Finite Group Databasebeta

← #14913792

Subgroups — #14913792

Order 2816.

5430 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4343C211yesmaximal, characteristic
2C2×#10623052C212yesmaximal, complemented
3#13071445C2116yesmaximal, complemented
4#13071202C211yesmaximal, characteristic, complemented
5#13071193C214yesmaximal, complemented
6#13070995C212yesmaximal, complemented
7D11×#381C214yesmaximal, complemented
8C11×#2310C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×#4343—216no—
11C22×#4343C4116yescomplemented
12C22×#4343C2218yes—
13C23×D44C2212yes—
14C23×D44C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C2×C11×#117C2212yes—
18C2×#66979C2212yes—
19#10623052—216no—
20C2×#66946C2218yescomplemented
21C2×C22⋊C4×D11C2218yes—
22C2×C4×D44C2218yescomplemented
23C11×#391C2218yescomplemented
24C11×#381C2214yes—
25#10622843C2218yescomplemented
26#10622824C2214yes—
27#10622600C2218yescomplemented
28#10622568C2214yes—
29#10622556C2214yes—
30C4×(C2×D11)⋊C4C2218yescomplemented
31#10622278C22132yescomplemented
32#10622277C22116yescomplemented
33D11×#95C22116yescomplemented
34C24×D11C2311yescharacteristic
35C24×D11C2312yes—
36C22×Q8×C11—28no—
37C22×Q8×C11C2×C418yescomplemented
38C22×Q8×C11C2314yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2311yescharacteristic
42C2×#4343—2128no—
43C2×#4343—232no—
44C2×#4343—232no—
45C2×#4343C2×C4164yescomplemented
46C22×D44—216no—
47C22×D44C2×C418yes—
48C22×D44C2×C4116yescomplemented
49C22×D44D4116yes—
50C22×D44C2318yes—
51C22×D44C2314yes—
52C22×C4×D11—216no—
53C22×C4×D11—28no—
54C22×C4×D11C2×C4116yescomplemented
55C22×C4×D11C2×C418yescomplemented
56C22×C4×D11C2318yes—
57C22×C4×D11C2314yes—
58C22×C4×D11C23116yes—
59C11×#117—28no—
60C2×C11×C4⋊C4C2314yes—
61C2×C11×C22⋊C4C2314yes—
62C2×C42×C11C2314yes—
63C2×C22⋊Dic11C2314yes—
64C2×(C2×D11)⋊C4C23116yes—
65C2×(C2×D11)⋊C4C23116yes—
66#66979—28no—
67C2×C4⋊Dic11C2314yes—
68C2×C4×Dic11C2314yes—
69#66946—232no—
70C22⋊C4×D11—232no—
71C4×D44—232no—
72C11×#95C23116yes—
73C11⋊#95C23116yes—
74C11⋊#95C23116yes—
75#34172—111nomaximal, Sylow
76C24×C11C2411yescharacteristic
77C23×D11—24no—
78C23×D11—48no—
79C23×D11—44no—
80C23×D11C22×C414yes—
81C23×D11C22×C418yes—
82C23×D11C2×D4116yes—
83C23×D11C2412yes—
84C23×D11C2414yes—
85C2×Q8×C11—232no—
86C2×Q8×C11—28no—
87C2×Q8×C11—28no—
88C2×Q8×C11C22×C4116yes—
89C22×C4×C11—28no—
90C22×C4×C11C22×C418yes—
91C22×C4×C11C22×C414yes—
92C22×C4×C11C2×D418yes—
93C22×C4×C11C2418yes—
94C22×C4×C11C2414yes—
95C22×C4×C11C2412yes—
96C22×Dic11—24no—
97C22×Dic11C22×C414yes—
98C22×Dic11C2418yes—
99C22×Dic11C2412yes—
100#4343—2256no—
101C2×D44—264no—
102C2×D44—232no—
103C2×D44C22⋊C4164yescomplemented
104C2×D44C22×C4132yes—
105C2×D44C22×C4116yes—
106C2×D44C2×D4116yes—
107C2×D44C2×D4116yes—
108C2×C4×D11—264no—
109C2×C4×D11—232no—
110C2×C4×D11—232no—
111C2×C4×D11—232no—
112C2×C4×D11—28no—
113C2×C4×D11—28no—
114C2×C4×D11—432no—
115C2×C4×D11C22×C4132yes—
116C2×C4×D11C22×C4116yes—
117C11×C4⋊C4—28no—
118C11×C22⋊C4—28no—
119C42×C11—28no—
120C22⋊Dic11—28no—
121(C2×D11)⋊C4—232no—
122(C2×D11)⋊C4—416no—
123C4⋊Dic11—28no—
124C4×Dic11—28no—
125C23×#41—111no—
126C2×#518—112no—
127#2339—1116no—
128#2310—111no—
129#2310D1111yescharacteristic, complemented
130#2308—114no—
131#2280—112no—
132C2×#381—114no—
133C23×C11—24no—
134C23×C11C23×C412yes—
135C23×C11C22×D414yes—
136C23×C11C2511yescharacteristic
137C22×D11—216no—
138C22×D11—28no—
139C22×D11—24no—
140C22×D11—28no—
141C22×D11—416no—
142C22×D11—48no—
143C22×D11—432no—
144C22×D11—416no—
145C22×D11C2×C22⋊C4132yes—
146C22×D11C23×C414yes—
147C22×D11C23×C418yes—
148C22×D11C22×D4116yes—
149Q8×C11—232no—
150C2×C4×C11—216no—
151C2×C4×C11—28no—
152C2×C4×C11—28no—
153C2×C4×C11—216no—
154C2×C4×C11C2×C22⋊C4116yes—
155C2×C4×C11C23×C418yes—
156C2×C4×C11C23×C414yes—
157C2×C4×C11C22×D414yes—
158C2×C4×C11C22×D414yes—
159C2×Dic11—28no—
160C2×Dic11—24no—
161C2×Dic11—28no—
162C2×Dic11—216no—
163C2×Dic11C23×C414yes—
164D44—264no—
165D44C2×C22⋊C4164yes—
166C4×D11—264no—
167C4×D11—232no—
168C4×D11—832no—
169C22×#41—118no—
170C22×#41—1116no—
171C22×#41—2216no—
172C23×Q8C2×D1111yescharacteristic
173C23×D4—111no—
174C23×D4—112no—
175C24×C4—112no—
176C24×C4—111no—
177#518—2216no—
178C2×C4×D4—118no—
179C2×C4×D4—118no—
180C2×#117—112no—
181C2×#117C2×D1112yes—
182C22×C22⋊C4—118no—
183#391—118no—
184#391C2×D1118yescomplemented
185#386—1132no—
186#381—114no—
187#381—114no—
188#381—1116no—
189#381C2×D1114yes—
190#380—118no—
191#379—114no—
192C4×C22⋊C4—118no—
193C2×#95—1116no—
194C22×C11—24no—
195C22×C11—28no—
196C22×C11C22×C22⋊C414yes—
197C22×C11C24×C411yescharacteristic
198C22×C11C23×D412yes—
199C22×C11#58514yes—
200C2×D11—216no—
201C2×D11—232no—
202C2×D11—24no—
203C2×D11—28no—
204C2×D11—432no—
205C2×D11—416no—
206C2×D11—48no—
207C2×D11C22×C22⋊C4116yes—
208C4×C11—28no—
209C4×C11—48no—
210C4×C11C22×C22⋊C418yes—
211Dic11—24no—
212Dic11—48no—
213C25—112no—
214C25—111no—
215C2×#41—1164no—
216C2×#41—22128no—
217C2×#41—2232no—
218C2×#41—2232no—
219C22×Q8—28no—
220C22×Q8C4×D1118yescomplemented
221C22×Q8C22×D1114yes—
222C22×D4—118no—
223C22×D4—1116no—
224C22×D4—1116no—
225C22×D4—114no—
226C22×D4—118no—
227C22×D4—2216no—
228C23×C4—111no—
229C23×C4—1116no—
230C23×C4—118no—
231C23×C4—118no—
232C23×C4—114no—
233C23×C4—1116no—
234C23×C4—2216no—
235C23×C4—228no—
236C23×C4C22×D1112yes—
237C23×C4C22×D1111yescharacteristic
238C4×D4—2232no—
239C4×D4—2232no—
240#117—28no—
241#117—228no—
242C2×C4⋊C4—114no—
243C2×C4⋊C4C22×D1114yes—
244C2×C22⋊C4—114no—
245C2×C22⋊C4—1116no—
246C2×C22⋊C4—1116no—
247C2×C22⋊C4—2232no—
248C2×C22⋊C4C22×D1114yes—
249C2×C42—114no—
250C2×C42C22×D1114yes—
251#95—1116no—
252#95—1116no—
253#95C22×D11116yes—
254C2×C11—24no—
255C2×C11C23×C22⋊C411yescharacteristic
256C2×C11#342812yes—
257C2×C11#348514yes—
258D11—216no—
259D11—44no—
260C24—114no—
261C24—118no—
262C24—1116no—
263C24—112no—
264C24—114no—
265C24—224no—
266C24—448no—
267C24—444no—
268C24C23×D1111yescharacteristic
269#41—22256no—
270C2×Q8—232no—
271C2×Q8—28no—
272C2×Q8—28no—
273C2×Q8C2×C4×D11116yes—
274C2×D4—1164no—
275C2×D4—1116no—
276C2×D4—1132no—
277C2×D4—1116no—
278C2×D4—1116no—
279C2×D4—2264no—
280C2×D4—2232no—
281C22×C4—28no—
282C22×C4—114no—
283C22×C4—112no—
284C22×C4—1132no—
285C22×C4—1116no—
286C22×C4—118no—
287C22×C4—2264no—
288C22×C4—2232no—
289C22×C4—2232no—
290C22×C4—224no—
291C22×C4—2232no—
292C22×C4—228no—
293C22×C4—228no—
294C22×C4—4432no—
295C22×C4C2×C4×D1118yes—
296C22×C4C2×C4×D1114yes—
297C22×C4D4×D1118yes—
298C22×C4C23×D1118yes—
299C22×C4C23×D1114yes—
300C22×C4C23×D1112yes—
301C4⋊C4—28no—
302C4⋊C4—228no—
303C22⋊C4—28no—
304C22⋊C4—2232no—
305C22⋊C4—228no—
306C22⋊C4—4416no—
307C42—28no—
308C42—228no—
309C11#3417211yescharacteristic, complemented, Sylow
310C23—24no—
311C23—118no—
312C23—1116no—
313C23—1132no—
314C23—114no—
315C23—2216no—
316C23—228no—
317C23—224no—
318C23—228no—
319C23—4432no—
320C23—4416no—
321C23—448no—
322C23—4416no—
323C23C22×C4×D1112yes—
324C23C2×D4×D1114yes—
325C23C24×D1111yescharacteristic
326Q8—232no—
327D4—1164no—
328D4—2264no—
329C2×C4—216no—
330C2×C4—28no—
331C2×C4—28no—
332C2×C4—216no—
333C2×C4—114no—
334C2×C4—2264no—
335C2×C4—228no—
336C2×C4—224no—
337C2×C4—2232no—
338C2×C4—228no—
339C2×C4—2216no—
340C2×C4—8832no—
341C2×C4C22⋊C4×D11116yes—
342C2×C4C22×C4×D1118yes—
343C2×C4C22×C4×D1114yes—
344C2×C4C2×D4×D1114yes—
345C2×C4C2×D4×D1114yes—
346C22—28no—
347C22—24no—
348C22—1116no—
349C22—2232no—
350C22—2216no—
351C22—224no—
352C22—228no—
353C22—4432no—
354C22—4416no—
355C22—448no—
356C22C2×C22⋊C4×D1114yes—
357C22C23×C4×D1111yescharacteristic
358C22C22×D4×D1112yes—
359C22#1062345714yes—
360C4—28no—
361C4—48no—
362C4—224no—
363C4—448no—
364C4C2×C22⋊C4×D1118yes—
365C2—24no—
366C2—2216no—
367C2—444no—
368C2C22×C22⋊C4×D1111yescharacteristic
369C2#1308181812yes—
370C2#1308225914yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2310C2
socle, cosocleC23×C11C25
prime radicalC23×#4343C2
hypercenter#2310D11
hypocenterC11#34172
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2310

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. #13071445C2semidirect
4. #13071202C2semidirect
5. #13071193C2semidirect
6. #13070995C2semidirect
7. D11×#381C2semidirect
8. C11×#2310C2semidirect
11. C22×#4343C4semidirect
20. C2×#66946C22semidirect
22. C2×C4×D44C22semidirect
23. C11×#391C22semidirect
25. #10622843C22semidirect
27. #10622600C22semidirect
30. C4×(C2×D11)⋊C4C22semidirect
31. #10622278C22semidirect
32. #10622277C22semidirect
33. D11×#95C22semidirect
37. C22×Q8×C11C2×C4semidirect
45. C2×#4343C2×C4semidirect
48. C22×D44C2×C4semidirect
54. C22×C4×D11C2×C4semidirect
55. C22×C4×D11C2×C4semidirect
103. C2×D44C22⋊C4semidirect
129. #2310D11semidirect
184. #391C2×D11semidirect
220. C22×Q8C4×D11semidirect
309. C11#34172semidirect

Maximal subgroups

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

subgroupindex
C23×#43432
C2×#106230522
#130714452
#130712022
#130711932
#130709952
D11×#3812
C11×#23102
#3417211