Finite Group Databasebeta

← #25103527

Subgroups — #25103527

Order 11008.

906 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583165C211yesmaximal, characteristic
2C4×#13063356C211yesmaximal, characteristic, complemented
3C4×#13063353C211yesmaximal, characteristic
4C2×#14582997C211yesmaximal, characteristic, complemented
5#19143024C211yesmaximal, characteristic, complemented
6#19135499C211yesmaximal, characteristic, complemented
7#19135379C211yesmaximal, characteristic, complemented
8#19135255C211yesmaximal, characteristic, complemented
9#19135252C211yesmaximal, characteristic, complemented
10#19135107C211yesmaximal, characteristic, complemented
11#19135104C211yesmaximal, characteristic
12#19134658C211yesmaximal, characteristic, complemented
13#19134502C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C4×#101×C43C211yesmaximal, characteristic, complemented
16C2×#13063356C2211yescharacteristic
17C2×#13063353C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063333C2211yescharacteristic
21C4×#10621898C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23#14583165C418yescomplemented
24#14583012—21no—
25#14583004—21no—
26#14583001—21no—
27#14582997—21no—
28#14582997—21no—
29#14582997—21no—
30#14582997—21no—
31#14582997—21no—
32C4×#10621885—21no—
33C4×#10621873—21no—
34C4×#10621884—21no—
35C4×D344—21no—
36C2×#13063260C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582939C2211yescharacteristic
40C2×#13063258C2211yescharacteristic
41#14582908C2211yescharacteristic
42#14582905C2211yescharacteristic
43#14582901C2211yescharacteristic
44#14582898C2211yescharacteristic
45C2×#13063249C2211yescharacteristic
46C2×#13063245C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48C2×#13063241C2211yescharacteristic
49#14582857C2211yescharacteristic
50#14582857C2211yescharacteristic
51#14582853—21no—
52#14582853—21no—
53C4×#10621877C2211yescharacteristic
54#14582851—21no—
55C2×#13063236C2211yescharacteristic
56#97×D43—21no—
57#14582667C2211yescharacteristic
58#14582667C2211yescharacteristic
59#14582663C2211yescharacteristic
60#14582663C2211yescharacteristic
61C2×C4×Q8×C43C2211yescharacteristic
62C2×#101×C43C2211yescharacteristic
63C2×#101×C43C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic
65C4×M16×C43C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#343C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C4×D43—21no—
71#13063356—22no—
72#13063356C2×C414yescomplemented
73#13063353—22no—
74#13063353C2×C414yes—
75C2×#10621885—21no—
76C2×#10621873—21no—
77C2×#10621884—21no—
78C2×#10621884—21no—
79C2×#10621884—21no—
80C2×#10621884—22no—
81C2×#10621884C2×C414yescomplemented
82C2×D344—21no—
83#13063333—22no—
84#13063333—22no—
85#13063333—22no—
86#13063333C2×C414yescomplemented
87C2×#10621877C2311yescharacteristic
88C2×#10621877C2311yescharacteristic
89C2×#10621872—21no—
90C2×#10621872—21no—
91C22×C43⋊C8C2311yescharacteristic
92C22×C43⋊C8C2311yescharacteristic
93C2×C8×D43—21no—
94C2×C8×D43—21no—
95C4×Dic86D411yescharacteristic
96C4×Dic86D411yescharacteristic
97C4×D172—21no—
98C4×D172—21no—
99C4×D172—21no—
100C4×D172—21no—
101C4×D172D411yescharacteristic
102C4×D172D411yescharacteristic
103C4×C22⋊D43—21no—
104C4×C22⋊D43—21no—
105#13063284C2311yescharacteristic
106#13063282—21no—
107C2×C4⋊Dic43C2311yescharacteristic
108C2×(C2×D43)⋊C4—21no—
109C42×D43—21no—
110#13063260—22no—
111#13063260C2×C414yescomplemented
112#13063259—21no—
113#13063258—21no—
114#13063258—21no—
115#13063258—21no—
116#13063257—21no—
117#13063256—21no—
118#13063250—21no—
119#13063249—21no—
120#13063249—21no—
121#13063249—21no—
122#13063249—21no—
123#13063248—21no—
124#13063247—21no—
125#13063247—21no—
126#13063247—21no—
127#13063245—21no—
128#13063245—21no—
129#13063245—21no—
130#13063241—22no—
131#13063241C2×C414yescomplemented
132#13063236—21no—
133#13063236D411yescharacteristic
134#13063236D411yescharacteristic
135#13063236D411yescharacteristic
136#13063236D411yescharacteristic
137#13063235—21no—
138#13063235—21no—
139C4×C43⋊C8—21no—
140C8×Dic43—21no—
141C8×Dic43—21no—
142C22×Q8×C43C2311yescharacteristic
143C2×M16×C43C2311yescharacteristic
144C2×M16×C43C2311yescharacteristic
145C2×M16×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C4×Q8×C43—21no—
148C4×Q8×C43—21no—
149C4×Q8×C43—21no—
150C4×Q8×C43—21no—
151C2×C4⋊C4×C43—21no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C42×C43—21no—
154C2×C42×C43C2311yescharacteristic
155#101×C43—22no—
156#101×C43C2×C414yescomplemented
157#97×C43—21no—
158#97×C43—21no—
159C4×C8×C43—21no—
160C4×C8×C43—21no—
161C23×D43—21no—
162C2×Q8×C43—21no—
163C2×Q8×C43—21no—
164C2×Q8×C43—21no—
165C2×Q8×C43—21no—
166C2×Q8×C43—21no—
167C2×Q8×C43C22×C412yes—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43#4111yescharacteristic
171C22×C4×C43#4111yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—21no—
174C22×Dic43—21no—
175#10621898—21no—
176#10621898—21no—
177#10621898C22×C412yes—
178#10621898#4112yes—
179C2×D172—21no—
180C2×D172—21no—
181C2×D172—21no—
182C2×D172—21no—
183C2×D172—21no—
184C2×D172C22×C412yes—
185C2×D172C2×D411yescharacteristic
186C2×C4×D43—21no—
187C2×C4×D43—21no—
188C2×C4×D43—21no—
189C2×C4×D43—41no—
190C2×C4×D43—41no—
191C2×C4×D43—82no—
192C2×Dic86C2×D411yescharacteristic
193M16×C43—21no—
194M16×C43—21no—
195M16×C43—21no—
196M16×C43—21no—
197M16×C43—21no—
198M16×C43C22×C412yes—
199M16×C43C22×C412yes—
200M16×C43#4112yes—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43—21no—
207C4⋊C4×C43—41no—
208C4⋊C4×C43—41no—
209C42×C43—41no—
210C42×C43—41no—
211C42×C43C2×D411yescharacteristic
212C42×C43C2×D411yescharacteristic
213C42×C43C2×D411yescharacteristic
214C42×C43C2×D411yescharacteristic
215C22⋊Dic43—21no—
216#10621885—24no—
217#10621884—24no—
218#10621884—24no—
219#10621884—24no—
220(C2×D43)⋊C4—21no—
221(C2×D43)⋊C4—21no—
222(C2×D43)⋊C4—41no—
223(C2×D43)⋊C4—41no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43C2×D411yescharacteristic
227C4⋊Dic43C2×D411yescharacteristic
228Dic43⋊C4—21no—
229Dic43⋊C4—21no—
230C4×Dic43—21no—
231C4×Dic43—21no—
232C4×Dic43—21no—
233#10621877—21no—
234#10621877—21no—
235#10621877—21no—
236#10621877C22×C412yes—
237C2×C43⋊C8—21no—
238C2×C43⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8C22×C412yes—
242C2×C43⋊C8C2×D411yescharacteristic
243C2×C43⋊C8C2×D411yescharacteristic
244C2×C43⋊C8C2×D411yescharacteristic
245C2×C43⋊C8C2×D411yescharacteristic
246C2×C43⋊C8#4112yes—
247D344—24no—
248#10621873—24no—
249#10621872—24no—
250#10621872—24no—
251C8×D43—24no—
252C8×D43—24no—
253C23×C43C2×#4111yescharacteristic
254C22×D43—21no—
255C22×D43—22no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—81no—
259C22×D43—81no—
260Q8×C43—22no—
261Q8×C43—22no—
262Q8×C43—41no—
263Q8×C43—41no—
264C2×C4×C43—22no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43—41no—
270C2×C4×C43—81no—
271C2×C4×C43#12111yescharacteristic
272C2×C4×C43#12111yescharacteristic
273C2×C4×C43#12111yescharacteristic
274C2×C4×C43#12111yescharacteristic
275C2×C4×C43C23×C411yescharacteristic
276C2×C4×C43C22×D411yescharacteristic
277C2×C4×C43C22×D411yescharacteristic
278C2×C4×C43C2×#4111yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C2×C4×C43C2×#4111yescharacteristic
281C22⋊D43—22no—
282C22⋊D43—22no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—41no—
287C2×Dic43—81no—
288D172—22no—
289D172—22no—
290D172—21no—
291D172—41no—
292D172—41no—
293D172C4×D412yes—
294C4×D43—22no—
295C4×D43—22no—
296C4×D43—81no—
297C4×D43—81no—
298C4×D43—82no—
299C4×D43—82no—
300Dic86—21no—
301Dic86C4×D412yes—
302C8×C43—22no—
303C8×C43—22no—
304C8×C43—22no—
305C8×C43—41no—
306C43⋊C8—22no—
307C43⋊C8—21no—
308C43⋊C8—21no—
309C43⋊C8—41no—
310C43⋊C8C4×D412yes—
311C43⋊C8C4×D412yes—
312#21557—431nomaximal, Sylow
313C22×C43—21no—
314C22×C43—21no—
315C22×C43C4×#4111yescharacteristic
316C22×C43C2×#12111yescharacteristic
317C22×C43#52911yescharacteristic
318C2×D43—22no—
319C2×D43—41no—
320C2×D43—41no—
321C2×D43—42no—
322C2×D43—82no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—82no—
326C4×C43—21no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—21no—
330C4×C43—42no—
331C4×C43—81no—
332C4×C43C2×C4×D411yescharacteristic
333C4×C43C2×C4×D411yescharacteristic
334C4×C43#52511yescharacteristic
335C4×C43#53211yescharacteristic
336Dic43—22no—
337Dic43—41no—
338Dic43—41no—
339Dic43—81no—
340C2×#471—431no—
341C4×#137—431no—
342C4×AGL(1,ℤ/8)—431no—
343C2×#440—431no—
344#2875—431no—
345#1977—431no—
346#1952—431no—
347#1931—431no—
348#1930—431no—
349#1908—431no—
350#1907—431no—
351#1816—431no—
352#1778—431no—
353C4×#101D4311yescharacteristic, complemented
354C4×#100—431no—
355C2×C43—21no—
356C2×C43—21no—
357C2×C43C4×#12111yescharacteristic
358C2×C43#306811yescharacteristic
359C2×C43#306911yescharacteristic
360D43—42no—
361D43—82no—
362C2×#137—431no—
363C2×AGL(1,ℤ/8)—431no—
364C22×SD16—431no—
365C2×#131—431no—
366C2×#131—431no—
367C4×#41—431no—
368C2×C4×Q8C2×D4311yescharacteristic
369C2×C4×D4—431no—
370#471—438no—
371#442—861no—
372#441—861no—
373#440—861no—
374#440—861no—
375#440—861no—
376#440—861no—
377#440—861no—
378#440—861no—
379C4×Q16—861no—
380C4×SD16—861no—
381C4×SD16—861no—
382C4×D8—861no—
383C2×#108—431no—
384C2×#108—431no—
385#428—431no—
386#428—431no—
387C2×#107—431no—
388#419—431no—
389#418—431no—
390#417—431no—
391#417—431no—
392C2×#103—431no—
393C2×#102—431no—
394C2×#101C2×D4311yescharacteristic
395C2×#101C2×D4311yescharacteristic
396C2×#100—431no—
397C2×#100—431no—
398#405—431no—
399#405—431no—
400#405—861no—
401#405—861no—
402C4×M16—431no—
403C4×M16—861no—
404C4×M16C2×D4311yescharacteristic
405C4×M16C2×D4311yescharacteristic
406C2×#97—431no—
407C2×#97—861no—
408#343—431no—
409#343—431no—
410#343C2×D4311yescharacteristic
411#343C2×D4311yescharacteristic
412#341—431no—
413#341—431no—
414C43#2155711yescharacteristic, complemented, Sylow
415C2×#41—431no—
416C22×Q8C22×D4311yescharacteristic
417C22×D4—431no—
418C23×C4—861no—
419#137—434no—
420#137—862no—
421AGL(1,ℤ/8)—434no—
422AGL(1,ℤ/8)—862no—
423C2×Q16—861no—
424C2×SD16—434no—
425C2×SD16—861no—
426C2×SD16—862no—
427C2×SD16—861no—
428C2×SD16—861no—
429C2×SD16—861no—
430C2×D8—861no—
431#131—434no—
432#131—862no—
433#131—862no—
434#131—862no—
435C2×M16—431no—
436C2×M16—431no—
437C2×M16—861no—
438C2×M16—861no—
439C2×M16C22×D4311yescharacteristic
440C2×M16C22×D4311yescharacteristic
441C2×M16C22×D4311yescharacteristic
442C2×M16C22×D4311yescharacteristic
443C22×C8—431no—
444C22×C8—431no—
445C22×C8—861no—
446C22×C8—861no—
447C4×Q8—21no—
448C4×Q8—21no—
449C4×Q8—21no—
450C4×Q8—21no—
451C4×Q8—431no—
452C4×Q8—431no—
453C4×D4—431no—
454C4×D4—431no—
455C4×D4—861no—
456C4×D4—861no—
457C4×D4—861no—
458C4×D4—861no—
459C4×D4—861no—
460C4×D4—861no—
461#117—431no—
462#117—861no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C22⋊C4—861no—
467C2×C42—21no—
468C2×C42—861no—
469C2×C42C22×D4311yescharacteristic
470#108—434no—
471#108—862no—
472#107—861no—
473#107—861no—
474#107—861no—
475#107—861no—
476#106—861no—
477#106—861no—
478#103—861no—
479#103—861no—
480#103—861no—
481#103—861no—
482#103—861no—
483#103—861no—
484#102—861no—
485#102—861no—
486#102—861no—
487#102—861no—
488#102—861no—
489#102—861no—
490#101—22no—
491#101C4×D4314yescomplemented
492#100—434no—
493#100—862no—
494#97—21no—
495#97—21no—
496#97—431no—
497#97—431no—
498#97—431no—
499#97—431no—
500#97—861no—
501#97—861no—
502#97—861no—
503C4×C8—21no—
504C4×C8—21no—
505C4×C8—861no—
506C4×C8—861no—
507C4×C8—861no—
508C24—861no—
509#41—432no—
510#41—432no—
511#41—861no—
512#41—861no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—431no—
519C2×Q8C2×C4×D4312yes—
520C2×D4—432no—
521C2×D4—431no—
522C2×D4—861no—
523C2×D4—861no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4—861no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—861no—
531C22×C4—861no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—3442no—
535C22×C4—1721no—
536C22×C4—1721no—
537C22×C4#1062189811yescharacteristic
538C22×C4#1062189811yescharacteristic
539C22×C4C23×D4311yescharacteristic
540Q16—864no—
541SD16—864no—
542SD16—864no—
543SD16—864no—
544SD16—864no—
545D8—864no—
546M16—21no—
547M16—21no—
548M16—21no—
549M16—21no—
550M16—21no—
551M16—432no—
552M16—864no—
553M16—864no—
554M16—861no—
555M16—861no—
556M16—861no—
557M16C2×C4×D4312yes—
558M16C2×C4×D4312yes—
559M16#1062189812yes—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—432no—
565C2×C8—431no—
566C2×C8—431no—
567C2×C8—432no—
568C2×C8—431no—
569C2×C8—431no—
570C2×C8—864no—
571C2×C8—864no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—41no—
579C4⋊C4—41no—
580C4⋊C4—431no—
581C4⋊C4—431no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—861no—
585C4⋊C4—861no—
586C22⋊C4—861no—
587C22⋊C4—861no—
588C22⋊C4—861no—
589C22⋊C4—1721no—
590C22⋊C4—1721no—
591C42—41no—
592C42—41no—
593C42—861no—
594C42—861no—
595C42—861no—
596C42D4×D4311yescharacteristic
597C42D4×D4311yescharacteristic
598C42D4×D4311yescharacteristic
599C42D4×D4311yescharacteristic
600C23—861no—
601C23—862no—
602C23—3441no—
603C23—3441no—
604C23—1721no—
605C23—1721no—
606C23C2×#1062189811yescharacteristic
607Q8—22no—
608Q8—22no—
609Q8—41no—
610Q8—41no—
611Q8—432no—
612Q8—861no—
613D4—432no—
614D4—862no—
615D4—862no—
616D4—862no—
617D4—862no—
618D4—861no—
619D4—1721no—
620D4—1721no—
621C2×C4—22no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—81no—
628C2×C4—861no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—3442no—
634C2×C4—3442no—
635C2×C4—3441no—
636C2×C4—3441no—
637C2×C4—3441no—
638C2×C4—1721no—
639C2×C4#1306329811yescharacteristic
640C2×C4#1306329811yescharacteristic
641C2×C4#1306329811yescharacteristic
642C2×C4#1306329811yescharacteristic
643C2×C4C22×C4×D4311yescharacteristic
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4C2×D4×D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4C2×#1062189811yescharacteristic
649C8—22no—
650C8—22no—
651C8—22no—
652C8—41no—
653C8—432no—
654C8—432no—
655C8—862no—
656C8—861no—
657C8—861no—
658C8—1721no—
659C22—21no—
660C22—21no—
661C22—862no—
662C22—3442no—
663C22—3442no—
664C22—3441no—
665C22—3441no—
666C22—1722no—
667C22—1721no—
668C22—1721no—
669C22C4×#1062189811yescharacteristic
670C22C2×#1306329811yescharacteristic
671C22#1458342711yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—42no—
677C4—81no—
678C4—862no—
679C4—3441no—
680C4—1721no—
681C4—1721no—
682C4C4×D4×D4311yescharacteristic
683C4C4×D4×D4311yescharacteristic
684C4#1458340811yescharacteristic
685C4#1458344611yescharacteristic
686C2—21no—
687C2—21no—
688C2—3442no—
689C2—1722no—
690C2C4×#1306329811yescharacteristic
691C2#1914432611yescharacteristic
692C2#1914433111yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#101×C43C2
socleC22×C43C2×#121
prime radicalC2×#13063353C22
cosocleC22×C4×C43C24
hypercenterC4×#101D43
hypocenterC43#21557
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
2. C4×#13063356C2semidirect
4. C2×#14582997C2semidirect
5. #19143024C2semidirect
6. #19135499C2semidirect
7. #19135379C2semidirect
8. #19135255C2semidirect
9. #19135252C2semidirect
10. #19135107C2semidirect
12. #19134658C2semidirect
13. #19134502C2semidirect
14. C4×#13063241C2semidirect
15. C4×#101×C43C2semidirect
23. #14583165C4semidirect
72. #13063356C2×C4semidirect
81. C2×#10621884C2×C4semidirect
86. #13063333C2×C4semidirect
111. #13063260C2×C4semidirect
131. #13063241C2×C4semidirect
156. #101×C43C2×C4semidirect
353. C4×#101D43semidirect
414. C43#21557semidirect
491. #101C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831652
C4×#130633562
C4×#130633532
C2×#145829972
#191430242
#191354992
#191353792
#191352552
#191352522
#191351072
#191351042
#191346582
#191345022
C4×#130632412
C4×#101×C432
#2155743