Finite Group Databasebeta

← #25103519

Subgroups — #25103519

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×#14583161C211yesmaximal, characteristic
2C4×#13063358C211yesmaximal, characteristic, complemented
3C4×#13063351C211yesmaximal, characteristic
4C2×#14582999C211yesmaximal, characteristic, complemented
5#19143024C211yesmaximal, characteristic, complemented
6#19135495C211yesmaximal, characteristic, complemented
7#19135379C211yesmaximal, characteristic, complemented
8#19135259C211yesmaximal, characteristic, complemented
9#19135248C211yesmaximal, characteristic, complemented
10#19135111C211yesmaximal, characteristic, complemented
11#19135100C211yesmaximal, characteristic
12#19134658C211yesmaximal, characteristic, complemented
13#19134502C211yesmaximal, characteristic, complemented
14C4×#13063243C211yesmaximal, characteristic, complemented
15C4×#100×C43C211yesmaximal, characteristic, complemented
16C2×#13063358C2211yescharacteristic
17C2×#13063351C2211yescharacteristic
18C22×#10621883C2211yescharacteristic
19C2×#13063333C2211yescharacteristic
20C2×#13063333C2211yescharacteristic
21C4×#10621898C2211yescharacteristic
22C2×C4×Dic86C2211yescharacteristic
23#14583161C418yescomplemented
24#14583009—21no—
25#14583007—21no—
26#14583001—21no—
27#14582999—21no—
28#14582999—21no—
29#14582999—21no—
30#14582999—21no—
31#14582999—21no—
32C4×Dic172—21no—
33C4×#10621873—21no—
34C4×#10621883—21no—
35C4×#10621882—21no—
36C2×#13063260C2211yescharacteristic
37C2×#13063260C2211yescharacteristic
38#14582941C2211yescharacteristic
39#14582939C2211yescharacteristic
40C2×#13063258C2211yescharacteristic
41#14582909C2211yescharacteristic
42#14582904C2211yescharacteristic
43#14582901C2211yescharacteristic
44#14582898C2211yescharacteristic
45C2×#13063248C2211yescharacteristic
46C2×#13063246C2211yescharacteristic
47C2×#13063243C2211yescharacteristic
48C2×#13063243C2211yescharacteristic
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×D4×C43C2211yescharacteristic
62C2×#100×C43C2211yescharacteristic
63C2×#100×C43C2211yescharacteristic
64C4×M16×C43C2211yescharacteristic
65C4×M16×C43C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#343C2211yescharacteristic
68C2×#10621898C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70#13063358—22no—
71#13063358C2×C414yescomplemented
72#13063351—22no—
73#13063351C2×C414yes—
74C2×Dic172—21no—
75C2×#10621873—21no—
76C2×#10621883—21no—
77C2×#10621883—21no—
78C2×#10621883—21no—
79C2×#10621883—22no—
80C2×#10621883C2×C414yescomplemented
81C2×#10621882—21no—
82#13063333—22no—
83#13063333—22no—
84#13063333—22no—
85#13063333C2×C414yescomplemented
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C2×#10621872—21no—
89C2×#10621872—21no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C2×C8×D43—21no—
93C2×C8×D43—21no—
94C4×Dic86—21no—
95C4×Dic86—21no—
96C4×Dic86—21no—
97C4×Dic86—21no—
98C4×Dic86D411yescharacteristic
99C4×Dic86D411yescharacteristic
100C4×D172D411yescharacteristic
101C4×D172D411yescharacteristic
102C4×C22⋊D43—21no—
103C4×C22⋊D43—21no—
104#13063284C2311yescharacteristic
105#13063282—21no—
106C2×C4⋊Dic43C2311yescharacteristic
107C2×Dic43⋊C4—21no—
108C2×C4×Dic43—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#13063250—21no—
120#13063250—21no—
121#13063248—21no—
122#13063248—21no—
123#13063248—21no—
124#13063247—21no—
125#13063246—21no—
126#13063246—21no—
127#13063246—21no—
128#13063246—21no—
129#13063245—21no—
130#13063243—22no—
131#13063243C2×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×D4×C43C2311yescharacteristic
143C23×C4×C43—21no—
144C2×M16×C43C2311yescharacteristic
145C2×M16×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C4×D4×C43—21no—
149C4×D4×C43—21no—
150C4×D4×C43—21no—
151C4×D4×C43—21no—
152C2×C4⋊C4×C43C2311yescharacteristic
153C2×C22⋊C4×C43—21no—
154C2×C42×C43C2311yescharacteristic
155#100×C43—22no—
156#100×C43C2×C414yescomplemented
157#97×C43—21no—
158#97×C43—21no—
159C4×C8×C43—21no—
160C4×C8×C43—21no—
161C24×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43—21no—
166C2×D4×C43—21no—
167C2×D4×C43C22×C412yes—
168C22×C4×C43—21no—
169C22×C4×C43—41no—
170C22×C4×C43—41no—
171C22×C4×C43—82no—
172C22×C4×C43#4111yescharacteristic
173C22×C4×C43#4111yescharacteristic
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—21no—
176C22×Dic43—21no—
177C22×Dic43—21no—
178#10621898—21no—
179#10621898—21no—
180#10621898C22×C412yes—
181#10621898#4112yes—
182C2×D172C2×D411yescharacteristic
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×Dic86—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86C22×C412yes—
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—
207C22⋊C4×C43—41no—
208C22⋊C4×C43—41no—
209C42×C43C2×D411yescharacteristic
210C42×C43C2×D411yescharacteristic
211C42×C43C2×D411yescharacteristic
212C42×C43C2×D411yescharacteristic
213C22⋊Dic43—21no—
214#10621883—24no—
215#10621883—24no—
216#10621883—24no—
217#10621882—24no—
218(C2×D43)⋊C4—21no—
219(C2×D43)⋊C4—21no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43C2×D411yescharacteristic
223C4⋊Dic43C2×D411yescharacteristic
224Dic43⋊C4—21no—
225Dic43⋊C4—21no—
226Dic43⋊C4—41no—
227Dic43⋊C4—41no—
228C4×Dic43—21no—
229C4×Dic43—21no—
230C4×Dic43—21no—
231C4×Dic43—41no—
232C4×Dic43—41no—
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—
247Dic172—24no—
248#10621873—24no—
249#10621872—24no—
250#10621872—24no—
251C8×D43—24no—
252C8×D43—24no—
253C23×C43—22no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43—81no—
257C23×C43—81no—
258C23×C43C2×#4111yescharacteristic
259C22×D43—21no—
260D4×C43—22no—
261D4×C43—22no—
262D4×C43—41no—
263D4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—82no—
268C2×C4×C43—82no—
269C2×C4×C43—81no—
270C2×C4×C43#12111yescharacteristic
271C2×C4×C43#12111yescharacteristic
272C2×C4×C43#12111yescharacteristic
273C2×C4×C43#12111yescharacteristic
274C2×C4×C43C23×C411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C2×C4×C43C22×D411yescharacteristic
277C2×C4×C43C2×#4111yescharacteristic
278C2×C4×C43C2×#4111yescharacteristic
279C2×C4×C43C2×#4111yescharacteristic
280C22⋊D43—22no—
281C22⋊D43—22no—
282C2×Dic43—21no—
283C2×Dic43—22no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—81no—
290D172—21no—
291D172C4×D412yes—
292C4×D43—22no—
293C4×D43—22no—
294C4×D43—81no—
295C4×D43—81no—
296Dic86—21no—
297Dic86—22no—
298Dic86—22no—
299Dic86—41no—
300Dic86—41no—
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×C43—42no—
316C22×C43—82no—
317C22×C43—82no—
318C22×C43—81no—
319C22×C43—81no—
320C22×C43C4×#4111yescharacteristic
321C22×C43C2×#12111yescharacteristic
322C22×C43#52911yescharacteristic
323C2×D43—22no—
324C2×D43—41no—
325C2×D43—41no—
326C4×C43—21no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—21no—
330C4×C43—81no—
331C4×C43C2×C4×D411yescharacteristic
332C4×C43C2×C4×D411yescharacteristic
333C4×C43#52511yescharacteristic
334C4×C43#53211yescharacteristic
335Dic43—22no—
336Dic43—42no—
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×#101—431no—
354C4×#100D4311yescharacteristic, complemented
355C2×C43—21no—
356C2×C43—21no—
357C2×C43—82no—
358C2×C43C4×#12111yescharacteristic
359C2×C43#306811yescharacteristic
360C2×C43#306911yescharacteristic
361D43—42no—
362C2×#137—431no—
363C2×AGL(1,ℤ/8)—431no—
364C22×SD16—431no—
365C2×#131—431no—
366C2×#131—431no—
367C4×#41—431no—
368C2×C4×Q8—431no—
369C2×C4×D4C2×D4311yescharacteristic
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×#101—431no—
395C2×#101—431no—
396C2×#100C2×D4311yescharacteristic
397C2×#100C2×D4311yescharacteristic
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×Q8—431no—
417C22×D4C22×D4311yescharacteristic
418C23×C4—21no—
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—431no—
448C4×Q8—431no—
449C4×Q8—861no—
450C4×Q8—861no—
451C4×Q8—861no—
452C4×Q8—861no—
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—21no—
456C4×D4—21no—
457C4×D4—431no—
458C4×D4—431no—
459C4×D4—861no—
460C4×D4—861no—
461#117—431no—
462#117—861no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C22⋊C4—21no—
467C2×C42—861no—
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—434no—
491#101—862no—
492#100—22no—
493#100C4×D4314yescomplemented
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—21no—
509#41—432no—
510#41—432no—
511#41—861no—
512#41—861no—
513C2×Q8—432no—
514C2×Q8—431no—
515C2×Q8—861no—
516C2×Q8—861no—
517C2×Q8—861no—
518C2×Q8—861no—
519C2×Q8—861no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—431no—
526C2×D4—861no—
527C2×D4C2×C4×D4312yes—
528C22×C4—21no—
529C22×C4—41no—
530C22×C4—41no—
531C22×C4—82no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
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—431no—
579C4⋊C4—431no—
580C4⋊C4—861no—
581C4⋊C4—861no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4—1721no—
585C4⋊C4—1721no—
586C22⋊C4—41no—
587C22⋊C4—41no—
588C22⋊C4—861no—
589C22⋊C4—861no—
590C22⋊C4—861no—
591C42—861no—
592C42—861no—
593C42—861no—
594C42—1721no—
595C42—1721no—
596C42D4×D4311yescharacteristic
597C42D4×D4311yescharacteristic
598C42D4×D4311yescharacteristic
599C42D4×D4311yescharacteristic
600C23—22no—
601C23—41no—
602C23—41no—
603C23—81no—
604C23—81no—
605C23—861no—
606C23C2×#1062189811yescharacteristic
607Q8—432no—
608Q8—861no—
609Q8—862no—
610Q8—862no—
611Q8—1721no—
612Q8—1721no—
613D4—22no—
614D4—22no—
615D4—41no—
616D4—41no—
617D4—432no—
618D4—862no—
619D4—862no—
620D4—861no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—82no—
625C2×C4—82no—
626C2×C4—81no—
627C2×C4—861no—
628C2×C4—862no—
629C2×C4—862no—
630C2×C4—862no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—3441no—
634C2×C4—3441no—
635C2×C4—3441no—
636C2×C4—1721no—
637C2×C4—1721no—
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—42no—
662C22—82no—
663C22—82no—
664C22—81no—
665C22—81no—
666C22—862no—
667C22—1721no—
668C22—1721no—
669C22C4×#1062189811yescharacteristic
670C22C2×#1306329811yescharacteristic
671C22#1458342711yescharacteristic
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—81no—
677C4—862no—
678C4—3441no—
679C4—1722no—
680C4—1721no—
681C4—1721no—
682C4C4×D4×D4311yescharacteristic
683C4C4×D4×D4311yescharacteristic
684C4#1458340811yescharacteristic
685C4#1458344611yescharacteristic
686C2—21no—
687C2—21no—
688C2—82no—
689C2—1722no—
690C2C4×#1306329811yescharacteristic
691C2#1914432211yescharacteristic
692C2#1914433511yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C2×#121
prime radicalC2×#13063351C22
cosocleC22×C4×C43C24
hypercenterC4×#100D43
hypocenterC43#21557
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

Complements

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

NH ≅ G/Ntype
2. C4×#13063358C2semidirect
4. C2×#14582999C2semidirect
5. #19143024C2semidirect
6. #19135495C2semidirect
7. #19135379C2semidirect
8. #19135259C2semidirect
9. #19135248C2semidirect
10. #19135111C2semidirect
12. #19134658C2semidirect
13. #19134502C2semidirect
14. C4×#13063243C2semidirect
15. C4×#100×C43C2semidirect
23. #14583161C4semidirect
71. #13063358C2×C4semidirect
80. C2×#10621883C2×C4semidirect
85. #13063333C2×C4semidirect
111. #13063260C2×C4semidirect
131. #13063243C2×C4semidirect
156. #100×C43C2×C4semidirect
354. C4×#100D43semidirect
414. C43#21557semidirect
493. #100C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831612
C4×#130633582
C4×#130633512
C2×#145829992
#191430242
#191354952
#191353792
#191352592
#191352482
#191351112
#191351002
#191346582
#191345022
C4×#130632432
C4×#100×C432
#2155743