Finite Group Databasebeta

← #14821813

Subgroups — #14821813

Order 2816.

832 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072957C211yesmaximal, characteristic, complemented
2#13069933C211yesmaximal, characteristic, complemented
3#13069795C211yesmaximal, characteristic
4#13069762C211yesmaximal, characteristic, complemented
5#13069619C211yesmaximal, characteristic
6#13069573C211yesmaximal, characteristic, complemented
7#13069291C211yesmaximal, characteristic, complemented
8#13069257C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic, complemented
10#13069184C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068923C211yesmaximal, characteristic, complemented
13#13068706C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2361C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#388—21no—
26C11×#386—21no—
27C11×#385—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622565—21no—
41#10622557—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622271—21no—
48#10622263—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C11×#121—22no—
66C11×#121—22no—
67C4×D4×C11—22no—
68C4×D4×C11—41no—
69C4×D4×C11—44no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×#4324—22no—
89C2×#4324—41no—
90C2×#4324—41no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94#66977—22no—
95#66977—41no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66923—22no—
105#66923—41no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#66896—22no—
111#66896—22no—
112#66896—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121#66874—22no—
122#66874—22no—
123#66874—41no—
124#66871—22no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#26721—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—81no—
153C22×C4×C11—81no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4—42no—
176C11×C4⋊C4#4112yes—
177C11×C4⋊C4#4112yes—
178C11×C22⋊C4—24no—
179C11×C22⋊C4—22no—
180C11×C22⋊C4—22no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—42no—
189C22⋊Dic11—42no—
190C22⋊Dic11—42no—
191#4324—44no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11#4112yes—
198Dic11⋊C4—42no—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201C4×Dic11—42no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214#2489—111no—
215#2361D1111yescharacteristic
216#2055—111no—
217#2033—111no—
218#2025—111no—
219#2000—111no—
220#1989—111no—
221#1933—111no—
222#1928—111no—
223#1923—111no—
224#1918—111no—
225#1877—111no—
226#1872—111no—
227#1824—111no—
228C4×#102—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11#13512yes—
243C23×C11C22×D411yescharacteristic
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—48no—
247D4×C11—41no—
248D4×C11—41no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—22no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—84no—
277C2×C4×C11—84no—
278C2×C4×C11AGL(1,ℤ/8)12yes—
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C2×C4×C11H(5,𝔽2)11yescharacteristic
285C2×Dic11—22no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297Dic22—41no—
298Dic22—41no—
299Dic22—41no—
300Dic22—41no—
301C11⋊C8—41no—
302C11⋊C8—41no—
303C11⋊C8—41no—
304C11⋊C8—41no—
305C22×SD16—111no—
306C2×#125—111no—
307C2×C22⋊Q8—111no—
308C2×#121C2×D1111yescharacteristic
309C2×C4×D4—21no—
310C2×C4×D4C2×D1111yescharacteristic
311C22×C4⋊C4C2×D1111yescharacteristic
312C2×#107—111no—
313C2×C4⋊C8—111no—
314C2×#103—111no—
315C2×#103—111no—
316C2×#103—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102—111no—
320C2×C22⋊C8—111no—
321C2×C22⋊C8—111no—
322C2×C4×C8—111no—
323#400—221no—
324#397—221no—
325#391—111no—
326#391—111no—
327#390C2×D1111yescharacteristic
328#389C2×D1111yescharacteristic
329#388—21no—
330#388—221no—
331#386—21no—
332#385—21no—
333#382—221no—
334#380—111no—
335C4×C4⋊C4—111no—
336C4×C4⋊C4C2×D1111yescharacteristic
337C4×C22⋊C4C2×D1111yescharacteristic
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#336—111no—
347#336—111no—
348C22×C11—22no—
349C22×C11—22no—
350C22×C11—22no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—42no—
356C22×C11—42no—
357C22×C11—42no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11—81no—
361C22×C11—81no—
362C22×C11#52511yescharacteristic
363C22×C11#54611yescharacteristic
364C22×C11#54611yescharacteristic
365C22×C11C2×#13511yescharacteristic
366C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57811yescharacteristic
369C4×C11—22no—
370C4×C11—41no—
371C4×C11—42no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—41no—
375C4×C11—42no—
376C4×C11—81no—
377C4×C11#52911yescharacteristic
378C4×C11#53811yescharacteristic
379C4×C11#55511yescharacteristic
380C4×C11#55911yescharacteristic
381Dic11—42no—
382Dic11—81no—
383Dic11—81no—
384Dic11—81no—
385C22×Q8—111no—
386C22×D4—21no—
387C22×D4C22×D1111yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4C22×D1111yescharacteristic
391C2×SD16—222no—
392C2×SD16—441no—
393C2×SD16—441no—
394C22×C8—111no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8—111no—
398#125—222no—
399#125—441no—
400C22⋊Q8—222no—
401C22⋊Q8—441no—
402#121—22no—
403#121—22no—
404C4×D4—22no—
405C4×D4—41no—
406C4×D4—44no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4C22⋊D1111yescharacteristic
427C2×C22⋊C4C22⋊D1111yescharacteristic
428C2×C42—21no—
429C2×C42—221no—
430C2×C42C22×D1111yescharacteristic
431C2×C42C22×D1111yescharacteristic
432#107—222no—
433C4⋊C8—441no—
434#103—222no—
435#103—222no—
436#103—441no—
437#102—222no—
438#102—222no—
439#102—441no—
440C22⋊C8—441no—
441C22⋊C8—441no—
442C4×C8—441no—
443#95—21no—
444#95—21no—
445#95—221no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95C22⋊D1111yescharacteristic
452#95C22⋊D1111yescharacteristic
453C2×C11—42no—
454C2×C11—82no—
455C2×C11#245911yescharacteristic
456C2×C11#310511yescharacteristic
457C2×C11#312011yescharacteristic
458C2×C11#330011yescharacteristic
459C2×C11#330111yescharacteristic
460C2×C11#331011yescharacteristic
461C2×C11#333011yescharacteristic
462C24—21no—
463C24C2×C22⋊D1111yescharacteristic
464C2×Q8—221no—
465C2×Q8—221no—
466C2×Q8—221no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×D4—24no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—42no—
477C2×D4—42no—
478C2×D4#433912yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—42no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—81no—
493C22×C4—81no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4C2×C22⋊D1111yescharacteristic
499C22×C4C2×C22⋊D1111yescharacteristic
500C22×C4C2×C22⋊D1111yescharacteristic
501C22×C4C2×C22⋊D1111yescharacteristic
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504SD16—444no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—42no—
522C4⋊C4—42no—
523C4⋊C4—112no—
524C4⋊C4—221no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4#433912yes—
533C4⋊C4#434112yes—
534C22⋊C4—24no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—42no—
538C22⋊C4—42no—
539C22⋊C4—81no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—42no—
547C42—442no—
548C11#2672111yescharacteristic, complemented, Sylow
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23#6700312yes—
563C23C22×C22⋊D1111yescharacteristic
564Q8—441no—
565Q8—441no—
566Q8—441no—
567Q8—441no—
568D4—22no—
569D4—22no—
570D4—48no—
571D4—41no—
572D4—41no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—84no—
601C2×C4—84no—
602C2×C4—222no—
603C2×C4—441no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4#6698512yes—
615C2×C4C2×#433911yescharacteristic
616C2×C4C2×#433911yescharacteristic
617C2×C4C2×#434111yescharacteristic
618C2×C4#6703711yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#6704211yescharacteristic
621C8—441no—
622C8—441no—
623C8—441no—
624C8—441no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22#1062332211yescharacteristic
640C22C2×#6698511yescharacteristic
641C22#1062333711yescharacteristic
642C22C2×#6700311yescharacteristic
643C22#1062336011yescharacteristic
644C22#1062336711yescharacteristic
645C22#1062336911yescharacteristic
646C4—22no—
647C4—42no—
648C4—41no—
649C4—42no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—81no—
654C4—442no—
655C4—881no—
656C4—881no—
657C4—881no—
658C4#1062306911yescharacteristic
659C4#1062309011yescharacteristic
660C4#1062309111yescharacteristic
661C4#1062309411yescharacteristic
662C2—42no—
663C2—82no—
664C2#1307254711yescharacteristic
665C2#1307866311yescharacteristic
666C2#1307883011yescharacteristic
667C2#1308050311yescharacteristic
668C2#1308051211yescharacteristic
669C2#1308063711yescharacteristic
670C2#1308091511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2361C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2361D11
hypocenterC11#26721
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. #13072957C2semidirect
2. #13069933C2semidirect
4. #13069762C2semidirect
6. #13069573C2semidirect
7. #13069291C2semidirect
8. #13069257C2semidirect
9. #13069224C2semidirect
10. #13069184C2semidirect
11. #13068950C2semidirect
12. #13068923C2semidirect
13. #13068706C2semidirect
14. C4×#66896C2semidirect
548. C11#26721semidirect

Maximal subgroups

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

subgroupindex
#130729572
#130699332
#130697952
#130697622
#130696192
#130695732
#130692912
#130692572
#130692242
#130691842
#130689502
#130689232
#130687062
C4×#668962
C11×#23612
#2672111