Finite Group Databasebeta

← #25146404

Subgroups — #25146404

Order 11008.

722 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144984C211yesmaximal, characteristic, complemented
2#19144388C211yesmaximal, characteristic, complemented
3C2×#14583115C211yesmaximal, characteristic
4#19135961C211yesmaximal, characteristic, complemented
5#19135954C211yesmaximal, characteristic, complemented
6#19135858C211yesmaximal, characteristic, complemented
7#19135851C211yesmaximal, characteristic
8#19135505C211yesmaximal, characteristic
9#19135498C211yesmaximal, characteristic, complemented
10#19135444C211yesmaximal, characteristic, complemented
11#19135371C211yesmaximal, characteristic, complemented
12#19135257C211yesmaximal, characteristic, complemented
13#19135250C211yesmaximal, characteristic, complemented
14C4×#13063241C211yesmaximal, characteristic, complemented
15C43×#2962C211yesmaximal, characteristic, complemented
16C22×#10621873C2211yescharacteristic
17C22×D344C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20#14583261—21no—
21#14583261—21no—
22#14583256—21no—
23#14583256—21no—
24#14583196—21no—
25#14583196—21no—
26#14583186—21no—
27#14583176—21no—
28#14583115—21no—
29#14583115—21no—
30#14583115—21no—
31#14583115—21no—
32C2×#13063261C2211yescharacteristic
33C2×#13063261C2211yescharacteristic
34#14582942C2211yescharacteristic
35#14582942C2211yescharacteristic
36#14582923C2211yescharacteristic
37#14582907C2211yescharacteristic
38#14582907C2211yescharacteristic
39#14582903C2211yescharacteristic
40#14582903C2211yescharacteristic
41#14582903C2211yescharacteristic
42#14582903C2211yescharacteristic
43C2×#13063250C2211yescharacteristic
44C2×#13063247C2211yescharacteristic
45C2×#13063243C2211yescharacteristic
46C2×#13063243C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48C2×#13063241C2211yescharacteristic
49C2×#13063241C2211yescharacteristic
50C2×#13063241C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52#14582667C2211yescharacteristic
53#14582667C2211yescharacteristic
54#14582664C2211yescharacteristic
55#14582664C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C43×#446—21no—
58C43×#446—21no—
59C43×#446—21no—
60C8×Q8×C43—21no—
61C43×#424C2211yescharacteristic
62C43×#424C2211yescharacteristic
63C2×C4⋊C8×C43C2211yescharacteristic
64C43×#405C2211yescharacteristic
65C43×#405C2211yescharacteristic
66C4×M16×C43C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C22×D172C2311yescharacteristic
70C22×C4×D43—21no—
71C2×#10621873—22no—
72C2×#10621873—21no—
73C2×#10621873—21no—
74C2×#10621873—41no—
75C2×D344—22no—
76C2×D344—21no—
77C2×D344—21no—
78C2×D344—41no—
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C2×#10621877C2311yescharacteristic
82C2×#10621877C2311yescharacteristic
83#13063313—21no—
84#13063313—21no—
85#13063313—21no—
86#13063313—21no—
87C4×D172—21no—
88C4×D172—21no—
89C4×D172—21no—
90C4×D172—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×(C2×D43)⋊C4—21no—
93C2×(C2×D43)⋊C4—21no—
94C2×(C2×D43)⋊C4—21no—
95#13063261—41no—
96#13063261—41no—
97#13063258—21no—
98#13063258—21no—
99#13063256—21no—
100#13063256—21no—
101C4⋊(C43⋊C8)—21no—
102C4⋊(C43⋊C8)—21no—
103#13063250—21no—
104#13063250—21no—
105#13063248—21no—
106#13063248—21no—
107#13063248—21no—
108#13063248—21no—
109#13063247—21no—
110#13063247—21no—
111#13063245—21no—
112#13063245—21no—
113#13063245—21no—
114#13063245—21no—
115#13063245—21no—
116#13063245—21no—
117#13063245—21no—
118#13063245—21no—
119#13063243—22no—
120#13063243—41no—
121#13063241—22no—
122#13063241—22no—
123#13063241—22no—
124#13063241—41no—
125#13063236—21no—
126C4×C43⋊C8—21no—
127C2×M16×C43C2311yescharacteristic
128C2×M16×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130C22×C8×C43C2311yescharacteristic
131C4⋊Q8×C43D411yescharacteristic
132C4⋊Q8×C43D411yescharacteristic
133#125×C43D411yescharacteristic
134#125×C43D411yescharacteristic
135C22⋊Q8×C43—21no—
136C22⋊Q8×C43—21no—
137C4×Q8×C43—21no—
138C4×Q8×C43—21no—
139#117×C43C2311yescharacteristic
140#117×C43C2311yescharacteristic
141C2×C42×C43C2311yescharacteristic
142C4⋊C8×C43—21no—
143C4⋊C8×C43—21no—
144C4⋊C8×C43—21no—
145C4⋊C8×C43—21no—
146C4⋊C8×C43D411yescharacteristic
147C4⋊C8×C43D411yescharacteristic
148C4⋊C8×C43D411yescharacteristic
149C4⋊C8×C43D411yescharacteristic
150#97×C43—21no—
151#97×C43—21no—
152#97×C43—21no—
153C4×C8×C43—21no—
154C4×C8×C43—21no—
155C4×C8×C43—21no—
156C23×D43—21no—
157C23×D43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C22×C4×C43#4111yescharacteristic
161C22×C4×C43#4111yescharacteristic
162C22×C4×C43C2411yescharacteristic
163C22×Dic43—21no—
164C22×Dic43—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×D172—21no—
170C2×D172—21no—
171C2×D172—21no—
172C2×D172—21no—
173C2×D172—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172#4112yes—
177C2×C4×D43—41no—
178C2×C4×D43—41no—
179C2×C4×D43—82no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86—21no—
186M16×C43—21no—
187M16×C43—21no—
188M16×C43—21no—
189M16×C43#4112yes—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43C2×D411yescharacteristic
197C2×C8×C43C2×D411yescharacteristic
198C2×C8×C43C2×D411yescharacteristic
199C2×C8×C43C2×D411yescharacteristic
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43—21no—
206C4⋊C4×C43C2×D411yescharacteristic
207C4⋊C4×C43C2×D411yescharacteristic
208C4⋊C4×C43C2×D411yescharacteristic
209C4⋊C4×C43C2×D411yescharacteristic
210C22⋊C4×C43—21no—
211C22⋊C4×C43—21no—
212C42×C43—21no—
213C42×C43—21no—
214C42×C43C2×D411yescharacteristic
215C42×C43C2×D411yescharacteristic
216C42×C43C2×D411yescharacteristic
217C42×C43C2×D411yescharacteristic
218(C2×D43)⋊C4—41no—
219(C2×D43)⋊C4—41no—
220(C2×D43)⋊C4—41no—
221(C2×D43)⋊C4—41no—
222(C2×D43)⋊C4—41no—
223(C2×D43)⋊C4—41no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877—21no—
230#10621877—21no—
231#10621877—21no—
232#10621877—21no—
233#10621877—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238D344—42no—
239D344—42no—
240#10621873—42no—
241#10621873—42no—
242C23×C43C2×#4111yescharacteristic
243C22×D43—22no—
244C22×D43—41no—
245C22×D43—41no—
246C22×D43—41no—
247C22×D43—41no—
248C22×D43—41no—
249C22×D43—81no—
250C22×D43—81no—
251C22×D43—81no—
252C22×D43—81no—
253Q8×C43—42no—
254Q8×C43—81no—
255C2×C4×C43—21no—
256C2×C4×C43—21no—
257C2×C4×C43—21no—
258C2×C4×C43—21no—
259C2×C4×C43—41no—
260C2×C4×C43—41no—
261C2×C4×C43#12111yescharacteristic
262C2×C4×C43#12111yescharacteristic
263C2×C4×C43#12111yescharacteristic
264C2×C4×C43#12111yescharacteristic
265C2×C4×C43C22×D411yescharacteristic
266C2×C4×C43C22×D411yescharacteristic
267C2×C4×C43C2×#4111yescharacteristic
268C2×C4×C43C2×#4111yescharacteristic
269C2×C4×C43H(5,𝔽2)11yescharacteristic
270C2×C4×C432−1+411yescharacteristic
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—81no—
276D172—22no—
277D172—22no—
278D172—41no—
279D172—41no—
280D172—41no—
281D172—41no—
282D172—41no—
283D172—41no—
284C4×D43—82no—
285C4×D43—82no—
286Dic86—41no—
287Dic86—41no—
288Dic86—41no—
289Dic86—41no—
290C8×C43—21no—
291C8×C43—21no—
292C8×C43—21no—
293C8×C43—21no—
294C8×C43—22no—
295C8×C43—41no—
296C43⋊C8—41no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#25316—431nomaximal, Sylow
301C22×C43—21no—
302C22×C43—21no—
303C22×C43C2×#12111yescharacteristic
304C22×C43#52911yescharacteristic
305C22×C43#54211yescharacteristic
306C2×D43—42no—
307C2×D43—82no—
308C2×D43—81no—
309C2×D43—81no—
310C2×D43—82no—
311C2×D43—81no—
312C2×D43—81no—
313C2×D43—81no—
314C2×D43—161no—
315C2×D43—161no—
316C4×C43—21no—
317C4×C43—21no—
318C4×C43—21no—
319C4×C43—21no—
320C4×C43—41no—
321C4×C43—41no—
322C4×C43—41no—
323C4×C43—41no—
324C4×C43#54611yescharacteristic
325C4×C43#54811yescharacteristic
326C4×C43#54811yescharacteristic
327C4×C43#55011yescharacteristic
328Dic43—81no—
329Dic43—81no—
330#3140—431no—
331#3077—431no—
332C2×#463—431no—
333#2962D4311yescharacteristic, complemented
334#2064—431no—
335#2063—431no—
336#2046—431no—
337#2045—431no—
338#1978—431no—
339#1977—431no—
340#1967—431no—
341#1950—431no—
342#1931—431no—
343#1930—431no—
344C4×#100—431no—
345C2×C43—21no—
346C2×C43—21no—
347C2×C43#242611yescharacteristic
348C2×C43#306711yescharacteristic
349C2×C43#306811yescharacteristic
350D43—82no—
351D43—161no—
352C22×SD16—431no—
353C22×D8—431no—
354#533C2×D4311yescharacteristic
355C2×#124—431no—
356C2×C4×D4—431no—
357#489—861no—
358#489—861no—
359#488—861no—
360#488—861no—
361#478—861no—
362#478—861no—
363#476—861no—
364#474—861no—
365#463—861no—
366#463—861no—
367#463—861no—
368#463—861no—
369#446—21no—
370#446—21no—
371#446—21no—
372C8×Q8—21no—
373C2×#108—431no—
374C2×#108—431no—
375#428—431no—
376#428—431no—
377#424C2×D4311yescharacteristic
378#424C2×D4311yescharacteristic
379#423—431no—
380C2×C4⋊C8C2×D4311yescharacteristic
381#419—431no—
382#419—431no—
383#418—431no—
384#418—431no—
385#418—431no—
386#418—431no—
387C2×#103—431no—
388C2×#102—431no—
389C2×#101—431no—
390C2×#101—431no—
391C2×#100—431no—
392C2×#100—431no—
393C2×#100—431no—
394C2×#100—431no—
395#405C2×D4311yescharacteristic
396#405C2×D4311yescharacteristic
397C4×M16—431no—
398C4×M16C2×D4311yescharacteristic
399#343—431no—
400#343—431no—
401#341—431no—
402#341—431no—
403C43#2531611yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×D4—431no—
406C22×D4—431no—
407C23×C4—861no—
408C2×SD16—862no—
409C2×SD16—861no—
410C2×SD16—861no—
411C2×SD16—1721no—
412C2×D8—862no—
413C2×D8—861no—
414C2×D8—861no—
415C2×D8—1721no—
416C2×M16—431no—
417C2×M16—431no—
418C2×M16—431no—
419C2×M16—431no—
420C2×M16C22×D4311yescharacteristic
421C2×M16C22×D4311yescharacteristic
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C4⋊Q8D17211yescharacteristic
425C4⋊Q8D17211yescharacteristic
426#125D17211yescharacteristic
427#125D17211yescharacteristic
428#124—861no—
429#124—861no—
430#124—861no—
431#124—861no—
432C22⋊Q8—21no—
433C22⋊Q8—21no—
434C4×Q8—21no—
435C4×Q8—21no—
436C4×D4—861no—
437C4×D4—861no—
438C4×D4—861no—
439C4×D4—861no—
440#117C22×D4311yescharacteristic
441#117C22×D4311yescharacteristic
442C2×C4⋊C4—431no—
443C2×C22⋊C4—861no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C42C22×D4311yescharacteristic
447#108—1721no—
448#108—1721no—
449#107—861no—
450#107—861no—
451#106—861no—
452#106—861no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—21no—
456C4⋊C8—21no—
457C4⋊C8—861no—
458C4⋊C8—861no—
459C4⋊C8C22⋊D4311yescharacteristic
460C4⋊C8C22⋊D4311yescharacteristic
461C4⋊C8C22⋊D4311yescharacteristic
462C4⋊C8C22⋊D4311yescharacteristic
463#103—861no—
464#103—861no—
465#103—861no—
466#103—861no—
467#103—861no—
468#103—861no—
469#102—861no—
470#102—861no—
471#102—861no—
472#102—861no—
473#102—861no—
474#102—861no—
475#102—861no—
476#102—861no—
477#102—861no—
478#102—861no—
479#101—862no—
480#101—1721no—
481#100—862no—
482#100—862no—
483#100—862no—
484#100—1721no—
485#97—21no—
486#97—21no—
487#97—21no—
488#97—861no—
489C4×C8—21no—
490C4×C8—21no—
491C4×C8—21no—
492C4×C8—861no—
493C24—861no—
494C24—861no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—861no—
500C2×Q8—861no—
501C2×Q8—861no—
502C2×Q8—861no—
503C2×D4—432no—
504C2×D4—861no—
505C2×D4—861no—
506C2×D4—861no—
507C2×D4—861no—
508C2×D4—861no—
509C2×D4—861no—
510C2×D4—861no—
511C2×D4—861no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—3442no—
518C22×C4—1721no—
519C22×C4—1721no—
520C22×C4#1062189811yescharacteristic
521C22×C4#1062189811yescharacteristic
522C22×C4C23×D4311yescharacteristic
523SD16—1722no—
524SD16—1722no—
525D8—1722no—
526D8—1722no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—861no—
531M16—861no—
532M16—861no—
533M16—861no—
534M16—861no—
535M16—861no—
536M16—861no—
537M16—861no—
538M16#1062190212yes—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8C2×C22⋊D4311yescharacteristic
550C2×C8C2×C22⋊D4311yescharacteristic
551C2×C8C2×C22⋊D4311yescharacteristic
552C2×C8C2×C22⋊D4311yescharacteristic
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—861no—
560C4⋊C4—861no—
561C4⋊C4C2×D17211yescharacteristic
562C4⋊C4C2×D17211yescharacteristic
563C4⋊C4C2×D17211yescharacteristic
564C4⋊C4C2×D17211yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—1721no—
568C22⋊C4—1721no—
569C22⋊C4—1721no—
570C22⋊C4—1721no—
571C22⋊C4—1721no—
572C22⋊C4—1721no—
573C42—21no—
574C42—21no—
575C42C2×D17211yescharacteristic
576C42C2×D17211yescharacteristic
577C42C2×C22⋊D4311yescharacteristic
578C42C2×C22⋊D4311yescharacteristic
579C23—862no—
580C23—3441no—
581C23—3441no—
582C23—3441no—
583C23—3441no—
584C23—1721no—
585C23—1721no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23C2×#1062189811yescharacteristic
590Q8—42no—
591Q8—81no—
592Q8—1721no—
593Q8—1721no—
594Q8—1721no—
595Q8—1721no—
596D4—862no—
597D4—862no—
598D4—1721no—
599D4—1721no—
600D4—1721no—
601D4—1721no—
602D4—1721no—
603D4—1721no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—3442no—
611C2×C4—3442no—
612C2×C4—3441no—
613C2×C4—1721no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4#1306329911yescharacteristic
618C2×C4#1306329911yescharacteristic
619C2×C4#1306329911yescharacteristic
620C2×C4#1306329911yescharacteristic
621C2×C4C22×C22⋊D4311yescharacteristic
622C2×C4C22×D17211yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C2×C4C2×#1062190211yescharacteristic
625C2×C4#1306337111yescharacteristic
626C2×C4#1306337311yescharacteristic
627C8—22no—
628C8—21no—
629C8—21no—
630C8—21no—
631C8—21no—
632C8—41no—
633C8—1721no—
634C8—1721no—
635C8—1721no—
636C8—1721no—
637C22—21no—
638C22—21no—
639C22—3442no—
640C22—3442no—
641C22—3441no—
642C22—3441no—
643C22—3441no—
644C22—3441no—
645C22—3441no—
646C22—1722no—
647C22—6881no—
648C22—6881no—
649C22C2×#1306329911yescharacteristic
650C22#1458343611yescharacteristic
651C22#1458352111yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—3441no—
661C4—3441no—
662C4#1458353711yescharacteristic
663C4#1458356011yescharacteristic
664C4#1458356111yescharacteristic
665C4#1458357111yescharacteristic
666C2—21no—
667C2—21no—
668C2—3442no—
669C2—6881no—
670C2#1913815511yescharacteristic
671C2#1914431511yescharacteristic
672C2#1914432311yescharacteristic
subgroupG/H
centerC22C2×#13063299
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2962C2
socleC22×C43C2×#121
prime radicalC22×D344C22
hypercenter#2962D43
hypocenterC43#25316
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2962

Complements

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

NH ≅ G/Ntype
1. #19144984C2semidirect
2. #19144388C2semidirect
4. #19135961C2semidirect
5. #19135954C2semidirect
6. #19135858C2semidirect
9. #19135498C2semidirect
10. #19135444C2semidirect
11. #19135371C2semidirect
12. #19135257C2semidirect
13. #19135250C2semidirect
14. C4×#13063241C2semidirect
15. C43×#2962C2semidirect
333. #2962D43semidirect
403. C43#25316semidirect

Maximal subgroups

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

subgroupindex
#191449842
#191443882
C2×#145831152
#191359612
#191359542
#191358582
#191358512
#191355052
#191354982
#191354442
#191353712
#191352572
#191352502
C4×#130632412
C43×#29622
#2531643