Finite Group Databasebeta

← #14724745

Subgroups — #14724745

Order 2816.

740 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078614C211yesmaximal, characteristic
2#13077361C211yesmaximal, characteristic, complemented
3D4×#4313C211yesmaximal, characteristic, complemented
4#13067529C211yesmaximal, characteristic, complemented
5#13067528C211yesmaximal, characteristic, complemented
6#13067482C211yesmaximal, characteristic, complemented
7#13067477C211yesmaximal, characteristic, complemented
8#13067477C211yesmaximal, characteristic, complemented
9#13067440C211yesmaximal, characteristic, complemented
10#13067438C211yesmaximal, characteristic, complemented
11#13067385C211yesmaximal, characteristic, complemented
12#13067065C211yesmaximal, characteristic, complemented
13D11×D4⋊C8C211yesmaximal, characteristic, complemented
14#13066902C211yesmaximal, characteristic, complemented
15C11×#1586C211yesmaximal, characteristic, complemented
16C2×#66960—21no—
17C22×#4313—21no—
18#10623079C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C11×#436C2211yescharacteristic, complemented
22C8×D4×C11C2211yescharacteristic
23#10622769C411yescharacteristic
24#10622763C411yescharacteristic
25#10622740—21no—
26#10622724—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29D4×C11⋊C8C2211yescharacteristic
30D4×C11⋊C8C2211yescharacteristic, complemented
31#10622503C411yescharacteristic
32#10622495C411yescharacteristic
33#10622451C2211yescharacteristic
34#10622451C2211yescharacteristic, complemented
35#10622450C2211yescharacteristic
36D11×C4⋊C8C2211yescharacteristic
37#10622399C411yescharacteristic
38#10622387C411yescharacteristic
39#10622386C411yescharacteristic
40#10622372C411yescharacteristic
41#10622343—21no—
42#10622343—21no—
43#10622340—21no—
44#10622339—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic
47C4×#4313C2211yescharacteristic
48C8×D44C2211yescharacteristic, complemented
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#334C2211yescharacteristic, complemented
52C11×D4⋊C8C2211yescharacteristic
53C11×D4⋊C8C2211yescharacteristic, complemented
54C11×#322C2211yescharacteristic, complemented
55D4⋊(C11⋊C8)C2211yescharacteristic
56D4⋊(C11⋊C8)C2211yescharacteristic, complemented
57#10622121C2211yescharacteristic
58#10622121C2211yescharacteristic, complemented
59#10622118C2211yescharacteristic, complemented
60#10622118C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic, complemented
63#10622095C2211yescharacteristic, complemented
64#10622093C2211yescharacteristic, complemented
65#10622093C2211yescharacteristic, complemented
66#10622092C2211yescharacteristic, complemented
67C2×D4×D11C2×C411yescharacteristic
68C2×#4339—21no—
69C22×C4×D11—21no—
70C2×C11×D8C2×C411yescharacteristic
71C2×C11×M16—21no—
72C22×C8×C11—21no—
73C4×D4×C11C2311yescharacteristic
74C4×D4×C11C2311yescharacteristic
75#66993C2×C411yescharacteristic
76#66991C2×C411yescharacteristic
77D4×Dic11C2×C411yescharacteristic
78C2×#4323C2×C411yescharacteristic
79C2×#4323C2×C411yescharacteristic
80C4×C22⋊D11—21no—
81C4×C22⋊D11—21no—
82C22×C11⋊C8—21no—
83C22×C11⋊C8—21no—
84#66960—44no—
85C2×D88C2×C411yescharacteristic
86C2×#4313—21no—
87C2×#4313—21no—
88C2×#4313—21no—
89C2×#4313—21no—
90C2×#4313—44no—
91C2×#4313D411yescharacteristic
92C2×#4313D411yescharacteristic
93C2×C8×D11—21no—
94C2×C8×D11—21no—
95C2×C8×D11—21no—
96#66948C2×C411yescharacteristic
97#66946C2×C411yescharacteristic
98C4⋊C4×D11C2×C411yescharacteristic
99#66941C2×C411yescharacteristic
100#66938—21no—
101#66937—21no—
102(C22⋊D11)⋊C4—21no—
103C22⋊C4×D11—21no—
104C4×D44C2311yescharacteristic
105C4×D44C2311yescharacteristic
106C42×D11C2311yescharacteristic
107C11×#107C2×C411yescharacteristic
108C11×C4⋊C8C2311yescharacteristic
109C11×C4⋊C8C2311yescharacteristic
110C11×#102C2×C411yescharacteristic
111C11×#102C2×C411yescharacteristic
112C11×C22⋊C8—21no—
113C11×C22⋊C8—21no—
114C4×C8×C11C2311yescharacteristic
115C4×C8×C11C2311yescharacteristic
116C4×C8×C11C2311yescharacteristic
117#66896C2×C411yescharacteristic
118#66896C2×C411yescharacteristic
119C22⋊(C11⋊C8)—21no—
120C22⋊(C11⋊C8)—21no—
121#66885C2×C411yescharacteristic
122#66885C2×C411yescharacteristic
123(C2×D11)⋊C8—21no—
124(C2×D11)⋊C8—21no—
125(C2×D11)⋊C8—21no—
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8C2×C411yescharacteristic
128(C2×D11)⋊C8C2×C411yescharacteristic
129#66882C2×C411yescharacteristic
130#66879D411yescharacteristic
131#66879D411yescharacteristic
132Dic11⋊C8—21no—
133Dic11⋊C8—21no—
134Dic11⋊C8C2×C411yescharacteristic
135Dic11⋊C8C2×C411yescharacteristic
136C8×Dic11—21no—
137#66873C2×C411yescharacteristic
138#66873C2×C411yescharacteristic
139#66871C2×C411yescharacteristic
140#66871C2×C411yescharacteristic
141C4⋊(C11⋊C8)C2311yescharacteristic
142C4⋊(C11⋊C8)C2311yescharacteristic
143C4×C11⋊C8C2311yescharacteristic
144C4×C11⋊C8C2311yescharacteristic
145C4×C11⋊C8C2311yescharacteristic
146#18001—111nomaximal, Sylow
147C23×D11—21no—
148C2×D4×C11C22×C411yescharacteristic
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C2×C22⋊D11—21no—
153C2×C22⋊D11—21no—
154C2×C22⋊D11—21no—
155C2×C22⋊D11—21no—
156C22×Dic11—21no—
157D4×D11—22no—
158D4×D11—41no—
159#4339—42no—
160#4339—42no—
161C2×D44—21no—
162C2×D44C22×C411yescharacteristic
163C2×D44C22×C411yescharacteristic
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—42no—
169C2×C4×D11—42no—
170C2×C4×D11C22×C411yescharacteristic
171C2×C4×D11C2×D411yescharacteristic
172C2×C4×D11#4111yescharacteristic
173C2×Dic22—21no—
174C11×D8—22no—
175C11×M16—42no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—42no—
180C2×C8×C11C22×C411yescharacteristic
181C2×C8×C11C22×C411yescharacteristic
182C2×C8×C11C2×D411yescharacteristic
183C2×C8×C11C2×D411yescharacteristic
184C11×C4⋊C4C22×C411yescharacteristic
185C11×C4⋊C4C22×C411yescharacteristic
186C11×C22⋊C4—21no—
187C11×C22⋊C4—21no—
188C42×C11C2411yescharacteristic
189C22⋊Dic11—21no—
190C22⋊Dic11—21no—
191#4323—22no—
192#4323—41no—
193(C2×D11)⋊C4—21no—
194(C2×D11)⋊C4—21no—
195(C2×D11)⋊C4—21no—
196(C2×D11)⋊C4—21no—
197C4⋊Dic11C22×C411yescharacteristic
198C4⋊Dic11C22×C411yescharacteristic
199Dic11⋊C4—21no—
200Dic11⋊C4—21no—
201C4×Dic11C22×C411yescharacteristic
202C4×Dic11C2×D411yescharacteristic
203C4×Dic11#4111yescharacteristic
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—42no—
208C2×C11⋊C8—42no—
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213D88—41no—
214#4313—22no—
215#4313—22no—
216#4313—42no—
217#4313—42no—
218#4313—42no—
219#4313—42no—
220C8×D11—42no—
221C8×D11—42no—
222C8×D11—42no—
223#3100—111no—
224#2935—111no—
225D4×M16—111no—
226#1594—111no—
227#1594—111no—
228#1586—111no—
229#1586—111no—
230#1586—111no—
231#1586D1111yescharacteristic, complemented
232#1580—111no—
233#1580—111no—
234#1570—111no—
235#1492—111no—
236C2×D4⋊C8—111no—
237#1451—111no—
238C23×C11—21no—
239C23×C11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—42no—
243C22×D11—42no—
244C22×D11—81no—
245C22×D11C4×D411yescharacteristic
246D4×C11—21no—
247D4×C11—21no—
248D4×C11—21no—
249D4×C11#13112yescomplemented
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11C23×C411yescharacteristic
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C22⋊D11—42no—
260C22⋊D11—42no—
261C22⋊D11—42no—
262C22⋊D11—81no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—42no—
266C2×Dic11C4×D411yescharacteristic
267C2×Dic11C4×D411yescharacteristic
268C2×Dic11C4×D411yescharacteristic
269D44—21no—
270D44—21no—
271D44—21no—
272D44—21no—
273D44—42no—
274C4×D11—21no—
275C4×D11—21no—
276C4×D11—41no—
277C4×D11—42no—
278C4×D11—41no—
279C4×D11—41no—
280C4×D11—41no—
281C4×D11—41no—
282C4×D11—42no—
283C4×D11AGL(1,ℤ/8)12yes—
284C4×D11AGL(1,ℤ/8)12yes—
285Dic22—42no—
286C8×C11—22no—
287C8×C11—21no—
288C8×C11—21no—
289C8×C11—21no—
290C8×C11—21no—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—21no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—21no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8—41no—
300C2×#131—221no—
301C22×M16—221no—
302#532—111no—
303C2×C4×D4—111no—
304#480—111no—
305#480—111no—
306#474—111no—
307#474—111no—
308#459—111no—
309#459—111no—
310#447—111no—
311#447—111no—
312C4×D8—111no—
313C4×D8—111no—
314C4×D8—111no—
315C4×D8C2×D1111yescharacteristic
316#436—111no—
317#436—111no—
318#436—111no—
319#436C2×D1111yescharacteristic, complemented
320#435—221no—
321#435—221no—
322#435—221no—
323#435—221no—
324C8×D4—111no—
325C8×D4—111no—
326C8×D4—111no—
327C8×D4C2×D1111yescharacteristic
328#431—111no—
329#423—111no—
330C2×C4⋊C8—111no—
331#408—221no—
332#407—221no—
333C4×M16—111no—
334C2×C4×C8—111no—
335#334—111no—
336#334—111no—
337#334—111no—
338#334C2×D1111yescharacteristic, complemented
339D4⋊C8—111no—
340D4⋊C8—111no—
341D4⋊C8—111no—
342D4⋊C8—111no—
343D4⋊C8—111no—
344D4⋊C8—111no—
345D4⋊C8C2×D1111yescharacteristic
346D4⋊C8C2×D1111yescharacteristic, complemented
347#322—111no—
348#322—111no—
349#322—111no—
350#322C2×D1111yescharacteristic, complemented
351C22×C11—22no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11C2×C4×D411yescharacteristic
358C2×D11—21no—
359C2×D11—21no—
360C2×D11—41no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—84no—
367C2×D11#44212yes—
368C4×C11—21no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11C2×#13111yescharacteristic
372C4×C11#56811yescharacteristic
373C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
374C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
375Dic11—21no—
376Dic11—21no—
377Dic11—41no—
378Dic11—41no—
379Dic11#44212yes—
380C2×#41—221no—
381C22×D4—111no—
382C23×C4—221no—
383C2×D8—111no—
384C2×D8—111no—
385C2×D8—111no—
386C2×D8C4×D1111yescharacteristic
387#131—444no—
388C2×M16—21no—
389C2×M16—111no—
390C2×M16—111no—
391C2×M16—221no—
392C2×M16—221no—
393C2×M16—221no—
394C2×M16—221no—
395C2×M16—444no—
396C22×C8—21no—
397C22×C8—221no—
398C22×C8—221no—
399C22×C8—221no—
400C22×C8—221no—
401C22×C8—221no—
402C4⋊Q8—111no—
403#127—111no—
404#124—221no—
405#121—111no—
406#121—111no—
407#121—221no—
408C4×D4—111no—
409C4×D4—111no—
410C4×D4—111no—
411C4×D4—111no—
412C4×D4—221no—
413C4×D4—221no—
414C4×D4—221no—
415C4×D4C22×D1111yescharacteristic
416C4×D4C22×D1111yescharacteristic
417C2×C4⋊C4—111no—
418C2×C22⋊C4—221no—
419C2×C42—111no—
420#107—111no—
421#107—111no—
422#107—111no—
423#107C4×D1111yescharacteristic
424C4⋊C8—111no—
425C4⋊C8—111no—
426C4⋊C8—111no—
427C4⋊C8—111no—
428C4⋊C8—221no—
429C4⋊C8—221no—
430C4⋊C8C22×D1111yescharacteristic
431C4⋊C8C22×D1111yescharacteristic
432#102—111no—
433#102—111no—
434#102—111no—
435#102—111no—
436#102—111no—
437#102—111no—
438#102C4×D1111yescharacteristic
439#102C4×D1111yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—111no—
443C22⋊C8—111no—
444C22⋊C8—221no—
445C22⋊C8—221no—
446C22⋊C8—221no—
447C22⋊C8—221no—
448C22⋊C8—221no—
449C22⋊C8—221no—
450#97—111no—
451#97—111no—
452C4×C8—111no—
453C4×C8—111no—
454C4×C8—111no—
455C4×C8—221no—
456C4×C8C22×D1111yescharacteristic
457C4×C8C22×D1111yescharacteristic
458C4×C8C22×D1111yescharacteristic
459C2×C11—42no—
460C2×C11—81no—
461C2×C11#293311yescharacteristic
462C2×C11C2×#44211yescharacteristic
463C2×C11#295611yescharacteristic
464D11—22no—
465D11—81no—
466D11—81no—
467C24—221no—
468#41—442no—
469#41—442no—
470C2×Q8—221no—
471C2×D4—111no—
472C2×D4—111no—
473C2×D4—221no—
474C2×D4—221no—
475C2×D4—221no—
476C2×D4—221no—
477C2×D4—222no—
478C2×D4—221no—
479C2×D4—441no—
480C2×D4C2×C4×D1111yescharacteristic
481C2×D4C2×C4×D1111yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—111no—
485C22×C4—111no—
486C22×C4—111no—
487C22×C4—221no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—442no—
493C22×C4—442no—
494D8—22no—
495D8—222no—
496D8—441no—
497D8—441no—
498M16—42no—
499M16—222no—
500M16—222no—
501M16—442no—
502M16—442no—
503M16—442no—
504M16—442no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—42no—
509C2×C8—111no—
510C2×C8—111no—
511C2×C8—111no—
512C2×C8—111no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—442no—
517C2×C8—442no—
518C2×C8—442no—
519C2×C8—442no—
520C2×C8—442no—
521C2×C8C2×C4×D1111yescharacteristic
522C2×C8C2×C4×D1111yescharacteristic
523C2×C8D4×D1111yescharacteristic
524C2×C8D4×D1111yescharacteristic
525C4⋊C4—111no—
526C4⋊C4—111no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4C2×C4×D1111yescharacteristic
530C4⋊C4C2×C4×D1111yescharacteristic
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—221no—
534C22⋊C4—221no—
535C22⋊C4—221no—
536C22⋊C4—221no—
537C22⋊C4—221no—
538C22⋊C4—221no—
539C42—111no—
540C42—111no—
541C42—111no—
542C42C23×D1111yescharacteristic
543C11#1800111yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—111no—
547C23—221no—
548C23—221no—
549C23—442no—
550C23—442no—
551C23—881no—
552Q8—442no—
553D4—21no—
554D4—21no—
555D4—21no—
556D4—221no—
557D4—221no—
558D4—221no—
559D4—221no—
560D4—442no—
561D4—442no—
562D4—442no—
563D4—442no—
564D4—881no—
565D4#6696012yescomplemented
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—111no—
573C2×C4—112no—
574C2×C4—112no—
575C2×C4—111no—
576C2×C4—111no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—441no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4C22×C4×D1111yescharacteristic
590C2×C4C2×D4×D1111yescharacteristic
591C2×C4#41×D1111yescharacteristic
592C8—22no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—21no—
597C8—41no—
598C8—41no—
599C8—221no—
600C8—221no—
601C8—221no—
602C8—221no—
603C8—441no—
604C8—441no—
605C8—441no—
606C22—22no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—112no—
613C22—221no—
614C22—221no—
615C22—441no—
616C22—441no—
617C22—441no—
618C22—441no—
619C22—441no—
620C22—441no—
621C22—884no—
622C22C4×D4×D1111yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—112no—
627C4—221no—
628C4—221no—
629C4—441no—
630C4—441no—
631C4C2×#6696011yescharacteristic
632C4#1062328111yescharacteristic
633C4D11×AGL(1,ℤ/8)11yescharacteristic
634C4D11×AGL(1,ℤ/8)11yescharacteristic
635C2—42no—
636C2—81no—
637C2—222no—
638C2—881no—
639C2—881no—
640C2#1307734211yescharacteristic
641C2D11×#44211yescharacteristic
642C2#1307752111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1586C2
socleC22×C11C2×C4×D4
prime radical#13078614C2
cosocleC42×C11C24
hypercenter#1586D11
hypocenterC11#18001
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1586

Complements

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

NH ≅ G/Ntype
2. #13077361C2semidirect
3. D4×#4313C2semidirect
4. #13067529C2semidirect
5. #13067528C2semidirect
6. #13067482C2semidirect
7. #13067477C2semidirect
8. #13067477C2semidirect
9. #13067440C2semidirect
10. #13067438C2semidirect
11. #13067385C2semidirect
12. #13067065C2semidirect
13. D11×D4⋊C8C2semidirect
14. #13066902C2semidirect
15. C11×#1586C2semidirect
21. C11×#436C22semidirect
30. D4×C11⋊C8C22semidirect
34. #10622451C22semidirect
48. C8×D44C22semidirect
51. C11×#334C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×#322C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622118C22semidirect
60. #10622118C22semidirect
62. #10622097C22semidirect
63. #10622095C22semidirect
64. #10622093C22semidirect
65. #10622093C22semidirect
66. #10622092C22semidirect
231. #1586D11semidirect
249. D4×C11#131semidirect
319. #436C2×D11semidirect
338. #334C2×D11semidirect
346. D4⋊C8C2×D11semidirect
350. #322C2×D11semidirect
543. C11#18001semidirect
565. D4#66960semidirect

Maximal subgroups

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

subgroupindex
#130786142
#130773612
D4×#43132
#130675292
#130675282
#130674822
#130674772
#130674402
#130674382
#130673852
#130670652
D11×D4⋊C82
#130669022
C11×#15862
#1800111