Finite Group Databasebeta

← #14916596

Subgroups — #14916596

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊Q8C211yesmaximal, characteristic
2#13071797C211yesmaximal, characteristic, complemented
3#13071796C212yesmaximal, complemented
4#13071704C214yesmaximal, complemented
5#13071482C218yesmaximal
6#13071361C218yesmaximal, complemented
7#13071199C214yesmaximal
8#13071013C212yesmaximal
9C11×#2381C211yesmaximal, characteristic, complemented
10C22×Q8×D11C2212yes—
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66997C2212yes—
13D11×C4⋊Q8C4116yescomplemented
14C2×#66945C2214yes—
15C2×C4⋊C4×D11C2214yes—
16C2×#66941C2214yes—
17C2×#66925C2214yes—
18C2×C42×D11C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#391C2214yes—
21C11×#387C2218yes—
22C11×#383C2212yes—
23#10622843C2214yes—
24#10622594C2218yes—
25#10622587C2214yes—
26#10622585C2218yes—
27#10622550C2212yes—
28C4×Dic11⋊C4C2218yes—
29#10622542C2214yes—
30#10622280C2214yes—
31#10622279C2214yes—
32#10622277C2214yes—
33#10622277C2218yes—
34#10622267C2218yes—
35#10622266C2218yes—
36#10622263C2214yes—
37#10622262C2218yes—
38#10622262C2214yes—
39#10622261C2214yes—
40#10622260C2218yes—
41#10622259C2218yes—
42#10622259C2218yes—
43C22×Q8×C11C2312yes—
44C2×Q8×D11—44no—
45C2×Q8×D11—44no—
46C2×Q8×D11C2×C4116yes—
47C22×C4×D11C2312yes—
48C22×C4×D11C2311yescharacteristic
49C22×C4×D11C2314yes—
50C22×Dic22C2312yes—
51C22×Dic22C2314yes—
52C11×C4⋊Q8C2×C418yes—
53C2×C11×C4⋊C4C2314yes—
54C2×C11×C4⋊C4C2314yes—
55C2×C42×C11C2314yes—
56C2×C42×C11C2311yescharacteristic
57#66997C2×C4116yes—
58C2×(C2×D11)⋊C4C2318yes—
59C2×C4⋊Dic11C2314yes—
60C2×C4⋊Dic11C2314yes—
61C2×Dic11⋊C4C2318yes—
62C2×Dic11⋊C4C2318yes—
63C2×Dic11⋊C4C2318yes—
64C2×C4×Dic11C2318yes—
65C2×C4×Dic11C2314yes—
66C2×C4×Dic11C2318yes—
67C2×C4×Dic11C2312yes—
68C2×C4×Dic11C2311yescharacteristic
69#66945—48no—
70C4⋊C4×D11C2×C4132yes—
71#66941C2×C4132yes—
72#66925—48no—
73C42×D11C2×C418yes—
74#66922C2×C418yes—
75C11×#95C2314yes—
76C11×#95C2318yes—
77C11×#95C2314yes—
78C11×#95C2314yes—
79C11⋊#95C2318yes—
80C11⋊#95C2314yes—
81C11⋊#95C2318yes—
82C11⋊#95C2318yes—
83C11⋊#95C2318yes—
84C11⋊#95C2314yes—
85C11⋊#95C2314yes—
86#34365—111nomaximal, Sylow
87C23×D11C2411yescharacteristic
88C2×Q8×C11—42no—
89C2×Q8×C11—42no—
90C2×Q8×C11C22×C418yes—
91C22×C4×C11C2418yes—
92C22×C4×C11C2412yes—
93C22×C4×C11C2411yescharacteristic
94C22×C4×C11C2414yes—
95C22×Dic11C2418yes—
96C22×Dic11C2411yescharacteristic
97C22×Dic11C2414yes—
98C22×Dic11C2412yes—
99Q8×D11—432no—
100C2×C4×D11—28no—
101C2×C4×D11—28no—
102C2×C4×D11—28no—
103C2×C4×D11—24no—
104C2×C4×D11C22×C418yes—
105C2×C4×D11C22×C414yes—
106C2×C4×D11C22×C4116yes—
107C2×Dic22—44no—
108C2×Dic22—44no—
109C2×Dic22—42no—
110C2×Dic22—42no—
111C2×Dic22C22×C418yes—
112C2×Dic22C22×C4116yes—
113C11×C4⋊C4—44no—
114C11×C4⋊C4C22×C4116yes—
115C42×C11—44no—
116C42×C11C22×C414yes—
117(C2×D11)⋊C4—216no—
118C4⋊Dic11—44no—
119C4⋊Dic11C22×C4116yes—
120Dic11⋊C4—216no—
121Dic11⋊C4—48no—
122Dic11⋊C4C22×C4132yes—
123C4×Dic11—216no—
124C4×Dic11—44no—
125C4×Dic11—48no—
126C4×Dic11C22×C418yes—
127C4×Dic11C22×C414yes—
128C22×C4⋊Q8—111no—
129#2381—112no—
130#2381—111no—
131#2381D1111yescharacteristic, complemented
132#2369—114no—
133#2344—118no—
134#2331—118no—
135#2310—114no—
136#2283—112no—
137C23×C11C2511yescharacteristic
138C22×D11—24no—
139C22×D11C23×C412yes—
140C22×D11H(5,𝔽2)14yes—
141Q8×C11—48no—
142C2×C4×C11—24no—
143C2×C4×C11—24no—
144C2×C4×C11—22no—
145C2×C4×C11—24no—
146C2×C4×C11—28no—
147C2×C4×C11—28no—
148C2×C4×C11—28no—
149C2×C4×C11C23×C414yes—
150C2×C4×C11C23×C412yes—
151C2×C4×C11C23×C418yes—
152C2×Dic11—24no—
153C2×Dic11—24no—
154C2×Dic11—22no—
155C2×Dic11—28no—
156C2×Dic11—28no—
157C2×Dic11—28no—
158C2×Dic11C23×C412yes—
159C2×Dic11C23×C418yes—
160C2×Dic11C23×C414yes—
161C2×Dic112−1+418yes—
162C4×D11—232no—
163C4×D11—28no—
164C4×D11—216no—
165Dic22—416no—
166Dic22—48no—
167C23×Q8—112no—
168C2×C4⋊Q8—112no—
169C2×C4⋊Q8—1116no—
170C2×C4⋊Q8—114no—
171C2×C4⋊Q8—111no—
172C2×C4⋊Q8C2×D1111yescharacteristic
173C2×#117—114no—
174C2×#117—114no—
175C22×C4⋊C4—114no—
176C22×C42—111no—
177#391—114no—
178#391—114no—
179#391—114no—
180#391—118no—
181#391—118no—
182#391C2×D1114yes—
183#389—118no—
184#389—118no—
185#387—118no—
186#387—118no—
187#387—118no—
188#387C2×D1118yes—
189#383—112no—
190#383C2×D1112yes—
191#382—114no—
192#381—114no—
193#381—118no—
194#380—114no—
195C4×C4⋊C4—118no—
196C4×C4⋊C4—118no—
197C4×C4⋊C4—114no—
198C4×C22⋊C4—114no—
199#376—114no—
200C22×C11C24×C411yescharacteristic
201C22×C11C2×H(5,𝔽2)12yes—
202C22×C11C2×2−1+414yes—
203C2×D11—24no—
204C2×D11—28no—
205C2×D11#51814yes—
206C4×C11—22no—
207C4×C11—28no—
208C4×C11—24no—
209C4×C11—48no—
210Dic11—22no—
211Dic11—28no—
212Dic11—48no—
213Dic11#51918yes—
214C22×Q8—1116no—
215C22×Q8—114no—
216C22×Q8—112no—
217C22×Q8—444no—
218C22×Q8—444no—
219C22×Q8C22×D1112yes—
220C23×C4—114no—
221C23×C4—112no—
222C23×C4—111no—
223C4⋊Q8—1116no—
224C4⋊Q8—1132no—
225C4⋊Q8—118no—
226C4⋊Q8C4×D1118yes—
227#117—448no—
228#117—448no—
229C2×C4⋊C4—118no—
230C2×C4⋊C4—114no—
231C2×C4⋊C4—1132no—
232C2×C4⋊C4—118no—
233C2×C4⋊C4—118no—
234C2×C4⋊C4—114no—
235C2×C4⋊C4C22×D1114yes—
236C2×C4⋊C4C22×D1114yes—
237C2×C22⋊C4—118no—
238C2×C42—112no—
239C2×C42—111no—
240C2×C42—118no—
241C2×C42—118no—
242C2×C42—118no—
243C2×C42—114no—
244C2×C42C22×D1114yes—
245C2×C42C22×D1111yescharacteristic
246#95—114no—
247#95—118no—
248#95—114no—
249#95—114no—
250#95—118no—
251#95—118no—
252#95—118no—
253#95C22×D1114yes—
254#95C22×D1114yes—
255#95C22×D1114yes—
256#95C22×D1118yes—
257C2×C11C2×#51811yescharacteristic
258C2×C11C2×#51912yes—
259C2×C11#354414yes—
260D11—24no—
261C24—111no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—1116no—
265C2×Q8—118no—
266C2×Q8—444no—
267C2×Q8—444no—
268C2×Q8—442no—
269C2×Q8—442no—
270C2×Q8—4432no—
271C2×Q8C2×C4×D1118yes—
272C22×C4—112no—
273C22×C4—111no—
274C22×C4—114no—
275C22×C4—118no—
276C22×C4—114no—
277C22×C4—1116no—
278C22×C4—118no—
279C22×C4—228no—
280C22×C4—228no—
281C22×C4—228no—
282C22×C4—224no—
283C22×C4C23×D1118yes—
284C22×C4C23×D1112yes—
285C22×C4C23×D1111yescharacteristic
286C22×C4C23×D1114yes—
287C4⋊C4—44no—
288C4⋊C4—1132no—
289C4⋊C4—1116no—
290C4⋊C4—2216no—
291C4⋊C4—448no—
292C4⋊C4—444no—
293C4⋊C4C2×C4×D11116yes—
294C22⋊C4—2216no—
295C42—44no—
296C42—114no—
297C42—118no—
298C42—2216no—
299C42—444no—
300C42—448no—
301C42C2×C4×D1114yes—
302C11#3436511yescharacteristic, complemented, Sylow
303C23—112no—
304C23—114no—
305C23—224no—
306C23C24×D1111yescharacteristic
307Q8—48no—
308Q8—448no—
309Q8—4416no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—22no—
313C2×C4—24no—
314C2×C4—28no—
315C2×C4—28no—
316C2×C4—28no—
317C2×C4—114no—
318C2×C4—118no—
319C2×C4—112no—
320C2×C4—118no—
321C2×C4—2216no—
322C2×C4—228no—
323C2×C4—2232no—
324C2×C4—224no—
325C2×C4—224no—
326C2×C4—222no—
327C2×C4—228no—
328C2×C4—228no—
329C2×C4—228no—
330C2×C4C22×C4×D1114yes—
331C2×C4C22×C4×D1112yes—
332C2×C4C22×C4×D1118yes—
333C22—114no—
334C22—228no—
335C22—224no—
336C22C23×C4×D1111yescharacteristic
337C22D11×H(5,𝔽2)12yes—
338C22D11×2−1+414yes—
339C4—22no—
340C4—28no—
341C4—24no—
342C4—48no—
343C4—118no—
344C4—222no—
345C4—228no—
346C4—448no—
347C2—224no—
348C2D11×#51811yescharacteristic
349C2D11×#51912yes—
350C2#1308295514yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2381C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2381D11
hypocenterC11#34365
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2381

Complements

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

NH ≅ G/Ntype
2. #13071797C2semidirect
3. #13071796C2semidirect
4. #13071704C2semidirect
6. #13071361C2semidirect
9. C11×#2381C2semidirect
13. D11×C4⋊Q8C4semidirect
131. #2381D11semidirect
302. C11#34365semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
#130717972
#130717962
#130717042
#130714822
#130713612
#130711992
#130710132
C11×#23812
#3436511