Finite Group Databasebeta

← #14656900

Subgroups — #14656900

Order 2816.

454 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 93 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#13071910C211yesmaximal, characteristic, complemented
2#13069447C211yesmaximal, characteristic
3#13067112C211yesmaximal, characteristic
4#13067110C211yesmaximal, characteristic
5#13066517C211yesmaximal, characteristic, complemented
6#13066444C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8#10623008C2211yescharacteristic
9C2×C4×Dic22—21no—
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13C2×#66889—21no—
14C2×#66889—21no—
15#10622597—21no—
16#10622592—21no—
17C4×C4⋊Dic11C2211yescharacteristic
18#10622545C2211yescharacteristic
19C4×Dic11⋊C4—21no—
20#10622538C2211yescharacteristic
21#10622270—21no—
22#10622269—21no—
23#10622108—21no—
24#10622108—21no—
25#10622089—21no—
26#10622089—21no—
27C2×#4339—21no—
28C22×Dic22—21no—
29C2×C11×M16—21no—
30C2×C11×C4⋊C4—21no—
31C2×C42×C11—21no—
32C2×C42×C11C2311yescharacteristic
33#66983—21no—
34#66983—21no—
35C2×C4⋊Dic11—21no—
36C2×C4⋊Dic11—21no—
37C2×Dic11⋊C4—21no—
38C2×Dic11⋊C4—21no—
39C2×Dic11⋊C4—21no—
40C2×Dic11⋊C4—21no—
41C2×C4×Dic11—21no—
42C2×C4×Dic11D411yescharacteristic
43C2×C4×Dic11D411yescharacteristic
44#66928—21no—
45#66927Q811yescharacteristic, complemented
46C4×D44—21no—
47C4×D44—21no—
48#66922Q811yescharacteristic, complemented
49C4×Dic22—42no—
50C4×Dic22—42no—
51C11×C4⋊C8—21no—
52C11×C4⋊C8—21no—
53C11×C4⋊C8—21no—
54C11×C22⋊C8—21no—
55C4×C8×C11—21no—
56C11×#95D411yescharacteristic
57C11×#95D411yescharacteristic
58C11⋊#95—21no—
59C11⋊#95—21no—
60C11⋊#95—21no—
61C11⋊#95—21no—
62C11⋊#95D411yescharacteristic
63C11⋊#95D411yescharacteristic
64C22⋊(C11⋊C8)—21no—
65#66889—42no—
66#66889—42no—
67C4⋊(C11⋊C8)—21no—
68C4×C11⋊C8—21no—
69#10370—111nomaximal, Sylow
70C22×C4×C11—21no—
71C22×C4×C11—21no—
72C22×C4×C11C2×D411yescharacteristic
73C22×C4×C11C2×D411yescharacteristic
74C22×C4×C11C2×D411yescharacteristic
75C2×C22⋊D11—41no—
76C22×Dic11—21no—
77C22×Dic11—21no—
78C22×Dic11—21no—
79C22×Dic11—21no—
80#4339—41no—
81#4339—41no—
82#4339—41no—
83#4339—41no—
84C2×D44—21no—
85C2×D44—21no—
86C2×D44—21no—
87C2×C4×D11—41no—
88C2×Dic22—21no—
89C2×Dic22—42no—
90C2×Dic22—42no—
91C2×Dic22—42no—
92C11×M16—41no—
93C11×M16—41no—
94C2×C8×C11—41no—
95C2×C8×C11—41no—
96C11×C4⋊C4—42no—
97C42×C11—41no—
98C42×C11—41no—
99C42×C11C2×Q811yescharacteristic
100C42×C11#4111yescharacteristic
101C42×C11#4111yescharacteristic
102C42×C11#4111yescharacteristic
103(C2×D11)⋊C4—41no—
104(C2×D11)⋊C4—41no—
105C4⋊Dic11—21no—
106C4⋊Dic11—21no—
107C4⋊Dic11—42no—
108C4⋊Dic11—42no—
109Dic11⋊C4—42no—
110Dic11⋊C4—42no—
111Dic11⋊C4—42no—
112Dic11⋊C4—42no—
113C4×Dic11—21no—
114C4×Dic11—21no—
115C4×Dic11—41no—
116C4×Dic11—41no—
117C4×Dic11D812yes—
118C4×Dic11SD1612yes—
119C2×C11⋊C8—41no—
120#2399—111no—
121#1963—111no—
122#1502—111no—
123#1502—111no—
124#1303—111no—
125#1303D1111yescharacteristic, complemented
126#1274—111no—
127C23×C11#12011yescharacteristic
128C22×D11—41no—
129C2×C4×C11—22no—
130C2×C4×C11—41no—
131C2×C4×C11—41no—
132C2×C4×C11—41no—
133C2×C4×C11—41no—
134C2×C4×C11—41no—
135C2×C4×C11—41no—
136C2×C4×C11—41no—
137C2×C4×C11C22⋊Q811yescharacteristic
138C2×C4×C11C22⋊Q811yescharacteristic
139C2×C4×C11C22⋊Q811yescharacteristic
140C2×C4×C11#12411yescharacteristic
141C2×C4×C11#12411yescharacteristic
142C2×C4×C11#12411yescharacteristic
143C2×C4×C11C2×D811yescharacteristic
144C2×C4×C11C2×SD1611yescharacteristic
145C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C11#13711yescharacteristic
147C22⋊D11—81no—
148C22⋊D11—81no—
149C2×Dic11—22no—
150C2×Dic11—22no—
151C2×Dic11—22no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160C2×Dic11—41no—
161C2×Dic11—41no—
162D44—41no—
163D44—41no—
164D44—81no—
165D44—81no—
166C4×D11—81no—
167C4×D11—81no—
168Dic22—48no—
169Dic22—41no—
170Dic22—41no—
171C8×C11—81no—
172C8×C11—81no—
173C11⋊C8—81no—
174#532—111no—
175C2×C4×Q8—221no—
176#431—111no—
177#431C2×D1111yescharacteristic
178#423C2×D1111yescharacteristic
179C2×#104—221no—
180C2×#104—221no—
181#398—221no—
182#398—221no—
183#395—221no—
184#395—221no—
185C4×C4⋊C4—111no—
186C4×C4⋊C4—221no—
187C4×C4⋊C4C2×D1111yescharacteristic
188#376—111no—
189#327—221no—
190#327—221no—
191#327—221no—
192#327—221no—
193C22×C11—21no—
194C22×C11—21no—
195C22×C11#39311yescharacteristic
196C22×C11#44711yescharacteristic
197C22×C11#44811yescharacteristic
198C2×D11—81no—
199C2×D11—81no—
200C2×D11—81no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—21no—
204C4×C11—21no—
205C4×C11—42no—
206C4×C11—81no—
207C4×C11#47411yescharacteristic
208C4×C11#47611yescharacteristic
209C4×C11#48611yescharacteristic
210C4×C11#48911yescharacteristic
211Dic11—42no—
212Dic11—42no—
213Dic11—42no—
214Dic11—81no—
215Dic11—81no—
216C2×#41—221no—
217C22×Q8—221no—
218C2×M16—21no—
219C4⋊Q8—111no—
220#127—111no—
221#124—221no—
222#121—221no—
223#121—221no—
224C4×Q8—442no—
225C4×Q8—442no—
226C4×D4—221no—
227C4×D4—221no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—221no—
230C2×C4⋊C4—221no—
231C2×C4⋊C4—221no—
232C2×C4⋊C4—221no—
233C2×C4⋊C4—221no—
234C2×C4⋊C4—221no—
235C2×C42—21no—
236C2×C42—111no—
237C2×C42—111no—
238C2×C42—221no—
239C2×C42C22×D1111yescharacteristic
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—221no—
244#104—442no—
245#104—442no—
246C22⋊C8—21no—
247C22⋊C8—221no—
248C4×C8—21no—
249C4×C8—221no—
250#95—111no—
251#95—111no—
252#95—221no—
253#95—221no—
254#95—221no—
255#95—221no—
256#95D4411yescharacteristic
257#95D4411yescharacteristic
258C2×C11—21no—
259C2×C11—21no—
260C2×C11#202311yescharacteristic
261C2×C11#203111yescharacteristic
262C2×C11#203111yescharacteristic
263D11—161no—
264#41—441no—
265#41—441no—
266#41—441no—
267#41—441no—
268C2×Q8—221no—
269C2×Q8—442no—
270C2×Q8—442no—
271C2×Q8—442no—
272C2×D4—221no—
273C2×D4—221no—
274C2×D4—221no—
275C2×D4—441no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—221no—
279C22×C4—221no—
280C22×C4—221no—
281C22×C4—221no—
282C22×C4—441no—
283C22×C4C2×D4411yescharacteristic
284C22×C4D4×D1111yescharacteristic
285C22×C4D4×D1111yescharacteristic
286M16—41no—
287M16—41no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—441no—
291C4⋊C4—42no—
292C4⋊C4—221no—
293C4⋊C4—221no—
294C4⋊C4—442no—
295C4⋊C4—442no—
296C4⋊C4—442no—
297C4⋊C4—442no—
298C4⋊C4—442no—
299C4⋊C4—442no—
300C22⋊C4—441no—
301C22⋊C4—441no—
302C42—41no—
303C42—41no—
304C42—112no—
305C42—112no—
306C42—221no—
307C42—221no—
308C42—441no—
309C42—441no—
310C42#433911yescharacteristic
311C42#433911yescharacteristic
312C42#434111yescharacteristic
313C42Q8×D1111yescharacteristic
314C11#1037011yescharacteristic, complemented, Sylow
315C23—441no—
316C23#6693511yescharacteristic
317Q8—448no—
318Q8—441no—
319Q8—441no—
320D4—441no—
321D4—441no—
322D4—881no—
323D4—881no—
324D4—881no—
325D4—881no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—222no—
335C2×C4—222no—
336C2×C4—222no—
337C2×C4—441no—
338C2×C4—441no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—881no—
348C2×C4—881no—
349C2×C4#6692811yescharacteristic
350C2×C4#6693811yescharacteristic
351C2×C4#6693811yescharacteristic
352C2×C4#6694911yescharacteristic
353C2×C4#6694911yescharacteristic
354C2×C4#6695011yescharacteristic
355C2×C4D8×D1111yescharacteristic
356C2×C4SD16×D1111yescharacteristic
357C2×C4#6696711yescharacteristic
358C2×C4#6697111yescharacteristic
359C8—81no—
360C8—81no—
361C8—881no—
362C22—21no—
363C22—21no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22#1062228611yescharacteristic
368C22#1062238611yescharacteristic
369C22#1062241911yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—42no—
375C4—81no—
376C4—442no—
377C4—442no—
378C4—442no—
379C4—881no—
380C4—881no—
381C4#1062237311yescharacteristic
382C4#1062240811yescharacteristic
383C4#1062248311yescharacteristic
384C4#1062250311yescharacteristic
385C2—21no—
386C2—21no—
387C2—1761no—
388C2#1306975111yescharacteristic
389C2#1306978911yescharacteristic
390C2#1306979111yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#393
prime radical#10623008C22
hypercenter#1303D11
hypocenterC11#10370
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
1. #13071910C2semidirect
5. #13066517C2semidirect
6. #13066444C2semidirect
7. C11×#1303C2semidirect
45. #66927Q8semidirect
48. #66922Q8semidirect
125. #1303D11semidirect
314. C11#10370semidirect

Maximal subgroups

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

subgroupindex
#130719102
#130694472
#130671122
#130671102
#130665172
#130664442
C11×#13032
#1037011