Finite Group Databasebeta

← #14666775

Subgroups — #14666775

Order 2816.

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

normal subgroups only

This group has 428 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#13074293C211yesmaximal, characteristic
2#13067624C211yesmaximal, characteristic, complemented
3#13067556C211yesmaximal, characteristic
4#13066621C211yesmaximal, characteristic, complemented
5#13066618C211yesmaximal, characteristic
6#13066560C211yesmaximal, characteristic, complemented
7C11×#2061C211yesmaximal, characteristic, complemented
8C11×#544C2211yescharacteristic
9C2×#66925—21no—
10C11×#428—21no—
11C11×#382C2211yescharacteristic
12#10622659—21no—
13#10622656—21no—
14#10622607—21no—
15#10622604C2211yescharacteristic
16#10622596C2211yescharacteristic
17#10622283—21no—
18#10622281—21no—
19#10622278—21no—
20#10622266—21no—
21C11×#343C2211yescharacteristic
22C11×#339—21no—
23#10622176—21no—
24#10622176—21no—
25#10622166C2211yescharacteristic
26#10622166C2211yescharacteristic
27C22×D44D411yescharacteristic
28C22×C4×D11—21no—
29C2×C11×M16—21no—
30C11×C4⋊Q8—41no—
31C11×#125—41no—
32C11×C22⋊Q8—21no—
33C11×C22⋊Q8—21no—
34C11×#117—21no—
35C2×C11×C4⋊C4D411yescharacteristic
36C2×C11×C4⋊C4C2311yescharacteristic
37C2×C42×C11D411yescharacteristic
38C2×#4325—41no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×(C2×D11)⋊C4—21no—
44C2×C4⋊Dic11—21no—
45C2×C4⋊Dic11D411yescharacteristic
46C2×Dic11⋊C4—21no—
47C2×Dic11⋊C4—21no—
48C2×C4×Dic11—21no—
49#66925—42no—
50#66925—42no—
51C11×#107—41no—
52C11×#106—41no—
53C11×#95—21no—
54C11×#95—21no—
55#66899—41no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95D411yescharacteristic
59C11⋊#95D411yescharacteristic
60C22⋊(C11⋊C8)—21no—
61C22⋊(C11⋊C8)—21no—
62#66873—41no—
63#66872—41no—
64#12248—111nomaximal, Sylow
65C23×D11—21no—
66C2×Q8×C11—21no—
67C2×Q8×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C2×D44—41no—
77C2×D44—42no—
78C2×C4×D11—42no—
79C2×C4×D11—42no—
80C2×C4×D11—42no—
81C11×M16—22no—
82C11×M16—41no—
83C2×C8×C11—41no—
84C11×C4⋊C4—21no—
85C11×C4⋊C4—21no—
86C11×C4⋊C4—21no—
87C11×C4⋊C4—21no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C22⋊C4—41no—
93C42×C11—21no—
94C42×C11—41no—
95C42×C11SD1612yescomplemented
96#4325—82no—
97(C2×D11)⋊C4—42no—
98(C2×D11)⋊C4—42no—
99(C2×D11)⋊C4—42no—
100(C2×D11)⋊C4—41no—
101(C2×D11)⋊C4—41no—
102(C2×D11)⋊C4—81no—
103C4⋊Dic11—41no—
104C4⋊Dic11—42no—
105Dic11⋊C4—42no—
106Dic11⋊C4—41no—
107Dic11⋊C4—41no—
108C4×Dic11—42no—
109C2×C11⋊C8—41no—
110C2×C11⋊C8—41no—
111#2609—111no—
112#2061D1111yescharacteristic, complemented
113#1611—111no—
114#1599—111no—
115#1346—111no—
116#1345—111no—
117#1324—111no—
118C23×C11#12011yescharacteristic
119C22×D11—22no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126Q8×C11—81no—
127Q8×C11—81no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—41no—
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×C11—41no—
142C2×C4×C11C2×SD1611yescharacteristic
143C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
144C2×Dic11—22no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150C2×Dic11—41no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153D44—42no—
154D44—81no—
155C4×D11—48no—
156C8×C11—42no—
157C11⋊C8—81no—
158C11⋊C8—81no—
159#544C2×D1111yescharacteristic
160C2×#117—221no—
161#483—221no—
162#450—221no—
163#428—21no—
164#398—111no—
165#396—221no—
166#394—111no—
167#388—221no—
168#387—221no—
169#386—221no—
170#385—221no—
171#382C2×D1111yescharacteristic
172#343C2×D1111yescharacteristic
173#339—21no—
174#328—221no—
175#328—221no—
176#324—111no—
177#324—111no—
178C22×C11—21no—
179C22×C11—21no—
180C22×C11#45011yescharacteristic
181C22×C11#45611yescharacteristic
182C22×C11B(4,𝔽2)11yescharacteristic
183C2×D11—42no—
184C2×D11—42no—
185C2×D11—42no—
186C2×D11—81no—
187C2×D11—81no—
188C2×D11—81no—
189C2×D11—81no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—42no—
193C4×C11—41no—
194C4×C11—41no—
195C4×C11—81no—
196C4×C11—81no—
197C4×C11—81no—
198Dic11—42no—
199Dic11—81no—
200Dic11—81no—
201C22×D4—111no—
202C23×C4—221no—
203C2×SD16—441no—
204C2×M16—21no—
205C4⋊Q8—41no—
206#125—41no—
207C22⋊Q8—21no—
208C22⋊Q8—21no—
209#117—21no—
210#117—442no—
211#117—442no—
212C2×C4⋊C4—111no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4C22⋊D1111yescharacteristic
217C2×C4⋊C4C22×D1111yescharacteristic
218C2×C22⋊C4—221no—
219C2×C22⋊C4—221no—
220C2×C22⋊C4—221no—
221C2×C22⋊C4—221no—
222C2×C22⋊C4—221no—
223C2×C42—221no—
224C2×C42C22⋊D1111yescharacteristic
225#107—41no—
226#106—41no—
227#106—441no—
228#103—441no—
229#102—441no—
230C22⋊C8—221no—
231C22⋊C8—221no—
232#95—21no—
233#95—21no—
234#95—111no—
235#95—111no—
236#95—221no—
237#95—221no—
238C2×C11—21no—
239C2×C11—21no—
240C2×C11#160411yescharacteristic
241C2×C11#219711yescharacteristic
242C2×C11#220411yescharacteristic
243D11—82no—
244C24—221no—
245C2×Q8—21no—
246C2×Q8—21no—
247C2×D4—441no—
248C2×D4—442no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—442no—
255C22×C4—442no—
256C22×C4—442no—
257C22×C4D4×D1111yescharacteristic
258C22×C4D4×D1111yescharacteristic
259C22×C4C2×C22⋊D1111yescharacteristic
260SD16—882no—
261M16—22no—
262M16—41no—
263C2×C8—41no—
264C2×C8—441no—
265C2×C8—441no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—441no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—441no—
278C4⋊C4—441no—
279C22⋊C4—41no—
280C22⋊C4—442no—
281C22⋊C4—442no—
282C22⋊C4—442no—
283C22⋊C4—441no—
284C22⋊C4—441no—
285C22⋊C4—881no—
286C42—21no—
287C42—41no—
288C42—442no—
289C42#432512yescomplemented
290C11#1224811yescharacteristic, complemented, Sylow
291C23—222no—
292C23—441no—
293C23—441no—
294C23—441no—
295C23—441no—
296C23—441no—
297C23—441no—
298C23#6699011yescharacteristic
299Q8—81no—
300Q8—81no—
301D4—442no—
302D4—881no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—222no—
318C2×C4—448no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—441no—
324C2×C4—441no—
325C2×C4—441no—
326C2×C4—441no—
327C2×C4C2×#432511yescharacteristic
328C2×C4#6700211yescharacteristic
329C8—42no—
330C8—881no—
331C8—881no—
332C22—21no—
333C22—21no—
334C22—442no—
335C22—442no—
336C22—442no—
337C22—881no—
338C22—881no—
339C22—881no—
340C22—881no—
341C22#1062264511yescharacteristic
342C22#1062265911yescharacteristic
343C22#1062270811yescharacteristic
344C4—21no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—41no—
349C4—81no—
350C4—81no—
351C4—81no—
352C4—442no—
353C4—881no—
354C4—881no—
355C2—21no—
356C2—21no—
357C2—882no—
358C2#1306758411yescharacteristic
359C2#1307060511yescharacteristic
360C2#1307064011yescharacteristic
subgroupG/H
centerC22#10622645
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#2061C2
socleC22×C11B(4,𝔽2)
prime radicalC22×D44D4
hypercenter#2061D11
hypocenterC11#12248
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2061

Complements

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

NH ≅ G/Ntype
2. #13067624C2semidirect
4. #13066621C2semidirect
6. #13066560C2semidirect
7. C11×#2061C2semidirect
95. C42×C11SD16semidirect
112. #2061D11semidirect
289. C42#4325semidirect
290. C11#12248semidirect

Maximal subgroups

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

subgroupindex
#130742932
#130676242
#130675562
#130666212
#130666182
#130665602
C11×#20612
#1224811