Finite Group Databasebeta

← #14666113

Subgroups — #14666113

Order 2816.

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

normal subgroups only

This group has 354 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#13076436C211yesmaximal, characteristic, complemented
2#13069840C211yesmaximal, characteristic
3#13067655C211yesmaximal, characteristic
4#13067621C211yesmaximal, characteristic
5#13066644C211yesmaximal, characteristic, complemented
6#13066623C211yesmaximal, characteristic, complemented
7C11×#1325C211yesmaximal, characteristic, complemented
8#10623041C2211yescharacteristic
9C11×#384C2211yescharacteristic
10#10622599C2211yescharacteristic
11#10622596C2211yescharacteristic
12#10622595—21no—
13#10622595—21no—
14#10622594—21no—
15#10622594—21no—
16#10622591—21no—
17#10622579—21no—
18#10622546—21no—
19C2×#66869—21no—
20#10622349—21no—
21#10622348—21no—
22C11×#324C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622108—21no—
26#10622108—21no—
27C2×#4339—21no—
28C2×C11×C4⋊C4—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32C2×C42×C11D411yescharacteristic
33#66983—21no—
34#66983—21no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×C4×Dic11—21no—
40C2×#4318—21no—
41#66950—41no—
42#66948—41no—
43C11×C22⋊C8—21no—
44C11×C22⋊C8—21no—
45C11⋊#95—21no—
46C11⋊#95—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95D411yescharacteristic
55C11⋊#95D411yescharacteristic
56#66885—41no—
57#66885—41no—
58#66882—41no—
59#66881—41no—
60#66874—41no—
61#66873—41no—
62#66869—42no—
63#12142—111nomaximal, Sylow
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11C2×D411yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C22×C4×C11C2×D411yescharacteristic
69C2×C22⋊D11—41no—
70C22×Dic11—21no—
71C22×Dic11—21no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74#4339—41no—
75#4339—41no—
76#4339—41no—
77#4339—41no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×C4×D11—41no—
82C2×Dic22—21no—
83C2×C8×C11—41no—
84C2×C8×C11—41no—
85C11×C4⋊C4—41no—
86C11×C4⋊C4—42no—
87C11×C4⋊C4—42no—
88C11×C4⋊C4—41no—
89C42×C11—21no—
90C42×C11—21no—
91(C2×D11)⋊C4—41no—
92(C2×D11)⋊C4—41no—
93C4⋊Dic11—21no—
94C4⋊Dic11—21no—
95C4⋊Dic11—41no—
96C4⋊Dic11—41no—
97Dic11⋊C4—42no—
98Dic11⋊C4—41no—
99Dic11⋊C4—41no—
100C4×Dic11—81no—
101#4318—41no—
102#4318—41no—
103C2×C11⋊C8—41no—
104#2794—111no—
105#2039—111no—
106#1616—111no—
107#1610—111no—
108#1353—111no—
109#1346—111no—
110#1325D1111yescharacteristic, complemented
111C23×C11#12011yescharacteristic
112C22×D11—41no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—22no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11#13511yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C22⋊D11—81no—
128C22⋊D11—81no—
129C2×Dic11—41no—
130C2×Dic11—41no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—42no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141D44—41no—
142D44—41no—
143D44—81no—
144D44—81no—
145C4×D11—81no—
146C4×D11—81no—
147Dic22—41no—
148Dic22—41no—
149C8×C11—81no—
150C8×C11—81no—
151C11⋊C8—81no—
152#537—111no—
153#481—221no—
154#480—221no—
155C2×#104—221no—
156#417—221no—
157#400—111no—
158#400—221no—
159#400—221no—
160#398—111no—
161#387—221no—
162#387—221no—
163#387—221no—
164#387—221no—
165#384C2×D1111yescharacteristic
166#343—111no—
167#327—221no—
168#327—221no—
169#324C2×D1111yescharacteristic
170#324C2×D1111yescharacteristic
171C22×C11—21no—
172C22×C11—21no—
173C22×C11#44911yescharacteristic
174C22×C11#45411yescharacteristic
175C22×C11B(4,𝔽2)11yescharacteristic
176C2×D11—81no—
177C2×D11—81no—
178C2×D11—81no—
179C4×C11—21no—
180C4×C11—21no—
181C4×C11—42no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—81no—
185Dic11—81no—
186Dic11—81no—
187Dic11—81no—
188Dic11—81no—
189Dic11—81no—
190C2×#41—221no—
191C2×M16—221no—
192C22⋊Q8—441no—
193#121—221no—
194#121—221no—
195#121—441no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—111no—
199C2×C4⋊C4—111no—
200C2×C4⋊C4—221no—
201C2×C4⋊C4—221no—
202C2×C4⋊C4D4411yescharacteristic
203C2×C4⋊C4C22×D1111yescharacteristic
204C2×C42—221no—
205C2×C42D4411yescharacteristic
206#107—441no—
207#106—441no—
208#104—442no—
209#103—441no—
210#102—441no—
211#102—441no—
212#102—441no—
213C22⋊C8—21no—
214C22⋊C8—21no—
215#95—111no—
216#95—111no—
217#95—221no—
218#95—221no—
219#95—221no—
220#95—221no—
221#95—221no—
222#95—221no—
223#95—221no—
224#95—221no—
225#95—221no—
226C2×C11—21no—
227C2×C11—21no—
228C2×C11#159711yescharacteristic
229C2×C11#219811yescharacteristic
230C2×C11#220311yescharacteristic
231D11—161no—
232#41—441no—
233#41—441no—
234#41—441no—
235#41—441no—
236C2×Q8—221no—
237C2×D4—221no—
238C2×D4—221no—
239C2×D4—221no—
240C2×D4—441no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—221no—
244C22×C4—221no—
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—441no—
248C22×C4C2×D4411yescharacteristic
249C22×C4D4×D1111yescharacteristic
250C22×C4D4×D1111yescharacteristic
251M16—441no—
252M16—441no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—441no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—221no—
261C4⋊C4—221no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—442no—
265C4⋊C4—441no—
266C4⋊C4—441no—
267C22⋊C4—441no—
268C22⋊C4—441no—
269C42—21no—
270C42—21no—
271C42—881no—
272C11#1214211yescharacteristic, complemented, Sylow
273C23—441no—
274C23#6693511yescharacteristic
275Q8—441no—
276Q8—441no—
277D4—441no—
278D4—441no—
279D4—881no—
280D4—881no—
281D4—881no—
282D4—881no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—441no—
296C2×C4—441no—
297C2×C4—441no—
298C2×C4—441no—
299C2×C4—442no—
300C2×C4—441no—
301C2×C4—441no—
302C2×C4—441no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4#6695711yescharacteristic
310C2×C4#6696111yescharacteristic
311C8—81no—
312C8—81no—
313C8—881no—
314C22—21no—
315C22—21no—
316C22—881no—
317C22—881no—
318C22—881no—
319C22#1062234711yescharacteristic
320C22#1062235411yescharacteristic
321C22#1062236611yescharacteristic
322C4—21no—
323C4—21no—
324C4—42no—
325C4—41no—
326C4—41no—
327C4—81no—
328C4—881no—
329C4—881no—
330C4—881no—
331C4—881no—
332C4—881no—
333C2—21no—
334C2—21no—
335C2—1761no—
336C2#1306754711yescharacteristic
337C2#1307061411yescharacteristic
338C2#1307063811yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1325C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#1325D11
hypocenterC11#12142
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1325

Complements

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

NH ≅ G/Ntype
1. #13076436C2semidirect
5. #13066644C2semidirect
6. #13066623C2semidirect
7. C11×#1325C2semidirect
110. #1325D11semidirect
272. C11#12142semidirect

Maximal subgroups

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

subgroupindex
#130764362
#130698402
#130676552
#130676212
#130666442
#130666232
C11×#13252
#1214211