Finite Group Databasebeta

← #14821868

Subgroups — #14821868

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072973C211yesmaximal, characteristic
2#13071620C211yesmaximal, characteristic, complemented
3#13069935C211yesmaximal, characteristic, complemented
4#13069814C211yesmaximal, characteristic, complemented
5#13069756C211yesmaximal, characteristic, complemented
6#13069622C211yesmaximal, characteristic
7#13069566C211yesmaximal, characteristic, complemented
8#13069298C211yesmaximal, characteristic, complemented
9#13069242C211yesmaximal, characteristic, complemented
10#13069220C211yesmaximal, characteristic, complemented
11#13068970C211yesmaximal, characteristic, complemented
12#13068932C211yesmaximal, characteristic
13#13068705C211yesmaximal, characteristic, complemented
14C4×#66874C211yesmaximal, characteristic, complemented
15C11×#1920C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C2×#66950C2211yescharacteristic
18C2×#66948C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×#66941C2211yescharacteristic
21C2×#66928—21no—
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×#66880C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622602—21no—
32#10622601C2211yescharacteristic
33#10622600C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35#10622587C2211yescharacteristic
36#10622586—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41#10622553—21no—
42#10622552C2211yescharacteristic
43C4×(C2×D11)⋊C4C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622286—21no—
46#10622285—21no—
47#10622279—21no—
48#10622267—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D44—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×Dic22—21no—
64C22×Dic22C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4D411yescharacteristic
82C2×(C2×D11)⋊C4D411yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×#4314—22no—
95C2×#4314—41no—
96C2×#4314—41no—
97#66950—22no—
98#66950—22no—
99#66948—22no—
100#66948—41no—
101C4⋊C4×D11—22no—
102C4⋊C4×D11—41no—
103#66941—22no—
104#66941—41no—
105#66928—44no—
106C4×Dic22—22no—
107C4×Dic22—41no—
108C11×#106—22no—
109C11×#95—21no—
110C11×#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95D411yescharacteristic
116C11⋊#95D411yescharacteristic
117#66885—22no—
118(C2×D11)⋊C8—41no—
119(C2×D11)⋊C8—41no—
120#66880—41no—
121Dic11⋊C8—41no—
122#66874—22no—
123#66874—22no—
124#66873—22no—
125#66873—41no—
126C4×C11⋊C8—41no—
127#26724—111nomaximal, Sylow
128C23×D11—21no—
129C23×D11C2×D411yescharacteristic
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2411yescharacteristic
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—81no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C2×C4×D11—21no—
158C2×C4×D11—42no—
159C2×C4×D11—42no—
160C2×C4×D11—81no—
161C2×Dic22—21no—
162C2×Dic22—21no—
163C2×Dic22—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—42no—
167C2×Dic22—42no—
168C2×Dic22—81no—
169C2×Dic22#4112yes—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—81no—
183C11×C4⋊C4#4112yes—
184C11×C4⋊C4#4112yes—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—42no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—41no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4SD1614yescomplemented
197C4⋊Dic11—24no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—81no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215#4314—44no—
216#2491—111no—
217#2360—111no—
218#2055—111no—
219#2035—111no—
220#2024—111no—
221#2000—111no—
222#1988—111no—
223#1934—111no—
224#1926—111no—
225#1923—111no—
226#1920D1111yescharacteristic, complemented
227#1880—111no—
228#1874—111no—
229#1824—111no—
230C4×#103—111no—
231C23×C11C22×D411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—41no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11C2×SD1612yes—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—22no—
249C2×C4×C11—21no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11C2×SD1612yes—
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—21no—
275C2×Dic11—22no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11C2×SD1612yes—
288D44—41no—
289D44—41no—
290D44—41no—
291D44—41no—
292D44—84no—
293C4×D11—41no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—84no—
298Dic22—22no—
299Dic22—22no—
300Dic22—41no—
301Dic22—41no—
302Dic22—84no—
303C8×C11—41no—
304C8×C11—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C22×SD16—111no—
308C2×C4⋊Q8—111no—
309C2×#124—221no—
310C2×C22⋊Q8—111no—
311C2×#121—111no—
312C2×C4×Q8—111no—
313C22×C4⋊C4—111no—
314C2×#106C2×D1111yescharacteristic
315C2×C4⋊C8—111no—
316C2×#103—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#102—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×C22⋊C8—111no—
323C2×C22⋊C8—111no—
324C2×C4×C8—111no—
325#394—221no—
326#393—221no—
327#391—111no—
328#390—111no—
329#390—111no—
330#389—221no—
331#389C2×D1111yescharacteristic
332#388—221no—
333#387—221no—
334#385—221no—
335#380—111no—
336C4×C4⋊C4—111no—
337C4×C4⋊C4C2×D1111yescharacteristic
338C4×C22⋊C4—111no—
339C4×C22⋊C4—221no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340C2×D1111yescharacteristic
346#340C2×D1111yescharacteristic
347#340C2×D1111yescharacteristic
348#336—111no—
349#336C2×D1111yescharacteristic
350C22×C11#52511yescharacteristic
351C22×C11#54611yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11C22×SD1611yescharacteristic
354C22×C11#57511yescharacteristic
355C22×C11#57611yescharacteristic
356C22×C11#57811yescharacteristic
357C2×D11—22no—
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—81no—
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C4×C11—22no—
372C4×C11—42no—
373C4×C11—42no—
374C4×C11—41no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11#52911yescharacteristic
378C4×C11#53811yescharacteristic
379C4×C11#55511yescharacteristic
380C4×C11#55911yescharacteristic
381Dic11—22no—
382Dic11—42no—
383Dic11—41no—
384Dic11—42no—
385Dic11—41no—
386Dic11—81no—
387C22×Q8—111no—
388C22×Q8—221no—
389C22×D4—111no—
390C22×D4—221no—
391C23×C4—111no—
392C23×C4—221no—
393C2×SD16—222no—
394C2×SD16—441no—
395C2×SD16—441no—
396C22×C8—111no—
397C22×C8—111no—
398C22×C8C22×D1111yescharacteristic
399C22×C8C22×D1111yescharacteristic
400C4⋊Q8—222no—
401C4⋊Q8—441no—
402#124—444no—
403C22⋊Q8—222no—
404C22⋊Q8—222no—
405#121—222no—
406#121—441no—
407C4×Q8—222no—
408C4×Q8—441no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—222no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—441no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C22⋊C4—111no—
423C2×C22⋊C4—111no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C42—21no—
432C2×C42—111no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42C22×D1111yescharacteristic
436#106—22no—
437C4⋊C8—441no—
438#103—222no—
439#103—222no—
440#103—441no—
441#102—222no—
442#102—222no—
443#102—441no—
444C22⋊C8—441no—
445C22⋊C8—441no—
446C4×C8—441no—
447#95—21no—
448#95—21no—
449#95—111no—
450#95—111no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455C2×C11#245911yescharacteristic
456C2×C11#310311yescharacteristic
457C2×C11#312411yescharacteristic
458C2×C11#329511yescharacteristic
459C2×C11#329811yescharacteristic
460C2×C11#331911yescharacteristic
461C2×C11#332711yescharacteristic
462D11—42no—
463D11—161no—
464C24—111no—
465C24—221no—
466C2×Q8—112no—
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—442no—
473C2×Q8—442no—
474C2×Q8—881no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—442no—
482C2×D4—442no—
483C2×D4—881no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—111no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—881no—
503C22×C4D4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506SD16—444no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—81no—
526C4⋊C4—112no—
527C4⋊C4—224no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4—442no—
534C4⋊C4#433912yes—
535C4⋊C4#434312yes—
536C22⋊C4—114no—
537C22⋊C4—224no—
538C22⋊C4—441no—
539C22⋊C4—442no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—881no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—221no—
549C42—221no—
550C42—442no—
551C42—881no—
552C11#2672411yescharacteristic, complemented, Sylow
553C23—112no—
554C23—221no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23C2×D4×D1111yescharacteristic
568Q8—222no—
569Q8—222no—
570Q8—441no—
571Q8—441no—
572Q8—884no—
573D4—441no—
574D4—441no—
575D4—441no—
576D4—441no—
577D4—884no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—112no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—222no—
605C2×C4—221no—
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—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—884no—
618C2×C4SD16×D1112yes—
619C2×C4C2×#433911yescharacteristic
620C2×C4C2×#434311yescharacteristic
621C2×C4#41×D1111yescharacteristic
622C2×C4#41×D1111yescharacteristic
623C2×C4#6704211yescharacteristic
624C2×C4#6704211yescharacteristic
625C8—41no—
626C8—41no—
627C8—441no—
628C8—441no—
629C22—222no—
630C22—222no—
631C22—222no—
632C22—441no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22—881no—
642C22—881no—
643C22#1062307811yescharacteristic
644C22#1062316111yescharacteristic
645C22#1062318511yescharacteristic
646C22C2×SD16×D1111yescharacteristic
647C22#1062329911yescharacteristic
648C22#1062330511yescharacteristic
649C22#1062331011yescharacteristic
650C4—22no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—81no—
655C4—81no—
656C4—222no—
657C4—441no—
658C4—441no—
659C4—442no—
660C4—442no—
661C4—881no—
662C4#1062306311yescharacteristic
663C4#1062311611yescharacteristic
664C4#1062322211yescharacteristic
665C4#1062323511yescharacteristic
666C2—442no—
667C2—1761no—
668C2#1307255711yescharacteristic
669C2#1307864511yescharacteristic
670C2#1307888211yescharacteristic
671C2#1308043711yescharacteristic
672C2#1308047911yescharacteristic
673C2#1308077011yescharacteristic
674C2#1308088111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1920C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1920D11
hypocenterC11#26724
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
2. #13071620C2semidirect
3. #13069935C2semidirect
4. #13069814C2semidirect
5. #13069756C2semidirect
7. #13069566C2semidirect
8. #13069298C2semidirect
9. #13069242C2semidirect
10. #13069220C2semidirect
11. #13068970C2semidirect
13. #13068705C2semidirect
14. C4×#66874C2semidirect
15. C11×#1920C2semidirect
196. (C2×D11)⋊C4SD16semidirect
226. #1920D11semidirect
552. C11#26724semidirect

Maximal subgroups

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

subgroupindex
#130729732
#130716202
#130699352
#130698142
#130697562
#130696222
#130695662
#130692982
#130692422
#130692202
#130689702
#130689322
#130687052
C4×#668742
C11×#19202
#2672411