Finite Group Databasebeta

← #14666210

Subgroups — #14666210

Order 2816.

372 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 57 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#13076682C211yesmaximal, characteristic, complemented
2#13069846C211yesmaximal, characteristic
3#13067621C211yesmaximal, characteristic
4#13067618C211yesmaximal, characteristic
5#13066621C211yesmaximal, characteristic, complemented
6#13066559C211yesmaximal, characteristic, complemented
7C11×#1346C211yesmaximal, characteristic, complemented
8#10623041C2211yescharacteristic
9C2×#66942—21no—
10C11×#398C2211yescharacteristic
11C2×#66889—21no—
12#10622746—21no—
13#10622597—21no—
14#10622597—21no—
15#10622596C2211yescharacteristic
16#10622590C2211yescharacteristic
17#10622580—21no—
18#10622349—21no—
19#10622273—21no—
20#10622271—21no—
21#10622270—21no—
22C11×#343C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622166C2211yescharacteristic
25#10622108—21no—
26#10622089—21no—
27C2×#4339—21no—
28C2×C11×M16—21no—
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C4⋊C4C2311yescharacteristic
32#66983—21no—
33#66983—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11D411yescharacteristic
36C2×C4⋊Dic11D411yescharacteristic
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×Dic11⋊C4—21no—
42C2×C4×Dic11D411yescharacteristic
43#66950—41no—
44#66948—41no—
45#66942—42no—
46#66942—42no—
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⋊#95D411yescharacteristic
57C22⋊(C11⋊C8)—21no—
58#66889—42no—
59#66885—41no—
60#66885—41no—
61#66882—41no—
62#66880—41no—
63#66873—41no—
64#66871—41no—
65#12157—111nomaximal, Sylow
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11C2×D411yescharacteristic
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C2×C22⋊D11—41no—
72C22×Dic11—21no—
73C22×Dic11—21no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76#4339—41no—
77#4339—41no—
78#4339—41no—
79#4339—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×C4×D11—41no—
84C2×Dic22—21no—
85C11×M16—41no—
86C11×M16—41no—
87C2×C8×C11—41no—
88C2×C8×C11—41no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—41no—
98C4⋊Dic11—41no—
99C4⋊Dic11—42no—
100Dic11⋊C4—42no—
101Dic11⋊C4—42no—
102Dic11⋊C4—42no—
103Dic11⋊C4—41no—
104Dic11⋊C4—41no—
105Dic11⋊C4—81no—
106C4×Dic11—21no—
107C4×Dic11D812yes—
108C2×C11⋊C8—41no—
109#2822—111no—
110#2040—111no—
111#1610—111no—
112#1610—111no—
113#1346—111no—
114#1346D1111yescharacteristic, complemented
115#1324—111no—
116C23×C11#12011yescharacteristic
117C22×D11—41no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
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×C11C2×D811yescharacteristic
131C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
132C22⋊D11—81no—
133C22⋊D11—81no—
134C2×Dic11—22no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—41no—
138C2×Dic11—41no—
139C2×Dic11—42no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146D44—41no—
147D44—41no—
148D44—81no—
149D44—81no—
150C4×D11—81no—
151C4×D11—81no—
152Dic22—41no—
153Dic22—41no—
154C8×C11—81no—
155C8×C11—81no—
156C11⋊C8—81no—
157#537—111no—
158C2×#125—221no—
159#480—221no—
160#480—221no—
161C2×#104—221no—
162#417—221no—
163#400—221no—
164#400—221no—
165#398—111no—
166#398—221no—
167#398—221no—
168#398—221no—
169#398C2×D1111yescharacteristic
170#382—111no—
171#343C2×D1111yescharacteristic
172#327—221no—
173#327—221no—
174#324—111no—
175#324C2×D1111yescharacteristic
176C22×C11—21no—
177C22×C11—21no—
178C22×C11#44711yescharacteristic
179C22×C11#45411yescharacteristic
180C22×C11B(4,𝔽2)11yescharacteristic
181C2×D11—81no—
182C2×D11—81no—
183C2×D11—81no—
184C4×C11—21no—
185C4×C11—21no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—81no—
189C4×C11—81no—
190Dic11—42no—
191Dic11—81no—
192Dic11—81no—
193Dic11—81no—
194Dic11—81no—
195C2×#41—221no—
196C2×M16—21no—
197#125—442no—
198#125—442no—
199C22⋊Q8—441no—
200#121—221no—
201#121—221no—
202#121—441no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—111no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4D4411yescharacteristic
213C2×C4⋊C4C22×D1111yescharacteristic
214C2×C42—111no—
215#107—441no—
216#107—441no—
217#104—442no—
218#103—441no—
219#102—441no—
220#102—441no—
221#102—441no—
222C22⋊C8—21no—
223C22⋊C8—221no—
224#95—21no—
225#95—111no—
226#95—221no—
227#95—221no—
228#95—221no—
229#95—221no—
230#95—221no—
231#95—221no—
232#95D4411yescharacteristic
233C2×C11—21no—
234C2×C11—21no—
235C2×C11#159811yescharacteristic
236C2×C11#220111yescharacteristic
237C2×C11#220311yescharacteristic
238D11—161no—
239#41—441no—
240#41—441no—
241#41—441no—
242#41—441no—
243C2×Q8—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—221no—
247C2×D4—441no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—221no—
254C22×C4—441no—
255C22×C4C2×D4411yescharacteristic
256C22×C4D4×D1111yescharacteristic
257C22×C4D4×D1111yescharacteristic
258M16—41no—
259M16—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—441no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—441no—
270C4⋊C4—441no—
271C4⋊C4—442no—
272C4⋊C4—442no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—441no—
276C4⋊C4—441no—
277C4⋊C4—881no—
278C22⋊C4—441no—
279C22⋊C4—441no—
280C42—112no—
281C42—221no—
282C11#1215711yescharacteristic, complemented, Sylow
283C23—441no—
284C23#6693511yescharacteristic
285Q8—441no—
286Q8—441no—
287D4—441no—
288D4—441no—
289D4—881no—
290D4—881no—
291D4—881no—
292D4—881no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—222no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—441no—
310C2×C4—442no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4D8×D1111yescharacteristic
320C2×C4#6696711yescharacteristic
321C8—81no—
322C8—81no—
323C8—881no—
324C22—21no—
325C22—21no—
326C22—881no—
327C22—881no—
328C22—881no—
329C22#1062235411yescharacteristic
330C22#1062238611yescharacteristic
331C22#1062244011yescharacteristic
332C4—21no—
333C4—21no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—442no—
339C4—881no—
340C4—881no—
341C4—881no—
342C4—881no—
343C2—21no—
344C2—21no—
345C2—1761no—
346C2#1306755211yescharacteristic
347C2#1307063011yescharacteristic
348C2#1307063811yescharacteristic
subgroupG/H
centerC22#10622354
commutator, cosocleC2×C11×C4⋊C4C23
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1346C2
socleC22×C11B(4,𝔽2)
prime radical#10623041C22
hypercenter#1346D11
hypocenterC11#12157
LCSG ▷ C2×C11×C4⋊C4 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #1346

Complements

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

NH ≅ G/Ntype
1. #13076682C2semidirect
5. #13066621C2semidirect
6. #13066559C2semidirect
7. C11×#1346C2semidirect
114. #1346D11semidirect
282. C11#12157semidirect

Maximal subgroups

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

subgroupindex
#130766822
#130698462
#130676212
#130676182
#130666212
#130665592
C11×#13462
#1215711