Finite Group Databasebeta

← #14792685

Subgroups — #14792685

Order 2816.

976 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078560C211yesmaximal, characteristic, complemented
2#13077270C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic
4#13069974C212yesmaximal, complemented
5#13069874C212yesmaximal, complemented
6#13069521C212yesmaximal, complemented
7#13069275C212yesmaximal, complemented
8#13069085C211yesmaximal, characteristic, complemented
9#13068823C211yesmaximal, characteristic, complemented
10#13068537C211yesmaximal, characteristic
11C2×C11×#450C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C22×C11×SD16C2212yes—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C22×#4318C2211yescharacteristic
17C11×#450—21no—
18C11×#450—21no—
19C11×#450—22no—
20C2×C11×#102C2212yes—
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×#66900C2212yescomplemented
23#10622838C2211yescharacteristic, complemented
24#10622838C2211yescharacteristic, complemented
25C2×#66897C2212yes—
26C2×#66897C2212yes—
27#10622828—21no—
28#10622828—21no—
29#10622828C2212yes—
30#10622828C2212yes—
31C2×#66896—21no—
32C2×#66896—21no—
33#10622820C2211yescharacteristic
34#10622820C2211yescharacteristic
35C2×#66883C2212yescomplemented
36#10622715C2212yescomplemented
37#10622714C2212yescomplemented
38#10622658—21no—
39#10622658—21no—
40#10622657—21no—
41#10622656—21no—
42#10622577C2211yescharacteristic, complemented
43#10622577C2211yescharacteristic, complemented
44#10622333—22no—
45#10622332—21no—
46#10622331—21no—
47#10622190C2212yescomplemented
48#10622168C2212yescomplemented
49C25×C11—21no—
50C22×Q8×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—21no—
53C22×D4×C11—21no—
54C22×D4×C11—21no—
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11—42no—
58C22×D4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C2×C11×SD16—24no—
61C2×C11×SD16—22no—
62C2×C11×SD16—22no—
63C2×C11×SD16—42no—
64C22×C8×C11C2312yes—
65C11×C22⋊Q8—21no—
66C11×C22⋊Q8—21no—
67C11×C22⋊Q8—21no—
68C11×C22⋊Q8—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C22⋊Dic11—21no—
73#66979—21no—
74#66979—21no—
75#66979D411yescharacteristic
76#66979D411yescharacteristic
77#66979C2311yescharacteristic
78#66979C2311yescharacteristic
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11D411yescharacteristic
81C2×C4×Dic11—21no—
82C2×#4318—21no—
83C2×#4318—42no—
84C2×#4318C2311yescharacteristic
85C2×#4318C2312yes—
86C2×#4318C2311yescharacteristic
87C2×#4318C2312yes—
88C22×C11⋊C8—21no—
89C11×#102—22no—
90C11×#102—22no—
91C11×C22⋊C8D411yescharacteristic
92C11×C22⋊C8D411yescharacteristic
93C11×C22⋊C8D412yes—
94#66900—42no—
95#66899—21no—
96#66899—21no—
97#66899—21no—
98#66899—21no—
99#66897—24no—
100#66897—42no—
101#66896—22no—
102#66896—22no—
103#66896—22no—
104#66896—22no—
105C22⋊(C11⋊C8)—21no—
106C22⋊(C11⋊C8)—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)—21no—
109#66883—42no—
110#66879—22no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114#66872—21no—
115#66872—21no—
116#66871—21no—
117#66871—21no—
118#24521—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—44no—
121C24×C11—41no—
122C24×C11—41no—
123C24×C11—82no—
124C24×C11—82no—
125C24×C11#4111yescharacteristic
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×D4×C11—24no—
131C2×D4×C11—24no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11—22no—
137C2×D4×C11—44no—
138C2×D4×C11—44no—
139C2×D4×C11—44no—
140C2×D4×C11—42no—
141C2×D4×C11—42no—
142C2×D4×C11—41no—
143C2×D4×C11—41no—
144C2×D4×C11#4114yes—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C11×SD16—44no—
158C11×SD16—44no—
159C2×C8×C11—22no—
160C2×C8×C11—22no—
161C2×C8×C11C2×D412yes—
162C2×C8×C11C2×D412yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—41no—
167C11×C22⋊C4—41no—
168C11×C22⋊C4—41no—
169C22⋊Dic11—21no—
170C22⋊Dic11—21no—
171C22⋊Dic11—21no—
172C22⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11C2×D411yescharacteristic
176C4⋊Dic11C2×D411yescharacteristic
177C4⋊Dic11C2×D411yescharacteristic
178C4⋊Dic11C2×D411yescharacteristic
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—21no—
182C4×Dic11—21no—
183#4318—22no—
184#4318—22no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—22no—
189#4318—42no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—22no—
194C2×C11⋊C8—42no—
195#3095—111no—
196C2×#450D1111yescharacteristic
197#2924—111no—
198C2×#418—111no—
199#2063—112no—
200#2046—112no—
201#1977—112no—
202#1931—112no—
203#1901—111no—
204#1855—111no—
205#1783—111no—
206C23×C11—22no—
207C23×C11—22no—
208C23×C11—24no—
209C23×C11—41no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—42no—
213C23×C11—42no—
214C23×C11—82no—
215C23×C11—82no—
216C23×C11—82no—
217C23×C11—82no—
218C23×C11—82no—
219C23×C11—816no—
220C23×C11—82no—
221C23×C11#12111yescharacteristic
222C23×C11#12111yescharacteristic
223C23×C11C2×#4111yescharacteristic
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×C11—42no—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—44no—
230D4×C11—44no—
231D4×C11—42no—
232D4×C11—42no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—81no—
244C2×C4×C11#12111yescharacteristic
245C2×C4×C11#12111yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C2×#4112yes—
249C2×C4×C11H(5,𝔽2)12yes—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—42no—
255C2×Dic11—81no—
256C8×C11—22no—
257C8×C11—22no—
258C11⋊C8—41no—
259C11⋊C8—42no—
260C11⋊C8—41no—
261C11⋊C8—42no—
262C23×D4C2×D1111yescharacteristic
263C22×SD16C2×D1112yes—
264C22×M16—111no—
265C2×C22⋊Q8C2×D1111yescharacteristic
266C2×#117—111no—
267#485—221no—
268#485—221no—
269#484—221no—
270#483—221no—
271#450—21no—
272#450—21no—
273#450—22no—
274#433—222no—
275#432—221no—
276#431—221no—
277C2×#108—112no—
278#428—111no—
279#428—111no—
280#424—112no—
281#419—111no—
282#419—111no—
283#418—112no—
284#418—112no—
285#418—221no—
286#418—221no—
287C2×#102—221no—
288C2×#102—221no—
289C2×#102C2×D1112yes—
290C2×#101—112no—
291C2×#100—112no—
292C2×#100—112no—
293#407—111no—
294#407—111no—
295C2×C22⋊C8C2×D1111yescharacteristic
296#405—112no—
297#343—112no—
298#341—112no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—21no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—84no—
309C22×C11—84no—
310C22×C11—88no—
311C22×C11—88no—
312C22×C11—82no—
313C22×C11—82no—
314C22×C11#47112yes—
315C22×C11C2×#12111yescharacteristic
316C22×C11#55112yes—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—81no—
320C4×C11—81no—
321C4×C11#52511yescharacteristic
322C4×C11#53511yescharacteristic
323C4×C11#54612yes—
324Dic11—41no—
325Dic11—41no—
326Dic11—41no—
327Dic11—41no—
328C25—21no—
329C22×Q8C22×D1111yescharacteristic
330C22×D4—24no—
331C22×D4—21no—
332C22×D4—21no—
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—42no—
337C22×D4C22×D1112yes—
338C23×C4C22×D1111yescharacteristic
339C2×SD16—24no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16—42no—
343C2×M16—112no—
344C2×M16—111no—
345C2×M16—112no—
346C2×M16—111no—
347C2×M16—221no—
348C2×M16—442no—
349C22×C8—221no—
350C22×C8C22×D1112yes—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—21no—
355#117—111no—
356#117—111no—
357#117—111no—
358#117—111no—
359#117—221no—
360#117—221no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C22⋊C4—21no—
366C2×C22⋊C4—221no—
367C2×C42—221no—
368#108—442no—
369#107—221no—
370#107—221no—
371#106—221no—
372#106—221no—
373C4⋊C8—222no—
374C4⋊C8—222no—
375#103—221no—
376#103—221no—
377#103—221no—
378#103—221no—
379#102—22no—
380#102—22no—
381#102—222no—
382#102—222no—
383#102—222no—
384#102—222no—
385#101—442no—
386#100—224no—
387#100—442no—
388C22⋊C8—221no—
389C22⋊C8—221no—
390C22⋊C8—221no—
391C22⋊C8—221no—
392C22⋊C8C22⋊D1111yescharacteristic
393C22⋊C8C22⋊D1111yescharacteristic
394C22⋊C8C22⋊D1112yes—
395#97—222no—
396C4×C8—222no—
397C2×C11—22no—
398C2×C11—22no—
399C2×C11—41no—
400C2×C11—84no—
401C2×C11#241111yescharacteristic
402C2×C11C2×#47111yescharacteristic
403C2×C11#306811yescharacteristic
404C24—22no—
405C24—44no—
406C24—41no—
407C24—41no—
408C24—82no—
409C24—82no—
410C24#434111yescharacteristic
411C2×Q8—21no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—21no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—41no—
428C2×D4—41no—
429C2×D4#434114yes—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4#434111yescharacteristic
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C23×D1111yescharacteristic
442SD16—44no—
443SD16—44no—
444M16—222no—
445M16—222no—
446M16—222no—
447M16—222no—
448M16—222no—
449M16—222no—
450M16—442no—
451C2×C8—22no—
452C2×C8—22no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—442no—
458C2×C8C2×C22⋊D1112yes—
459C2×C8C2×C22⋊D1112yes—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—111no—
465C4⋊C4—111no—
466C4⋊C4—111no—
467C4⋊C4—111no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—221no—
473C22⋊C4—221no—
474C22⋊C4—221no—
475C22⋊C4—221no—
476C42—221no—
477C42—221no—
478C42—221no—
479C42—221no—
480C11#2452111yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—24no—
484C23—41no—
485C23—44no—
486C23—44no—
487C23—42no—
488C23—42no—
489C23—82no—
490C23—82no—
491C23—82no—
492C23—82no—
493C23—82no—
494C23—816no—
495C23—82no—
496C23#6699111yescharacteristic
497C23#6699111yescharacteristic
498C23C2×#434111yescharacteristic
499Q8—42no—
500Q8—41no—
501Q8—41no—
502D4—24no—
503D4—24no—
504D4—44no—
505D4—44no—
506D4—42no—
507D4—42no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—81no—
519C2×C4—221no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—442no—
524C2×C4—881no—
525C2×C4#6699111yescharacteristic
526C2×C4#6699111yescharacteristic
527C2×C4C2×D4×D1111yescharacteristic
528C2×C4C2×#434112yes—
529C2×C4#6703712yes—
530C2×C4C22×C22⋊D1111yescharacteristic
531C8—22no—
532C8—22no—
533C8—442no—
534C8—441no—
535C8—442no—
536C8—441no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—44no—
545C22—44no—
546C22—84no—
547C22—88no—
548C22—84no—
549C22—88no—
550C22—82no—
551C22—82no—
552C22#1062279012yes—
553C22#1062311812yes—
554C22C2×#6699111yescharacteristic
555C4—21no—
556C4—21no—
557C4—81no—
558C4—81no—
559C4—441no—
560C4—441no—
561C4—441no—
562C4—441no—
563C4#1062311711yescharacteristic
564C4#1062312311yescharacteristic
565C4#1062333712yes—
566C2—22no—
567C2—22no—
568C2—41no—
569C2—84no—
570C2#1307199711yescharacteristic
571C2C2×#1062279011yescharacteristic
572C2#1307834011yescharacteristic
subgroupG/H
centerC22C2×#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#450C2
socleC22×C11C2×#121
prime radicalC23×D4×C11C22
hypercenterC2×#450D11
hypocenterC11#24521
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. #13078560C2semidirect
2. #13077270C2semidirect
4. #13069974C2semidirect
5. #13069874C2semidirect
6. #13069521C2semidirect
7. #13069275C2semidirect
8. #13069085C2semidirect
9. #13068823C2semidirect
22. C2×#66900C22semidirect
23. #10622838C22semidirect
24. #10622838C22semidirect
35. C2×#66883C22semidirect
36. #10622715C22semidirect
37. #10622714C22semidirect
42. #10622577C22semidirect
43. #10622577C22semidirect
47. #10622190C22semidirect
48. #10622168C22semidirect
480. C11#24521semidirect

Maximal subgroups

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

subgroupindex
#130785602
#130772702
C2×#106228282
#130699742
#130698742
#130695212
#130692752
#130690852
#130688232
#130685372
C2×C11×#4502
#2452111