Finite Group Databasebeta

← #14666537

Subgroups — #14666537

Order 2816.

414 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 59 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#13075585C211yesmaximal, characteristic
2#13069777C211yesmaximal, characteristic, complemented
3#13067626C211yesmaximal, characteristic, complemented
4#13067558C211yesmaximal, characteristic
5#13066623C211yesmaximal, characteristic, complemented
6#13066620C211yesmaximal, characteristic
7C11×#1319C211yesmaximal, characteristic, complemented
8C2×#66999—21no—
9#10623031C2211yescharacteristic
10C11×#391C2211yescharacteristic
11#10622838—21no—
12#10622604C2211yescharacteristic
13#10622596C2211yescharacteristic
14#10622553—21no—
15#10622344—21no—
16#10622334—21no—
17#10622287—21no—
18#10622281—21no—
19#10622278—21no—
20#10622272—21no—
21C11×#324C2211yescharacteristic
22C11×#324C2211yescharacteristic
23#10622168C2211yescharacteristic
24#10622161—21no—
25#10622105—21no—
26#10622105—21no—
27C22×Q8×C11D411yescharacteristic
28C22×D44D411yescharacteristic
29C22×C4×D11—21no—
30C2×C11×C4⋊C4C2311yescharacteristic
31C2×C42×C11D411yescharacteristic
32#66999—42no—
33#66999—42no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—21no—
36C2×(C2×D11)⋊C4—21no—
37C2×(C2×D11)⋊C4—21no—
38C2×(C2×D11)⋊C4—21no—
39#66979—21no—
40C2×C4⋊Dic11—21no—
41C2×C4⋊Dic11D411yescharacteristic
42#66977—21no—
43#66977—21no—
44C2×Dic11⋊C4—21no—
45C2×Dic11⋊C4—21no—
46C2×#4318—21no—
47C2×#4314—41no—
48#66943—41no—
49#66941—41no—
50C11×C22⋊C8—21no—
51C11×C22⋊C8—21no—
52C11×#95—21no—
53C11×#95—21no—
54#66899—41no—
55#66899—41no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95D411yescharacteristic
60C11⋊#95D411yescharacteristic
61#66885—41no—
62#66881—41no—
63#66880—41no—
64#12210—111nomaximal, Sylow
65C23×D11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—41no—
68C2×Q8×C11—41no—
69C2×Q8×C11SD1612yescomplemented
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C2×D44—41no—
79C2×D44—42no—
80C2×C4×D11—42no—
81C2×C4×D11—81no—
82C2×C4×D11—81no—
83C2×Dic22—21no—
84C2×Dic22—21no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—41no—
88C42×C11—41no—
89C22⋊Dic11—41no—
90(C2×D11)⋊C4—42no—
91(C2×D11)⋊C4—42no—
92(C2×D11)⋊C4—42no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95(C2×D11)⋊C4—81no—
96C4⋊Dic11—21no—
97C4⋊Dic11—21no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—41no—
101C4⋊Dic11—42no—
102Dic11⋊C4—41no—
103Dic11⋊C4—41no—
104Dic11⋊C4—42no—
105Dic11⋊C4—41no—
106Dic11⋊C4—41no—
107C4×Dic11—41no—
108#4318—41no—
109#4318—41no—
110C2×C11⋊C8—41no—
111#4314—82no—
112#2728—111no—
113#2028—111no—
114#1611—111no—
115#1599—111no—
116#1346—111no—
117#1345—111no—
118#1319D1111yescharacteristic, complemented
119C23×C11#12011yescharacteristic
120C22×D11—22no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C22×D11—41no—
127Q8×C11—42no—
128Q8×C11—81no—
129C2×C4×C11—21no—
130C2×C4×C11—21no—
131C2×C4×C11—22no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11C2×SD1611yescharacteristic
142C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154D44—42no—
155D44—81no—
156C4×D11—84no—
157Dic22—81no—
158Dic22—81no—
159C8×C11—81no—
160C8×C11—81no—
161C11⋊C8—81no—
162#544—111no—
163C2×C22⋊Q8—221no—
164#483—221no—
165#450—221no—
166#419—221no—
167#400—221no—
168#398—111no—
169#397—221no—
170#394—111no—
171#391C2×D1111yescharacteristic
172#388—221no—
173#386—221no—
174#385—221no—
175#343—111no—
176#339—221no—
177#328—221no—
178#328—221no—
179#324C2×D1111yescharacteristic
180#324C2×D1111yescharacteristic
181C22×C11—21no—
182C22×C11—21no—
183C22×C11#45011yescharacteristic
184C22×C11#45511yescharacteristic
185C22×C11B(4,𝔽2)11yescharacteristic
186C2×D11—42no—
187C2×D11—42no—
188C2×D11—42no—
189C2×D11—81no—
190C2×D11—81no—
191C2×D11—81no—
192C2×D11—81no—
193C4×C11—21no—
194C4×C11—21no—
195C4×C11—42no—
196C4×C11—41no—
197C4×C11—41no—
198C4×C11—81no—
199Dic11—81no—
200Dic11—81no—
201Dic11—81no—
202Dic11—81no—
203Dic11—81no—
204C22×Q8D4411yescharacteristic
205C22×D4—111no—
206C23×C4—221no—
207C2×SD16—441no—
208C2×M16—221no—
209C4⋊Q8—441no—
210#125—441no—
211C22⋊Q8—221no—
212C22⋊Q8—221no—
213C22⋊Q8—442no—
214C22⋊Q8—442no—
215#117—221no—
216C2×C4⋊C4—111no—
217C2×C4⋊C4—221no—
218C2×C4⋊C4—221no—
219C2×C4⋊C4—221no—
220C2×C4⋊C4C22×D1111yescharacteristic
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C22⋊C4—221no—
224C2×C22⋊C4—221no—
225C2×C22⋊C4—221no—
226C2×C42D4411yescharacteristic
227#106—441no—
228#103—441no—
229#103—441no—
230#103—441no—
231#102—441no—
232C22⋊C8—21no—
233C22⋊C8—21no—
234#95—21no—
235#95—21no—
236#95—111no—
237#95—111no—
238#95—221no—
239#95—221no—
240#95—221no—
241C2×C11—21no—
242C2×C11—21no—
243C2×C11#160111yescharacteristic
244C2×C11#219711yescharacteristic
245C2×C11#220311yescharacteristic
246D11—82no—
247C24—221no—
248C2×Q8—21no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—221no—
252C2×Q8—221no—
253C2×Q8#431412yescomplemented
254C2×D4—441no—
255C2×D4—442no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—442no—
262C22×C4—881no—
263C22×C4—881no—
264C22×C4C2×D4411yescharacteristic
265C22×C4D4×D1111yescharacteristic
266C22×C4D4×D1111yescharacteristic
267SD16—882no—
268M16—441no—
269M16—441no—
270C2×C8—41no—
271C2×C8—41no—
272C2×C8—441no—
273C4⋊C4—41no—
274C4⋊C4—221no—
275C4⋊C4—221no—
276C4⋊C4—221no—
277C4⋊C4—221no—
278C4⋊C4—441no—
279C4⋊C4—442no—
280C4⋊C4—442no—
281C4⋊C4—441no—
282C4⋊C4—441no—
283C4⋊C4—441no—
284C4⋊C4—441no—
285C22⋊C4—442no—
286C22⋊C4—442no—
287C22⋊C4—442no—
288C22⋊C4—441no—
289C22⋊C4—441no—
290C22⋊C4—441no—
291C22⋊C4—881no—
292C42—41no—
293C42—441no—
294C11#1221011yescharacteristic, complemented, Sylow
295C23—222no—
296C23—441no—
297C23—441no—
298C23—441no—
299C23—441no—
300C23—441no—
301C23—441no—
302C23#6693511yescharacteristic
303Q8—42no—
304Q8—81no—
305Q8—881no—
306Q8—881no—
307D4—442no—
308D4—881no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4—441no—
328C2×C4—441no—
329C2×C4—441no—
330C2×C4—441no—
331C2×C4—441no—
332C2×C4—884no—
333C2×C4C2×#431411yescharacteristic
334C2×C4#6696111yescharacteristic
335C8—81no—
336C8—81no—
337C8—881no—
338C22—21no—
339C22—21no—
340C22—442no—
341C22—442no—
342C22—442no—
343C22—881no—
344C22—881no—
345C22—881no—
346C22—881no—
347C22#1062234411yescharacteristic
348C22#1062235411yescharacteristic
349C22#1062235911yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—42no—
355C4—81no—
356C4—881no—
357C4—881no—
358C4—881no—
359C4—881no—
360C4—881no—
361C2—21no—
362C2—21no—
363C2—882no—
364C2#1306757011yescharacteristic
365C2#1307060911yescharacteristic
366C2#1307063811yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1319C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D44D4
hypercenter#1319D11
hypocenterC11#12210
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1319

Complements

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

NH ≅ G/Ntype
2. #13069777C2semidirect
3. #13067626C2semidirect
5. #13066623C2semidirect
7. C11×#1319C2semidirect
69. C2×Q8×C11SD16semidirect
118. #1319D11semidirect
253. C2×Q8#4314semidirect
294. C11#12210semidirect

Maximal subgroups

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

subgroupindex
#130755852
#130697772
#130676262
#130675582
#130666232
#130666202
C11×#13192
#1221011