C11×C4⋊C4C2314yes—
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C22⋊C4C2314yes—
56C2×C42×C11C2314yes—
57C2×C42×C11C2318yes—
58C2×C22⋊Dic11C2314yes—
59C2×(C2×D11)⋊C4C2×C4116yes—
60C2×(C2×D11)⋊C4C23116yes—
61C2×(C2×D11)⋊C4C23116yes—
62C2×(C2×D11)⋊C4C2318yes—
63#66979—28no—
64C2×C4⋊Dic11C2314yes—
65C2×Dic11⋊C4C2318yes—
66C2×Dic11⋊C4C2318yes—
67C2×C4×Dic11C2×C418yes—
68C2×C4×Dic11C2314yes—
69C2×C4×Dic11C2318yes—
70C2×C4×Dic11C2312yes—
71C2×C4×Dic11C2312yes—
72#66946C2×C4132yes—
73#66946C2×C4132yes—
74#66925—416no—
75C11×#95C2318yes—
76C11⋊#95C2318yes—
77C11⋊#95C2318yes—
78C11⋊#95C2318yes—
79#34186—111nomaximal, Sylow
80C24×C11C2411yescharacteristic
81C23×D11—28no—
82C23×D11—44no—
83C23×D11—44no—
84C23×D11C22×C418yes—
85C23×D11C2414yes—
86C22×C4×C11—44no—
87C22×C4×C11C22×C418yes—
88C22×C4×C11C22×C414yes—
89C22×C4×C11#4118yes—
90C22×C4×C11C2418yes—
91C22×C4×C11C2414yes—
92C22×C4×C11C2412yes—
93C22×Dic11—24no—
94C22×Dic11—42no—
95C22×Dic11C22×C414yes—
96C22×Dic11C22×C414yes—
97C22×Dic11C2418yes—
98C22×Dic11C2411yescharacteristic
99C22×Dic11C2412yes—
100C22×Dic11C2411yescharacteristic
101C2×D44—232no—
102C2×D44—28no—
103C2×D44—28no—
104C2×D44C22×C4116yes—
105C2×C4×D11—216no—
106C2×C4×D11—48no—
107C2×C4×D11—432no—
108C2×C4×D11C22×C4116yes—
109C2×C4×D11C22×C4116yes—
110C11×C4⋊C4—28no—
111C11×C4⋊C4C22×C4116yes—
112C11×C22⋊C4—28no—
113C42×C11—28no—
114C42×C11—48no—
115C22⋊Dic11—28no—
116(C2×D11)⋊C4—416no—
117(C2×D11)⋊C4—416no—
118(C2×D11)⋊C4C22×C4132yes—
119C4⋊Dic11—28no—
120Dic11⋊C4—216no—
121Dic11⋊C4—48no—
122C4×Dic11—28no—
123C4×Dic11—48no—
124C4×Dic11C22×C418yes—
125C4×Dic11C22×C418yes—
126C22×C4×D4—111no—
127#2357—118no—
128#2354—118no—
129#2312—114no—
130#2309—112no—
131#2285—112no—
132#2280—114no—
133#2274—111no—
134#2274D1111yescharacteristic, complemented
135C23×C11—22no—
136C23×C11—22no—
137C23×C11C23×C412yes—
138C23×C11C2×#4114yes—
139C23×C11C2511yescharacteristic
140C22×D11—216no—
141C22×D11—28no—
142C22×D11—28no—
143C22×D11—28no—
144C22×D11—48no—
145C22×D11—48no—
146C22×D11—432no—
147C22×D11C23×C418yes—
148C2×C4×C11—28no—
149C2×C4×C11—28no—
150C2×C4×C11—28no—
151C2×C4×C11—28no—
152C2×C4×C11—48no—
153C2×C4×C11#117116yescomplemented
154C2×C4×C11C23×C418yes—
155C2×C4×C11C23×C414yes—
156C2×C4×C11C2×#4114yes—
157C2×C4×C11C2×#4114yes—
158C2×Dic11—22no—
159C2×Dic11—24no—
160C2×Dic11—28no—
161C2×Dic11—28no—
162C2×Dic11—28no—
163C2×Dic11—28no—
164C2×Dic11—44no—
165C2×Dic11C23×C414yes—
166C2×Dic11C23×C412yes—
167C2×Dic11C23×C412yes—
168C2×Dic11H(5,𝔽2)14yes—
169D44—232no—
170C4×D11—232no—
171C4×D11—416no—
172C23×D4—111no—
173C24×C4—112no—
174C2×C4×D4—114no—
175C2×C4×D4—114no—
176C2×C4×D4—1116no—
177C2×#117—112no—
178C2×#117—118no—
179C2×#117C2×D1112yes—
180C22×C4⋊C4C2×D1111yescharacteristic
181C22×C22⋊C4—112no—
182C22×C42—111no—
183#390—118no—
184#390—118no—
185#388—1116no—
186#388—1116no—
187#384—114no—
188#382—114no—
189#381—118no—
190#380—114no—
191#380—114no—
192#380—118no—
193#379—118no—
194C4×C4⋊C4—118no—
195C4×C4⋊C4—114no—
196C4×C4⋊C4—114no—
197C4×C4⋊C4C2×D1118yescomplemented
198C4×C22⋊C4—114no—
199C4×C22⋊C4—118no—
200C4×C22⋊C4C2×D1114yes—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—28no—
204C22×C11C2×#11714yes—
205C22×C11C24×C411yescharacteristic
206C22×C11C22×#4112yes—
207C22×C11C2×H(5,𝔽2)12yes—
208C22×C11#58512yes—
209C2×D11—28no—
210C2×D11—28no—
211C2×D11—28no—
212C2×D11—432no—
213C2×D11—416no—
214C4×C11—28no—
215C4×C11—48no—
216C4×C11C2×#11718yes—
217Dic11—22no—
218Dic11—24no—
219Dic11—48no—
220Dic11#51814yes—
221C25—112no—
222C22×D4—118no—
223C22×D4—114no—
224C22×D4—228no—
225C23×C4—111no—
226C23×C4—111no—
227C23×C4—114no—
228C23×C4—1116no—
229C23×C4—114no—
230C23×C4—448no—
231C23×C4C22×D1112yes—
232C23×C4C22×D1111yescharacteristic
233C4×D4—1132no—
234C4×D4—1132no—
235#117—28no—
236#117—228no—
237#117—4416no—
238C2×C4⋊C4—118no—
239C2×C4⋊C4—114no—
240C2×C4⋊C4—118no—
241C2×C4⋊C4C4×D1118yes—
242C2×C4⋊C4C22×D1114yes—
243C2×C4⋊C4C22×D1114yes—
244C2×C22⋊C4—1116no—
245C2×C22⋊C4—118no—
246C2×C22⋊C4—114no—
247C2×C22⋊C4—1116no—
248C2×C22⋊C4—1116no—
249C2×C22⋊C4C22×D1114yes—
250C2×C42—118no—
251C2×C42—112no—
252C2×C42—112no—
253C2×C42—114no—
254C2×C42—118no—
255C2×C42C22×D1114yes—
256C2×C42C22×D1118yes—
257#95—118no—
258#95—118no—
259#95—118no—
260#95C22×D1118yes—
261C2×C11—24no—
262C2×C11C22×#11711yescharacteristic
263C2×C11C2×#51811yescharacteristic
264C2×C11#342811yescharacteristic
265C2×C11#350614yes—
266D11—48no—
267C24—114no—
268C24—118no—
269C24—228no—
270C24—444no—
271C24—444no—
272C24C23×D1111yescharacteristic
273C2×D4—1116no—
274C2×D4—2232no—
275C2×D4—228no—
276C2×D4—228no—
277C22×C4—44no—
278C22×C4—111no—
279C22×C4—114no—
280C22×C4—111no—
281C22×C4—112no—
282C22×C4—114no—
283C22×C4—1116no—
284C22×C4—1116no—
285C22×C4—118no—
286C22×C4—2216no—
287C22×C4—224no—
288C22×C4—448no—
289C22×C4—4432no—
290C22×C4—442no—
291C22×C4C2×C4×D1118yes—
292C22×C4C2×C4×D1114yes—
293C22×C4#433918yes—
294C22×C4C23×D1118yes—
295C22×C4C23×D1114yes—
296C22×C4C23×D1112yes—
297C4⋊C4—28no—
298C4⋊C4—2216no—
299C4⋊C4—228no—
300C4⋊C4—448no—
301C4⋊C4C2×C4×D11116yes—
302C22⋊C4—28no—
303C22⋊C4—1132no—
304C22⋊C4—228no—
305C22⋊C4—4416no—
306C22⋊C4—4416no—
307C42—28no—
308C42—48no—
309C42—118no—
310C42—118no—
311C42—228no—
312C42—448no—
313C11#3418611yescharacteristic, complemented, Sylow
314C23—22no—
315C23—22no—
316C23—118no—
317C23—2216no—
318C23—228no—
319C23—228no—
320C23—228no—
321C23—448no—
322C23—448no—
323C23—4432no—
324C23C22×C4×D1112yes—
325C23C2×#433914yes—
326C23C24×D1111yescharacteristic
327D4—2232no—
328C2×C4—28no—
329C2×C4—28no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—48no—
333C2×C4—112no—
334C2×C4—114no—
335C2×C4—114no—
336C2×C4—112no—
337C2×C4—2232no—
338C2×C4—228no—
339C2×C4—222no—
340C2×C4—224no—
341C2×C4—228no—
342C2×C4—228no—
343C2×C4—228no—
344C2×C4—4416no—
345C2×C4—444no—
346C2×C4#66925116yescomplemented
347C2×C4C22×C4×D1118yes—
348C2×C4C22×C4×D1114yes—
349C2×C4C2×#433914yes—
350C2×C4C2×#433914yes—
351C22—28no—
352C22—22no—
353C22—22no—
354C22—228no—
355C22—228no—
356C22—228no—
357C22—4432no—
358C22—4416no—
359C22C2×#6692514yes—
360C22C23×C4×D1111yescharacteristic
361C22C22×#433912yes—
362C22D11×H(5,𝔽2)12yes—
363C22#1062345712yes—
364C4—28no—
365C4—48no—
366C4—114no—
367C4—222no—
368C4—224no—
369C4—448no—
370C4C2×#6692518yes—
371C2—24no—
372C2—448no—
373C2C22×#6692511yescharacteristic
374C2D11×#51811yescharacteristic
375C2#1308181811yescharacteristic
376C2#1308246114yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2274C2
socle, cosocleC23×C11C25
prime radicalC23×D44C22
hypercenter#2274D11
hypocenterC11#34186
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2274

Complements

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

NH ≅ G/Ntype
2. #13071585C2semidirect
3. #13071561C2semidirect
4. #13071211C2semidirect
6. #13071019C2semidirect
7. #13070997C2semidirect
8. #13070973C2semidirect
9. C11×#2274C2semidirect
17. C2×#66946C4semidirect
20. C2×#66925C22semidirect
21. C4×C11×C4⋊C4C22semidirect
25. #10622590C22semidirect
26. #10622589C22semidirect
27. C4⋊C4×Dic11C22semidirect
31. #10622553C22semidirect
33. C4×(C2×D11)⋊C4C22semidirect
34. C4×Dic11⋊C4C22semidirect
35. C4×Dic11⋊C4C22semidirect
36. #10622282C22semidirect
37. #10622280C22semidirect
38. #10622277C22semidirect
134. #2274D11semidirect
153. C2×C4×C11#117semidirect
197. C4×C4⋊C4C2×D11semidirect
313. C11#34186semidirect
346. C2×C4#66925semidirect

Maximal subgroups

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

subgroupindex
C22×#669462
#130715852
#130715612
#130712112
#130711962
#130710192
#130709972
#130709732
C11×#22742
#3418611