Finite Group Databasebeta

← #14913819

Subgroups — #14913819

Order 2816.

4110 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071465C2116yesmaximal, complemented
2#13071230C212yesmaximal, complemented
3#13071214C214yesmaximal, complemented
4#13070999C214yesmaximal, complemented
5C2×#10622860C212yesmaximal
6#13070969C212yesmaximal, complemented
7C23×C11×C22⋊C4C211yesmaximal, characteristic
8C26×C11C2211yescharacteristic
9C24×C4×C11C2212yes—
10C22×C11×C22⋊C4C4116yescomplemented
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×C11×C22⋊C4C2211yescharacteristic
13C22×C11×C22⋊C4C2218yes—
14C22×C11×C22⋊C4C2212yes—
15C22×C22⋊Dic11C2214yes—
16C22×C22⋊Dic11C2218yes—
17C2×#66979C2218yescomplemented
18#10622860C2218yes—
19#10622860C2214yes—
20#10622860C2214yes—
21#10622825C2218yescomplemented
22#10622825C2218yescomplemented
23#10622824C2218yescomplemented
24C4×C22⋊Dic11C2218yescomplemented
25C4×C22⋊Dic11C2218yescomplemented
26#10622564C22132yescomplemented
27#10622563C22116yescomplemented
28C22⋊C4×Dic11C22116yescomplemented
29C25×C11—28no—
30C25×C11—48no—
31C25×C11C2×C418yes—
32C25×C11C2311yescharacteristic
33C25×C11C2314yes—
34C25×C11C2311yescharacteristic
35C25×C11C2311yescharacteristic
36C23×C4×C11—48no—
37C23×C4×C11C2×C4116yescomplemented
38C23×C4×C11C2314yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2314yes—
41C23×C4×C11C2312yes—
42C23×Dic11C2318yes—
43C2×C11×C22⋊C4C2×C418yes—
44C2×C11×C22⋊C4C2×C418yes—
45C2×C11×C22⋊C4C2×C4164yescomplemented
46C2×C11×C22⋊C4C2×C4116yescomplemented
47C2×C11×C22⋊C4C2314yes—
48C2×C11×C22⋊C4C2314yes—
49C2×C11×C22⋊C4C2318yes—
50C2×C22⋊Dic11—216no—
51C2×C22⋊Dic11—416no—
52C2×C22⋊Dic11C23116yes—
53C2×C22⋊Dic11C2318yes—
54C2×C22⋊Dic11C2318yes—
55C2×C22⋊Dic11C23116yes—
56#66979—416no—
57C2×C4⋊Dic11C23116yescomplemented
58C2×C4×Dic11C23116yescomplemented
59C11⋊#95C23116yescomplemented
60C11⋊#95C23116yescomplemented
61#34176—111nomaximal, Sylow
62C24×C11—24no—
63C24×C11—28no—
64C24×C11—232no—
65C24×C11—216no—
66C24×C11—24no—
67C24×C11—216no—
68C24×C11—432no—
69C24×C11—44no—
70C24×C11—48no—
71C24×C11—44no—
72C24×C11—464no—
73C24×C11C22×C414yes—
74C24×C11C22×C4116yes—
75C24×C11C22×C414yes—
76C24×C11C22×C414yes—
77C24×C11#4118yes—
78C24×C11C2412yes—
79C24×C11C2411yescharacteristic
80C24×C11C2412yes—
81C24×C11C2412yes—
82C22×C4×C11—216no—
83C22×C4×C11—432no—
84C22×C4×C11—44no—
85C22×C4×C11—48no—
86C22×C4×C11—44no—
87C22×C4×C11C22×C4116yes—
88C22×C4×C11C22×C418yes—
89C22×C4×C11C22×C418yes—
90C22×C4×C11C22×C4116yes—
91C22×C4×C11C2414yes—
92C22×C4×C11C2414yes—
93C22×Dic11—216no—
94C22×Dic11—416no—
95C22×Dic11C24116yes—
96C11×C22⋊C4C22×C4116yes—
97C11×C22⋊C4C22×C4116yes—
98C11×C22⋊C4C22×C4132yes—
99C22⋊Dic11—216no—
100C22⋊Dic11—216no—
101C22⋊Dic11—232no—
102C22⋊Dic11—416no—
103C4⋊Dic11—416no—
104C4×Dic11—416no—
105C23×C22⋊C4D1111yescharacteristic
106#2342—1116no—
107#2315—112no—
108#2312—114no—
109#2280—114no—
110C2×#379—112no—
111#2273—112no—
112C23×C11—232no—
113C23×C11—28no—
114C23×C11—216no—
115C23×C11—24no—
116C23×C11—28no—
117C23×C11—24no—
118C23×C11—24no—
119C23×C11—232no—
120C23×C11—28no—
121C23×C11—232no—
122C23×C11—24no—
123C23×C11—28no—
124C23×C11—48no—
125C23×C11—416no—
126C23×C11—48no—
127C23×C11—416no—
128C23×C11—464no—
129C23×C11—4128no—
130C23×C11—416no—
131C23×C11#117116yescomplemented
132C23×C11C23×C414yes—
133C23×C11C23×C414yes—
134C23×C11C23×C412yes—
135C23×C11C23×C414yes—
136C23×C11C2×#4114yes—
137C23×C11C2×#4118yes—
138C23×C11H(5,𝔽2)18yes—
139C23×C11C2511yescharacteristic
140C2×C4×C11—232no—
141C2×C4×C11—28no—
142C2×C4×C11—28no—
143C2×C4×C11—48no—
144C2×C4×C11—48no—
145C2×C4×C11—416no—
146C2×C4×C11C23×C418yes—
147C2×C4×C11C23×C418yes—
148C2×Dic11—216no—
149C2×Dic11—232no—
150C2×Dic11—816no—
151C26C2×D1111yescharacteristic
152C24×C4C2×D1112yes—
153C2×#117—118no—
154C22×C22⋊C4—114no—
155C22×C22⋊C4—118no—
156C22×C22⋊C4Dic11116yescomplemented
157C22×C22⋊C4C2×D1111yescharacteristic
158C22×C22⋊C4C2×D1111yescharacteristic
159C22×C22⋊C4C2×D1112yes—
160C22×C22⋊C4C2×D1118yes—
161#388—1132no—
162#385—1116no—
163#381—118no—
164#380—118no—
165#380—118no—
166#379—114no—
167#379—118no—
168#379—114no—
169C4×C22⋊C4—118no—
170C4×C22⋊C4—118no—
171C4×C22⋊C4—1116no—
172C22×C11—232no—
173C22×C11—24no—
174C22×C11—24no—
175C22×C11—24no—
176C22×C11—28no—
177C22×C11—28no—
178C22×C11—216no—
179C22×C11—216no—
180C22×C11—24no—
181C22×C11—28no—
182C22×C11—416no—
183C22×C11—464no—
184C22×C11—416no—
185C22×C11—48no—
186C22×C11C2×#11714yes—
187C22×C11C2×#11718yes—
188C22×C11#51818yes—
189C22×C11C24×C411yescharacteristic
190C22×C11C22×#4112yes—
191C22×C11C2×H(5,𝔽2)14yes—
192C4×C11—28no—
193C4×C11—28no—
194Dic11—416no—
195C25—28no—
196C25—48no—
197C25C2×Dic1118yes—
198C25C22×D1111yescharacteristic
199C25C22×D1114yes—
200C25C22×D1111yescharacteristic
201C25C22×D1111yescharacteristic
202C23×C4—48no—
203C23×C4—118no—
204C23×C4C2×Dic11116yescomplemented
205C23×C4C22×D1114yes—
206C23×C4C22×D1112yes—
207C23×C4C22×D1114yes—
208C23×C4C22×D1112yes—
209#117—4416no—
210C2×C4⋊C4—1116no—
211C2×C22⋊C4—1116no—
212C2×C22⋊C4—118no—
213C2×C22⋊C4—118no—
214C2×C22⋊C4—1116no—
215C2×C22⋊C4—2216no—
216C2×C22⋊C4—4416no—
217C2×C22⋊C4C2×Dic1118yes—
218C2×C22⋊C4C2×Dic1118yes—
219C2×C22⋊C4C2×Dic11164yescomplemented
220C2×C22⋊C4C2×Dic11116yescomplemented
221C2×C22⋊C4C22×D1114yes—
222C2×C22⋊C4C22×D1114yes—
223C2×C22⋊C4C22×D1118yes—
224C2×C42—1116no—
225#95—1116no—
226#95—1116no—
227C2×C11—24no—
228C2×C11—28no—
229C2×C11—28no—
230C2×C11—44no—
231C2×C11C22×#11711yescharacteristic
232C2×C11C2×#51812yes—
233C2×C11#349014yes—
234C24—24no—
235C24—28no—
236C24—232no—
237C24—216no—
238C24—24no—
239C24—216no—
240C24—44no—
241C24—48no—
242C24—44no—
243C24—432no—
244C24—464no—
245C24#433918yes—
246C24C22×Dic1114yes—
247C24C22×Dic11116yes—
248C24C22×Dic1114yes—
249C24C22×Dic1114yes—
250C24C23×D1112yes—
251C24C23×D1111yescharacteristic
252C24C23×D1112yes—
253C24C23×D1112yes—
254C22×C4—216no—
255C22×C4—44no—
256C22×C4—48no—
257C22×C4—44no—
258C22×C4—432no—
259C22×C4—1116no—
260C22×C4—2216no—
261C22×C4—4416no—
262C22×C4C22×Dic11116yes—
263C22×C4C22×Dic1118yes—
264C22×C4C22×Dic1118yes—
265C22×C4C22×Dic11116yes—
266C22×C4C23×D1114yes—
267C22×C4C23×D1114yes—
268C4⋊C4—4416no—
269C22⋊C4—2216no—
270C22⋊C4—2216no—
271C22⋊C4—2232no—
272C22⋊C4—4416no—
273C22⋊C4C22×Dic11116yes—
274C22⋊C4C22×Dic11116yes—
275C22⋊C4C22×Dic11132yes—
276C42—4416no—
277C11#3417611yescharacteristic, complemented, Sylow
278C23—232no—
279C23—28no—
280C23—216no—
281C23—24no—
282C23—24no—
283C23—24no—
284C23—28no—
285C23—232no—
286C23—28no—
287C23—232no—
288C23—24no—
289C23—28no—
290C23—416no—
291C23—48no—
292C23—416no—
293C23—48no—
294C23—464no—
295C23—4128no—
296C23—416no—
297C23#66979116yescomplemented
298C23C2×#433914yes—
299C23C2×#433918yes—
300C23#6703718yes—
301C23C23×Dic1114yes—
302C23C23×Dic1114yes—
303C23C23×Dic1112yes—
304C23C23×Dic1114yes—
305C23C24×D1111yescharacteristic
306C2×C4—232no—
307C2×C4—28no—
308C2×C4—28no—
309C2×C4—48no—
310C2×C4—48no—
311C2×C4—416no—
312C2×C4—2216no—
313C2×C4—2232no—
314C2×C4—8816no—
315C2×C4C23×Dic1118yes—
316C2×C4C23×Dic1118yes—
317C22—232no—
318C22—24no—
319C22—216no—
320C22—28no—
321C22—216no—
322C22—24no—
323C22—24no—
324C22—28no—
325C22—24no—
326C22—28no—
327C22—416no—
328C22—464no—
329C22—416no—
330C22—48no—
331C22C2×#6697914yes—
332C22C2×#6697918yes—
333C22#1062332918yes—
334C22C22×#433912yes—
335C22C2×#6703714yes—
336C22C24×Dic1111yescharacteristic
337C4—28no—
338C4—28no—
339C4—4416no—
340C2—24no—
341C2—28no—
342C2—28no—
343C2—44no—
344C2C22×#6697911yescharacteristic
345C2C2×#1062332912yes—
346C2#1308230514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC23×C11×C22⋊C4C2
socle, cosocleC23×C11C25
prime radicalC26×C11C22
hypercenterC23×C22⋊C4D11
hypocenterC11#34176
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #13071465C2semidirect
2. #13071230C2semidirect
3. #13071214C2semidirect
4. #13070999C2semidirect
6. #13070969C2semidirect
10. C22×C11×C22⋊C4C4semidirect
17. C2×#66979C22semidirect
21. #10622825C22semidirect
22. #10622825C22semidirect
23. #10622824C22semidirect
24. C4×C22⋊Dic11C22semidirect
25. C4×C22⋊Dic11C22semidirect
26. #10622564C22semidirect
27. #10622563C22semidirect
28. C22⋊C4×Dic11C22semidirect
37. C23×C4×C11C2×C4semidirect
45. C2×C11×C22⋊C4C2×C4semidirect
46. C2×C11×C22⋊C4C2×C4semidirect
57. C2×C4⋊Dic11C23semidirect
58. C2×C4×Dic11C23semidirect
59. C11⋊#95C23semidirect
60. C11⋊#95C23semidirect
131. C23×C11#117semidirect
156. C22×C22⋊C4Dic11semidirect
204. C23×C4C2×Dic11semidirect
219. C2×C22⋊C4C2×Dic11semidirect
220. C2×C22⋊C4C2×Dic11semidirect
277. C11#34176semidirect
297. C23#66979semidirect

Maximal subgroups

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

subgroupindex
#130714652
#130712302
#130712142
#130709992
C2×#106228602
#130709692
C23×C11×C22⋊C42
#3417611