Finite Group Databasebeta

← #25103525

Subgroups — #25103525

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×#14583164C211yesmaximal, characteristic
2C4×#13063350C211yesmaximal, characteristic
3C2×#14582997C211yesmaximal, characteristic, complemented
4#19143023C211yesmaximal, characteristic, complemented
5#19135497C211yesmaximal, characteristic, complemented
6#19135377C211yesmaximal, characteristic, complemented
7#19135256C211yesmaximal, characteristic, complemented
8#19135253C211yesmaximal, characteristic, complemented
9#19135112C211yesmaximal, characteristic, complemented
10#19135101C211yesmaximal, characteristic
11#19134657C211yesmaximal, characteristic, complemented
12#19134502C211yesmaximal, characteristic, complemented
13C4×#13063244C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C4×#137×C43C211yesmaximal, characteristic, complemented
16C2×#13063350C2211yescharacteristic
17C22×#10621884C2211yescharacteristic
18C2×#13063332C2211yescharacteristic
19C2×#13063332C2211yescharacteristic
20C2×C4×D172C2211yescharacteristic
21#14583164C418yescomplemented
22#14583009—21no—
23#14582997—21no—
24#14582997—21no—
25#14582997—21no—
26#14582997—21no—
27#14582997—21no—
28C4×#10621884—21no—
29C4×#10621882—21no—
30C2×#13063260C2211yescharacteristic
31C2×#13063260C2211yescharacteristic
32#14582942C2211yescharacteristic
33C2×#13063258C2211yescharacteristic
34#14582903C2211yescharacteristic
35#14582900C2211yescharacteristic
36C2×#13063249C2211yescharacteristic
37C2×#13063245C2211yescharacteristic
38C2×#13063244C2211yescharacteristic
39C2×#13063244C2211yescharacteristic
40C2×#13063241C2211yescharacteristic
41C2×#13063241C2211yescharacteristic
42#14582855—21no—
43#14582855—21no—
44#14582855C2211yescharacteristic
45#14582855C2211yescharacteristic
46C4×#10621877—21no—
47C4×#10621877C2211yescharacteristic
48C4×#10621877C2211yescharacteristic
49C2×#13063236—21no—
50C2×#13063236C2211yescharacteristic
51#14582668C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582667C2211yescharacteristic
55#14582663C2211yescharacteristic
56#14582663C2211yescharacteristic
57C2×#137×C43C2211yescharacteristic
58C4×#41×C43C2211yescharacteristic
59C2×C4×Q8×C43C2211yescharacteristic
60C43×#441—21no—
61C43×#440—21no—
62C4×Q16×C43—21no—
63C4×SD16×C43—21no—
64C43×#428C2211yescharacteristic
65C43×#419C2211yescharacteristic
66C43×#417C2211yescharacteristic
67C4×M16×C43C2211yescharacteristic
68C22×D172C2311yescharacteristic
69C22×C4×D43—21no—
70#13063350—22no—
71#13063350C2×C414yes—
72C2×#10621884—21no—
73C2×#10621884—21no—
74C2×#10621884—21no—
75C2×#10621884—22no—
76C2×#10621884C2×C414yescomplemented
77C2×#10621882—21no—
78#13063332—22no—
79#13063332—22no—
80#13063332—22no—
81#13063332C2×C414yescomplemented
82C2×#10621877—21no—
83C2×#10621877—21no—
84C2×#10621877C2311yescharacteristic
85C2×#10621877C2311yescharacteristic
86C2×#10621877C2311yescharacteristic
87C2×#10621877C2311yescharacteristic
88C22×C43⋊C8—21no—
89C22×C43⋊C8—21no—
90C22×C43⋊C8C2311yescharacteristic
91C22×C43⋊C8C2311yescharacteristic
92C4×D172—21no—
93C4×D172—21no—
94C4×D172—21no—
95C4×D172—21no—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×(C2×D43)⋊C4—21no—
98#13063260—22no—
99#13063260C2×C414yescomplemented
100#13063258—21no—
101#13063258—21no—
102#13063258—21no—
103#13063256—21no—
104#13063249—21no—
105#13063249—21no—
106#13063249—21no—
107#13063246—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—21no—
111#13063245—21no—
112#13063244—22no—
113#13063244C2×C414yescomplemented
114#13063241—22no—
115#13063241C2×C414yescomplemented
116#13063236—21no—
117#13063236—21no—
118#13063236—21no—
119#13063236—21no—
120#13063236D411yescharacteristic
121#13063236D411yescharacteristic
122#13063236D411yescharacteristic
123#13063236D411yescharacteristic
124C4×C43⋊C8—21no—
125C4×C43⋊C8—21no—
126C4×C43⋊C8—21no—
127C4×C43⋊C8—21no—
128C2×#41×C43C2311yescharacteristic
129C22×Q8×C43C2311yescharacteristic
130#137×C43—22no—
131#137×C43C2×C414yescomplemented
132C2×Q16×C43—21no—
133C2×SD16×C43—21no—
134C2×M16×C43C2311yescharacteristic
135C2×M16×C43C2311yescharacteristic
136C4×Q8×C43—21no—
137C4×Q8×C43—21no—
138C4×Q8×C43—21no—
139C4×Q8×C43—21no—
140C4×Q8×C43D411yescharacteristic
141C4×Q8×C43D411yescharacteristic
142C4×D4×C43—21no—
143C4×D4×C43—21no—
144C4×D4×C43D411yescharacteristic
145C4×D4×C43D411yescharacteristic
146#117×C43—21no—
147#117×C43C2311yescharacteristic
148C2×C4⋊C4×C43—21no—
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C42×C43—21no—
151C2×C42×C43—21no—
152C2×C42×C43C2311yescharacteristic
153#107×C43—21no—
154#106×C43—21no—
155#103×C43—21no—
156#103×C43—21no—
157#103×C43—21no—
158#102×C43—21no—
159#97×C43—21no—
160C4×C8×C43—21no—
161C23×D43—21no—
162#41×C43—21no—
163#41×C43—21no—
164#41×C43C22×C412yes—
165#41×C43#4112yes—
166C2×Q8×C43—21no—
167C2×Q8×C43—21no—
168C2×Q8×C43—21no—
169C2×Q8×C43—21no—
170C2×Q8×C43—21no—
171C2×Q8×C43C22×C412yes—
172C2×Q8×C43C2×D411yescharacteristic
173C2×D4×C43—21no—
174C2×D4×C43C2×D411yescharacteristic
175C22×C4×C43—21no—
176C22×C4×C43—21no—
177C22×C4×C43—21no—
178C22×C4×C43—21no—
179C22×C4×C43—21no—
180C22×C4×C43#4111yescharacteristic
181C22×C4×C43#4111yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C22×Dic43—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172C22×C412yes—
190C2×C4×D43—41no—
191C2×C4×D43—41no—
192C2×C4×D43—82no—
193Q16×C43—24no—
194SD16×C43—24no—
195M16×C43—21no—
196M16×C43—21no—
197M16×C43—21no—
198M16×C43C22×C412yes—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—41no—
206C4⋊C4×C43—41no—
207C4⋊C4×C43C2×D411yescharacteristic
208C4⋊C4×C43C2×D411yescharacteristic
209C22⋊C4×C43—21no—
210C22⋊C4×C43—21no—
211C22⋊C4×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43—21no—
215C42×C43—41no—
216C42×C43—41no—
217C42×C43C2×D411yescharacteristic
218C42×C43C2×D411yescharacteristic
219C42×C43C2×D411yescharacteristic
220C42×C43C2×D411yescharacteristic
221#10621884—24no—
222#10621884—24no—
223#10621884—24no—
224#10621882—24no—
225(C2×D43)⋊C4—41no—
226(C2×D43)⋊C4—41no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229#10621877—24no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—24no—
234#10621877—21no—
235#10621877—21no—
236#10621877C22×C412yes—
237#10621877C22×C412yes—
238#10621877#4112yes—
239C2×C43⋊C8—24no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—24no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8C22×C412yes—
248C2×C43⋊C8C2×D411yescharacteristic
249C2×C43⋊C8C2×D411yescharacteristic
250C2×C43⋊C8C2×D411yescharacteristic
251C2×C43⋊C8C2×D411yescharacteristic
252C2×C43⋊C8#4112yes—
253C23×C43—21no—
254C23×C43C2×#4111yescharacteristic
255C22×D43—22no—
256C22×D43—41no—
257C22×D43—41no—
258C22×D43—81no—
259C22×D43—81no—
260Q8×C43—21no—
261Q8×C43—22no—
262Q8×C43—22no—
263Q8×C43—41no—
264Q8×C43—41no—
265Q8×C43C4×D412yes—
266D4×C43—22no—
267D4×C43—22no—
268D4×C43—21no—
269D4×C43C4×D412yes—
270C2×C4×C43—21no—
271C2×C4×C43—22no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—41no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—81no—
282C2×C4×C43—81no—
283C2×C4×C43—81no—
284C2×C4×C43#12111yescharacteristic
285C2×C4×C43#12111yescharacteristic
286C2×C4×C43#12111yescharacteristic
287C2×C4×C43#12111yescharacteristic
288C2×C4×C43C23×C411yescharacteristic
289C2×C4×C43C22×D411yescharacteristic
290C2×C4×C43C22×D411yescharacteristic
291C2×C4×C43C2×#4111yescharacteristic
292C2×C4×C43C2×#4111yescharacteristic
293C2×C4×C43C2×#4111yescharacteristic
294C2×Dic43—41no—
295C2×Dic43—81no—
296D172—22no—
297D172—22no—
298D172—41no—
299D172—41no—
300C4×D43—82no—
301C4×D43—82no—
302C8×C43—22no—
303C8×C43—41no—
304C43⋊C8—22no—
305C43⋊C8—22no—
306C43⋊C8—21no—
307C43⋊C8—22no—
308C43⋊C8—21no—
309C43⋊C8—41no—
310C43⋊C8C4×D412yes—
311C43⋊C8C4×D412yes—
312#21557—431nomaximal, Sylow
313C22×C43—21no—
314C22×C43—21no—
315C22×C43—22no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43C4×#4111yescharacteristic
319C22×C43C2×#12111yescharacteristic
320C22×C43#52911yescharacteristic
321C2×D43—42no—
322C2×D43—82no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—82no—
326C4×C43—22no—
327C4×C43—21no—
328C4×C43—21no—
329C4×C43—21no—
330C4×C43—21no—
331C4×C43—42no—
332C4×C43—41no—
333C4×C43—41no—
334C4×C43—81no—
335C4×C43C2×C4×D411yescharacteristic
336C4×C43C2×C4×D411yescharacteristic
337C4×C43#52511yescharacteristic
338C4×C43#53211yescharacteristic
339Dic43—81no—
340C2×#471—431no—
341C4×#137D4311yescharacteristic, complemented
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×#100—431no—
355C2×C43—21no—
356C2×C43—21no—
357C2×C43—42no—
358C2×C43C4×#12111yescharacteristic
359C2×C43#306811yescharacteristic
360C2×C43#306911yescharacteristic
361D43—82no—
362C2×#137C2×D4311yescharacteristic
363C2×AGL(1,ℤ/8)—431no—
364C22×SD16—431no—
365C2×#131—431no—
366C2×#131—431no—
367C4×#41C2×D4311yescharacteristic
368C2×C4×Q8C2×D4311yescharacteristic
369C2×C4×D4—431no—
370#471—438no—
371#442—861no—
372#441—21no—
373#440—21no—
374#440—861no—
375#440—861no—
376#440—861no—
377#440—861no—
378#440—861no—
379C4×Q16—21no—
380C4×SD16—21no—
381C4×SD16—861no—
382C4×D8—861no—
383C2×#108—431no—
384C2×#108—431no—
385#428—431no—
386#428C2×D4311yescharacteristic
387C2×#107—431no—
388#419C2×D4311yescharacteristic
389#418—431no—
390#417—431no—
391#417C2×D4311yescharacteristic
392C2×#103—431no—
393C2×#102—431no—
394C2×#101—431no—
395C2×#101—431no—
396C2×#100—431no—
397C2×#100—431no—
398#405—431no—
399#405—431no—
400#405—861no—
401#405—861no—
402C4×M16—431no—
403C4×M16—431no—
404C4×M16—861no—
405C4×M16C2×D4311yescharacteristic
406C2×#97—431no—
407C2×#97—861no—
408#343—431no—
409#343—431no—
410#343—431no—
411#343—431no—
412#341—431no—
413#341—431no—
414C43#2155711yescharacteristic, complemented, Sylow
415C2×#41C22×D4311yescharacteristic
416C22×Q8C22×D4311yescharacteristic
417C22×D4—431no—
418C23×C4—861no—
419#137—22no—
420#137C4×D4314yescomplemented
421AGL(1,ℤ/8)—434no—
422AGL(1,ℤ/8)—862no—
423C2×Q16—21no—
424C2×SD16—21no—
425C2×SD16—434no—
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—431no—
438C2×M16—431no—
439C2×M16—861no—
440C2×M16—861no—
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×Q8C22⋊D4311yescharacteristic
452C4×Q8C22⋊D4311yescharacteristic
453C4×D4—21no—
454C4×D4—21no—
455C4×D4—861no—
456C4×D4—861no—
457C4×D4—861no—
458C4×D4—861no—
459C4×D4C22⋊D4311yescharacteristic
460C4×D4C22⋊D4311yescharacteristic
461#117—21no—
462#117C22×D4311yescharacteristic
463C2×C4⋊C4—21no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C22⋊C4—861no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42C22×D4311yescharacteristic
470#108—434no—
471#108—862no—
472#107—21no—
473#107—861no—
474#107—861no—
475#107—861no—
476#106—21no—
477#106—861no—
478#103—21no—
479#103—21no—
480#103—21no—
481#103—861no—
482#103—861no—
483#103—861no—
484#102—21no—
485#102—861no—
486#102—861no—
487#102—861no—
488#102—861no—
489#102—861no—
490#101—434no—
491#101—862no—
492#100—434no—
493#100—862no—
494#97—21no—
495#97—431no—
496#97—431no—
497#97—431no—
498#97—431no—
499#97—861no—
500#97—861no—
501#97—861no—
502#97—861no—
503C4×C8—21no—
504C4×C8—861no—
505C4×C8—861no—
506C4×C8—861no—
507C4×C8—861no—
508C24—861no—
509#41—21no—
510#41—21no—
511#41C2×C4×D4312yes—
512#41#1062189812yes—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8C2×C4×D4312yes—
519C2×Q8C2×C22⋊D4311yescharacteristic
520C2×D4—21no—
521C2×D4—432no—
522C2×D4—861no—
523C2×D4—861no—
524C2×D4—861no—
525C2×D4—861no—
526C2×D4—861no—
527C2×D4C2×C22⋊D4311yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—861no—
534C22×C4—3442no—
535C22×C4—1721no—
536C22×C4—1721no—
537C22×C4#1062190011yescharacteristic
538C22×C4#1062190011yescharacteristic
539C22×C4C23×D4311yescharacteristic
540Q16—24no—
541SD16—24no—
542SD16—864no—
543SD16—864no—
544SD16—864no—
545D8—864no—
546M16—21no—
547M16—21no—
548M16—21no—
549M16—432no—
550M16—432no—
551M16—432no—
552M16—864no—
553M16—864no—
554M16—861no—
555M16—861no—
556M16—861no—
557M16—861no—
558M16—861no—
559M16C2×C4×D4312yes—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—432no—
563C2×C8—431no—
564C2×C8—431no—
565C2×C8—432no—
566C2×C8—431no—
567C2×C8—431no—
568C2×C8—864no—
569C2×C8—864no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C4⋊C4—21no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—41no—
581C4⋊C4—41no—
582C4⋊C4—861no—
583C4⋊C4—861no—
584C4⋊C4C2×C22⋊D4311yescharacteristic
585C4⋊C4C2×C22⋊D4311yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—21no—
588C22⋊C4—21no—
589C22⋊C4—1721no—
590C22⋊C4—1721no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—41no—
595C42—41no—
596C42D4×D4311yescharacteristic
597C42D4×D4311yescharacteristic
598C42C2×C22⋊D4311yescharacteristic
599C42C2×C22⋊D4311yescharacteristic
600C23—21no—
601C23—862no—
602C23—3441no—
603C23—3441no—
604C23—1721no—
605C23—1721no—
606C23C2×#1062190011yescharacteristic
607Q8—21no—
608Q8—22no—
609Q8—22no—
610Q8—41no—
611Q8—41no—
612Q8C4×C22⋊D4312yes—
613D4—22no—
614D4—22no—
615D4—21no—
616D4—862no—
617D4—862no—
618D4—1721no—
619D4—1721no—
620D4C4×C22⋊D4312yes—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—81no—
633C2×C4—81no—
634C2×C4—81no—
635C2×C4—3442no—
636C2×C4—3442no—
637C2×C4—3441no—
638C2×C4—1721no—
639C2×C4#1306329711yescharacteristic
640C2×C4#1306329711yescharacteristic
641C2×C4#1306329711yescharacteristic
642C2×C4#1306329711yescharacteristic
643C2×C4C22×C4×D4311yescharacteristic
644C2×C4C2×D4×D4311yescharacteristic
645C2×C4C22×C22⋊D4311yescharacteristic
646C2×C4#41×D4311yescharacteristic
647C2×C4#41×D4311yescharacteristic
648C2×C4C2×#1062189811yescharacteristic
649C8—22no—
650C8—41no—
651C8—432no—
652C8—432no—
653C8—862no—
654C8—862no—
655C8—861no—
656C8—861no—
657C8—862no—
658C8—1721no—
659C22—21no—
660C22—21no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—3442no—
665C22—3442no—
666C22—3441no—
667C22—3441no—
668C22—1722no—
669C22C4×#1062190011yescharacteristic
670C22C2×#1306329711yescharacteristic
671C22#1458342911yescharacteristic
672C4—22no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—42no—
678C4—41no—
679C4—41no—
680C4—81no—
681C4—3441no—
682C4C4×D4×D4311yescharacteristic
683C4C2×C4×C22⋊D4311yescharacteristic
684C4#1458340811yescharacteristic
685C4#1458344511yescharacteristic
686C2—21no—
687C2—21no—
688C2—42no—
689C2—3442no—
690C2C4×#1306329711yescharacteristic
691C2#1914432511yescharacteristic
692C2#1914432911yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#137×C43C2
socleC22×C43C2×#121
prime radicalC2×#13063350C22
cosocleC22×C4×C43C24
hypercenterC4×#137D43
hypocenterC43#21557
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#137

Complements

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

NH ≅ G/Ntype
3. C2×#14582997C2semidirect
4. #19143023C2semidirect
5. #19135497C2semidirect
6. #19135377C2semidirect
7. #19135256C2semidirect
8. #19135253C2semidirect
9. #19135112C2semidirect
11. #19134657C2semidirect
12. #19134502C2semidirect
13. C4×#13063244C2semidirect
14. C4×#13063241C2semidirect
15. C4×#137×C43C2semidirect
21. #14583164C4semidirect
76. C2×#10621884C2×C4semidirect
81. #13063332C2×C4semidirect
99. #13063260C2×C4semidirect
113. #13063244C2×C4semidirect
115. #13063241C2×C4semidirect
131. #137×C43C2×C4semidirect
341. C4×#137D43semidirect
414. C43#21557semidirect
420. #137C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145831642
C4×#130633502
C2×#145829972
#191430232
#191354972
#191353772
#191352562
#191352532
#191351122
#191351012
#191346572
#191345022
C4×#130632442
C4×#130632412
C4×#137×C432
#2155743