Finite Group Databasebeta

← #25099158

Subgroups — #25099158

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19143182C211yesmaximal, characteristic
2C2×#14582906C211yesmaximal, characteristic
3#419×D43C211yesmaximal, characteristic
4C2×#101×D43C211yesmaximal, characteristic
5#19143011C211yesmaximal, characteristic
6#19135253C211yesmaximal, characteristic, complemented
7#19135252C211yesmaximal, characteristic, complemented
8#19135251C211yesmaximal, characteristic, complemented
9#19135250C211yesmaximal, characteristic, complemented
10#19135249C211yesmaximal, characteristic, complemented
11#19135248C211yesmaximal, characteristic, complemented
12#19135247C211yesmaximal, characteristic, complemented
13#19134332C211yesmaximal, characteristic
14#19134320C211yesmaximal, characteristic
15C43×#1930C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19C2×M16×D43C2211yescharacteristic
20C2×M16×D43C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22#117×D43C2211yescharacteristic
23#14582942C2211yescharacteristic
24#14582941C2211yescharacteristic
25#14582940—21no—
26#14582939C2211yescharacteristic
27#14582938—21no—
28#14582936—21no—
29#14582934—21no—
30#14582909C2211yescharacteristic
31#14582908C2211yescharacteristic
32#14582907C2211yescharacteristic
33#14582906—21no—
34#14582906—21no—
35#14582906—21no—
36#14582906—21no—
37#14582906—21no—
38#14582906—21no—
39C2×#13063250C2211yescharacteristic
40C2×#13063249C2211yescharacteristic
41C2×#13063248C2211yescharacteristic
42#103×D43—21no—
43#103×D43—21no—
44C2×#13063244C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47#101×D43C418yescomplemented
48#14582857C2211yescharacteristic
49#14582856—21no—
50#14582855C2211yescharacteristic
51#14582854C2211yescharacteristic
52#14582853—21no—
53#14582851—21no—
54C4×#10621872—21no—
55#14582668C2211yescharacteristic
56#14582667C2211yescharacteristic
57#14582667C2211yescharacteristic
58#14582664C2211yescharacteristic
59#14582663C2211yescharacteristic
60#14582663C2211yescharacteristic
61C43×#428C2211yescharacteristic
62C43×#419C2211yescharacteristic
63C2×#103×C43C2211yescharacteristic
64C2×#101×C43C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C43×#343C2211yescharacteristic
67C43×#341C2211yescharacteristic
68C22×Dic86—21no—
69C22×Dic86C2311yescharacteristic
70C2×Q8×D43—22no—
71C2×Q8×D43—21no—
72C2×Q8×D43—21no—
73C2×Q8×D43—21no—
74C2×Q8×D43—21no—
75C2×Q8×D43—22no—
76C2×Q8×D43—22no—
77C2×Q8×D43C2×C414yes—
78C22×C4×D43—21no—
79C22×C4×D43C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83C2×#10621872—21no—
84C2×#10621872—21no—
85C2×#10621872—22no—
86C2×#10621872—22no—
87C2×#10621872—21no—
88C2×#10621872D411yescharacteristic
89C2×#10621872D411yescharacteristic
90C2×#10621872D411yescharacteristic
91C2×#10621872D411yescharacteristic
92M16×D43—22no—
93M16×D43—22no—
94M16×D43—22no—
95M16×D43—22no—
96M16×D43C2×C414yes—
97M16×D43C2×C414yes—
98C22×C43⋊C8C2311yescharacteristic
99C2×C8×D43—21no—
100C2×C8×D43—21no—
101C2×C8×D43—21no—
102#13063284C2311yescharacteristic
103#13063283—21no—
104#13063283—21no—
105#13063283—21no—
106#13063283—21no—
107#13063283D411yescharacteristic
108#13063283D411yescharacteristic
109#13063282—21no—
110#13063281—21no—
111C2×C4⋊Dic43C2311yescharacteristic
112C4⋊C4×D43D411yescharacteristic
113C4⋊C4×D43D411yescharacteristic
114C2×(C2×D43)⋊C4—21no—
115C22⋊C4×D43—21no—
116C2×C4×Dic43—21no—
117C42×D43—21no—
118#13063259—21no—
119#13063258—21no—
120#13063258—21no—
121#13063257—21no—
122#13063256—21no—
123#13063256—21no—
124#13063250—21no—
125#13063250—21no—
126#13063250—21no—
127#13063250—21no—
128#13063249—21no—
129#13063249—21no—
130#13063249—21no—
131#13063249—21no—
132#13063248—21no—
133#13063248—21no—
134#13063248—21no—
135#13063248—21no—
136#13063244C2×C414yescomplemented
137#13063243C2×C414yescomplemented
138#13063243C2×C414yescomplemented
139#13063236—21no—
140#13063235—21no—
141#13063235—21no—
142C4×C43⋊C8—21no—
143C8×Dic43—21no—
144C8×Dic43—21no—
145C22×Q8×C43C2311yescharacteristic
146C2×M16×C43C2311yescharacteristic
147C2×M16×C43C2311yescharacteristic
148C2×M16×C43C2311yescharacteristic
149C22×C8×C43C2311yescharacteristic
150#117×C43C2311yescharacteristic
151C2×C4⋊C4×C43C2311yescharacteristic
152#107×C43—21no—
153#106×C43—21no—
154#103×C43—21no—
155#103×C43—21no—
156#103×C43—21no—
157#103×C43—21no—
158#101×C43C2×C414yescomplemented
159#97×C43—21no—
160C4×C8×C43—21no—
161C23×D43#4111yescharacteristic
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×C43C2411yescharacteristic
171C22×Dic43—21no—
172C22×Dic43—21no—
173C22×Dic43#4111yescharacteristic
174Q8×D43—24no—
175Q8×D43—24no—
176Q8×D43—24no—
177Q8×D43—24no—
178Q8×D43—42no—
179Q8×D43—42no—
180Q8×D43—42no—
181Q8×D43—42no—
182C2×C4×D43—24no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—41no—
186C2×C4×D43—41no—
187C2×C4×D43—42no—
188C2×C4×D43C22×C412yes—
189C2×C4×D43C2×D411yescharacteristic
190C2×C4×D43C2×D411yescharacteristic
191C2×C4×D43C2×D411yescharacteristic
192C2×C4×D43C2×D411yescharacteristic
193C2×C4×D43#4112yes—
194C2×C4×D43#4112yes—
195C2×C4×D43#4112yes—
196C2×Dic86—21no—
197C2×Dic86—21no—
198C2×Dic86—21no—
199C2×Dic86—21no—
200C2×Dic86—21no—
201C2×Dic86—24no—
202C2×Dic86—41no—
203C2×Dic86—41no—
204C2×Dic86—42no—
205C2×Dic86C22×C412yes—
206M16×C43—21no—
207M16×C43—21no—
208M16×C43—21no—
209M16×C43—21no—
210M16×C43C22×C412yes—
211M16×C43C22×C412yes—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43—21no—
215C2×C8×C43—21no—
216C2×C8×C43—21no—
217C2×C8×C43C2×D411yescharacteristic
218C2×C8×C43C2×D411yescharacteristic
219C4⋊C4×C43—21no—
220C4⋊C4×C43—21no—
221C4⋊C4×C43C2×D411yescharacteristic
222C4⋊C4×C43C2×D411yescharacteristic
223C22⋊C4×C43—21no—
224C42×C43—21no—
225C22⋊Dic43—21no—
226(C2×D43)⋊C4—21no—
227(C2×D43)⋊C4—21no—
228(C2×D43)⋊C4—41no—
229(C2×D43)⋊C4—41no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43C2×D411yescharacteristic
233C4⋊Dic43C2×D411yescharacteristic
234Dic43⋊C4—21no—
235Dic43⋊C4—21no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—41no—
240C4×Dic43—41no—
241#10621877—21no—
242#10621877—21no—
243#10621877—21no—
244#10621877—21no—
245#10621877C22×C412yes—
246#10621877C22×C412yes—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8C2×D411yescharacteristic
253C2×C43⋊C8C2×D411yescharacteristic
254#10621872—24no—
255#10621872—24no—
256#10621872—22no—
257#10621872—22no—
258#10621872—22no—
259#10621872—22no—
260#10621872—42no—
261C8×D43—24no—
262C8×D43—24no—
263C8×D43—42no—
264C23×C43C2×#4111yescharacteristic
265C22×D43—41no—
266C22×D43—41no—
267C22×D43#11712yes—
268C22×D43#12111yescharacteristic
269C22×D43#12111yescharacteristic
270C22×D43#12612yes—
271Q8×C43—22no—
272Q8×C43—22no—
273Q8×C43—41no—
274Q8×C43—41no—
275C2×C4×C43—22no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—81no—
282C2×C4×C43C23×C411yescharacteristic
283C2×C4×C43C22×D411yescharacteristic
284C2×C4×C43C22×D411yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43C2×#4111yescharacteristic
287C2×C4×C43C2×#4111yescharacteristic
288C2×Dic43—22no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—81no—
295C2×Dic43#11712yes—
296C2×Dic43#12111yescharacteristic
297C2×Dic43#12111yescharacteristic
298C2×Dic43#12612yes—
299C4×D43—44no—
300C4×D43—44no—
301C4×D43—81no—
302C4×D43—81no—
303C4×D43C4×D412yes—
304C4×D43C4×D412yes—
305C4×D43C4×D412yes—
306C4×D43C4×D412yes—
307C4×D43#12312yes—
308C4×D43#12312yes—
309C4×D43#12412yes—
310C4×D43#12412yes—
311Dic86—22no—
312Dic86—22no—
313Dic86—41no—
314Dic86—41no—
315Dic86—44no—
316Dic86—44no—
317C8×C43—22no—
318C8×C43—22no—
319C8×C43—21no—
320C8×C43—21no—
321C8×C43—41no—
322C43⋊C8—22no—
323C43⋊C8—22no—
324C43⋊C8—21no—
325C43⋊C8—21no—
326C43⋊C8—41no—
327#21077—431nomaximal, Sylow
328C22×C43—21no—
329C22×C43—21no—
330C22×C43C2×#11711yescharacteristic
331C22×C43C2×#12111yescharacteristic
332C22×C43C2×#12611yescharacteristic
333C2×D43—21no—
334C2×D43—21no—
335C2×D43—21no—
336C2×D43—21no—
337C2×D43—42no—
338C2×D43—42no—
339C2×D43#38812yes—
340C2×D43#38812yes—
341C4×C43—42no—
342C4×C43—41no—
343C4×C43—41no—
344C4×C43—81no—
345C4×C43C2×C4×D411yescharacteristic
346C4×C43C2×C4×D411yescharacteristic
347C4×C43C2×#12311yescharacteristic
348C4×C43C2×#12411yescharacteristic
349Dic43—42no—
350Dic43—41no—
351Dic43—41no—
352Dic43—81no—
353Dic43#38812yes—
354Dic43#38812yes—
355#2911—431no—
356C2×#419—431no—
357C2×#419—431no—
358C22×#101—431no—
359#2873—431no—
360#1930—431no—
361#1930—431no—
362#1930—431no—
363#1930—431no—
364#1930—431no—
365#1930—431no—
366#1930—431no—
367#1930D4311yescharacteristic, complemented
368#1742—431no—
369#1738—431no—
370C2×C43—21no—
371C2×C43—21no—
372C2×C43C2×#38811yescharacteristic
373C2×C43#306911yescharacteristic
374C2×C43#306911yescharacteristic
375D43—22no—
376D43—22no—
377C23×Q8—431no—
378C22×M16—431no—
379C22×M16—431no—
380C22×M16—431no—
381C22×M16—431no—
382C2×#117—431no—
383C2×#117—431no—
384#428—431no—
385#428—431no—
386#428—431no—
387#428—861no—
388#428—861no—
389#428C2×D4311yescharacteristic
390#427—861no—
391#427—861no—
392#419—431no—
393#419—431no—
394#419—431no—
395#419—861no—
396#419—861no—
397#419—861no—
398#419—861no—
399#419—861no—
400#419—861no—
401#419C2×D4311yescharacteristic
402C2×#103—431no—
403C2×#103—431no—
404C2×#103—431no—
405C2×#103—861no—
406C2×#103—861no—
407C2×#103C2×D4311yescharacteristic
408C2×#101—431no—
409C2×#101—431no—
410C2×#101—431no—
411C2×#101—438no—
412C2×#101C2×D4311yescharacteristic
413#405—431no—
414#405—431no—
415#405—431no—
416#405—861no—
417#405—861no—
418#405C2×D4311yescharacteristic
419C4×M16—861no—
420C4×M16—861no—
421#343—431no—
422#343—431no—
423#343—431no—
424#343C2×D4311yescharacteristic
425#341—431no—
426#341—431no—
427#341—431no—
428#341C2×D4311yescharacteristic
429C43#2107711yescharacteristic, complemented, Sylow
430C22×Q8—434no—
431C22×Q8—431no—
432C22×Q8—861no—
433C22×Q8—862no—
434C22×Q8—861no—
435C22×Q8—861no—
436C22×Q8—861no—
437C22×Q8—861no—
438C22×Q8—862no—
439C22×Q8—862no—
440C22×Q8C22×D4311yescharacteristic
441C23×C4—431no—
442C23×C4—861no—
443C2×M16—431no—
444C2×M16—431no—
445C2×M16—431no—
446C2×M16—431no—
447C2×M16—431no—
448C2×M16—431no—
449C2×M16—434no—
450C2×M16—434no—
451C2×M16—431no—
452C2×M16—861no—
453C2×M16—862no—
454C2×M16—862no—
455C2×M16—861no—
456C2×M16—861no—
457C2×M16—862no—
458C2×M16—862no—
459C2×M16—862no—
460C2×M16—862no—
461C2×M16C22×D4311yescharacteristic
462C2×M16C22×D4311yescharacteristic
463C2×M16C22×D4311yescharacteristic
464C22×C8—431no—
465C22×C8—861no—
466C22×C8—861no—
467C22×C8—861no—
468C22×C8C22×D4311yescharacteristic
469#117—431no—
470#117—431no—
471#117—431no—
472#117—861no—
473#117—861no—
474#117—861no—
475#117—861no—
476#117—861no—
477#117—861no—
478#117C22×D4311yescharacteristic
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—431no—
482C2×C4⋊C4C22×D4311yescharacteristic
483C2×C22⋊C4—861no—
484C2×C22⋊C4—861no—
485C2×C42—861no—
486C2×C42—861no—
487#107—21no—
488#107—861no—
489#107—861no—
490#107—861no—
491#106—21no—
492#106—861no—
493#106—861no—
494#106—861no—
495#103—21no—
496#103—21no—
497#103—21no—
498#103—21no—
499#103—861no—
500#103—861no—
501#103—861no—
502#103—861no—
503#103—861no—
504#103—861no—
505#103—861no—
506#103—861no—
507#103—861no—
508#103—861no—
509#103—861no—
510#103—861no—
511#101—434no—
512#101—434no—
513#101—434no—
514#101C4×D4314yescomplemented
515#97—21no—
516#97—861no—
517#97—861no—
518#97—861no—
519C4×C8—21no—
520C4×C8—861no—
521C4×C8—861no—
522C4×C8—861no—
523C24—431no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—432no—
530C2×Q8—864no—
531C2×Q8—864no—
532C2×Q8—864no—
533C2×Q8—864no—
534C2×Q8—864no—
535C2×Q8—861no—
536C2×Q8—861no—
537C2×Q8—861no—
538C2×Q8—861no—
539C2×Q8—861no—
540C2×Q8—1721no—
541C2×Q8—1721no—
542C2×Q8—1722no—
543C2×Q8—1722no—
544C2×Q8—1722no—
545C2×Q8—1722no—
546C2×Q8—1722no—
547C2×Q8C2×C4×D4312yes—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—431no—
551C22×C4—432no—
552C22×C4—431no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—431no—
556C22×C4—432no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—864no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—1721no—
565C22×C4—1721no—
566C22×C4—1722no—
567C22×C4C23×D4311yescharacteristic
568M16—21no—
569M16—21no—
570M16—21no—
571M16—21no—
572M16—432no—
573M16—432no—
574M16—864no—
575M16—864no—
576M16—862no—
577M16—862no—
578M16—862no—
579M16—862no—
580M16—861no—
581M16—861no—
582M16—861no—
583M16—861no—
584M16—1722no—
585M16C2×C4×D4312yes—
586M16C2×C4×D4312yes—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—431no—
593C2×C8—431no—
594C2×C8—864no—
595C2×C8—864no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—861no—
600C2×C8—861no—
601C2×C8—1722no—
602C2×C8D4×D4311yescharacteristic
603C2×C8D4×D4311yescharacteristic
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—431no—
607C4⋊C4—431no—
608C4⋊C4—861no—
609C4⋊C4—861no—
610C4⋊C4—861no—
611C4⋊C4—861no—
612C4⋊C4D4×D4311yescharacteristic
613C4⋊C4D4×D4311yescharacteristic
614C22⋊C4—21no—
615C22⋊C4—861no—
616C22⋊C4—861no—
617C22⋊C4—861no—
618C22⋊C4—1721no—
619C22⋊C4—1721no—
620C42—21no—
621C42—861no—
622C42—861no—
623C42—861no—
624C42—1721no—
625C42—1721no—
626C23—431no—
627C23—431no—
628C23—432no—
629C23—432no—
630C23—1721no—
631C23—1721no—
632C23#41×D4311yescharacteristic
633Q8—22no—
634Q8—22no—
635Q8—41no—
636Q8—41no—
637Q8—862no—
638Q8—862no—
639Q8—1724no—
640Q8—1724no—
641Q8—1721no—
642Q8—1721no—
643C2×C4—22no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—81no—
650C2×C4—432no—
651C2×C4—431no—
652C2×C4—431no—
653C2×C4—432no—
654C2×C4—432no—
655C2×C4—432no—
656C2×C4—432no—
657C2×C4—432no—
658C2×C4—432no—
659C2×C4—432no—
660C2×C4—432no—
661C2×C4—432no—
662C2×C4—862no—
663C2×C4—861no—
664C2×C4—861no—
665C2×C4—3441no—
666C2×C4—3441no—
667C2×C4—3441no—
668C2×C4—1724no—
669C2×C4—1724no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4C22×C4×D4311yescharacteristic
674C2×C4C2×D4×D4311yescharacteristic
675C2×C4C2×D4×D4311yescharacteristic
676C2×C4#41×D4311yescharacteristic
677C2×C4#41×D4311yescharacteristic
678C2×C4#41×D4311yescharacteristic
679C8—22no—
680C8—22no—
681C8—21no—
682C8—21no—
683C8—41no—
684C8—862no—
685C8—862no—
686C8—861no—
687C8—861no—
688C8—1721no—
689C22—21no—
690C22—21no—
691C22—432no—
692C22—432no—
693C22—861no—
694C22—861no—
695C22—861no—
696C22—861no—
697C22—1722no—
698C22—1722no—
699C22#117×D4311yescharacteristic
700C22#121×D4311yescharacteristic
701C22#126×D4311yescharacteristic
702C4—41no—
703C4—41no—
704C4—42no—
705C4—81no—
706C4—432no—
707C4—432no—
708C4—3441no—
709C4—1721no—
710C4—1721no—
711C4—1722no—
712C4C4×D4×D4311yescharacteristic
713C4C4×D4×D4311yescharacteristic
714C4#123×D4311yescharacteristic
715C4#124×D4311yescharacteristic
716C2—21no—
717C2—21no—
718C2—862no—
719C2—862no—
720C2#388×D4311yescharacteristic
721C2#1914432711yescharacteristic
722C2#1914433011yescharacteristic
subgroupG/H
centerC22#121×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1930C2
socleC22×C43C2×#121
prime radicalC23×D43#41
cosocleC22×C4×C43C24
hypercenter#1930D43
hypocenterC43#21077
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #1930

Complements

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

NH ≅ G/Ntype
6. #19135253C2semidirect
7. #19135252C2semidirect
8. #19135251C2semidirect
9. #19135250C2semidirect
10. #19135249C2semidirect
11. #19135248C2semidirect
12. #19135247C2semidirect
15. C43×#1930C2semidirect
47. #101×D43C4semidirect
136. #13063244C2×C4semidirect
137. #13063243C2×C4semidirect
138. #13063243C2×C4semidirect
158. #101×C43C2×C4semidirect
367. #1930D43semidirect
429. C43#21077semidirect
514. #101C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191431822
C2×#145829062
#419×D432
C2×#101×D432
#191430112
#191352532
#191352522
#191352512
#191352502
#191352492
#191352482
#191352472
#191343322
#191343202
C43×#19302
#2107743