Finite Group Databasebeta

← #14664713

Subgroups — #14664713

Order 2816.

378 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 89 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#13079190C211yesmaximal, characteristic
2#13070412C211yesmaximal, characteristic, complemented
3#13068742C211yesmaximal, characteristic, complemented
4#13066626C211yesmaximal, characteristic, complemented
5#13066625C211yesmaximal, characteristic, complemented
6#13066624C211yesmaximal, characteristic, complemented
7C11×#1347C211yesmaximal, characteristic, complemented
8#10623127—21no—
9C11×#466C2211yescharacteristic
10#10622764C411yescharacteristic, complemented
11D8×Dic11C411yescharacteristic, complemented
12#10622728C2211yescharacteristic
13C2×C8×Dic11C2211yescharacteristic
14#10622651—21no—
15#10622589—21no—
16#10622487C411yescharacteristic, complemented
17#10622485C411yescharacteristic, complemented
18#10622373—21no—
19#10622369—21no—
20C11×C22⋊C16C2211yescharacteristic
21C11×#340C2211yescharacteristic
22#10622189C2211yescharacteristic
23C22⋊(C11⋊C16)C2211yescharacteristic
24#10622167—21no—
25Dic11⋊C16—21no—
26C16×Dic11—21no—
27C2×#4341—41no—
28C2×C11×D8C2×C411yescharacteristic
29C22×C8×C11C2311yescharacteristic
30C11×#121—21no—
31C2×C11×C4⋊C4—21no—
32#66993—21no—
33#66992—41no—
34D4×Dic11—21no—
35C2×#4323—21no—
36#66983—21no—
37C2×C4⋊Dic11—21no—
38C2×Dic11⋊C4—41no—
39C2×Dic11⋊C4—41no—
40C2×C4×Dic11D411yescharacteristic
41C22×C11⋊C8D411yescharacteristic
42C2×D88C2×C411yescharacteristic
43#66946—21no—
44#66941—21no—
45#66938—41no—
46(C22⋊D11)⋊C4—41no—
47C2×C11×C16—21no—
48C11×#107C2×C411yescharacteristic
49C11×#102—21no—
50#66896—21no—
51#66885—21no—
52#66882C2×C411yescharacteristic
53C8×Dic11C2×C411yescharacteristic
54C8×Dic11C2×C411yescharacteristic
55C8×Dic11D411yescharacteristic
56C8×Dic11D411yescharacteristic
57C2×C11⋊C16—21no—
58#66873—21no—
59#66871—21no—
60#11856—111nomaximal, Sylow
61C2×D4×C11—21no—
62C2×D4×C11—41no—
63C22×C4×C11—41no—
64C22×C4×C11C2×D411yescharacteristic
65C2×C22⋊D11—41no—
66C2×C22⋊D11—41no—
67C2×C22⋊D11—41no—
68C22×Dic11—41no—
69C22×Dic11—41no—
70C22×Dic11D811yescharacteristic
71C22×Dic11D811yescharacteristic
72#4341—82no—
73#4341—82no—
74C2×D44—21no—
75C2×C4×D11—41no—
76C2×Dic22—41no—
77C11×D8—41no—
78C2×C8×C11—41no—
79C2×C8×C11C22×C411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4—41no—
83C11×C4⋊C4—41no—
84C11×C22⋊C4—41no—
85C22⋊Dic11—41no—
86#4323—42no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89C4⋊Dic11—21no—
90C4⋊Dic11—41no—
91C4⋊Dic11—41no—
92Dic11⋊C4—41no—
93Dic11⋊C4—82no—
94Dic11⋊C4—82no—
95C4×Dic11C22⋊C411yescharacteristic
96C4×Dic11C22⋊C411yescharacteristic
97C4×Dic11SD1611yescharacteristic
98C4×Dic11SD1611yescharacteristic
99C2×C11⋊C8—41no—
100C2×C11⋊C8C22⋊C411yescharacteristic
101C2×C11⋊C8C22⋊C411yescharacteristic
102D88—41no—
103C11×C16—41no—
104C11⋊C16—41no—
105#3169—111no—
106#2162—111no—
107#1834—111no—
108#1347—111no—
109#1347—111no—
110#1347—111no—
111#1347D1111yescharacteristic, complemented
112C23×C11—41no—
113C23×C11C2×D811yescharacteristic
114C22×D11—41no—
115D4×C11—41no—
116D4×C11—41no—
117D4×C11—81no—
118D4×C11—81no—
119C2×C4×C11—21no—
120C2×C4×C11—21no—
121C2×C4×C11—41no—
122C2×C4×C11—81no—
123C2×C4×C11—81no—
124C2×C4×C11—81no—
125C2×C4×C11C2×C22⋊C411yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C22⋊D11—81no—
128C22⋊D11—81no—
129C22⋊D11—82no—
130C22⋊D11—82no—
131C2×Dic11—22no—
132C2×Dic11—41no—
133C2×Dic11—82no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11—81no—
137C2×Dic11#10211yescharacteristic
138C2×Dic11#10211yescharacteristic
139C2×Dic11#10211yescharacteristic
140C2×Dic11#10211yescharacteristic
141C2×Dic11D1612yes—
142C2×Dic11SD3212yes—
143D44—41no—
144D44—41no—
145C4×D11—82no—
146Dic22—82no—
147C8×C11—21no—
148C8×C11—21no—
149C11⋊C8—21no—
150C11⋊C8—21no—
151#532—221no—
152#500—111no—
153#493—111no—
154#486—221no—
155#466—111no—
156#466—221no—
157#466C2×D1111yescharacteristic
158C4×D8—111no—
159C4×D8—111no—
160C4×D8—221no—
161C2×C4×C8—111no—
162#384—221no—
163C4⋊C16—221no—
164C22⋊C16—111no—
165C22⋊C16C2×D1111yescharacteristic
166C4×C16—221no—
167#340—111no—
168#340—221no—
169#340C2×D1111yescharacteristic
170C22×C11—21no—
171C22×C11—21no—
172C22×C11—81no—
173C22×C11—81no—
174C22×C11—81no—
175C22×C11C2×#10211yescharacteristic
176C22×C11C2×D1611yescharacteristic
177C22×C11C2×SD3211yescharacteristic
178C2×D11—81no—
179C2×D11—81no—
180C2×D11—81no—
181C4×C11—21no—
182C4×C11—81no—
183C4×C11—161no—
184C4×C11#41011yescharacteristic
185C4×C11#42111yescharacteristic
186Dic11—21no—
187Dic11—81no—
188Dic11—161no—
189Dic11#35712yes—
190Dic11#35712yes—
191Dic11#36012yes—
192C2×#41—441no—
193C2×D8—111no—
194C2×D8—221no—
195C2×D8C4×D1111yescharacteristic
196C22×C8—111no—
197C22×C8C22×D1111yescharacteristic
198C4⋊Q8—221no—
199#127—221no—
200#124—441no—
201#121—21no—
202#121—221no—
203#121—441no—
204C4×D4—221no—
205C4×D4—221no—
206C4×D4—441no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—221no—
209C2×C4⋊C4—441no—
210C2×C4⋊C4—441no—
211C2×C42—111no—
212C2×C16—21no—
213C2×C16—221no—
214#107—111no—
215#107—221no—
216#107C4×D1111yescharacteristic
217#102—21no—
218#102—221no—
219#102—221no—
220#102—221no—
221C4×C8—111no—
222C4×C8—111no—
223C4×C8—111no—
224C4×C8—111no—
225C2×C11—21no—
226C2×C11—21no—
227C2×C11—161no—
228C2×C11#151711yescharacteristic
229C2×C11C2×#35711yescharacteristic
230C2×C11C2×#36011yescharacteristic
231D11—161no—
232#41—882no—
233#41—882no—
234C2×Q8—441no—
235C2×D4—21no—
236C2×D4—41no—
237C2×D4—221no—
238C2×D4—441no—
239C2×D4—441no—
240C2×D4—441no—
241C22×C4—41no—
242C22×C4—111no—
243C22×C4—111no—
244C22×C4—441no—
245C22×C4—441no—
246C22×C4—441no—
247C22×C4D4×D1111yescharacteristic
248D8—41no—
249D8—441no—
250D8—442no—
251C2×C8—41no—
252C2×C8—111no—
253C2×C8—111no—
254C2×C8—441no—
255C2×C8C2×C4×D1111yescharacteristic
256C2×C8D4×D1111yescharacteristic
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—221no—
261C4⋊C4—441no—
262C4⋊C4—441no—
263C4⋊C4—441no—
264C4⋊C4—882no—
265C4⋊C4—882no—
266C22⋊C4—41no—
267C22⋊C4—441no—
268C22⋊C4—441no—
269C22⋊C4—441no—
270C42—111no—
271C42—111no—
272C42—111no—
273C42—111no—
274C16—41no—
275C16—441no—
276C11#1185611yescharacteristic, complemented, Sylow
277C23—41no—
278C23—441no—
279C23D8×D1111yescharacteristic
280Q8—882no—
281D4—41no—
282D4—41no—
283D4—81no—
284D4—81no—
285D4—441no—
286D4—441no—
287D4—882no—
288D4—882no—
289D4—881no—
290D4—881no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—112no—
298C2×C4—112no—
299C2×C4—111no—
300C2×C4—111no—
301C2×C4—111no—
302C2×C4—111no—
303C2×C4—222no—
304C2×C4—441no—
305C2×C4—882no—
306C2×C4—882no—
307C2×C4—881no—
308C2×C4—881no—
309C2×C4—881no—
310C2×C4C22⋊C4×D1111yescharacteristic
311C2×C4SD16×D1111yescharacteristic
312C8—21no—
313C8—21no—
314C8—221no—
315C8—221no—
316C22—21no—
317C22—21no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—881no—
322C22—881no—
323C22—881no—
324C22D11×#10211yescharacteristic
325C22D11×D1611yescharacteristic
326C22D11×SD3211yescharacteristic
327C4—21no—
328C4—81no—
329C4—112no—
330C4—112no—
331C4—112no—
332C4—161no—
333C4—221no—
334C4—881no—
335C4—1761no—
336C4#1062235311yescharacteristic
337C4#1062243411yescharacteristic
338C2—21no—
339C2—21no—
340C2—161no—
341C2—1761no—
342C2#1306717411yescharacteristic
343C2D11×#35711yescharacteristic
344C2D11×#36011yescharacteristic
subgroupG/H
centerC22D11×#102
commutatorC2×C8×C11C22×C4
FrattiniC22×C8C22×D11
FittingC11×#1347C2
socleC22×C11C2×#102
prime radical#13079190C2
cosocleC22×C8×C11C23
hypercenter#1347D11
hypocenterC11#11856
LCSG ▷ C2×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1347

Complements

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

NH ≅ G/Ntype
2. #13070412C2semidirect
3. #13068742C2semidirect
4. #13066626C2semidirect
5. #13066625C2semidirect
6. #13066624C2semidirect
7. C11×#1347C2semidirect
10. #10622764C4semidirect
11. D8×Dic11C4semidirect
16. #10622487C4semidirect
17. #10622485C4semidirect
111. #1347D11semidirect
276. C11#11856semidirect

Maximal subgroups

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

subgroupindex
#130791902
#130704122
#130687422
#130666262
#130666252
#130666242
C11×#13472
#1185611