Finite Group Databasebeta

← #14656320

Subgroups — #14656320

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×#10622621C211yesmaximal, characteristic, complemented
3#13069411C211yesmaximal, characteristic, complemented
4C2×#10622119C211yesmaximal, characteristic, complemented
5C2×#10622182C211yesmaximal, characteristic, complemented
6#13066450C211yesmaximal, characteristic, complemented
7C2×C11×#459C211yesmaximal, characteristic
8C22×C11×D8—21no—
9C2×C11×#127C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C2×#66922C2211yescharacteristic
12C11×#459—22no—
13C11×#459—22no—
14C2×C11×C4⋊C8C2211yescharacteristic
15C2×C11×#102—21no—
16C2×#66896—21no—
17C2×#66896—22no—
18C2×C22⋊(C11⋊C8)—22no—
19#10622683—22no—
20#10622683—22no—
21#10622621—22no—
22#10622621—22no—
23C2×#66872—21no—
24C2×C4⋊(C11⋊C8)C2211yescharacteristic
25C2×C4⋊(C11⋊C8)C2211yescharacteristic
26C2×C4×C11⋊C8C2211yescharacteristic
27#10622182—22no—
28#10622119—22no—
29C22×D4×C11—21no—
30C22×D4×C11—21no—
31C22×D4×C11—21no—
32C22×D4×C11D411yescharacteristic
33C23×C4×C11—21no—
34C22×Dic22—21no—
35C2×C11×D8—24no—
36C2×C11×D8—42no—
37C2×C11×D8—42no—
38C22×C8×C11—21no—
39C11×#127—21no—
40C11×#127—21no—
41C11×#127—21no—
42C11×#127D412yes—
43C4×D4×C11—21no—
44C4×D4×C11—21no—
45C4×D4×C11—21no—
46C4×D4×C11—21no—
47C2×C11×C4⋊C4D411yescharacteristic
48C2×C11×C22⋊C4—21no—
49C2×C42×C11C2311yescharacteristic
50C2×C4⋊Dic11—21no—
51C2×C4⋊Dic11—21no—
52C22×C11⋊C8—21no—
53C22×C11⋊C8—21no—
54C22×C11⋊C8D412yes—
55#66922—21no—
56#66922—21no—
57#66922—21no—
58#66922D412yes—
59C11×C4⋊C8—21no—
60C11×C4⋊C8D412yes—
61C11×#102—24no—
62#66896—24no—
63#66896—28no—
64C22⋊(C11⋊C8)—44no—
65#66872—24no—
66C4⋊(C11⋊C8)—21no—
67C4⋊(C11⋊C8)—21no—
68C4⋊(C11⋊C8)—21no—
69C4⋊(C11⋊C8)D412yes—
70C4×C11⋊C8—21no—
71C4×C11⋊C8—21no—
72#10267—111nomaximal, Sylow
73C24×C11—21no—
74C24×C11—41no—
75C2×D4×C11—21no—
76C2×D4×C11—21no—
77C2×D4×C11—22no—
78C2×D4×C11—22no—
79C2×D4×C11—22no—
80C2×D4×C11—21no—
81C2×D4×C11—21no—
82C2×D4×C11—21no—
83C2×D4×C11—41no—
84C2×D4×C11—41no—
85C2×D4×C11—41no—
86C2×D4×C11—41no—
87C2×D4×C11—42no—
88C2×D4×C11—41no—
89C2×D4×C11—41no—
90C2×D4×C11—42no—
91C2×D4×C11—41no—
92C2×D4×C11—82no—
93C2×D4×C11SD1612yes—
94C22×C4×C11—21no—
95C22×C4×C11—41no—
96C22×C4×C11—41no—
97C22×C4×C11—42no—
98C22×C4×C11—42no—
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11#4111yescharacteristic
102C22×Dic11—41no—
103C2×Dic22—22no—
104C2×Dic22—41no—
105C2×Dic22—82no—
106C11×D8—48no—
107C2×C8×C11—22no—
108C2×C8×C11—41no—
109C2×C8×C11—41no—
110C11×C4⋊C4—21no—
111C11×C4⋊C4—21no—
112C11×C22⋊C4—41no—
113C11×C22⋊C4—41no—
114C42×C11C2×D411yescharacteristic
115C42×C11C2×D411yescharacteristic
116C42×C11C2×D411yescharacteristic
117C42×C11C2×D411yescharacteristic
118C4⋊Dic11—22no—
119C4⋊Dic11—22no—
120C4⋊Dic11—41no—
121C4⋊Dic11—41no—
122C2×C11⋊C8—22no—
123C2×C11⋊C8—22no—
124C2×C11⋊C8—22no—
125C2×C11⋊C8—22no—
126C2×C11⋊C8—41no—
127C2×C11⋊C8—41no—
128C2×C11⋊C8—41no—
129C2×C11⋊C8—42no—
130C2×#486—111no—
131C2×#476—111no—
132C2×#459D1111yescharacteristic
133#1954—111no—
134C2×#333—111no—
135C2×#331—111no—
136#1277—111no—
137C23×C11—22no—
138C23×C11—41no—
139C23×C11—42no—
140C23×C11—41no—
141C23×C11—42no—
142C23×C11—42no—
143C23×C11—82no—
144C23×C11—81no—
145C23×C11—81no—
146C23×C11—82no—
147C23×C11#12111yescharacteristic
148D4×C11—22no—
149D4×C11—22no—
150D4×C11—41no—
151D4×C11—44no—
152D4×C11—42no—
153D4×C11—41no—
154D4×C11—42no—
155D4×C11—82no—
156D4×C11—82no—
157D4×C11—81no—
158D4×C11—81no—
159D4×C11—81no—
160D4×C11—81no—
161C2×C4×C11—22no—
162C2×C4×C11—41no—
163C2×C4×C11—42no—
164C2×C4×C11—82no—
165C2×C4×C11—81no—
166C2×C4×C11—81no—
167C2×C4×C11#12011yescharacteristic
168C2×C4×C11#12011yescharacteristic
169C2×C4×C11#12011yescharacteristic
170C2×C4×C11#12111yescharacteristic
171C2×C4×C11#12111yescharacteristic
172C2×C4×C11#12711yescharacteristic
173C2×C4×C11C2×SD1611yescharacteristic
174C2×C4×C11#13512yes—
175C2×C4×C11#13511yescharacteristic
176C2×C4×C11AGL(1,ℤ/8)12yes—
177C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C11#13711yescharacteristic
179C2×Dic11—42no—
180C2×Dic11—82no—
181Dic22—82no—
182Dic22—82no—
183C8×C11—42no—
184C11⋊C8—42no—
185C11⋊C8—42no—
186C11⋊C8—81no—
187C22×D8—21no—
188C2×C4⋊Q8—111no—
189C2×#127C2×D1111yescharacteristic
190C2×C4×D4C2×D1111yescharacteristic
191#486—222no—
192#486—222no—
193#476—222no—
194#476—222no—
195#459—22no—
196#459—22no—
197C2×#106—221no—
198C2×C4⋊C8—111no—
199C2×C4⋊C8—111no—
200C2×C4⋊C8C2×D1111yescharacteristic
201C2×#102—21no—
202C2×#102—222no—
203C2×#102—221no—
204C2×C22⋊C8—222no—
205C2×C4×C8—111no—
206#333—222no—
207#331—222no—
208C22×C11—44no—
209C22×C11—42no—
210C22×C11—82no—
211C22×C11—81no—
212C22×C11—81no—
213C22×C11—82no—
214C22×C11—82no—
215C22×C11—82no—
216C22×C11—162no—
217C22×C11—162no—
218C22×C11#39211yescharacteristic
219C22×C11#46312yes—
220C22×C11#46511yescharacteristic
221C22×C11#46811yescharacteristic
222C22×C11#47212yes—
223C4×C11—21no—
224C4×C11—21no—
225C4×C11—81no—
226C4×C11#44811yescharacteristic
227C4×C11#44912yes—
228C4×C11#44911yescharacteristic
229C4×C11#45011yescharacteristic
230C4×C11#45211yescharacteristic
231C4×C11#49511yescharacteristic
232C4×C11#49611yescharacteristic
233Dic11—82no—
234C22×Q8—221no—
235C22×D4—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C22⋊D1111yescharacteristic
239C23×C4—21no—
240C2×D8—24no—
241C2×D8—42no—
242C2×D8—42no—
243C22×C8—21no—
244C22×C8—112no—
245C22×C8—221no—
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#127C22⋊D1112yes—
255C4×D4—21no—
256C4×D4—21no—
257C4×D4—21no—
258C4×D4—21no—
259C2×C4⋊C4—221no—
260C2×C4⋊C4—221no—
261C2×C4⋊C4C22⋊D1111yescharacteristic
262C2×C22⋊C4—21no—
263C2×C42C22×D1111yescharacteristic
264#106—224no—
265C4⋊C8—21no—
266C4⋊C8—112no—
267C4⋊C8—221no—
268C4⋊C8—221no—
269C4⋊C8—221no—
270C4⋊C8C22⋊D1112yes—
271#102—24no—
272#102—224no—
273#102—228no—
274C22⋊C8—444no—
275C4×C8—221no—
276C4×C8—221no—
277C2×C11—82no—
278C2×C11—162no—
279C2×C11#167712yes—
280C2×C11#169712yes—
281C2×C11#200011yescharacteristic
282C2×C11#201211yescharacteristic
283C2×C11#201811yescharacteristic
284C24—21no—
285C24—41no—
286C2×Q8—222no—
287C2×Q8—441no—
288C2×Q8—882no—
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—21no—
296C2×D4—22no—
297C2×D4—42no—
298C2×D4—42no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—82no—
307C2×D4#432412yes—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—42no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—441no—
314C22×C4D4×D1111yescharacteristic
315C22×C4#434111yescharacteristic
316C22×C4C2×C22⋊D1111yescharacteristic
317D8—48no—
318C2×C8—22no—
319C2×C8—41no—
320C2×C8—41no—
321C2×C8—222no—
322C2×C8—222no—
323C2×C8—222no—
324C2×C8—222no—
325C2×C8—441no—
326C2×C8—441no—
327C2×C8—442no—
328C2×C8—441no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—222no—
332C4⋊C4—222no—
333C4⋊C4—441no—
334C4⋊C4—441no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C42D4×D1111yescharacteristic
338C42D4×D1111yescharacteristic
339C42C2×C22⋊D1111yescharacteristic
340C42C2×C22⋊D1111yescharacteristic
341C11#1026711yescharacteristic, complemented, Sylow
342C23—22no—
343C23—42no—
344C23—42no—
345C23—41no—
346C23—41no—
347C23—42no—
348C23—82no—
349C23—82no—
350C23—81no—
351C23—81no—
352C23#6699211yescharacteristic
353Q8—882no—
354Q8—882no—
355D4—22no—
356D4—22no—
357D4—44no—
358D4—42no—
359D4—41no—
360D4—42no—
361D4—41no—
362D4—82no—
363D4—82no—
364D4—81no—
365D4—81no—
366D4—81no—
367D4—81no—
368C2×C4—22no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—82no—
374C2×C4—442no—
375C2×C4—882no—
376C2×C4#6696412yes—
377C2×C4#6696512yes—
378C2×C4#6698511yescharacteristic
379C2×C4C2×#432411yescharacteristic
380C2×C4#6699011yescharacteristic
381C2×C4#6699011yescharacteristic
382C2×C4#6699111yescharacteristic
383C2×C4#6699211yescharacteristic
384C2×C4#6699311yescharacteristic
385C2×C4#6700311yescharacteristic
386C2×C4#6700411yescharacteristic
387C2×C4#6700611yescharacteristic
388C8—42no—
389C8—442no—
390C8—442no—
391C8—881no—
392C22—42no—
393C22—44no—
394C22—82no—
395C22—81no—
396C22—81no—
397C22—82no—
398C22—82no—
399C22—82no—
400C22—162no—
401C22—162no—
402C22#1062265411yescharacteristic
403C22#1062265511yescharacteristic
404C22#1062276612yes—
405C22#1062281212yes—
406C22#1062283611yescharacteristic
407C4—21no—
408C4—21no—
409C4—81no—
410C4—882no—
411C4#1062265011yescharacteristic
412C4#1062265311yescharacteristic
413C4#1062276711yescharacteristic
414C4#1062276811yescharacteristic
415C4#1062277112yes—
416C4#1062283111yescharacteristic
417C4#1062285211yescharacteristic
418C2—82no—
419C2—162no—
420C2#1306802312yes—
421C2#1306814712yes—
422C2#1306961911yescharacteristic
423C2#1306969111yescharacteristic
424C2#1306972211yescharacteristic
subgroupG/H
centerC23#66992
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11#121
hypercenterC2×#459D11
hypocenterC11#10267
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10622683C2semidirect
2. C2×#10622621C2semidirect
3. #13069411C2semidirect
4. C2×#10622119C2semidirect
5. C2×#10622182C2semidirect
6. #13066450C2semidirect
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×#106226212
#130694112
C2×#106221192
C2×#106221822
#130664502
C2×C11×#4592
#1026711