Finite Group Databasebeta

← #14769818

Subgroups — #14769818

Order 2816.

1316 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622809C211yesmaximal, characteristic, complemented
2#13077492C211yesmaximal, characteristic, complemented
3#13077149C212yesmaximal, complemented
4#13069532C211yesmaximal, characteristic, complemented
5#13069478C211yesmaximal, characteristic, complemented
6#13069133C212yesmaximal, complemented
7#13068987C212yesmaximal, complemented
8#13068680C211yesmaximal, characteristic, complemented
9#13068575C212yesmaximal, complemented
10#13068451C211yesmaximal, characteristic, complemented
11C2×C11×#578C211yesmaximal, characteristic
12C2×C11×2−1+4C2212yes—
13C11×#578—24no—
14C11×#578C418yescomplemented
15C2×C11×#137—22no—
16C2×C11×#137C2212yes—
17C2×C11×#135—21no—
18C2×C11×#135C2211yescharacteristic
19C22×C11×Q16—21no—
20C22×C11×Q16C2211yescharacteristic
21C2×C11×#131C2211yescharacteristic
22#10623358C2212yes—
23C2×#67001C2212yes—
24C2×#66901C2212yes—
25C2×#66901C2211yescharacteristic
26#10622846—22no—
27#10622846C2211yescharacteristic
28#10622845—22no—
29#10622845C2212yes—
30#10622845C2212yes—
31#10622843C2212yes—
32C2×#66900C2212yes—
33#10622838—22no—
34#10622838C2212yes—
35C2×#66899—22no—
36C2×#66899C2212yes—
37#10622809—24no—
38Q16×Dic11—21no—
39#10622777—22no—
40D8×Dic11—21no—
41C2×#66883C2211yescharacteristic
42C2×#66882C2211yescharacteristic
43#10622714C2211yescharacteristic
44C2×C8×Dic11C2211yescharacteristic
45#10622196C2211yescharacteristic
46#10622193C2211yescharacteristic
47#10622192C2212yes—
48C11×2−1+4—24no—
49C11×2−1+4—24no—
50C11×2−1+4—42no—
51C11×2−1+4C2×C418yescomplemented
52C2×C11×#41—22no—
53C2×C11×#41—22no—
54C2×C11×#41—42no—
55C2×C11×#41C2312yes—
56C2×C11×#41C2311yescharacteristic
57C22×Q8×C11—22no—
58C22×Q8×C11—22no—
59C22×Q8×C11C2312yes—
60C11×#137—24no—
61C11×#137—216no—
62C11×#137C2×C418yescomplemented
63C11×#135—28no—
64C11×#135C2×C414yes—
65C11×#135D414yes—
66C2×C11×Q16—22no—
67C2×C11×Q16—28no—
68C2×C11×Q16—21no—
69C2×C11×Q16—21no—
70C2×C11×Q16—22no—
71C2×C11×Q16C2×C414yescomplemented
72C2×C11×Q16D411yescharacteristic
73C2×C11×SD16—22no—
74C2×C11×SD16D412yes—
75C2×C11×D8D411yescharacteristic
76C11×#131—22no—
77C11×#131C2×C414yescomplemented
78C2×C11×M16—21no—
79C2×C11×M16C2311yescharacteristic
80C22×C8×C11—21no—
81C22×C8×C11C2311yescharacteristic
82#67001—24no—
83#67001—42no—
84Q8×Dic11—22no—
85D4×Dic11—22no—
86D4×Dic11—42no—
87#66979—22no—
88#66979C2311yescharacteristic
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11C2312yes—
91C2×C4×Dic11C2311yescharacteristic
92C2×#4318—22no—
93C2×#4318C2312yes—
94C2×#4318C2311yescharacteristic
95C22×C11⋊C8—22no—
96C22×C11⋊C8C2311yescharacteristic
97#66901—24no—
98#66901—22no—
99#66900—42no—
100#66899—22no—
101#66899—22no—
102#66899—22no—
103#66899—22no—
104#66899—22no—
105#66899—22no—
106#66899D411yescharacteristic
107#66899D411yescharacteristic
108#66896—22no—
109#66896—22no—
110#66896D411yescharacteristic
111#66896D411yescharacteristic
112C11⋊#95—42no—
113#66883—22no—
114#66882—21no—
115#66882—21no—
116#66879—21no—
117C8×Dic11—21no—
118C8×Dic11—22no—
119#22468—111nomaximal, Sylow
120C11×#41—21no—
121C11×#41—22no—
122C11×#41—22no—
123C11×#41—21no—
124C11×#41—28no—
125C11×#41—28no—
126C11×#41—48no—
127C11×#41—44no—
128C11×#41—44no—
129C11×#41—48no—
130C11×#41C22×C414yes—
131C11×#41C22×C412yes—
132C11×#41C2×D414yes—
133C11×#41#4112yes—
134C2×Q8×C11—22no—
135C2×Q8×C11—28no—
136C2×Q8×C11—28no—
137C2×Q8×C11—22no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—42no—
142C2×Q8×C11—44no—
143C2×Q8×C11—44no—
144C2×Q8×C11C22×C414yes—
145C2×Q8×C11C2×D412yes—
146C2×Q8×C11C2×D411yescharacteristic
147C2×D4×C11—22no—
148C2×D4×C11—21no—
149C2×D4×C11—42no—
150C2×D4×C11C2×D412yes—
151C2×D4×C11C2×D411yescharacteristic
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—22no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—42no—
161C11×Q16—24no—
162C11×Q16—24no—
163C11×Q16—28no—
164C11×Q16C22⋊C414yes—
165C11×SD16—28no—
166C11×SD16C22⋊C418yes—
167C11×D8C22⋊C414yes—
168C11×M16—24no—
169C11×M16—21no—
170C11×M16C22×C412yes—
171C2×C8×C11—24no—
172C2×C8×C11—21no—
173C2×C8×C11C22×C412yes—
174C2×C8×C11C2×D411yescharacteristic
175C2×C8×C11C2×D412yes—
176C2×C8×C11C2×D411yescharacteristic
177C22⋊Dic11—21no—
178C22⋊Dic11—42no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—42no—
182C4⋊Dic11C2×D411yescharacteristic
183C4⋊Dic11C2×D411yescharacteristic
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188#4318—22no—
189#4318—21no—
190#4318—21no—
191#4318—22no—
192#4318—44no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—44no—
198C2×C11⋊C8C2×D411yescharacteristic
199C2×C11⋊C8C2×D411yescharacteristic
200C2×#578D1111yescharacteristic
201C2×#443—111no—
202#2951—111no—
203#2898—112no—
204#1979—111no—
205#1969—111no—
206#1908—112no—
207#1882—112no—
208#1816—111no—
209#1793—112no—
210#1764—111no—
211C23×C11—22no—
212C23×C11—21no—
213C23×C11H(5,𝔽2)11yescharacteristic
214Q8×C11—21no—
215Q8×C11—22no—
216Q8×C11—24no—
217Q8×C11—24no—
218Q8×C11—48no—
219Q8×C11—42no—
220Q8×C11—42no—
221Q8×C11C2×C22⋊C414yes—
222Q8×C11C4×D412yes—
223D4×C11—22no—
224D4×C11—24no—
225D4×C11—22no—
226D4×C11—24no—
227D4×C11—21no—
228D4×C11—22no—
229D4×C11—48no—
230D4×C11C2×C22⋊C414yes—
231D4×C11C4×D412yes—
232C2×C4×C11—22no—
233C2×C4×C11—21no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—48no—
240C2×C4×C11—48no—
241C2×C4×C11—42no—
242C2×C4×C11—42no—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11H(5,𝔽2)11yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—42no—
255C2×Dic11—82no—
256C2×Dic11—162no—
257C8×C11—22no—
258C8×C11C2×C22⋊C412yes—
259C8×C11C2×C22⋊C412yes—
260C11⋊C8—21no—
261C11⋊C8—21no—
262C11⋊C8—42no—
263C11⋊C8—41no—
264C2×2−1+4C2×D1112yes—
265#578—24no—
266#578Dic1118yescomplemented
267C2×#137—22no—
268C2×#137C2×D1112yes—
269C2×#135—21no—
270C2×#135C2×D1111yescharacteristic
271C22×Q16—21no—
272C22×Q16C2×D1111yescharacteristic
273C2×#131—112no—
274C2×#131C2×D1111yescharacteristic
275#520—112no—
276#443—224no—
277#440—222no—
278C4×Q16—221no—
279C4×D8—221no—
280C2×#108—111no—
281C2×#107—111no—
282C2×#104—111no—
283C2×#104—112no—
284#419—112no—
285#419—222no—
286#417—112no—
287#417—112no—
288#417—222no—
289#416—111no—
290#416—222no—
291C2×#103—112no—
292C2×#103—222no—
293C2×#101—112no—
294#405—111no—
295C2×C4×C8—111no—
296#391—112no—
297#343—112no—
298#341—111no—
299#339—111no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—22no—
303C22×C11—24no—
304C22×C11—41no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—41no—
308C22×C11#51811yescharacteristic
309C22×C11D4211yescharacteristic
310C22×C11#54611yescharacteristic
311C4×C11—22no—
312C4×C11—24no—
313C4×C11—44no—
314C4×C11C22×C22⋊C411yescharacteristic
315C4×C11C2×C4×D411yescharacteristic
316C4×C11D4211yescharacteristic
317C4×C11#54611yescharacteristic
318Dic11—42no—
319Dic11—41no—
320Dic11—41no—
321Dic11—82no—
3222−1+4—24no—
3232−1+4—24no—
3242−1+4—42no—
3252−1+4C2×Dic1118yescomplemented
326C2×#41—22no—
327C2×#41—22no—
328C2×#41—42no—
329C2×#41C22×D1111yescharacteristic
330C2×#41C22×D1112yes—
331C22×Q8—22no—
332C22×Q8—22no—
333C22×Q8C22×D1112yes—
334#137—24no—
335#137—216no—
336#137C2×Dic1118yescomplemented
337#135—28no—
338#135C2×Dic1114yes—
339#135C22⋊D1114yes—
340C2×Q16—22no—
341C2×Q16—28no—
342C2×Q16—21no—
343C2×Q16—21no—
344C2×Q16—22no—
345C2×Q16C2×Dic1114yescomplemented
346C2×Q16C22⋊D1111yescharacteristic
347C2×SD16—22no—
348C2×SD16C22⋊D1112yes—
349C2×D8C22⋊D1111yescharacteristic
350#131—22no—
351#131—224no—
352#131—442no—
353#131C2×Dic1114yescomplemented
354C2×M16—21no—
355C2×M16—112no—
356C2×M16—111no—
357C2×M16—222no—
358C2×M16C22×D1111yescharacteristic
359C22×C8—21no—
360C22×C8—111no—
361C22×C8—222no—
362C22×C8C22×D1111yescharacteristic
363C4×Q8—222no—
364C4×D4—222no—
365C4×D4—442no—
366#117—111no—
367#117—222no—
368C2×C4⋊C4—112no—
369C2×C4⋊C4—222no—
370C2×C42—111no—
371#108—222no—
372#107—221no—
373#107—221no—
374#104—222no—
375#104—224no—
376#103—111no—
377#103—111no—
378#103—222no—
379#103—222no—
380#103—222no—
381#103—222no—
382#103—222no—
383#103—222no—
384#102—111no—
385#102—111no—
386#102—222no—
387#102—222no—
388#101—442no—
389#97—221no—
390C4×C8—222no—
391C4×C8—221no—
392#95—442no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—42no—
396C2×C11—44no—
397C2×C11D4×C22⋊C411yescharacteristic
398C2×C11#329011yescharacteristic
399C2×C11#329311yescharacteristic
400#41—22no—
401#41—22no—
402#41—21no—
403#41—21no—
404#41—28no—
405#41—28no—
406#41—48no—
407#41—44no—
408#41—44no—
409#41—48no—
410#41#434112yes—
411#41C22×Dic1112yes—
412#41C22×Dic1114yes—
413#41C2×C22⋊D1114yes—
414C2×Q8—22no—
415C2×Q8—28no—
416C2×Q8—28no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—22no—
421C2×Q8—42no—
422C2×Q8—44no—
423C2×Q8—44no—
424C2×Q8D4×D1111yescharacteristic
425C2×Q8C22×Dic1114yes—
426C2×Q8C2×C22⋊D1112yes—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—42no—
430C2×D4D4×D1111yescharacteristic
431C2×D4C2×C22⋊D1112yes—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—442no—
440C22×C4C23×D1111yescharacteristic
441Q16—28no—
442Q16—24no—
443Q16—24no—
444Q16C22⋊Dic1114yes—
445SD16—28no—
446SD16C22⋊Dic1118yes—
447D8C22⋊Dic1114yes—
448M16—21no—
449M16—24no—
450M16—221no—
451M16—221no—
452M16—222no—
453M16—222no—
454M16—444no—
455M16C22×Dic1112yes—
456C2×C8—21no—
457C2×C8—24no—
458C2×C8—111no—
459C2×C8—111no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—222no—
463C2×C8—221no—
464C2×C8—444no—
465C2×C8C22×Dic1112yes—
466C2×C8C2×C22⋊D1111yescharacteristic
467C2×C8C2×C22⋊D1112yes—
468C2×C8C2×C22⋊D1111yescharacteristic
469C4⋊C4—111no—
470C4⋊C4—111no—
471C4⋊C4—222no—
472C4⋊C4—222no—
473C4⋊C4—442no—
474C22⋊C4—221no—
475C22⋊C4—442no—
476C42—221no—
477C42—221no—
478C42—221no—
479C42—442no—
480C11#2246811yescharacteristic, complemented, Sylow
481C23—22no—
482C23—21no—
483C23#6703711yescharacteristic
484Q8—21no—
485Q8—22no—
486Q8—24no—
487Q8—24no—
488Q8—48no—
489Q8—42no—
490Q8—42no—
491Q8D4×Dic1112yes—
492Q8C2×C22⋊Dic1114yes—
493D4—22no—
494D4—24no—
495D4—22no—
496D4—24no—
497D4—21no—
498D4—22no—
499D4—48no—
500D4D4×Dic1112yes—
501D4C2×C22⋊Dic1114yes—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—48no—
510C2×C4—48no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—222no—
514C2×C4—221no—
515C2×C4—221no—
516C2×C4—441no—
517C2×C4—441no—
518C2×C4—442no—
519C2×C4—882no—
520C2×C4—1762no—
521C2×C4C2×D4×D1111yescharacteristic
522C2×C4C2×#434111yescharacteristic
523C2×C4#6703711yescharacteristic
524C2×C4C23×Dic1111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C2×C4C22×C22⋊D1111yescharacteristic
527C8—22no—
528C8—221no—
529C8—221no—
530C8—442no—
531C8—441no—
532C8C2×C22⋊Dic1112yes—
533C8C2×C22⋊Dic1112yes—
534C22—21no—
535C22—21no—
536C22—22no—
537C22—24no—
538C22—42no—
539C22—41no—
540C22—42no—
541C22—41no—
542C22#1062332911yescharacteristic
543C22D4×C22⋊D1111yescharacteristic
544C22#1062333711yescharacteristic
545C4—22no—
546C4—24no—
547C4—44no—
548C4—442no—
549C4—441no—
550C4—441no—
551C4—882no—
552C4C2×D4×Dic1111yescharacteristic
553C4D4×C22⋊D1111yescharacteristic
554C4#1062333711yescharacteristic
555C4C22×C22⋊Dic1111yescharacteristic
556C2—21no—
557C2—21no—
558C2—42no—
559C2—44no—
560C2D4×C22⋊Dic1111yescharacteristic
561C2#1308040211yescharacteristic
562C2#1308041811yescharacteristic
subgroupG/H
centerC22D4×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#578C2
socleC22×C11D42
cosocleC22×C4×C11C24
hypercenterC2×#578D11
hypocenterC11#22468
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#578

Complements

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

NH ≅ G/Ntype
1. C2×#10622809C2semidirect
2. #13077492C2semidirect
3. #13077149C2semidirect
4. #13069532C2semidirect
5. #13069478C2semidirect
6. #13069133C2semidirect
7. #13068987C2semidirect
8. #13068680C2semidirect
9. #13068575C2semidirect
10. #13068451C2semidirect
14. C11×#578C4semidirect
51. C11×2−1+4C2×C4semidirect
62. C11×#137C2×C4semidirect
71. C2×C11×Q16C2×C4semidirect
77. C11×#131C2×C4semidirect
266. #578Dic11semidirect
325. 2−1+4C2×Dic11semidirect
336. #137C2×Dic11semidirect
345. C2×Q16C2×Dic11semidirect
353. #131C2×Dic11semidirect
480. C11#22468semidirect

Maximal subgroups

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

subgroupindex
C2×#106228092
#130774922
#130771492
#130695322
#130694782
#130691332
#130689872
#130686802
#130685752
#130684512
C2×C11×#5782
#2246811