Finite Group Databasebeta

← #14803538

Subgroups — #14803538

Order 2816.

764 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078990C211yesmaximal, characteristic, complemented
2#13078413C211yesmaximal, characteristic, complemented
3#13077559C211yesmaximal, characteristic, complemented
4#13069974C212yesmaximal, complemented
5#13069869C212yesmaximal, complemented
6#13069527C212yesmaximal, complemented
7#13069457C211yesmaximal, characteristic, complemented
8#13069392C211yesmaximal, characteristic, complemented
9#13069275C212yesmaximal, complemented
10C4×#66897C211yesmaximal, characteristic, complemented
11C2×C11×#459C211yesmaximal, characteristic
12C22×C11×D8C2212yes—
13C2×C11×#127C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15#10623001C2211yescharacteristic
16C11×#459—22no—
17C11×#459—21no—
18C11×#459—21no—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#102C2212yes—
21C2×#66897C2211yescharacteristic
22C2×#66897C2211yescharacteristic
23C2×#66897C2212yes—
24C2×#66897C2212yes—
25#10622828C2212yes—
26#10622828C2212yes—
27#10622828C2212yes—
28C2×#66883C2212yes—
29#10622715C2212yes—
30#10622714C2212yes—
31#10622684—22no—
32#10622683—21no—
33#10622683—21no—
34#10622622—22no—
35#10622621—21no—
36#10622620—21no—
37#10622577C2212yes—
38#10622537C2211yescharacteristic
39C4×#4318C2211yescharacteristic
40C4×#4318C2211yescharacteristic
41#10622444—21no—
42#10622443—21no—
43#10622441—22no—
44#10622190C2212yes—
45#10622168C2211yescharacteristic
46#10622168C2211yescharacteristic
47C22×D4×C11—21no—
48C22×D4×C11—21no—
49C22×D4×C11C2312yes—
50C22×D4×C11C2311yescharacteristic
51C23×C4×C11—21no—
52C2×C11×D8—24no—
53C2×C11×D8—22no—
54C2×C11×D8—22no—
55C2×C11×D8—42no—
56C22×C8×C11C2312yes—
57C11×#127—21no—
58C11×#127—21no—
59C11×#127—21no—
60C11×#127—21no—
61C4×D4×C11—21no—
62C4×D4×C11—21no—
63C4×D4×C11—21no—
64C4×D4×C11—21no—
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C22⋊C4—21no—
67C2×C42×C11C2311yescharacteristic
68#66979C2312yes—
69#66977—21no—
70#66977—21no—
71C2×#4318C2311yescharacteristic
72C2×#4318C2312yes—
73C2×#4318C2311yescharacteristic
74C2×#4318C2311yescharacteristic
75C2×#4318C2311yescharacteristic
76#66923D412yes—
77#66922D411yescharacteristic
78#66922D411yescharacteristic
79C4×Dic22—21no—
80C4×Dic22—21no—
81C11×C4⋊C8D412yes—
82C11×C4⋊C8D411yescharacteristic
83C11×C4⋊C8D411yescharacteristic
84C11×#102—22no—
85C11×#102—22no—
86#66897—22no—
87#66897—22no—
88#66897—24no—
89#66897—42no—
90#66896—22no—
91#66896—22no—
92#66896—22no—
93#66896—22no—
94#66896—22no—
95#66896—22no—
96#66883—42no—
97#66879—22no—
98Dic11⋊C8—22no—
99Dic11⋊C8—22no—
100C8×Dic11—22no—
101#66872—22no—
102#66871—22no—
103C4⋊(C11⋊C8)—21no—
104C4⋊(C11⋊C8)—21no—
105#66867—21no—
106#66867—21no—
107C4×C11⋊C8—21no—
108C4×C11⋊C8—21no—
109#25312—111nomaximal, Sylow
110C24×C11—21no—
111C24×C11—22no—
112C2×D4×C11—21no—
113C2×D4×C11—21no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—21no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—21no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—41no—
124C2×D4×C11—41no—
125C2×D4×C11—41no—
126C2×D4×C11—41no—
127C2×D4×C11—82no—
128C2×D4×C11—82no—
129C2×D4×C11#4112yes—
130C22×C4×C11—21no—
131C22×C4×C11—41no—
132C22×C4×C11—41no—
133C22×C4×C11—82no—
134C22×C4×C11#4111yescharacteristic
135C22×C4×C11#4111yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C2×Dic22—21no—
138C2×Dic22—21no—
139C11×D8—44no—
140C11×D8—44no—
141C2×C8×C11—22no—
142C2×C8×C11—22no—
143C2×C8×C11C2×D412yes—
144C2×C8×C11C2×D412yes—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C22⋊C4—41no—
148C11×C22⋊C4—41no—
149C42×C11C2×D411yescharacteristic
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C22⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11C2×D412yes—
157C4⋊Dic11C2×D412yes—
158Dic11⋊C4—22no—
159Dic11⋊C4—22no—
160C4×Dic11—22no—
161#4318—21no—
162#4318—21no—
163#4318—21no—
164#4318—22no—
165#4318—21no—
166#4318—22no—
167#4318—21no—
168#4318—21no—
169#4318—21no—
170#4318#4112yes—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—22no—
176#3138—111no—
177#3077—111no—
178C2×#459D1111yescharacteristic
179#2962—111no—
180#2063—112no—
181#2045—112no—
182#1978—112no—
183#1965—111no—
184#1950—111no—
185#1931—112no—
186C4×#100—111no—
187C23×C11—22no—
188C23×C11—41no—
189C23×C11—41no—
190C23×C11—42no—
191C23×C11—42no—
192C23×C11—42no—
193C23×C11—81no—
194C23×C11—81no—
195C23×C11—82no—
196C23×C11—82no—
197C23×C11C2×#4111yescharacteristic
198D4×C11—22no—
199D4×C11—22no—
200D4×C11—42no—
201D4×C11—41no—
202D4×C11—42no—
203D4×C11—42no—
204D4×C11—41no—
205D4×C11—42no—
206D4×C11—82no—
207D4×C11—82no—
208D4×C11—82no—
209D4×C11—82no—
210C2×C4×C11—22no—
211C2×C4×C11—41no—
212C2×C4×C11—41no—
213C2×C4×C11—82no—
214C2×C4×C11—82no—
215C2×C4×C11—81no—
216C2×C4×C11#12111yescharacteristic
217C2×C4×C11#12111yescharacteristic
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×C4×C11H(5,𝔽2)11yescharacteristic
225C2×C4×C112−1+411yescharacteristic
226C2×Dic11—22no—
227C2×Dic11—22no—
228Dic22—42no—
229Dic22—81no—
230C8×C11—22no—
231C8×C11—22no—
232C11⋊C8—22no—
233C11⋊C8—41no—
234C11⋊C8—41no—
235C11⋊C8—41no—
236C11⋊C8—42no—
237C22×D8C2×D1112yes—
238#533—111no—
239C2×#127C2×D1111yescharacteristic
240C2×C4×D4C2×D1111yescharacteristic
241#490—222no—
242#486—221no—
243#486—221no—
244#478—222no—
245#476—221no—
246#474—221no—
247#459—21no—
248#459—22no—
249#459—21no—
250#446—222no—
251#446—221no—
252C8×Q8—221no—
253C2×#108—112no—
254#428—112no—
255#424—112no—
256#423—111no—
257C2×C4⋊C8C2×D1111yescharacteristic
258#418—112no—
259#418—112no—
260#418—112no—
261C2×#102C2×D1112yes—
262C2×#100—112no—
263C2×#100—111no—
264C2×#100—111no—
265C2×#100—112no—
266#405—112no—
267C4×M16—111no—
268C4×M16—111no—
269#343—111no—
270#343—111no—
271#341—112no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—42no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—81no—
278C22×C11—81no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11—82no—
282C22×C11—162no—
283C22×C11—162no—
284C22×C11C2×#12111yescharacteristic
285C22×C11#52911yescharacteristic
286C22×C11#54211yescharacteristic
287C4×C11—21no—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—81no—
291C4×C11#47212yes—
292C4×C11#54611yescharacteristic
293C4×C11#54811yescharacteristic
294C4×C11#54811yescharacteristic
295C4×C11#55011yescharacteristic
296Dic11—42no—
297Dic11—42no—
298C22×D4—21no—
299C22×D4—21no—
300C22×D4C22×D1112yes—
301C22×D4C22×D1111yescharacteristic
302C23×C4—21no—
303C2×D8—24no—
304C2×D8—22no—
305C2×D8—22no—
306C2×D8—42no—
307C2×M16—111no—
308C2×M16—111no—
309C2×M16—112no—
310C2×M16—111no—
311C2×M16—111no—
312C22×C8C22×D1112yes—
313C4⋊Q8—111no—
314C4⋊Q8—111no—
315#127—21no—
316#127—21no—
317#127—21no—
318#127—21no—
319#125—112no—
320C22⋊Q8—221no—
321C22⋊Q8—221no—
322C4×Q8—221no—
323C4×Q8—221no—
324C4×D4—21no—
325C4×D4—21no—
326C4×D4—21no—
327C4×D4—21no—
328#117—112no—
329C2×C4⋊C4C22×D1111yescharacteristic
330C2×C22⋊C4—21no—
331C2×C42C22×D1111yescharacteristic
332#108—442no—
333#107—222no—
334#106—222no—
335C4⋊C8—222no—
336C4⋊C8—222no—
337C4⋊C8—221no—
338C4⋊C8—221no—
339C4⋊C8C22⋊D1111yescharacteristic
340C4⋊C8C22⋊D1111yescharacteristic
341C4⋊C8C22⋊D1112yes—
342#102—22no—
343#102—22no—
344#102—222no—
345#102—222no—
346#102—222no—
347#102—222no—
348#102—222no—
349#102—222no—
350#100—222no—
351#100—224no—
352#100—222no—
353#100—442no—
354#97—222no—
355#97—221no—
356#97—221no—
357C4×C8—222no—
358C4×C8—221no—
359C4×C8—221no—
360C2×C11—21no—
361C2×C11—21no—
362C2×C11—82no—
363C2×C11—162no—
364C2×C11#242611yescharacteristic
365C2×C11C2×#47211yescharacteristic
366C2×C11#306811yescharacteristic
367C24—21no—
368C24—22no—
369C2×Q8—221no—
370C2×Q8—221no—
371C2×D4—21no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—22no—
376C2×D4—21no—
377C2×D4—22no—
378C2×D4—21no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—22no—
382C2×D4—41no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—82no—
387C2×D4—82no—
388C2×D4#434112yes—
389C22×C4—21no—
390C22×C4—41no—
391C22×C4—41no—
392C22×C4—82no—
393C22×C4#434111yescharacteristic
394C22×C4#434111yescharacteristic
395C22×C4C23×D1111yescharacteristic
396D8—44no—
397D8—44no—
398M16—112no—
399M16—221no—
400M16—221no—
401M16—221no—
402M16—221no—
403M16—222no—
404M16—221no—
405M16—222no—
406M16—221no—
407M16—221no—
408C2×C8—22no—
409C2×C8—22no—
410C2×C8—221no—
411C2×C8—221no—
412C2×C8—221no—
413C2×C8—222no—
414C2×C8—221no—
415C2×C8C2×C22⋊D1112yes—
416C2×C8C2×C22⋊D1112yes—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—112no—
420C4⋊C4—112no—
421C4⋊C4—222no—
422C4⋊C4—222no—
423C4⋊C4—221no—
424C4⋊C4—221no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—222no—
428C42—222no—
429C42D4×D1111yescharacteristic
430C42D4×D1111yescharacteristic
431C42C2×C22⋊D1111yescharacteristic
432C42C2×C22⋊D1111yescharacteristic
433C11#2531211yescharacteristic, complemented, Sylow
434C23—22no—
435C23—41no—
436C23—41no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—81no—
441C23—81no—
442C23—82no—
443C23—82no—
444C23C2×#434111yescharacteristic
445Q8—442no—
446Q8—881no—
447D4—22no—
448D4—22no—
449D4—42no—
450D4—41no—
451D4—42no—
452D4—42no—
453D4—41no—
454D4—42no—
455D4—82no—
456D4—82no—
457D4—82no—
458D4—82no—
459C2×C4—22no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—82no—
463C2×C4—82no—
464C2×C4—81no—
465C2×C4—222no—
466C2×C4—222no—
467C2×C4#6699111yescharacteristic
468C2×C4#6699111yescharacteristic
469C2×C4#6699111yescharacteristic
470C2×C4#6699111yescharacteristic
471C2×C4C2×D4×D1111yescharacteristic
472C2×C4C2×#434111yescharacteristic
473C2×C4#6703711yescharacteristic
474C2×C4#41×D1111yescharacteristic
475C2×C4#6704311yescharacteristic
476C2×C4C22×C22⋊D1111yescharacteristic
477C8—22no—
478C8—22no—
479C8—222no—
480C8—441no—
481C8—441no—
482C8—441no—
483C8—442no—
484C22—21no—
485C22—21no—
486C22—42no—
487C22—82no—
488C22—82no—
489C22—81no—
490C22—81no—
491C22—82no—
492C22—82no—
493C22—82no—
494C22—162no—
495C22—162no—
496C22#1062313111yescharacteristic
497C22#1062313411yescharacteristic
498C22C2×#6699111yescharacteristic
499C4—21no—
500C4—21no—
501C4—21no—
502C4—81no—
503C4—442no—
504C4—442no—
505C4#1062277312yes—
506C4#1062312911yescharacteristic
507C4#1062313011yescharacteristic
508C4#1062333711yescharacteristic
509C4#1062336211yescharacteristic
510C2—21no—
511C2—21no—
512C2—82no—
513C2—162no—
514C2#1307217811yescharacteristic
515C2C2×#1062277311yescharacteristic
516C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#459C2
socleC22×C11C2×#121
hypercenterC2×#459D11
hypocenterC11#25312
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #13078990C2semidirect
2. #13078413C2semidirect
3. #13077559C2semidirect
4. #13069974C2semidirect
5. #13069869C2semidirect
6. #13069527C2semidirect
7. #13069457C2semidirect
8. #13069392C2semidirect
9. #13069275C2semidirect
10. C4×#66897C2semidirect
433. C11#25312semidirect

Maximal subgroups

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

subgroupindex
#130789902
#130784132
#130775592
#130699742
#130698692
#130695272
#130694572
#130693922
#130692752
C4×#668972
C2×C11×#4592
#2531211