Finite Group Databasebeta

← #14666364

Subgroups — #14666364

Order 2816.

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

normal subgroups only

This group has 362 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#13076885C211yesmaximal, characteristic, complemented
2#13069840C211yesmaximal, characteristic
3#13067655C211yesmaximal, characteristic
4#13067587C211yesmaximal, characteristic
5#13066647C211yesmaximal, characteristic, complemented
6#13066644C211yesmaximal, characteristic, complemented
7C11×#1325C211yesmaximal, characteristic, complemented
8#10623041C2211yescharacteristic
9C11×#384C2211yescharacteristic
10#10622599—21no—
11#10622599C2211yescharacteristic
12#10622597—21no—
13#10622597—21no—
14#10622597—21no—
15#10622592—21no—
16#10622592C2211yescharacteristic
17#10622579—21no—
18#10622550—21no—
19C2×#66869—21no—
20#10622351—21no—
21#10622348—21no—
22C11×#324C2211yescharacteristic
23C11×#324C2211yescharacteristic
24#10622168C2211yescharacteristic
25#10622108—21no—
26#10622108—21no—
27C2×#4339—21no—
28C22×Dic22D411yescharacteristic
29C2×C11×C4⋊C4—21no—
30C2×C11×C4⋊C4—21no—
31C2×C11×C4⋊C4D411yescharacteristic
32C2×C11×C4⋊C4C2311yescharacteristic
33C2×C42×C11D411yescharacteristic
34#66983—21no—
35#66983—21no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11D411yescharacteristic
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×#4318—21no—
42C2×#4314—41no—
43#66950—41no—
44#66948—41no—
45C11×C22⋊C8—21no—
46C11×C22⋊C8—21no—
47C11⋊#95—21no—
48C11⋊#95—21no—
49C11⋊#95—21no—
50C11⋊#95—21no—
51C11⋊#95—21no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95D411yescharacteristic
56C11⋊#95D411yescharacteristic
57#66885—41no—
58#66881—41no—
59#66880—41no—
60#66874—41no—
61#66873—41no—
62#66869—42no—
63#12183—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×Dic22—41no—
84C2×Dic22—81no—
85C2×C8×C11—41no—
86C2×C8×C11—41no—
87C11×C4⋊C4—41no—
88C11×C4⋊C4—41no—
89C11×C4⋊C4—81no—
90C11×C4⋊C4—81no—
91C42×C11—21no—
92C42×C11SD1612yescomplemented
93(C2×D11)⋊C4—41no—
94(C2×D11)⋊C4—41no—
95C4⋊Dic11—21no—
96C4⋊Dic11—21no—
97C4⋊Dic11—41no—
98C4⋊Dic11—81no—
99Dic11⋊C4—81no—
100Dic11⋊C4—81no—
101Dic11⋊C4—81no—
102#4318—41no—
103#4318—41no—
104C2×C11⋊C8—41no—
105#4314—82no—
106#2843—111no—
107#2039—111no—
108#1616—111no—
109#1604—111no—
110#1354—111no—
111#1353—111no—
112#1325D1111yescharacteristic, complemented
113C23×C11#12011yescharacteristic
114C22×D11—41no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—22no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11—41no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—41no—
124C2×C4×C11—41no—
125C2×C4×C11—41no—
126C2×C4×C11—41no—
127C2×C4×C11C2×SD1611yescharacteristic
128C2×C4×C11#13711yescharacteristic
129C22⋊D11—81no—
130C22⋊D11—81no—
131C2×Dic11—41no—
132C2×Dic11—41no—
133C2×Dic11—41no—
134C2×Dic11—41no—
135C2×Dic11—41no—
136C2×Dic11—41no—
137C2×Dic11—42no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143D44—41no—
144D44—41no—
145D44—81no—
146D44—81no—
147C4×D11—81no—
148C4×D11—81no—
149Dic22—41no—
150Dic22—41no—
151Dic22—42no—
152Dic22—81no—
153C8×C11—81no—
154C8×C11—81no—
155C11⋊C8—81no—
156#537—111no—
157#481—221no—
158#448—221no—
159C2×#104—221no—
160#417—221no—
161#400—111no—
162#400—221no—
163#398—221no—
164#398—221no—
165#398—221no—
166#395—111no—
167#395—221no—
168#384C2×D1111yescharacteristic
169#383—221no—
170#343—111no—
171#327—221no—
172#327—221no—
173#324C2×D1111yescharacteristic
174#324C2×D1111yescharacteristic
175C22×C11—21no—
176C22×C11—21no—
177C22×C11#44811yescharacteristic
178C22×C11#45411yescharacteristic
179C22×C11B(4,𝔽2)11yescharacteristic
180C2×D11—81no—
181C2×D11—81no—
182C2×D11—81no—
183C4×C11—21no—
184C4×C11—21no—
185C4×C11—42no—
186C4×C11—41no—
187C4×C11—41no—
188C4×C11—81no—
189Dic11—81no—
190Dic11—81no—
191Dic11—81no—
192Dic11—81no—
193Dic11—81no—
194C2×#41—221no—
195C22×Q8—111no—
196C2×SD16—441no—
197C2×M16—221no—
198C22⋊Q8—441no—
199#121—221no—
200#121—221no—
201#121—441no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—111no—
205C2×C4⋊C4—221no—
206C2×C4⋊C4—221no—
207C2×C4⋊C4—221no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4D4411yescharacteristic
210C2×C4⋊C4C22×D1111yescharacteristic
211C2×C42D4411yescharacteristic
212#106—441no—
213#104—442no—
214#103—441no—
215#103—441no—
216#102—441no—
217#102—441no—
218C22⋊C8—21no—
219C22⋊C8—21no—
220#95—111no—
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—221no—
230C2×C11—21no—
231C2×C11—21no—
232C2×C11#159911yescharacteristic
233C2×C11#220011yescharacteristic
234C2×C11#220311yescharacteristic
235D11—161no—
236#41—441no—
237#41—441no—
238#41—441no—
239#41—441no—
240C2×Q8—221no—
241C2×Q8—441no—
242C2×Q8—881no—
243C2×D4—221no—
244C2×D4—221no—
245C2×D4—221no—
246C2×D4—441no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4—221no—
252C22×C4—221no—
253C22×C4—441no—
254C22×C4C2×D4411yescharacteristic
255C22×C4D4×D1111yescharacteristic
256C22×C4D4×D1111yescharacteristic
257SD16—882no—
258M16—441no—
259M16—441no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—441no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—441no—
270C4⋊C4—881no—
271C4⋊C4—881no—
272C4⋊C4—881no—
273C4⋊C4—881no—
274C22⋊C4—441no—
275C22⋊C4—441no—
276C42—21no—
277C42#431412yescomplemented
278C11#1218311yescharacteristic, complemented, Sylow
279C23—441no—
280C23#6693511yescharacteristic
281Q8—441no—
282Q8—441no—
283Q8—442no—
284Q8—881no—
285D4—441no—
286D4—441no—
287D4—881no—
288D4—881no—
289D4—881no—
290D4—881no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—441no—
304C2×C4—441no—
305C2×C4—441no—
306C2×C4—441no—
307C2×C4—441no—
308C2×C4—441no—
309C2×C4—442no—
310C2×C4—441no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—881no—
316C2×C4—881no—
317C2×C4C2×#431411yescharacteristic
318C2×C4#6696211yescharacteristic
319C8—81no—
320C8—81no—
321C8—881no—
322C22—21no—
323C22—21no—
324C22—881no—
325C22—881no—
326C22—881no—
327C22#1062235111yescharacteristic
328C22#1062235411yescharacteristic
329C22#1062236611yescharacteristic
330C4—21no—
331C4—21no—
332C4—42no—
333C4—41no—
334C4—41no—
335C4—81no—
336C4—881no—
337C4—881no—
338C4—881no—
339C4—881no—
340C4—881no—
341C2—21no—
342C2—21no—
343C2—1761no—
344C2#1306755811yescharacteristic
345C2#1307062611yescharacteristic
346C2#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#12183
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. #13076885C2semidirect
5. #13066647C2semidirect
6. #13066644C2semidirect
7. C11×#1325C2semidirect
92. C42×C11SD16semidirect
112. #1325D11semidirect
277. C42#4314semidirect
278. C11#12183semidirect

Maximal subgroups

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

subgroupindex
#130768852
#130698402
#130676552
#130675872
#130666472
#130666442
C11×#13252
#1218311