Finite Group Databasebeta

← #14959850

Subgroups — #14959850

Order 2816.

2782 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2#13076993C212yesmaximal, complemented
3#13076989C214yesmaximal, complemented
4#13076974C212yesmaximal, complemented
5#13076919C218yesmaximal, complemented
6C4×#67000C218yesmaximal, complemented
7#13071104C214yesmaximal, complemented
8C2×C42×Dic11C211yesmaximal, characteristic, complemented
9C2×C11×#533C211yesmaximal, characteristic, complemented
10C22×#4339C2212yes—
11C11×#533—28no—
12C2×C11×C4⋊Q8C2212yes—
13C2×C11×#125C2212yes—
14C2×C11×C22⋊Q8C2214yes—
15C2×C4×Q8×C11C2214yes—
16C2×C11×#117C2212yes—
17C22×C42×C11C2211yescharacteristic
18C2×#67000C2218yes—
19C2×#66983C2214yes—
20C22×C4×Dic11C2212yes—
21C22×C4×Dic11C2214yes—
22#10623008—28no—
23C2×#66928C2212yes—
24C2×#66927C2211yescharacteristic
25C2×C4×D44C2214yes—
26C2×#66922C2211yescharacteristic
27#10622843C2218yes—
28#10622603C22132yes—
29#10622601C2218yes—
30#10622601C2218yes—
31#10622590C2218yes—
32#10622587C2218yes—
33#10622571C22116yes—
34C4×(C2×D11)⋊C4C22116yes—
35C42×Dic11C2212yes—
36C42×Dic11C2214yes—
37C42×Dic11C2212yes—
38C22×Q8×C11C2314yes—
39C23×C4×C11C2312yes—
40C23×C4×C11C2311yescharacteristic
41C22×C22⋊D11C2314yes—
42C23×Dic11C2314yes—
43C2×#4339—28no—
44C2×#4339—216no—
45C22×D44C2314yes—
46C22×D44C2312yes—
47C22×C4×D11C2314yes—
48C22×Dic22C2312yes—
49C11×C4⋊Q8—28no—
50C11×#125—28no—
51C11×C22⋊Q8—216no—
52C4×Q8×C11—216no—
53C11×#117—28no—
54C2×C11×C4⋊C4C2314yes—
55C2×C11×C4⋊C4C2314yes—
56C2×C11×C4⋊C4C2318yes—
57C2×C11×C22⋊C4C2314yes—
58C2×C42×C11D418yes—
59C2×C42×C11C2314yes—
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2312yes—
62C2×C42×C11C2311yescharacteristic
63#67000—232no—
64#66983—216no—
65C2×(C2×D11)⋊C4C2318yes—
66C2×(C2×D11)⋊C4C23132yes—
67C2×C4⋊Dic11C2314yes—
68C2×C4×Dic11—28no—
69C2×C4×Dic11—216no—
70C2×C4×Dic11C2314yes—
71C2×C4×Dic11C2314yes—
72C2×C4×Dic11C2314yes—
73C2×C4×Dic11C2318yes—
74C2×C4×Dic11C2314yes—
75#66928—28no—
76#66927—24no—
77C4×D44—216no—
78#66922—24no—
79C11⋊#95C23132yes—
80#36639—111nomaximal, Sylow
81C24×C11C2411yescharacteristic
82C23×D11C2414yes—
83C2×Q8×C11—28no—
84C2×Q8×C11—216no—
85C22×C4×C11—28no—
86C22×C4×C11C2×D418yes—
87C22×C4×C11C2×D414yes—
88C22×C4×C11#4118yes—
89C22×C4×C11C2418yes—
90C22×C4×C11C2412yes—
91C22×C4×C11C2412yes—
92C22×C4×C11C2411yescharacteristic
93C22×C4×C11C2411yescharacteristic
94C2×C22⋊D11—28no—
95C2×C22⋊D11—216no—
96C22×Dic11—216no—
97C22×Dic11—28no—
98C22×Dic11C2414yes—
99C22×Dic11C2418yes—
100#4339—432no—
101C2×D44—28no—
102C2×D44—24no—
103C2×D44—216no—
104C2×D44—28no—
105C2×C4×D11—28no—
106C2×C4×D11—216no—
107C2×Dic22—24no—
108C2×Dic22—28no—
109C11×C4⋊C4—28no—
110C11×C4⋊C4—216no—
111C11×C4⋊C4—28no—
112C11×C22⋊C4—28no—
113C42×C11—28no—
114C42×C11C2×D414yes—
115C42×C11C2×D418yes—
116C42×C11C2×D414yes—
117(C2×D11)⋊C4—264no—
118(C2×D11)⋊C4—216no—
119C4⋊Dic11—28no—
120C4×Dic11—216no—
121C4×Dic11—28no—
122C4×Dic11—28no—
123C4×Dic11—28no—
124C4×Dic11#41116yescomplemented
125C2×#533D1111yescharacteristic, complemented
126C2×#532—111no—
127#2862—112no—
128#2861—114no—
129#2858—112no—
130#2850—118no—
131C4×#124—118no—
132#2297—114no—
133C2×C43—111no—
134C23×C11—24no—
135C23×C11C22×D412yes—
136C23×C11C2×#4114yes—
137C23×C11C2511yescharacteristic
138C22×D11—24no—
139C22×D11—216no—
140C22×D11—28no—
141Q8×C11—416no—
142C2×C4×C11—24no—
143C2×C4×C11—216no—
144C2×C4×C11—28no—
145C2×C4×C11—216no—
146C2×C4×C11#124116yescomplemented
147C2×C4×C11C22×D414yes—
148C2×C4×C11C22×D412yes—
149C2×C4×C11C22×D412yes—
150C2×C4×C11C22×D414yes—
151C2×C4×C11C2×#4114yes—
152C2×C4×C11C2×#4114yes—
153C2×C4×C11C2×#4118yes—
154C22⋊D11—416no—
155C2×Dic11—232no—
156C2×Dic11—28no—
157C2×Dic11—28no—
158C2×Dic11—24no—
159C2×Dic11—28no—
160C2×Dic11C2×#41116yes—
161D44—48no—
162D44—416no—
163C4×D11—416no—
164Dic22—48no—
165C22×#41—112no—
166#533—28no—
167#532—228no—
168C2×C4⋊Q8—111no—
169C2×C4⋊Q8C2×D1112yes—
170C2×#127—111no—
171C2×#125C2×D1112yes—
172C2×#124—118no—
173C2×#124—112no—
174C2×C22⋊Q8C2×D1114yes—
175C2×#121—114no—
176C2×C4×Q8C2×D1114yes—
177C2×C4×D4—114no—
178C2×#117C2×D1112yes—
179C22×C42—114no—
180C22×C42—112no—
181C22×C42C2×D1111yescharacteristic
182#391—118no—
183#391—118no—
184#390—118no—
185#390—118no—
186#388—1132no—
187#386—1116no—
188#382—118no—
189C4×C22⋊C4—1116no—
190C43—112no—
191C43—112no—
192C43—114no—
193C22×C11—24no—
194C22×C11—28no—
195C22×C11C2×#12414yes—
196C22×C11C23×D411yescharacteristic
197C22×C11C22×#4112yes—
198C22×C11C22×#4114yes—
199C2×D11—44no—
200C2×D11—48no—
201C2×D11—416no—
202C4×C11—24no—
203C4×C11—48no—
204C4×C11C2×#12414yes—
205C4×C11C2×#12414yes—
206C4×C11#53218yes—
207Dic11—216no—
208Dic11—44no—
209C2×#41—2216no—
210C2×#41—228no—
211C22×Q8—112no—
212C22×Q8C22×D1114yes—
213C22×D4—114no—
214C22×D4—114no—
215C22×D4—112no—
216C23×C4—114no—
217C23×C4—114no—
218C23×C4C22×D1112yes—
219C23×C4C22×D1111yescharacteristic
220C4⋊Q8—28no—
221C4⋊Q8—224no—
222#127—224no—
223#125—28no—
224#124—2232no—
225#124—228no—
226C22⋊Q8—216no—
227#121—2216no—
228C4×Q8—216no—
229C4×D4—2216no—
230#117—28no—
231C2×C4⋊C4—114no—
232C2×C4⋊C4C22×D1114yes—
233C2×C4⋊C4C22×D1118yes—
234C2×C4⋊C4C22×D1114yes—
235C2×C22⋊C4—118no—
236C2×C22⋊C4—1132no—
237C2×C22⋊C4C22×D1114yes—
238C2×C42—114no—
239C2×C42—118no—
240C2×C42—114no—
241C2×C42—114no—
242C2×C42—114no—
243C2×C42—2216no—
244C2×C42—228no—
245C2×C42C22⋊D1118yes—
246C2×C42C22×D1114yes—
247C2×C42C22×D1111yescharacteristic
248C2×C42C22×D1111yescharacteristic
249C2×C42C22×D1112yes—
250#95—1132no—
251C2×C11—24no—
252C2×C11C22×#12411yescharacteristic
253C2×C11C2×#53212yes—
254C2×C11#344414yes—
255D11—84no—
256C24—114no—
257C24C23×D1111yescharacteristic
258#41—4432no—
259C2×Q8—216no—
260C2×Q8—28no—
261C2×Q8—228no—
262C2×Q8—224no—
263C2×D4—2216no—
264C2×D4—228no—
265C2×D4—228no—
266C2×D4—2216no—
267C2×D4—228no—
268C2×D4—224no—
269C22×C4—28no—
270C22×C4—118no—
271C22×C4—114no—
272C22×C4—2216no—
273C22×C4—228no—
274C22×C4—2216no—
275C22×C4—228no—
276C22×C4#434318yes—
277C22×C4C2×C22⋊D1118yes—
278C22×C4C2×C22⋊D1114yes—
279C22×C4C23×D1118yes—
280C22×C4C23×D1112yes—
281C22×C4C23×D1111yescharacteristic
282C22×C4C23×D1112yes—
283C22×C4C23×D1111yescharacteristic
284C4⋊C4—28no—
285C4⋊C4—216no—
286C4⋊C4—28no—
287C4⋊C4—228no—
288C22⋊C4—28no—
289C22⋊C4—2264no—
290C22⋊C4—2216no—
291C42—28no—
292C42—1116no—
293C42—2216no—
294C42—228no—
295C42—228no—
296C42—228no—
297C42C2×C22⋊D1118yes—
298C42C2×C22⋊D1114yes—
299C42C2×C22⋊D1114yes—
300C11#3663911yescharacteristic, complemented, Sylow
301C23—24no—
302C23—228no—
303C23—2216no—
304C23—224no—
305C23C2×#434314yes—
306C23C22×C22⋊D1112yes—
307C23C24×D1111yescharacteristic
308Q8—416no—
309Q8—448no—
310D4—4416no—
311D4—448no—
312D4—4416no—
313C2×C4—24no—
314C2×C4—216no—
315C2×C4—216no—
316C2×C4—28no—
317C2×C4—1116no—
318C2×C4—2232no—
319C2×C4—228no—
320C2×C4—228no—
321C2×C4—228no—
322C2×C4—224no—
323C2×C4—4416no—
324C2×C4#67000116yescomplemented
325C2×C4C2×#434314yes—
326C2×C4C2×#434314yes—
327C2×C4#41×D1118yes—
328C2×C4C22×C22⋊D1114yes—
329C2×C4C22×C22⋊D1112yes—
330C2×C4C22×C22⋊D1112yes—
331C2×C4C22×C22⋊D1114yes—
332C22—24no—
333C22—28no—
334C22—444no—
335C22—448no—
336C22—4416no—
337C22C2×#6700014yes—
338C22C22×#434312yes—
339C22C2×#41×D1114yes—
340C22C23×C22⋊D1111yescharacteristic
341C4—24no—
342C4—48no—
343C4—2216no—
344C4—444no—
345C4C2×#6700014yes—
346C4C2×#6700014yes—
347C4#1062336318yes—
348C2—24no—
349C2—884no—
350C2C22×#6700011yescharacteristic
351C2C2×#1062336312yes—
352C2#1308191314yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#533C2
prime radicalC2×#10623008C2
hypercenterC2×#533D11
hypocenterC11#36639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13076993C2semidirect
3. #13076989C2semidirect
4. #13076974C2semidirect
5. #13076919C2semidirect
6. C4×#67000C2semidirect
7. #13071104C2semidirect
8. C2×C42×Dic11C2semidirect
9. C2×C11×#533C2semidirect
124. C4×Dic11#41semidirect
125. C2×#533D11semidirect
146. C2×C4×C11#124semidirect
300. C11#36639semidirect
324. C2×C4#67000semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
#130769932
#130769892
#130769742
#130769192
C4×#670002
#130711042
C2×C42×Dic112
C2×C11×#5332
#3663911