Finite Group Databasebeta

← #14666909

Subgroups — #14666909

Order 2816.

372 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 55 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#13076043C211yesmaximal, characteristic
2#13069782C211yesmaximal, characteristic
3#13067573C211yesmaximal, characteristic
4#13066638C211yesmaximal, characteristic
5#13066616C211yesmaximal, characteristic
6#13066545C211yesmaximal, characteristic
7C11×#1608C211yesmaximal, characteristic
8C11×#543C2211yescharacteristic
9C11×#483—21no—
10C11×#397C2211yescharacteristic
11#10622663—21no—
12#10622597—21no—
13#10622564—21no—
14#10622560C2211yescharacteristic
15#10622559—21no—
16#10622556—21no—
17#10622556C2211yescharacteristic
18#10622272—21no—
19#10622264—21no—
20#10622259—21no—
21C11×#328—21no—
22C11×#323C2211yescharacteristic
23#10622176—21no—
24#10622164—21no—
25#10622164C2211yescharacteristic
26#10622163C2211yescharacteristic
27C23×Dic11D411yescharacteristic
28C22×Dic22D411yescharacteristic
29C11×C22⋊Q8—21no—
30C11×C22⋊Q8—21no—
31C11×C22⋊Q8—41no—
32C11×C22⋊Q8—41no—
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C22⋊C4—21no—
35C2×C11×C22⋊C4—21no—
36C2×C11×C22⋊C4C2311yescharacteristic
37C2×C22⋊Dic11—21no—
38C2×C22⋊Dic11—21no—
39C2×C22⋊Dic11D411yescharacteristic
40C2×#4326—41no—
41C2×C4⋊Dic11—21no—
42C2×Dic11⋊C4—21no—
43C2×Dic11⋊C4—21no—
44C2×C4×Dic11—21no—
45C11×#106—41no—
46C11×#103—41no—
47C11×C22⋊C8—21no—
48C11×#95—21no—
49C11×#95D411yescharacteristic
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—41no—
58C11⋊#95—41no—
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61#66874—41no—
62#12269—111nomaximal, Sylow
63C24×C11C2×D411yescharacteristic
64C2×Q8×C11—21no—
65C2×Q8×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—41no—
79C22×Dic11—41no—
80C22×Dic11—41no—
81C2×Dic22—41no—
82C2×Dic22—42no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C22⋊C4—41no—
90C11×C22⋊C4—41no—
91C11×C22⋊C4—41no—
92C11×C22⋊C4—41no—
93C11×C22⋊C4—41no—
94C22⋊Dic11—41no—
95C22⋊Dic11—41no—
96C22⋊Dic11—42no—
97C22⋊Dic11—41no—
98#4326—82no—
99C4⋊Dic11—81no—
100Dic11⋊C4—81no—
101Dic11⋊C4—81no—
102C4×Dic11—42no—
103C2×C11⋊C8—41no—
104#2764—111no—
105#2030—111no—
106#1608D1111yescharacteristic
107#1602—111no—
108#1351—111no—
109#1344—111no—
110#1317—111no—
111C23×C11—21no—
112C23×C11—21no—
113C23×C11—41no—
114C23×C11—41no—
115C23×C11#12011yescharacteristic
116C23×C11#13511yescharacteristic
117C23×C11#13711yescharacteristic
118Q8×C11—81no—
119Q8×C11—81no—
120C2×C4×C11—21no—
121C2×C4×C11—21no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11—41no—
128C2×C4×C11—41no—
129C2×C4×C11—41no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—81no—
133C2×C4×C11—81no—
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—42no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—81no—
148C2×Dic11—81no—
149C2×Dic11—81no—
150C2×Dic11—81no—
151Dic22—42no—
152Dic22—81no—
153C8×C11—81no—
154C11⋊C8—81no—
155#543C2×D1111yescharacteristic
156#483—21no—
157#451—221no—
158#400—221no—
159#398—221no—
160#397C2×D1111yescharacteristic
161#393—111no—
162#391—221no—
163#388—221no—
164#385—221no—
165#383—221no—
166#381—111no—
167#381—221no—
168#342—111no—
169#342—221no—
170#328—21no—
171#328—221no—
172#323—111no—
173#323C2×D1111yescharacteristic
174C22×C11—21no—
175C22×C11—21no—
176C22×C11—21no—
177C22×C11—21no—
178C22×C11—41no—
179C22×C11—41no—
180C22×C11—41no—
181C22×C11—41no—
182C22×C11—81no—
183C22×C11#45211yescharacteristic
184C22×C11#45511yescharacteristic
185C22×C11B(4,𝔽2)11yescharacteristic
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—81no—
189C4×C11—81no—
190C4×C11—81no—
191C4×C11—81no—
192Dic11—42no—
193Dic11—81no—
194Dic11—81no—
195Dic11—81no—
196Dic11—161no—
197C22×Q8—111no—
198C23×C4—111no—
199C2×Q16—441no—
200C22⋊Q8—21no—
201C22⋊Q8—21no—
202C22⋊Q8—41no—
203C22⋊Q8—41no—
204C2×C4⋊C4—221no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4C22⋊D1111yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—111no—
211C2×C22⋊C4—221no—
212C2×C22⋊C4—221no—
213C2×C22⋊C4C22×D1111yescharacteristic
214C2×C42—221no—
215#106—41no—
216#103—41no—
217#103—441no—
218C22⋊C8—21no—
219C22⋊C8—221no—
220#95—21no—
221#95—111no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—441no—
230#95—441no—
231#95C22⋊D1111yescharacteristic
232C2×C11—21no—
233C2×C11—21no—
234C2×C11—41no—
235C2×C11—41no—
236C2×C11#160611yescharacteristic
237C2×C11#219711yescharacteristic
238C2×C11#220111yescharacteristic
239C24D4×D1111yescharacteristic
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—441no—
243C2×Q8—442no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—441no—
255C22×C4—441no—
256C22×C4—441no—
257C22×C4D4×D1111yescharacteristic
258C22×C4C2×C22⋊D1111yescharacteristic
259Q16—882no—
260C2×C8—41no—
261C2×C8—441no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—881no—
268C4⋊C4—881no—
269C4⋊C4—881no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—41no—
275C22⋊C4—442no—
276C22⋊C4—441no—
277C22⋊C4—441no—
278C22⋊C4—441no—
279C42—442no—
280C11#1226911yescharacteristic, complemented, Sylow
281C23—21no—
282C23—21no—
283C23—41no—
284C23—41no—
285C23#6696811yescharacteristic
286C23#6696911yescharacteristic
287C23#6699011yescharacteristic
288Q8—81no—
289Q8—81no—
290Q8—442no—
291Q8—881no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—222no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—441no—
311C2×C4—442no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—881no—
320C2×C4—881no—
321C2×C4—881no—
322C2×C4—881no—
323C8—81no—
324C8—881no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22#1062264511yescharacteristic
335C22#1062278611yescharacteristic
336C22#1062281511yescharacteristic
337C4—41no—
338C4—41no—
339C4—81no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—442no—
344C4—881no—
345C4—881no—
346C4—881no—
347C4—1761no—
348C2—21no—
349C2—21no—
350C2—41no—
351C2—41no—
352C2#1306759311yescharacteristic
353C2#1307060511yescharacteristic
354C2#1307062711yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C22⋊C4C23
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1608C2
socleC22×C11B(4,𝔽2)
prime radicalC24×C11C2×D4
hypercenter#1608D11
hypocenterC11#12269
LCSG ▷ C2×C11×C22⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1608

Complements

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

NH ≅ G/Ntype
280. C11#12269semidirect

Maximal subgroups

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

subgroupindex
#130760432
#130697822
#130675732
#130666382
#130666162
#130665452
C11×#16082
#1226911