Finite Group Databasebeta

← #14656322

Subgroups — #14656322

Order 2816.

646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622683C211yesmaximal, characteristic, complemented
2C2×#10622455C211yesmaximal, characteristic, complemented
3C2×#10622685C211yesmaximal, characteristic
4#13069409C211yesmaximal, characteristic, complemented
5C2×#10622119C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#331C211yesmaximal, characteristic, complemented
8C2×C11×#127C2211yescharacteristic
9C22×#4323—21no—
10C2×C4×D44C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C2×C11×C4⋊C8C2211yescharacteristic
13C2×C11×C4⋊C8C2211yescharacteristic
14C2×#66896—21no—
15C2×#66896—22no—
16C2×#66885—21no—
17C2×(C2×D11)⋊C8—22no—
18C2×#66881—21no—
19#10622685—22no—
20#10622685—22no—
21#10622683—22no—
22#10622683—22no—
23C2×C4⋊(C11⋊C8)C2211yescharacteristic
24C2×C4×C11⋊C8C2211yescharacteristic
25#10622455—22no—
26#10622455—22no—
27C11×#331—22no—
28#10622119—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D44D411yescharacteristic
33C22×C4×D11—21no—
34C22×Dic22—21no—
35C22×C8×C11—21no—
36C22×C8×C11—21no—
37C11×#127—21no—
38C11×#127—21no—
39C11×#127—21no—
40C11×#127D412yes—
41C2×C42×C11C2311yescharacteristic
42C2×#4323—24no—
43C2×#4323—42no—
44C2×#4323—42no—
45C2×(C2×D11)⋊C4—21no—
46C2×C4⋊Dic11—21no—
47C2×C4⋊Dic11—21no—
48C2×C4⋊Dic11D411yescharacteristic
49C22×C11⋊C8—21no—
50C22×C11⋊C8D412yes—
51C4×D44—21no—
52C4×D44—21no—
53C4×D44—21no—
54C4×D44—21no—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922D412yes—
59C11×C4⋊C8—21no—
60C11×C4⋊C8—21no—
61C11×C4⋊C8—21no—
62C11×C4⋊C8D412yes—
63#66896—28no—
64#66896—24no—
65#66885—24no—
66(C2×D11)⋊C8—44no—
67#66881—24no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10267—111nomaximal, Sylow
73C24×C11—41no—
74C23×D11—21no—
75C2×D4×C11—22no—
76C2×D4×C11—22no—
77C2×D4×C11—22no—
78C2×D4×C11—41no—
79C2×D4×C11—41no—
80C2×D4×C11—41no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—42no—
84C2×D4×C11—41no—
85C2×D4×C11—42no—
86C2×D4×C11—41no—
87C2×D4×C11—82no—
88C22×C4×C11C2×D411yescharacteristic
89C22×C4×C11C2×D411yescharacteristic
90C22×C4×C11#4111yescharacteristic
91C22×Dic11—21no—
92C22×Dic11—41no—
93C2×D44—21no—
94C2×D44—21no—
95C2×D44—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44SD1612yes—
99C2×C4×D11—41no—
100C2×C4×D11—41no—
101C2×C4×D11—42no—
102C2×C4×D11—42no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—82no—
106C2×C8×C11—22no—
107C2×C8×C11—41no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C2×C8×C11—42no—
111C42×C11C2×D411yescharacteristic
112C42×C11C2×D411yescharacteristic
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115#4323—48no—
116(C2×D11)⋊C4—41no—
117(C2×D11)⋊C4—41no—
118C4⋊Dic11—21no—
119C4⋊Dic11—22no—
120C4⋊Dic11—22no—
121C4⋊Dic11—21no—
122C4⋊Dic11—41no—
123C4⋊Dic11—41no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—22no—
127C2×C11⋊C8—22no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—41no—
130C2×#486—111no—
131C2×#476—111no—
132C2×#459—111no—
133#1954—111no—
134C2×#333—111no—
135C2×#331D1111yescharacteristic, complemented
136#1277—111no—
137C23×C11—42no—
138C23×C11—82no—
139C23×C11—81no—
140C23×C11—81no—
141C23×C11—82no—
142C23×C11#12111yescharacteristic
143C22×D11—22no—
144C22×D11—41no—
145C22×D11—42no—
146C22×D11—41no—
147C22×D11—42no—
148D4×C11—44no—
149D4×C11—42no—
150D4×C11—42no—
151D4×C11—82no—
152D4×C11—82no—
153D4×C11—81no—
154D4×C11—81no—
155D4×C11—81no—
156D4×C11—81no—
157C2×C4×C11—22no—
158C2×C4×C11#12011yescharacteristic
159C2×C4×C11#12011yescharacteristic
160C2×C4×C11#12011yescharacteristic
161C2×C4×C11#12111yescharacteristic
162C2×C4×C11#12111yescharacteristic
163C2×C4×C11#12711yescharacteristic
164C2×C4×C11C2×SD1611yescharacteristic
165C2×C4×C11#13511yescharacteristic
166C2×C4×C11#13512yes—
167C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C11AGL(1,ℤ/8)12yes—
169C2×C4×C11#13711yescharacteristic
170C2×Dic11—42no—
171C2×Dic11—41no—
172C2×Dic11—42no—
173C2×Dic11—82no—
174D44—22no—
175D44—22no—
176D44—41no—
177D44—41no—
178C4×D11—82no—
179C4×D11—81no—
180C4×D11—81no—
181Dic22—82no—
182Dic22—82no—
183C8×C11—42no—
184C8×C11—81no—
185C11⋊C8—42no—
186C11⋊C8—42no—
187C22×D8—221no—
188C2×C4⋊Q8—111no—
189C2×#127C2×D1111yescharacteristic
190C2×C4×D4—111no—
191#486—222no—
192#486—222no—
193#476—222no—
194#476—222no—
195#459—222no—
196#459—222no—
197C2×#106—221no—
198C2×C4⋊C8—111no—
199C2×C4⋊C8C2×D1111yescharacteristic
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#102—221no—
202C2×#102—221no—
203C2×#102—222no—
204C2×C22⋊C8—222no—
205C2×C4×C8—111no—
206#333—222no—
207#331—22no—
208C22×C11—82no—
209C22×C11—82no—
210C22×C11—82no—
211C22×C11—162no—
212C22×C11—162no—
213C22×C11#39211yescharacteristic
214C22×C11#46312yes—
215C22×C11#46511yescharacteristic
216C22×C11#46811yescharacteristic
217C22×C11#47212yes—
218C2×D11—44no—
219C2×D11—42no—
220C2×D11—82no—
221C2×D11—81no—
222C2×D11—81no—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11#44811yescharacteristic
226C4×C11#44911yescharacteristic
227C4×C11#44912yes—
228C4×C11#45011yescharacteristic
229C4×C11#45211yescharacteristic
230C4×C11#49511yescharacteristic
231C4×C11#49611yescharacteristic
232Dic11—81no—
233Dic11—82no—
234C22×Q8—221no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4—111no—
239C23×C4—221no—
240C2×D8—224no—
241C2×D8—442no—
242C2×D8—442no—
243C22×C8—21no—
244C22×C8—21no—
245C22×C8—112no—
246C22×C8—221no—
247C4⋊Q8—112no—
248C4⋊Q8—221no—
249C4⋊Q8—221no—
250C4⋊Q8—221no—
251#127—21no—
252#127—21no—
253#127—21no—
254#127D4412yes—
255C4×D4—221no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4—221no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#106—224no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8—21no—
268C4⋊C8—112no—
269C4⋊C8—221no—
270C4⋊C8C22⋊D1112yes—
271#102—224no—
272#102—224no—
273#102—228no—
274C22⋊C8—444no—
275C4×C8—221no—
276C4×C8—221no—
277C2×C11—162no—
278C2×C11#167712yes—
279C2×C11#169712yes—
280C2×C11#200011yescharacteristic
281C2×C11#201211yescharacteristic
282C2×C11#201811yescharacteristic
283D11—82no—
284C24—41no—
285C24—221no—
286C2×Q8—222no—
287C2×Q8—441no—
288C2×Q8—882no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—82no—
302C2×D4—112no—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—221no—
308C22×C4—221no—
309C22×C4—441no—
310C22×C4—441no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—441no—
314C22×C4#433911yescharacteristic
315C22×C4D4×D1111yescharacteristic
316C22×C4D4×D1111yescharacteristic
317D8—448no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—42no—
322C2×C8—41no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—222no—
326C2×C8—222no—
327C2×C8—441no—
328C2×C8—441no—
329C4⋊C4—221no—
330C4⋊C4—222no—
331C4⋊C4—222no—
332C4⋊C4—221no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42C2×D4411yescharacteristic
338C42D4×D1111yescharacteristic
339C42D4×D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C11#1026711yescharacteristic, complemented, Sylow
342C23—42no—
343C23—82no—
344C23—81no—
345C23—81no—
346C23—82no—
347C23—222no—
348C23—441no—
349C23—442no—
350C23—441no—
351C23—442no—
352C23#6693711yescharacteristic
353Q8—882no—
354Q8—882no—
355D4—42no—
356D4—44no—
357D4—42no—
358D4—82no—
359D4—82no—
360D4—81no—
361D4—81no—
362D4—81no—
363D4—81no—
364D4—222no—
365D4—222no—
366D4—441no—
367D4—441no—
368C2×C4—22no—
369C2×C4—441no—
370C2×C4—442no—
371C2×C4—442no—
372C2×C4—882no—
373C2×C4—881no—
374C2×C4—881no—
375C2×C4—882no—
376C2×C4#6693511yescharacteristic
377C2×C4#6693511yescharacteristic
378C2×C4#6693711yescharacteristic
379C2×C4#6696412yes—
380C2×C4#6696411yescharacteristic
381C2×C4#6696511yescharacteristic
382C2×C4SD16×D1111yescharacteristic
383C2×C4#6696811yescharacteristic
384C2×C4#6696912yes—
385C2×C4#6698311yescharacteristic
386C2×C4#6699011yescharacteristic
387C2×C4#6699311yescharacteristic
388C8—42no—
389C8—81no—
390C8—442no—
391C8—442no—
392C22—82no—
393C22—82no—
394C22—82no—
395C22—162no—
396C22—162no—
397C22—442no—
398C22—444no—
399C22—882no—
400C22—881no—
401C22—881no—
402C22#1062236212yes—
403C22#1062239111yescharacteristic
404C22#1062239311yescharacteristic
405C22#1062240012yes—
406C22#1062257311yescharacteristic
407C4—21no—
408C4—21no—
409C4—881no—
410C4—882no—
411C4#1062238911yescharacteristic
412C4#1062239412yes—
413C4#1062239611yescharacteristic
414C4#1062276711yescharacteristic
415C4#1062277111yescharacteristic
416C4#1062278111yescharacteristic
417C4#1062278311yescharacteristic
418C2—162no—
419C2—882no—
420C2#1306802412yes—
421C2#1306814812yes—
422C2#1306962011yescharacteristic
423C2#1306969511yescharacteristic
424C2#1306972411yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#331C2
socleC23×C11#121
prime radicalC2×#10622685C2
hypercenterC2×#331D11
hypocenterC11#10267
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
1. C2×#10622683C2semidirect
2. C2×#10622455C2semidirect
4. #13069409C2semidirect
5. C2×#10622119C2semidirect
6. #13066450C2semidirect
7. C2×C11×#331C2semidirect
135. C2×#331D11semidirect
341. C11#10267semidirect

Maximal subgroups

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

subgroupindex
C2×#106226832
C2×#106224552
C2×#106226852
#130694092
C2×#106221192
#130664502
C2×C11×#3312
#1026711