Finite Group Databasebeta

← #14959872

Subgroups — #14959872

Order 2816.

4086 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C216yesmaximal, complemented
2#13077013C211yesmaximal, characteristic, complemented
3#13077010C211yesmaximal, characteristic, complemented
4#13076970C216yesmaximal, complemented
5#13076961C211yesmaximal, characteristic, complemented
6#13076959C216yesmaximal, complemented
7#127×Dic11C211yesmaximal, characteristic, complemented
8#13071180C216yesmaximal, complemented
9#13071178C211yesmaximal, characteristic, complemented
10C2×C42×Dic11C211yesmaximal, characteristic, complemented
11C11×#2856C211yesmaximal, characteristic, complemented
12C22×#4341C2214yes—
13C2×C11×#127C2211yescharacteristic
14C2×C11×#121C2216yes—
15C22×C42×C11C2211yescharacteristic
16C2×#66993C2216yes—
17C2×#66993C2216yes—
18C2×#66992C22112yes—
19C2×D4×Dic11C2216yes—
20C2×#66983C2216yes—
21C22×C4×Dic11C2213yes—
22C22×C4×Dic11C2213yes—
23#10623127—248no—
24C2×#66946C2216yes—
25C2×#66941C2216yes—
26C2×#66938C22112yes—
27C2×(C22⋊D11)⋊C4C22112yes—
28C2×#66927C2211yescharacteristic
29C11×#390C2216yes—
30C11×#384C2211yescharacteristic
31#10622834C2216yes—
32#10622601C2216yes—
33#10622589C2216yes—
34#10622570C22124yes—
35#10622552C2216yes—
36#10622548C2211yescharacteristic
37C42×Dic11C2211yescharacteristic
38C42×Dic11C2211yescharacteristic
39C42×Dic11C2213yes—
40C42×Dic11C2213yes—
41C22×D4×C11C2316yes—
42C22×D4×C11C2314yes—
43C23×C4×C11C2313yes—
44C22×C22⋊D11C23112yes—
45C22×C22⋊D11C2314yes—
46C22×C22⋊D11C2314yes—
47C23×Dic11C2314yes—
48C23×Dic11C2313yes—
49C23×Dic11C2311yescharacteristic
50C2×#4341—248no—
51C22×D44C2316yes—
52C22×C4×D11C2314yes—
53C22×Dic22C2314yes—
54C11×#127—24no—
55C11×#121—224no—
56C2×C11×C4⋊C4C2316yes—
57C2×C11×C22⋊C4C23112yes—
58C2×C42×C11—24no—
59C2×C42×C11C2313yes—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11C23112yes—
62#66993—224no—
63#66993—224no—
64#66992—248no—
65D4×Dic11—224no—
66#66983—224no—
67C2×(C2×D11)⋊C4C23112yes—
68C2×(C2×D11)⋊C4C23112yes—
69C2×C4⋊Dic11C2316yes—
70C2×Dic11⋊C4C23112yes—
71C2×C4×Dic11—212no—
72C2×C4×Dic11D4124yescomplemented
73C2×C4×Dic11C2316yes—
74C2×C4×Dic11C2313yes—
75C2×C4×Dic11C2313yes—
76C2×C4×Dic11C2313yes—
77C2×C4×Dic11C2313yes—
78C2×C4×Dic11C2313yes—
79C2×C4×Dic11C2313yes—
80#66946—224no—
81#66941—224no—
82#66938—248no—
83(C22⋊D11)⋊C4—248no—
84#66927—24no—
85#36644—111nomaximal, Sylow
86C24×C11C2414yes—
87C24×C11C2411yescharacteristic
88C23×D11C2414yes—
89C2×D4×C11—224no—
90C2×D4×C11—212no—
91C2×D4×C11—212no—
92C2×D4×C11—212no—
93C22×C4×C11—26no—
94C22×C4×C11—26no—
95C22×C4×C11C2×D4112yes—
96C22×C4×C11C2414yes—
97C22×C4×C11C2413yes—
98C22×C4×C11C2413yes—
99C2×C22⋊D11—224no—
100C2×C22⋊D11—224no—
101C2×C22⋊D11—248no—
102C2×C22⋊D11—224no—
103C22×Dic11—212no—
104C22×Dic11—224no—
105C22×Dic11C2×D4112yes—
106C22×Dic11C2×D4112yes—
107C22×Dic11C2414yes—
108C22×Dic11C2413yes—
109C22×Dic11C2411yescharacteristic
110C22×Dic11C2411yescharacteristic
111C22×Dic11C2413yes—
112#4341—464no—
113C2×D44—212no—
114C2×D44—212no—
115C2×D44—212no—
116C2×C4×D11—224no—
117C2×Dic22—224no—
118C11×C4⋊C4—212no—
119C11×C22⋊C4—224no—
120C42×C11—26no—
121C42×C11#4114yescomplemented
122C22⋊Dic11—224no—
123(C2×D11)⋊C4—224no—
124(C2×D11)⋊C4—224no—
125C4⋊Dic11—212no—
126Dic11⋊C4—224no—
127C4×Dic11—212no—
128C4×Dic11—26no—
129C4×Dic11C2×D4112yes—
130C4×Dic11C2×D4112yes—
131C4×Dic11C2×D4112yes—
132C4×Dic11C2×D4112yes—
133C4×Dic11#41112yescomplemented
134C2×#532—116no—
135#2868—111no—
136#2867—111no—
137#2858—116no—
138#2856—111no—
139#2856—116no—
140#2856D1111yescharacteristic, complemented
141C4×#127—116no—
142C4×#127—111no—
143C4×#127—111no—
144C2×C43—111no—
145C23×C11—23no—
146C23×C11—21no—
147C23×C11—212no—
148C23×C11—212no—
149C23×C11—24no—
150C23×C11C22×D416yes—
151C23×C11C2511yescharacteristic
152C22×D11—212no—
153C22×D11—24no—
154C22×D11—212no—
155D4×C11—416no—
156D4×C11—424no—
157C2×C4×C11—23no—
158C2×C4×C11—23no—
159C2×C4×C11—224no—
160C2×C4×C11—212no—
161C2×C4×C11C22×D416yes—
162C2×C4×C11C22×D416yes—
163C2×C4×C11C2×#4116yes—
164C2×C4×C11C2×#4116yes—
165C22⋊D11—416no—
166C22⋊D11—416no—
167C22⋊D11—448no—
168C2×Dic11—26no—
169C2×Dic11—224no—
170C2×Dic11—212no—
171C2×Dic11—416no—
172C2×Dic11#127116yescomplemented
173C2×Dic11C22×D416yes—
174C2×Dic11C22×D416yes—
175C2×Dic11C22×D416yes—
176C2×Dic11C22×D416yes—
177C2×Dic11C2×#41112yes—
178D44—424no—
179C4×D11—416no—
180Dic22—416no—
181C22×#41—114no—
182#532—2248no—
183C2×C4⋊Q8—116no—
184C2×#127—116no—
185C2×#127—116no—
186C2×#127—111no—
187C2×#127C2×D1111yescharacteristic
188C2×#124—1112no—
189C2×#121—1112no—
190C2×#121—116no—
191C2×#121C2×D1116yes—
192C2×C4×D4—116no—
193C2×C4×D4—116no—
194C2×C4×D4—1112no—
195C22×C42—113no—
196C22×C42—113no—
197C22×C42C2×D1111yescharacteristic
198#390—116no—
199#390—116no—
200#390—1124no—
201#390—116no—
202#390C2×D1116yes—
203#384—116no—
204#384—111no—
205#384C2×D1111yescharacteristic
206C43—113no—
207C43—111no—
208C43—113no—
209C43—111no—
210C22×C11—26no—
211C22×C11—26no—
212C22×C11—44no—
213C22×C11—412no—
214C22×C11—412no—
215C22×C11C2×#12714yes—
216C22×C11C23×D413yes—
217C22×C11C22×#4111yescharacteristic
218C22×C11C22×#4113yes—
219C2×D11—44no—
220C2×D11—412no—
221C2×D11—412no—
222C4×C11—26no—
223C4×C11—44no—
224C4×C11#532112yescomplemented
225Dic11—26no—
226Dic11—44no—
227Dic11C2×#12714yes—
228Dic11C2×#12714yes—
229Dic11#532112yescomplemented
230C2×#41—2248no—
231C22×Q8—114no—
232C22×D4—1112no—
233C22×D4—114no—
234C22×D4—114no—
235C22×D4—116no—
236C22×D4C22×D1116yes—
237C22×D4C22×D1114yes—
238C23×C4—111no—
239C23×C4—113no—
240C23×C4—114no—
241C23×C4—114no—
242C23×C4C22×D1113yes—
243C4⋊Q8—2224no—
244#127—24no—
245#127—2224no—
246#127—2224no—
247#127—224no—
248#124—2248no—
249#121—224no—
250#121—2248no—
251#121—2224no—
252C4×D4—2248no—
253C4×D4—2224no—
254C4×D4—2224no—
255C2×C4⋊C4—1112no—
256C2×C4⋊C4—116no—
257C2×C4⋊C4C22×D1116yes—
258C2×C22⋊C4—1112no—
259C2×C22⋊C4—1112no—
260C2×C22⋊C4—1112no—
261C2×C22⋊C4C22×D11112yes—
262C2×C42—24no—
263C2×C42—1124no—
264C2×C42—113no—
265C2×C42—113no—
266C2×C42—113no—
267C2×C42—113no—
268C2×C42—113no—
269C2×C42—116no—
270C2×C42—113no—
271C2×C42—2212no—
272C2×C42C22×D1113yes—
273C2×C42C22×D1111yescharacteristic
274C2×C11—24no—
275C2×C11—84no—
276C2×C11C22×#12711yescharacteristic
277C2×C11C2×#53213yes—
278C2×C11C2×#53213yes—
279D11—84no—
280C24—114no—
281C24C23×D1114yes—
282C24C23×D1111yescharacteristic
283#41—4464no—
284C2×Q8—2224no—
285C2×D4—224no—
286C2×D4—212no—
287C2×D4—212no—
288C2×D4—212no—
289C2×D4—2224no—
290C2×D4—2224no—
291C2×D4—2248no—
292C2×D4—2224no—
293C2×D4—2212no—
294C2×D4—2212no—
295C2×D4—2212no—
296C22×C4—26no—
297C22×C4—26no—
298C22×C4—1112no—
299C22×C4—113no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—1112no—
303C22×C4—113no—
304C22×C4—114no—
305C22×C4—2224no—
306C22×C4—2212no—
307C22×C4—2224no—
308C22×C4D4×D11112yes—
309C22×C4C23×D1114yes—
310C22×C4C23×D1113yes—
311C22×C4C23×D1113yes—
312C4⋊C4—212no—
313C4⋊C4—2224no—
314C4⋊C4—2212no—
315C22⋊C4—224no—
316C22⋊C4—2224no—
317C22⋊C4—2224no—
318C22⋊C4—2224no—
319C42—26no—
320C42—1112no—
321C42—1112no—
322C42—1112no—
323C42—1112no—
324C42—1112no—
325C42—2212no—
326C42—226no—
327C42#434114yescomplemented
328C11#3664411yescharacteristic, complemented, Sylow
329C23—21no—
330C23—23no—
331C23—212no—
332C23—24no—
333C23—212no—
334C23—2212no—
335C23—224no—
336C23—2212no—
337C23C2×D4×D1116yes—
338C23C24×D1111yescharacteristic
339Q8—4416no—
340D4—416no—
341D4—424no—
342D4—4416no—
343D4—4448no—
344D4—4416no—
345D4—4424no—
346C2×C4—23no—
347C2×C4—23no—
348C2×C4—224no—
349C2×C4—212no—
350C2×C4—1116no—
351C2×C4—116no—
352C2×C4—116no—
353C2×C4—116no—
354C2×C4—1112no—
355C2×C4—116no—
356C2×C4—2224no—
357C2×C4—226no—
358C2×C4—2212no—
359C2×C4—4416no—
360C2×C4—4416no—
361C2×C4C2×D4×D1116yes—
362C2×C4C2×D4×D1116yes—
363C2×C4C2×#434116yes—
364C2×C4#41×D1116yes—
365C22—26no—
366C22—26no—
367C22—44no—
368C22—412no—
369C22—412no—
370C22—444no—
371C22—4412no—
372C22—4412no—
373C22D11×#12714yes—
374C22C22×D4×D1113yes—
375C22C22×#434111yescharacteristic
376C22C2×#41×D1113yes—
377C4—26no—
378C4—44no—
379C4—114no—
380C4—114no—
381C4—1112no—
382C4—226no—
383C4—444no—
384C4#10623127112yescomplemented
385C2—24no—
386C2—84no—
387C2—884no—
388C2C2×D11×#12711yescharacteristic
389C2D11×#53213yes—
390C2C2×#1062312713yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2856C2
hypercenter#2856D11
hypocenterC11#36644
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#10623127C2semidirect
2. #13077013C2semidirect
3. #13077010C2semidirect
4. #13076970C2semidirect
5. #13076961C2semidirect
6. #13076959C2semidirect
7. #127×Dic11C2semidirect
8. #13071180C2semidirect
9. #13071178C2semidirect
10. C2×C42×Dic11C2semidirect
11. C11×#2856C2semidirect
72. C2×C4×Dic11D4semidirect
121. C42×C11#41semidirect
133. C4×Dic11#41semidirect
140. #2856D11semidirect
172. C2×Dic11#127semidirect
224. C4×C11#532semidirect
229. Dic11#532semidirect
327. C42#4341semidirect
328. C11#36644semidirect
384. C4#10623127semidirect

Maximal subgroups

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

subgroupindex
C2×#106231272
#130770132
#130770102
#130769702
#130769612
#130769592
#127×Dic112
#130711802
#130711782
C2×C42×Dic112
C11×#28562
#3664411