Finite Group Databasebeta

← #14665994

Subgroups — #14665994

Order 2816.

542 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13069742C211yesmaximal, characteristic
2#13067635C212yesmaximal, complemented
3#13066640C212yesmaximal, complemented
4#13066544C211yesmaximal, characteristic, complemented
5C11×#2842C211yesmaximal, characteristic, complemented
6C2×#67006—21no—
7#10623024C2211yescharacteristic
8C11×#399—21no—
9C11×#399C2212yes—
10C11×#396—22no—
11C11×#396—22no—
12C11×#379—21no—
13C11×#379C2211yescharacteristic
14#10622581—22no—
15C2×#66870—21no—
16#10622164C2211yescharacteristic
17#10622163C2212yes—
18#10622089—22no—
19C25×C11D411yescharacteristic
20C22×C22⋊D11—21no—
21C22×C22⋊D11—41no—
22C2×C11×C4⋊C4—22no—
23C2×C11×C4⋊C4—21no—
24C2×C11×C4⋊C4—22no—
25C2×C11×C4⋊C4D412yescomplemented
26C2×C11×C22⋊C4—21no—
27C2×C11×C22⋊C4—22no—
28C2×C11×C22⋊C4—21no—
29C2×C11×C22⋊C4—22no—
30C2×C11×C22⋊C4—22no—
31C2×C11×C22⋊C4D411yescharacteristic
32C2×C11×C22⋊C4C2311yescharacteristic
33#67006—42no—
34#67006—42no—
35C2×C22⋊Dic11—21no—
36C2×C22⋊Dic11—41no—
37#66983—22no—
38#66939—41no—
39#66935—41no—
40C11×#95—21no—
41C11×#95D412yescomplemented
42C22⋊(C11⋊C8)—22no—
43#66873—42no—
44#66872—42no—
45#66870—42no—
46#12124—111nomaximal, Sylow
47C24×C11—21no—
48C24×C11—21no—
49C24×C11—41no—
50C24×C11—41no—
51C24×C11—82no—
52C24×C11SD1612yes—
53C24×C11C2×D411yescharacteristic
54C23×D11—21no—
55C22×C4×C11—22no—
56C22×C4×C11—21no—
57C22×C4×C11—22no—
58C22×C4×C11C2×D412yes—
59C2×C22⋊D11—41no—
60C2×C22⋊D11—41no—
61C2×C22⋊D11—41no—
62C2×C22⋊D11—44no—
63C2×C22⋊D11—41no—
64C2×C22⋊D11—41no—
65C2×C22⋊D11—41no—
66C2×C22⋊D11—84no—
67C22×Dic11—21no—
68C22×Dic11—41no—
69C2×D44—22no—
70C11×C4⋊C4—42no—
71C11×C4⋊C4—82no—
72C11×C4⋊C4—82no—
73C11×C4⋊C4—81no—
74C11×C22⋊C4—41no—
75C11×C22⋊C4—41no—
76C11×C22⋊C4—82no—
77C11×C22⋊C4—82no—
78C11×C22⋊C4—82no—
79C11×C22⋊C4—81no—
80C11×C22⋊C4—81no—
81C22⋊Dic11—22no—
82C22⋊Dic11—44no—
83C22⋊Dic11—41no—
84(C2×D11)⋊C4—42no—
85C4⋊Dic11—22no—
86C2×C11⋊C8—42no—
87#2842D1111yescharacteristic, complemented
88#2021—111no—
89#1613—112no—
90#1352—112no—
91#1316—111no—
92C23×C11—21no—
93C23×C11—21no—
94C23×C11—22no—
95C23×C11—42no—
96C23×C11—42no—
97C23×C11—42no—
98C23×C11—42no—
99C23×C11—44no—
100C23×C11—41no—
101C23×C11—41no—
102C23×C11—81no—
103C23×C11—82no—
104C23×C11—82no—
105C23×C11—82no—
106C23×C11—84no—
107C23×C11#12011yescharacteristic
108C23×C11C2×SD1611yescharacteristic
109C23×C11#13711yescharacteristic
110C22×D11—41no—
111C22×D11—41no—
112C22×D11—41no—
113C22×D11—82no—
114C2×C4×C11—22no—
115C2×C4×C11—42no—
116C2×C4×C11—42no—
117C2×C4×C11—42no—
118C2×C4×C11—42no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—42no—
123C2×C4×C11—42no—
124C22⋊D11—81no—
125C22⋊D11—81no—
126C22⋊D11—88no—
127C22⋊D11—81no—
128C22⋊D11—81no—
129C2×Dic11—42no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—82no—
134D44—82no—
135C11⋊C8—82no—
136#534—111no—
137C2×#120—221no—
138#481—222no—
139C2×#99—221no—
140#399—21no—
141#399C2×D1112yes—
142#396—22no—
143#396—22no—
144#379—21no—
145#379C2×D1111yescharacteristic
146#342—111no—
147#327—222no—
148#323—112no—
149C22×C11—22no—
150C22×C11—21no—
151C22×C11—21no—
152C22×C11—41no—
153C22×C11—41no—
154C22×C11—42no—
155C22×C11—42no—
156C22×C11—42no—
157C22×C11—44no—
158C22×C11—42no—
159C22×C11—81no—
160C22×C11—82no—
161C22×C11—82no—
162C22×C11—84no—
163C22×C11—82no—
164C22×C11#44811yescharacteristic
165C22×C11#45311yescharacteristic
166C22×C11B(4,𝔽2)11yescharacteristic
167C2×D11—82no—
168C2×D11—81no—
169C2×D11—82no—
170C2×D11—161no—
171C4×C11—42no—
172C4×C11—81no—
173C4×C11—82no—
174C4×C11—82no—
175Dic11—82no—
176Dic11—81no—
177C25C22⋊D1111yescharacteristic
178C22×D4—221no—
179C22×D4—441no—
180#123—441no—
181#121—222no—
182#120—441no—
183#120—442no—
184#120—442no—
185C2×C4⋊C4—22no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4C22⋊D1112yescomplemented
189C2×C22⋊C4—21no—
190C2×C22⋊C4—22no—
191C2×C22⋊C4—21no—
192C2×C22⋊C4—22no—
193C2×C22⋊C4—22no—
194C2×C22⋊C4—221no—
195C2×C22⋊C4—441no—
196C2×C22⋊C4C22⋊D1111yescharacteristic
197C2×C22⋊C4C22×D1111yescharacteristic
198#106—442no—
199#102—442no—
200#99—442no—
201C22⋊C8—222no—
202#95—21no—
203#95C22⋊D1112yescomplemented
204C2×C11—21no—
205C2×C11—21no—
206C2×C11—41no—
207C2×C11—41no—
208C2×C11—82no—
209C2×C11#159611yescharacteristic
210C2×C11#220012yes—
211D11—161no—
212C24—21no—
213C24—21no—
214C24—41no—
215C24—41no—
216C24—82no—
217C24—221no—
218C24#432512yes—
219C24C2×C22⋊D1111yescharacteristic
220C2×D4—222no—
221C2×D4—441no—
222C2×D4—441no—
223C2×D4—441no—
224C2×D4—444no—
225C2×D4—441no—
226C2×D4—441no—
227C2×D4—441no—
228C2×D4—884no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—22no—
232C22×C4—221no—
233C22×C4—441no—
234C22×C4C2×C22⋊D1112yes—
235C2×C8—442no—
236C4⋊C4—42no—
237C4⋊C4—82no—
238C4⋊C4—82no—
239C4⋊C4—81no—
240C4⋊C4—222no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—82no—
244C22⋊C4—82no—
245C22⋊C4—82no—
246C22⋊C4—81no—
247C22⋊C4—81no—
248C22⋊C4—222no—
249C22⋊C4—442no—
250C22⋊C4—444no—
251C22⋊C4—441no—
252C11#1212411yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—22no—
256C23—42no—
257C23—42no—
258C23—42no—
259C23—42no—
260C23—44no—
261C23—41no—
262C23—41no—
263C23—81no—
264C23—82no—
265C23—82no—
266C23—82no—
267C23—84no—
268C23—441no—
269C23—441no—
270C23—441no—
271C23—882no—
272C23C2×#432511yescharacteristic
273C23#6699511yescharacteristic
274C23#6700611yescharacteristic
275D4—882no—
276D4—881no—
277D4—881no—
278D4—888no—
279D4—881no—
280D4—881no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—442no—
292C2×C4—441no—
293C2×C4—441no—
294C2×C4—441no—
295C2×C4—882no—
296C8—882no—
297C22—22no—
298C22—21no—
299C22—21no—
300C22—41no—
301C22—41no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—44no—
306C22—42no—
307C22—81no—
308C22—82no—
309C22—82no—
310C22—84no—
311C22—82no—
312C22—882no—
313C22—881no—
314C22—882no—
315C22—1761no—
316C22#1062284011yescharacteristic
317C22#1062285411yescharacteristic
318C22#1062285711yescharacteristic
319C4—42no—
320C4—81no—
321C4—82no—
322C4—82no—
323C4—882no—
324C4—881no—
325C2—21no—
326C2—21no—
327C2—41no—
328C2—41no—
329C2—82no—
330C2—1761no—
331C2#1306753911yescharacteristic
332C2#1307062312yes—
subgroupG/H
centerC22#10622857
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#2842C2
socleC22×C11B(4,𝔽2)
prime radical#13069742C2
hypercenter#2842D11
hypocenterC11#12124
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2842

Complements

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

NH ≅ G/Ntype
2. #13067635C2semidirect
3. #13066640C2semidirect
4. #13066544C2semidirect
5. C11×#2842C2semidirect
25. C2×C11×C4⋊C4D4semidirect
41. C11×#95D4semidirect
87. #2842D11semidirect
188. C2×C4⋊C4C22⋊D11semidirect
203. #95C22⋊D11semidirect
252. C11#12124semidirect

Maximal subgroups

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

subgroupindex
#130697422
#130676352
#130666402
#130665442
C11×#28422
#1212411