Finite Group Databasebeta

← #14656318

Subgroups — #14656318

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×#10622697C211yesmaximal, characteristic, complemented
2C2×#10622685C211yesmaximal, characteristic
3#13069410C211yesmaximal, characteristic, complemented
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×#10622182C211yesmaximal, characteristic, complemented
6#13066451C211yesmaximal, characteristic, complemented
7C2×C11×#486C211yesmaximal, characteristic, complemented
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C22×#4323—21no—
11C2×C4×D44C2211yescharacteristic
12C11×#486—22no—
13C11×#486—22no—
14C2×C11×#102—22no—
15C2×C4×C8×C11C2211yescharacteristic
16C2×#66896—21no—
17C2×(C2×D11)⋊C8—22no—
18#10622697—22no—
19#10622697—22no—
20#10622685—22no—
21#10622685—22no—
22C2×#66873—21no—
23C2×#66872—21no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4⋊(C11⋊C8)C2211yescharacteristic
27#10622184—22no—
28#10622182—22no—
29C22×Q8×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11—21no—
33C22×D44D411yescharacteristic
34C22×C4×D11—21no—
35C22×C8×C11D412yes—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8—21no—
38C11×C4⋊Q8—21no—
39C11×C4⋊Q8D412yes—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127—21no—
43C11×#127D412yes—
44C2×C11×C4⋊C4—21no—
45C2×C11×C4⋊C4—21no—
46C2×C42×C11C2311yescharacteristic
47C2×#4323—24no—
48C2×#4323—42no—
49C2×#4323—42no—
50C2×(C2×D11)⋊C4—21no—
51C2×C4⋊Dic11D411yescharacteristic
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C22×C11⋊C8—21no—
55C4×D44—21no—
56C4×D44—21no—
57C4×D44—21no—
58C4×D44—21no—
59C11×#102—28no—
60C4×C8×C11—21no—
61C4×C8×C11—21no—
62#66896—24no—
63(C2×D11)⋊C8—44no—
64#66873—24no—
65#66872—24no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)—21no—
70C4⋊(C11⋊C8)D412yes—
71C4⋊(C11⋊C8)D412yes—
72#10267—111nomaximal, Sylow
73C24×C11—41no—
74C23×D11—21no—
75C2×Q8×C11—22no—
76C2×Q8×C11—41no—
77C2×Q8×C11—82no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—22no—
81C2×D4×C11—41no—
82C2×D4×C11—41no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—42no—
87C2×D4×C11—41no—
88C2×D4×C11—42no—
89C2×D4×C11—41no—
90C2×D4×C11—82no—
91C22×C4×C11—41no—
92C22×C4×C11C2×D411yescharacteristic
93C22×C4×C11C2×D411yescharacteristic
94C22×C4×C11#4111yescharacteristic
95C22×Dic11—21no—
96C2×D44—21no—
97C2×D44—21no—
98C2×D44—21no—
99C2×D44—21no—
100C2×D44—21no—
101C2×D44SD1612yes—
102C2×C4×D11—41no—
103C2×C4×D11—41no—
104C2×C4×D11—42no—
105C2×C4×D11—42no—
106C2×C8×C11—22no—
107C2×C8×C11—22no—
108C2×C8×C11—22no—
109C11×C4⋊C4—22no—
110C11×C4⋊C4—22no—
111C11×C4⋊C4—41no—
112C11×C4⋊C4—41no—
113C42×C11C2×D411yescharacteristic
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117#4323—48no—
118(C2×D11)⋊C4—41no—
119(C2×D11)⋊C4—41no—
120C4⋊Dic11—21no—
121C4⋊Dic11—21no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—41no—
125C2×C11⋊C8—41no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—42no—
130C2×#486D1111yescharacteristic, complemented
131C2×#476—111no—
132C2×#459—111no—
133#1954—111no—
134C2×#333—111no—
135C2×#331—111no—
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—
148Q8×C11—82no—
149Q8×C11—82no—
150D4×C11—44no—
151D4×C11—42no—
152D4×C11—42no—
153D4×C11—82no—
154D4×C11—82no—
155D4×C11—81no—
156D4×C11—81no—
157D4×C11—81no—
158D4×C11—81no—
159C2×C4×C11—22no—
160C2×C4×C11—42no—
161C2×C4×C11—82no—
162C2×C4×C11#12011yescharacteristic
163C2×C4×C11#12011yescharacteristic
164C2×C4×C11#12011yescharacteristic
165C2×C4×C11#12111yescharacteristic
166C2×C4×C11#12111yescharacteristic
167C2×C4×C11#12711yescharacteristic
168C2×C4×C11C2×SD1611yescharacteristic
169C2×C4×C11#13511yescharacteristic
170C2×C4×C11#13512yes—
171C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
172C2×C4×C11AGL(1,ℤ/8)12yes—
173C2×C4×C11#13711yescharacteristic
174C2×Dic11—41no—
175C2×Dic11—42no—
176D44—22no—
177D44—22no—
178D44—41no—
179D44—41no—
180C4×D11—82no—
181C4×D11—81no—
182C4×D11—81no—
183C8×C11—42no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186C11⋊C8—81no—
187C22×D8—221no—
188C2×C4⋊Q8C2×D1111yescharacteristic
189C2×#127C2×D1111yescharacteristic
190C2×C4×D4—111no—
191#486—22no—
192#486—22no—
193#476—222no—
194#476—222no—
195#459—222no—
196#459—222no—
197C2×#106—221no—
198C2×C4⋊C8—111no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8—111no—
201C2×#102—22no—
202C2×#102—221no—
203C2×#102—221no—
204C2×C22⋊C8—222no—
205C2×C4×C8C2×D1111yescharacteristic
206#333—222no—
207#331—222no—
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—82no—
226C4×C11#44811yescharacteristic
227C4×C11#44911yescharacteristic
228C4×C11#44912yes—
229C4×C11#45011yescharacteristic
230C4×C11#45211yescharacteristic
231C4×C11#49511yescharacteristic
232C4×C11#49611yescharacteristic
233Dic11—81no—
234C22×Q8—21no—
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—221no—
244C22×C8—221no—
245C22×C8—221no—
246C22×C8C22⋊D1112yes—
247C4⋊Q8—21no—
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8C22⋊D1112yes—
251#127—21no—
252#127—21no—
253#127—21no—
254#127C22⋊D1112yes—
255C4×D4—221no—
256C4×D4—221no—
257C4×D4—221no—
258C4×D4—221no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—111no—
262C2×C22⋊C4—221no—
263C2×C42C22×D1111yescharacteristic
264#106—224no—
265C4⋊C8—112no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8—221no—
271#102—28no—
272#102—224no—
273#102—224no—
274C22⋊C8—444no—
275C4×C8—21no—
276C4×C8—21no—
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—22no—
287C2×Q8—41no—
288C2×Q8—82no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—42no—
300C2×D4—42no—
301C2×D4—82no—
302C2×D4—112no—
303C2×D4—221no—
304C2×D4—221no—
305C2×D4—221no—
306C2×D4—221no—
307C2×D4—221no—
308C22×C4—41no—
309C22×C4—221no—
310C22×C4—441no—
311C22×C4—442no—
312C22×C4—442no—
313C22×C4—441no—
314C22×C4D4×D1111yescharacteristic
315C22×C4#434111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317D8—448no—
318C2×C8—22no—
319C2×C8—22no—
320C2×C8—22no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—441no—
324C2×C8—441no—
325C2×C8—441no—
326C2×C8—441no—
327C2×C8—441no—
328C2×C8—442no—
329C4⋊C4—22no—
330C4⋊C4—22no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—221no—
334C4⋊C4—221no—
335C22⋊C4—441no—
336C22⋊C4—441no—
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C11#1026711yescharacteristic, complemented, Sylow
342C23—42no—
343C23—82no—
344C23—81no—
345C23—81no—
346C23—82no—
347C23—222no—
348C23—442no—
349C23—441no—
350C23—441no—
351C23—442no—
352C23#6699111yescharacteristic
353Q8—82no—
354Q8—82no—
355D4—42no—
356D4—42no—
357D4—44no—
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—42no—
370C2×C4—82no—
371C2×C4—441no—
372C2×C4—442no—
373C2×C4—882no—
374C2×C4—881no—
375C2×C4—881no—
376C2×C4SD16×D1111yescharacteristic
377C2×C4#6696711yescharacteristic
378C2×C4#6696811yescharacteristic
379C2×C4#6696911yescharacteristic
380C2×C4#6699011yescharacteristic
381C2×C4#6699011yescharacteristic
382C2×C4#6699211yescharacteristic
383C2×C4#6699211yescharacteristic
384C2×C4#6699311yescharacteristic
385C2×C4#6700212yes—
386C2×C4#6700312yes—
387C2×C4#6700611yescharacteristic
388C8—42no—
389C8—442no—
390C8—442no—
391C8—881no—
392C22—82no—
393C22—82no—
394C22—82no—
395C22—162no—
396C22—162no—
397C22—442no—
398C22—444no—
399C22—882no—
400C22—881no—
401C22—881no—
402C22#1062267012yes—
403C22#1062277312yes—
404C22#1062278411yescharacteristic
405C22#1062278711yescharacteristic
406C22#1062283611yescharacteristic
407C4—21no—
408C4—21no—
409C4—82no—
410C4—881no—
411C4#1062267111yescharacteristic
412C4#1062267211yescharacteristic
413C4#1062278211yescharacteristic
414C4#1062278311yescharacteristic
415C4#1062278511yescharacteristic
416C4#1062278611yescharacteristic
417C4#1062285112yes—
418C2—162no—
419C2—882no—
420C2#1306802212yes—
421C2#1306814612yes—
422C2#1306961611yescharacteristic
423C2#1306969311yescharacteristic
424C2#1306972311yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#486C2
socleC23×C11#121
prime radicalC2×#10622685C2
hypercenterC2×#486D11
hypocenterC11#10267
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#10622697C2semidirect
3. #13069410C2semidirect
4. C2×#10622184C2semidirect
5. C2×#10622182C2semidirect
6. #13066451C2semidirect
7. C2×C11×#486C2semidirect
130. C2×#486D11semidirect
341. C11#10267semidirect

Maximal subgroups

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

subgroupindex
C2×#106226972
C2×#106226852
#130694102
C2×#106221842
C2×#106221822
#130664512
C2×C11×#4862
#1026711