Finite Group Databasebeta

← #14656966

Subgroups — #14656966

Order 2816.

390 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 73 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#13074273C211yesmaximal, characteristic, complemented
2#13069535C211yesmaximal, characteristic
3#13067164C211yesmaximal, characteristic
4#13067123C211yesmaximal, characteristic
5#13066481C211yesmaximal, characteristic, complemented
6#13066471C211yesmaximal, characteristic, complemented
7C11×#1300C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C11×#432C2211yescharacteristic
10C4×C11×M16C2211yescharacteristic
11C11×#376C2211yescharacteristic
12C2×#66889—21no—
13C2×#66889—21no—
14#10622550C2211yescharacteristic
15C4×C4⋊Dic11C2211yescharacteristic
16#10622546—21no—
17#10622541—21no—
18#10622539C2211yescharacteristic
19#10622274—21no—
20#10622270—21no—
21#10622267—21no—
22#10622260—21no—
23#10622108—21no—
24#10622108—21no—
25#10622089—21no—
26#10622089—21no—
27C2×#4339—21no—
28C2×C11×M16—21no—
29C2×C42×C11—21no—
30C2×C42×C11C2311yescharacteristic
31#66983—21no—
32#66983—21no—
33C2×C4⋊Dic11—21no—
34C2×C4⋊Dic11—21no—
35C2×C4⋊Dic11—21no—
36C2×Dic11⋊C4—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×C4×Dic11D411yescharacteristic
41C2×C4×Dic11D411yescharacteristic
42#66928—21no—
43#66927Q811yescharacteristic
44C4×D44—21no—
45C4×D44—21no—
46#66922Q811yescharacteristic
47C11×C4⋊C8—21no—
48C11×C22⋊C8—21no—
49C11×#97—21no—
50C11×#97—21no—
51C4×C8×C11—21no—
52C11×#95—21no—
53C11×#95D411yescharacteristic
54C11×#95D411yescharacteristic
55C11⋊#95—21no—
56C11⋊#95—21no—
57C11⋊#95—21no—
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95D411yescharacteristic
61C11⋊#95D411yescharacteristic
62C22⋊(C11⋊C8)—21no—
63#66889—42no—
64#66889—42no—
65C4⋊(C11⋊C8)—21no—
66#66867—21no—
67#10380—111nomaximal, Sylow
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—41no—
74C22×Dic11—21no—
75C22×Dic11—21no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78#4339—41no—
79#4339—41no—
80#4339—41no—
81#4339—41no—
82C2×D44—21no—
83C2×D44—21no—
84C2×D44—21no—
85C2×C4×D11—41no—
86C2×Dic22—21no—
87C11×M16—22no—
88C11×M16—41no—
89C2×C8×C11—41no—
90C2×C8×C11—41no—
91C42×C11—42no—
92C42×C11C2×Q811yescharacteristic
93C42×C11#4111yescharacteristic
94C42×C11#4111yescharacteristic
95C42×C11#4111yescharacteristic
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98C4⋊Dic11—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11—42no—
101C4⋊Dic11—42no—
102C4⋊Dic11—42no—
103Dic11⋊C4—42no—
104Dic11⋊C4—42no—
105Dic11⋊C4—81no—
106Dic11⋊C4—81no—
107C4×Dic11—41no—
108C4×Dic11—41no—
109C2×C11⋊C8—41no—
110#2606—111no—
111#1980—111no—
112#1514—111no—
113#1505—111no—
114#1300D1111yescharacteristic, complemented
115#1288—111no—
116#1285—111no—
117C23×C11#12011yescharacteristic
118C22×D11—41no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—22no—
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×C11C22⋊Q811yescharacteristic
130C2×C4×C11C22⋊Q811yescharacteristic
131C2×C4×C11C22⋊Q811yescharacteristic
132C2×C4×C11#12411yescharacteristic
133C2×C4×C11#12411yescharacteristic
134C2×C4×C11#12411yescharacteristic
135C22⋊D11—81no—
136C22⋊D11—81no—
137C2×Dic11—22no—
138C2×Dic11—41no—
139C2×Dic11—41no—
140C2×Dic11—41no—
141C2×Dic11—41no—
142C2×Dic11—41no—
143C2×Dic11—41no—
144C2×Dic11—41no—
145C2×Dic11—41no—
146C2×Dic11—41no—
147C2×Dic11—41no—
148C2×Dic11—41no—
149C2×Dic11—41no—
150D44—41no—
151D44—41no—
152D44—81no—
153D44—81no—
154C4×D11—81no—
155C4×D11—81no—
156Dic22—41no—
157Dic22—41no—
158C8×C11—42no—
159C8×C11—81no—
160C11⋊C8—81no—
161#532—111no—
162#432—111no—
163#432C2×D1111yescharacteristic
164C2×#104—221no—
165C2×#104—221no—
166C4×M16C2×D1111yescharacteristic
167#398—221no—
168#398—221no—
169#389—221no—
170#389—221no—
171#387—221no—
172#387—221no—
173#383—111no—
174C4×C4⋊C4—111no—
175#376C2×D1111yescharacteristic
176#327—221no—
177#327—221no—
178#327—221no—
179#327—221no—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11#39311yescharacteristic
183C22×C11#45311yescharacteristic
184C22×C11#45411yescharacteristic
185C2×D11—81no—
186C2×D11—81no—
187C2×D11—81no—
188C4×C11—21no—
189C4×C11—21no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11—21no—
193C4×C11—21no—
194C4×C11—42no—
195C4×C11—81no—
196Dic11—42no—
197Dic11—81no—
198Dic11—81no—
199Dic11—81no—
200Dic11—81no—
201C2×#41—221no—
202C2×M16—21no—
203C4⋊Q8—111no—
204#127—111no—
205#124—221no—
206#121—221no—
207#121—221no—
208C4×D4—221no—
209C4×D4—221no—
210C2×C4⋊C4—221no—
211C2×C4⋊C4—221no—
212C2×C4⋊C4—221no—
213C2×C4⋊C4—221no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4—221no—
216C2×C4⋊C4—221no—
217C2×C42—21no—
218C2×C42—111no—
219C2×C42—111no—
220C2×C42C22×D1111yescharacteristic
221C4⋊C8—21no—
222C4⋊C8—221no—
223#104—442no—
224#104—442no—
225C22⋊C8—21no—
226C22⋊C8—221no—
227#97—21no—
228#97—21no—
229#97—221no—
230C4×C8—21no—
231#95—21no—
232#95—111no—
233#95—111no—
234#95—221no—
235#95—221no—
236#95—221no—
237#95—221no—
238#95—221no—
239#95D4411yescharacteristic
240#95D4411yescharacteristic
241C2×C11—21no—
242C2×C11—21no—
243C2×C11#202711yescharacteristic
244C2×C11#203111yescharacteristic
245C2×C11#203111yescharacteristic
246D11—161no—
247#41—441no—
248#41—441no—
249#41—441no—
250#41—441no—
251C2×Q8—221no—
252C2×D4—221no—
253C2×D4—221no—
254C2×D4—221no—
255C2×D4—441no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—221no—
259C22×C4—221no—
260C22×C4—221no—
261C22×C4—221no—
262C22×C4—441no—
263C22×C4C2×D4411yescharacteristic
264C22×C4D4×D1111yescharacteristic
265C22×C4D4×D1111yescharacteristic
266M16—22no—
267M16—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—441no—
271C4⋊C4—221no—
272C4⋊C4—221no—
273C4⋊C4—442no—
274C4⋊C4—442no—
275C4⋊C4—442no—
276C4⋊C4—442no—
277C4⋊C4—442no—
278C4⋊C4—881no—
279C4⋊C4—881no—
280C22⋊C4—441no—
281C22⋊C4—441no—
282C42—42no—
283C42—441no—
284C42—441no—
285C42#433911yescharacteristic
286C42#433911yescharacteristic
287C42#434111yescharacteristic
288C42Q8×D1111yescharacteristic
289C11#1038011yescharacteristic, complemented, Sylow
290C23—441no—
291C23#6693511yescharacteristic
292Q8—441no—
293Q8—441no—
294D4—441no—
295D4—441no—
296D4—881no—
297D4—881no—
298D4—881no—
299D4—881no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—222no—
311C2×C4—441no—
312C2×C4—441no—
313C2×C4—441no—
314C2×C4—441no—
315C2×C4—441no—
316C2×C4—441no—
317C2×C4—441no—
318C2×C4—441no—
319C2×C4—441no—
320C2×C4—441no—
321C2×C4—441no—
322C2×C4—441no—
323C2×C4—881no—
324C2×C4—881no—
325C2×C4#6692811yescharacteristic
326C2×C4#6693811yescharacteristic
327C2×C4#6693811yescharacteristic
328C2×C4#6694911yescharacteristic
329C2×C4#6694911yescharacteristic
330C2×C4#6695011yescharacteristic
331C8—42no—
332C8—81no—
333C8—881no—
334C22—21no—
335C22—21no—
336C22—881no—
337C22—881no—
338C22—881no—
339C22#1062228611yescharacteristic
340C22#1062243511yescharacteristic
341C22#1062244011yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—42no—
349C4—81no—
350C4—442no—
351C4—881no—
352C4—881no—
353C4—881no—
354C4—881no—
355C2—21no—
356C2—21no—
357C2—1761no—
358C2#1306977111yescharacteristic
359C2#1306978911yescharacteristic
360C2#1306979111yescharacteristic
subgroupG/H
centerC22#10622286
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1300C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1300D11
hypocenterC11#10380
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1300

Complements

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

NH ≅ G/Ntype
1. #13074273C2semidirect
5. #13066481C2semidirect
6. #13066471C2semidirect
7. C11×#1300C2semidirect
114. #1300D11semidirect
289. C11#10380semidirect

Maximal subgroups

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

subgroupindex
#130742732
#130695352
#130671642
#130671232
#130664812
#130664712
C11×#13002
#1038011