Finite Group Databasebeta

← #14724657

Subgroups — #14724657

Order 2816.

748 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#13077355C211yesmaximal, characteristic, complemented
3#13077352C211yesmaximal, characteristic, complemented
4#13067501C211yesmaximal, characteristic, complemented
5#13067499C211yesmaximal, characteristic, complemented
6#13067448C211yesmaximal, characteristic, complemented
7#13067448C211yesmaximal, characteristic, complemented
8#13067447C211yesmaximal, characteristic, complemented
9#13067410C211yesmaximal, characteristic, complemented
10C8×#4323C211yesmaximal, characteristic, complemented
11#13067389C211yesmaximal, characteristic, complemented
12#13067065C211yesmaximal, characteristic, complemented
13D11×D4⋊C8C211yesmaximal, characteristic, complemented
14#13066895C211yesmaximal, characteristic, complemented
15C11×#1581C211yesmaximal, characteristic, complemented
16C2×M16×D11—21no—
17C2×#66954—21no—
18#10623079C2211yescharacteristic
19C4×D4×D11C2211yescharacteristic
20C4×C11×D8C2211yescharacteristic
21C11×#436C2211yescharacteristic
22C8×D4×C11C2211yescharacteristic, complemented
23#10622769C411yescharacteristic
24#10622763C411yescharacteristic
25#10622740—21no—
26#10622724—21no—
27C4×#4323C2211yescharacteristic
28C4×#4323C2211yescharacteristic
29#10622625C2211yescharacteristic
30#10622625C2211yescharacteristic, complemented
31#10622503C411yescharacteristic
32#10622495C411yescharacteristic
33#10622450C2211yescharacteristic
34#10622447C2211yescharacteristic
35#10622447C2211yescharacteristic, complemented
36D11×C4⋊C8C2211yescharacteristic
37#10622399C411yescharacteristic
38#10622387C411yescharacteristic
39#10622386C411yescharacteristic
40#10622372C411yescharacteristic
41#10622341—21no—
42#10622341—21no—
43#10622340—21no—
44#10622339—21no—
45C4×D88C2211yescharacteristic
46#10622301C2211yescharacteristic, complemented
47C4×#4313C2211yescharacteristic
48C8×D44C2211yescharacteristic
49#10622298C2211yescharacteristic
50C4×C8×D11C2211yescharacteristic
51C11×#335C2211yescharacteristic, 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#10622117C2211yescharacteristic, complemented
60#10622117C2211yescharacteristic, complemented
61#10622097C2211yescharacteristic
62#10622097C2211yescharacteristic, complemented
63#10622096C2211yescharacteristic, complemented
64#10622092C2211yescharacteristic, complemented
65C8×C11⋊C8C2211yescharacteristic, complemented
66C8×C11⋊C8C2211yescharacteristic, 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—
82C2×#4318—21no—
83C2×#4318—21no—
84M16×D11—44no—
85C2×D88C2×C411yescharacteristic
86#66954—44no—
87C2×#4313—21no—
88C2×#4313—21no—
89C2×#4313D411yescharacteristic
90C2×#4313D411yescharacteristic
91C2×C8×D11—21no—
92C2×C8×D11—21no—
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#17994—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—41no—
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
204#4318—42no—
205#4318—42no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8C22×C411yescharacteristic
210C2×C11⋊C8C22×C411yescharacteristic
211C2×C11⋊C8C2×D411yescharacteristic
212C2×C11⋊C8C2×D411yescharacteristic
213D88—22no—
214#4313—22no—
215#4313—42no—
216#4313—42no—
217#4313D814yescomplemented
218C8×D11—42no—
219C8×D11—42no—
220C8×D11—42no—
221C8×D11—42no—
222C8×D11—42no—
223#3100—111no—
224#2935—111no—
225D4×M16—111no—
226#1589—111no—
227#1589—111no—
228#1581—111no—
229#1581—111no—
230#1581—111no—
231#1581D1111yescharacteristic, complemented
232C8×D8—111no—
233C8×D8—111no—
234#1571—111no—
235#1492—111no—
236C2×D4⋊C8—111no—
237C8×M16—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—21no—
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—42no—
273D44#13112yescomplemented
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×D11C2×D812yes—
284C4×D11#13512yes—
285Dic22—42no—
286C8×C11—21no—
287C8×C11—21no—
288C8×C11—21no—
289C8×C11—41no—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11C2×D812yes—
293C11⋊C8—22no—
294C11⋊C8—21no—
295C11⋊C8—21no—
296C11⋊C8—21no—
297C11⋊C8—41no—
298C11⋊C8—41no—
299C11⋊C8C2×D812yes—
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
320#435—221no—
321#435—221no—
322#435—221no—
323#435—221no—
324C8×D4—111no—
325C8×D4—111no—
326C8×D4—111no—
327C8×D4C2×D1111yescharacteristic, complemented
328#431—111no—
329#423—111no—
330C2×C4⋊C8—111no—
331#408—221no—
332#407—221no—
333C4×M16—111no—
334C2×C4×C8—111no—
335#335—111no—
336#335—111no—
337#335—111no—
338#335C2×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#322C2×D1111yescharacteristic, complemented
349C82—111no—
350C82—111no—
351C22×C11—41no—
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—22no—
361C2×D11—41no—
362C2×D11—41no—
363C2×D11—41no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—84no—
367C2×D11C4×D812yes—
368C4×C11—21no—
369C4×C11—41no—
370C4×C11—41no—
371C4×C11C2×#13111yescharacteristic
372C4×C11#56811yescharacteristic
373C4×C11C22×D811yescharacteristic
374C4×C11C2×#13511yescharacteristic
375Dic11—21no—
376Dic11—21no—
377Dic11—41no—
378Dic11—41no—
379Dic11C4×D812yes—
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—81no—
460C2×C11—81no—
461C2×C11#293311yescharacteristic
462C2×C11C2×C4×D811yescharacteristic
463C2×C11#295611yescharacteristic
464D11—22no—
465D11—42no—
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—41no—
495D8—222no—
496D8—222no—
497D8—441no—
498M16—42no—
499M16—114no—
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#1799411yescharacteristic, 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—21no—
557D4—112no—
558D4—221no—
559D4—221no—
560D4—221no—
561D4—442no—
562D4—442no—
563D4—442no—
564D4—442no—
565D4—881no—
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—21no—
593C8—21no—
594C8—21no—
595C8—41no—
596C8—41no—
597C8—41no—
598C8—112no—
599C8—222no—
600C8—221no—
601C8—221no—
602C8—221no—
603C8—441no—
604C8—441no—
605C8D8×D1112yes—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—112no—
613C22—221no—
614C22—221no—
615C22—222no—
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—
631C4#1062327611yescharacteristic
632C4D11×#13111yescharacteristic
633C4C2×D8×D1111yescharacteristic
634C4D11×#13511yescharacteristic
635C2—81no—
636C2—81no—
637C2—222no—
638C2—442no—
639C2—881no—
640C2#1307733911yescharacteristic
641C2C4×D8×D1111yescharacteristic
642C2#1307752411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC42C23×D11
FittingC11×#1581C2
socleC22×C11C2×C4×D4
prime radical#13078614C2
cosocleC42×C11C24
hypercenter#1581D11
hypocenterC11#17994
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1581

Complements

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

NH ≅ G/Ntype
2. #13077355C2semidirect
3. #13077352C2semidirect
4. #13067501C2semidirect
5. #13067499C2semidirect
6. #13067448C2semidirect
7. #13067448C2semidirect
8. #13067447C2semidirect
9. #13067410C2semidirect
10. C8×#4323C2semidirect
11. #13067389C2semidirect
12. #13067065C2semidirect
13. D11×D4⋊C8C2semidirect
14. #13066895C2semidirect
15. C11×#1581C2semidirect
22. C8×D4×C11C22semidirect
30. #10622625C22semidirect
35. #10622447C22semidirect
46. #10622301C22semidirect
51. C11×#335C22semidirect
53. C11×D4⋊C8C22semidirect
54. C11×#322C22semidirect
56. D4⋊(C11⋊C8)C22semidirect
58. #10622121C22semidirect
59. #10622117C22semidirect
60. #10622117C22semidirect
62. #10622097C22semidirect
63. #10622096C22semidirect
64. #10622092C22semidirect
65. C8×C11⋊C8C22semidirect
66. C8×C11⋊C8C22semidirect
217. #4313D8semidirect
231. #1581D11semidirect
273. D44#131semidirect
327. C8×D4C2×D11semidirect
338. #335C2×D11semidirect
346. D4⋊C8C2×D11semidirect
348. #322C2×D11semidirect
543. C11#17994semidirect

Maximal subgroups

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

subgroupindex
#130786142
#130773552
#130773522
#130675012
#130674992
#130674482
#130674472
#130674102
C8×#43232
#130673892
#130670652
D11×D4⋊C82
#130668952
C11×#15812
#1799411