Finite Group Databasebeta

← #25146414

Subgroups — #25146414

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
2C2×#14583114C211yesmaximal, characteristic
3#19143544C211yesmaximal, characteristic, complemented
4#19135959C211yesmaximal, characteristic, complemented
5#19135952C211yesmaximal, characteristic, complemented
6#19135857C211yesmaximal, characteristic, complemented
7#19135850C211yesmaximal, characteristic
8#19135504C211yesmaximal, characteristic
9#19135501C211yesmaximal, characteristic, complemented
10#19135442C211yesmaximal, characteristic, complemented
11#19135368C211yesmaximal, characteristic, complemented
12#19135256C211yesmaximal, characteristic, complemented
13#19135249C211yesmaximal, characteristic, complemented
14C4×#13063242C211yesmaximal, characteristic, complemented
15C43×#3077C211yesmaximal, characteristic, complemented
16C22×#10621883C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19#14583261—21no—
20#14583261—21no—
21#14583256—21no—
22#14583256—21no—
23#14583114—21no—
24#14583114—21no—
25#14583114—21no—
26#14583114—21no—
27#14583030—21no—
28#14583030—21no—
29#14583030—21no—
30Q8×C43⋊C8—21no—
31C2×#13063260C2211yescharacteristic
32C2×#13063260C2211yescharacteristic
33#14582926C2211yescharacteristic
34#14582926C2211yescharacteristic
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36#14582907C2211yescharacteristic
37#14582907C2211yescharacteristic
38#14582903C2211yescharacteristic
39#14582903C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×#13063245C2211yescharacteristic
42C2×#13063243C2211yescharacteristic
43C2×#13063243C2211yescharacteristic
44C2×#13063242C2211yescharacteristic
45C2×#13063242C2211yescharacteristic
46C2×#13063241C2211yescharacteristic
47C2×#13063241C2211yescharacteristic
48#14582855C2211yescharacteristic
49#14582855C2211yescharacteristic
50C4×#10621877C2211yescharacteristic
51C4×#10621877C2211yescharacteristic
52#14582668C2211yescharacteristic
53#14582668C2211yescharacteristic
54#14582663C2211yescharacteristic
55#14582663C2211yescharacteristic
56C43×#533C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#478—21no—
59C43×#478—21no—
60C43×#476—21no—
61C43×#474—21no—
62C43×#428C2211yescharacteristic
63C43×#428C2211yescharacteristic
64C43×#423C2211yescharacteristic
65C43×#418C2211yescharacteristic
66C43×#418C2211yescharacteristic
67C22×Dic86C2311yescharacteristic
68C22×D172C2311yescharacteristic
69C2×#10621883—22no—
70C2×#10621883—21no—
71C2×#10621883—21no—
72C2×#10621883—41no—
73C2×#10621882—22no—
74C2×#10621882—21no—
75C2×#10621882—21no—
76C2×#10621882—41no—
77C2×#10621877C2311yescharacteristic
78C2×#10621877C2311yescharacteristic
79C2×#10621877C2311yescharacteristic
80C2×#10621877C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063313—21no—
84#13063313—21no—
85#13063313—21no—
86#13063313—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89#13063260—41no—
90#13063260—41no—
91C4⋊(C43⋊C8)—21no—
92C4⋊(C43⋊C8)—21no—
93C4⋊(C43⋊C8)—21no—
94C4⋊(C43⋊C8)—21no—
95C4⋊(C43⋊C8)D411yescharacteristic
96C4⋊(C43⋊C8)D411yescharacteristic
97C4⋊(C43⋊C8)D411yescharacteristic
98C4⋊(C43⋊C8)D411yescharacteristic
99#13063248—21no—
100#13063248—21no—
101#13063248—21no—
102#13063248—21no—
103#13063248—21no—
104#13063248—21no—
105#13063245—21no—
106#13063245—21no—
107#13063245—21no—
108#13063245—21no—
109#13063245—21no—
110#13063245—21no—
111#13063243—22no—
112#13063243—41no—
113#13063242—22no—
114#13063242—22no—
115#13063241—22no—
116#13063241—41no—
117#13063236—21no—
118#13063236—21no—
119#13063236—21no—
120#13063236—21no—
121C4×C43⋊C8—21no—
122C4×C43⋊C8—21no—
123C4×C43⋊C8—21no—
124C4×C43⋊C8—21no—
125C22×D4×C43C2311yescharacteristic
126C23×C4×C43—21no—
127C2×M16×C43C2311yescharacteristic
128C2×M16×C43C2311yescharacteristic
129C4⋊Q8×C43D411yescharacteristic
130C4⋊Q8×C43D411yescharacteristic
131#125×C43D411yescharacteristic
132#125×C43D411yescharacteristic
133C22⋊Q8×C43—21no—
134C22⋊Q8×C43—21no—
135C4×Q8×C43—21no—
136C4×Q8×C43—21no—
137C4×D4×C43—21no—
138C4×D4×C43—21no—
139C4×D4×C43—21no—
140C4×D4×C43—21no—
141#117×C43C2311yescharacteristic
142#117×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C22⋊C4×C43—21no—
145C2×C42×C43C2311yescharacteristic
146#107×C43—21no—
147#107×C43—21no—
148#106×C43—21no—
149#106×C43—21no—
150C4⋊C8×C43—21no—
151C4⋊C8×C43—21no—
152#102×C43—21no—
153#102×C43—21no—
154#102×C43—21no—
155#102×C43—21no—
156C24×C43—21no—
157C23×D43—21no—
158C2×Q8×C43—21no—
159C2×Q8×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—21no—
164C2×D4×C43—21no—
165C2×D4×C43#4112yes—
166C22×C4×C43—21no—
167C22×C4×C43—41no—
168C22×C4×C43—41no—
169C22×C4×C43—82no—
170C22×C4×C43#4111yescharacteristic
171C22×C4×C43#4111yescharacteristic
172C22×C4×C43C2411yescharacteristic
173C22×Dic43—21no—
174C2×D172—21no—
175C2×D172—21no—
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—21no—
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—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43C2×D411yescharacteristic
201C4⋊C4×C43C2×D411yescharacteristic
202C4⋊C4×C43C2×D411yescharacteristic
203C4⋊C4×C43C2×D411yescharacteristic
204C22⋊C4×C43—21no—
205C22⋊C4×C43—21no—
206C22⋊C4×C43—41no—
207C22⋊C4×C43—41no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43C2×D411yescharacteristic
211C42×C43C2×D411yescharacteristic
212C42×C43C2×D411yescharacteristic
213C42×C43C2×D411yescharacteristic
214#10621883—42no—
215#10621883—42no—
216#10621882—42no—
217#10621882—42no—
218(C2×D43)⋊C4—41no—
219(C2×D43)⋊C4—41no—
220(C2×D43)⋊C4—41no—
221(C2×D43)⋊C4—41no—
222#10621877—21no—
223#10621877—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877—21no—
228#10621877—21no—
229#10621877#4112yes—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8C2×D411yescharacteristic
239C2×C43⋊C8C2×D411yescharacteristic
240C2×C43⋊C8C2×D411yescharacteristic
241C2×C43⋊C8C2×D411yescharacteristic
242C23×C43—22no—
243C23×C43—41no—
244C23×C43—41no—
245C23×C43—81no—
246C23×C43—81no—
247C23×C43C2×#4111yescharacteristic
248C22×D43—41no—
249C22×D43—41no—
250C22×D43—41no—
251C22×D43—81no—
252C22×D43—81no—
253Q8×C43—42no—
254Q8×C43—81no—
255D4×C43—22no—
256D4×C43—22no—
257D4×C43—41no—
258D4×C43—41no—
259C2×C4×C43—21no—
260C2×C4×C43—21no—
261C2×C4×C43—21no—
262C2×C4×C43—21no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—82no—
267C2×C4×C43—82no—
268C2×C4×C43—81no—
269C2×C4×C43#12111yescharacteristic
270C2×C4×C43#12111yescharacteristic
271C2×C4×C43#12111yescharacteristic
272C2×C4×C43#12111yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C2×#4111yescharacteristic
276C2×C4×C43C2×#4111yescharacteristic
277C2×C4×C43H(5,𝔽2)11yescharacteristic
278C2×C4×C432−1+411yescharacteristic
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282D172—41no—
283D172—41no—
284D172—41no—
285D172—41no—
286Dic86—41no—
287Dic86—41no—
288Dic86—41no—
289Dic86—41no—
290C8×C43—41no—
291C8×C43—41no—
292C43⋊C8—21no—
293C43⋊C8—21no—
294C43⋊C8—21no—
295C43⋊C8—21no—
296C43⋊C8—22no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#25316—431nomaximal, Sylow
301C22×C43—21no—
302C22×C43—21no—
303C22×C43—42no—
304C22×C43—82no—
305C22×C43—82no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43C2×#12111yescharacteristic
309C22×C43#52911yescharacteristic
310C22×C43#54211yescharacteristic
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—81no—
325C4×C43#54611yescharacteristic
326C4×C43#54811yescharacteristic
327C4×C43#54811yescharacteristic
328C4×C43#55011yescharacteristic
329Dic43—81no—
330#3140—431no—
331#3077D4311yescharacteristic, complemented
332C2×#463—431no—
333#2962—431no—
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—82no—
348C2×C43#242611yescharacteristic
349C2×C43#306711yescharacteristic
350C2×C43#306811yescharacteristic
351D43—161no—
352C22×SD16—431no—
353C22×D8—431no—
354#533C2×D4311yescharacteristic
355C2×#124—431no—
356C2×C4×D4C2×D4311yescharacteristic
357#489—861no—
358#489—861no—
359#488—861no—
360#488—861no—
361#478—21no—
362#478—21no—
363#476—21no—
364#474—21no—
365#463—861no—
366#463—861no—
367#463—861no—
368#463—861no—
369#446—861no—
370#446—861no—
371#446—861no—
372C8×Q8—861no—
373C2×#108—431no—
374C2×#108—431no—
375#428C2×D4311yescharacteristic
376#428C2×D4311yescharacteristic
377#424—431no—
378#424—431no—
379#423C2×D4311yescharacteristic
380C2×C4⋊C8—431no—
381#419—431no—
382#419—431no—
383#418—431no—
384#418—431no—
385#418C2×D4311yescharacteristic
386#418C2×D4311yescharacteristic
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#405—431no—
396#405—431no—
397C4×M16—431no—
398C4×M16—431no—
399#343—431no—
400#343—431no—
401#341—431no—
402#341—431no—
403C43#2531611yescharacteristic, complemented, Sylow
404C22×Q8—431no—
405C22×D4—431no—
406C22×D4C22×D4311yescharacteristic
407C23×C4—21no—
408C2×SD16—861no—
409C2×SD16—861no—
410C2×SD16—862no—
411C2×SD16—1721no—
412C2×D8—861no—
413C2×D8—861no—
414C2×D8—862no—
415C2×D8—1721no—
416C2×M16—431no—
417C2×M16—431no—
418C2×M16—431no—
419C2×M16—431no—
420C2×M16C22×D4311yescharacteristic
421C2×M16C22×D4311yescharacteristic
422C22×C8—431no—
423C22×C8—431no—
424C4⋊Q8C22⋊D4311yescharacteristic
425C4⋊Q8C22⋊D4311yescharacteristic
426#125C22⋊D4311yescharacteristic
427#125C22⋊D4311yescharacteristic
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—21no—
437C4×D4—21no—
438C4×D4—21no—
439C4×D4—21no—
440#117C22×D4311yescharacteristic
441#117C22×D4311yescharacteristic
442C2×C4⋊C4C22×D4311yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—861no—
445C2×C22⋊C4—861no—
446C2×C42C22×D4311yescharacteristic
447#108—1721no—
448#108—1721no—
449#107—21no—
450#107—21no—
451#106—21no—
452#106—21no—
453C4⋊C8—21no—
454C4⋊C8—21no—
455C4⋊C8—431no—
456C4⋊C8—431no—
457C4⋊C8—431no—
458C4⋊C8—431no—
459C4⋊C8—861no—
460C4⋊C8—861no—
461C4⋊C8—861no—
462C4⋊C8—861no—
463#103—861no—
464#103—861no—
465#103—861no—
466#103—861no—
467#103—861no—
468#103—861no—
469#102—21no—
470#102—21no—
471#102—21no—
472#102—21no—
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—861no—
486#97—861no—
487#97—861no—
488#97—861no—
489C4×C8—861no—
490C4×C8—861no—
491C4×C8—861no—
492C4×C8—861no—
493C24—21no—
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—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—861no—
509C2×D4—861no—
510C2×D4—861no—
511C2×D4—861no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4#1062190212yes—
515C22×C4—21no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—82no—
519C22×C4—861no—
520C22×C4#1062190011yescharacteristic
521C22×C4#1062190011yescharacteristic
522C22×C4C23×D4311yescharacteristic
523SD16—1722no—
524SD16—1722no—
525D8—1722no—
526D8—1722no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—432no—
532M16—861no—
533M16—861no—
534M16—861no—
535M16—861no—
536M16—861no—
537M16—861no—
538M16—861no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—431no—
542C2×C8—431no—
543C2×C8—431no—
544C2×C8—431no—
545C2×C8—861no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8—861no—
552C2×C8—861no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4C2×C22⋊D4311yescharacteristic
562C4⋊C4C2×C22⋊D4311yescharacteristic
563C4⋊C4C2×C22⋊D4311yescharacteristic
564C4⋊C4C2×C22⋊D4311yescharacteristic
565C22⋊C4—21no—
566C22⋊C4—21no—
567C22⋊C4—41no—
568C22⋊C4—41no—
569C22⋊C4—1721no—
570C22⋊C4—1721no—
571C22⋊C4—1721no—
572C22⋊C4—1721no—
573C42—21no—
574C42—21no—
575C42D4×D4311yescharacteristic
576C42D4×D4311yescharacteristic
577C42C2×C22⋊D4311yescharacteristic
578C42C2×C22⋊D4311yescharacteristic
579C23—22no—
580C23—41no—
581C23—41no—
582C23—81no—
583C23—81no—
584C23—3441no—
585C23—3441no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23C2×#1062190011yescharacteristic
590Q8—42no—
591Q8—81no—
592Q8—1721no—
593Q8—1721no—
594Q8—1721no—
595Q8—1721no—
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
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—41no—
611C2×C4—82no—
612C2×C4—82no—
613C2×C4—81no—
614C2×C4—1721no—
615C2×C4—1721no—
616C2×C4—1721no—
617C2×C4#1306329711yescharacteristic
618C2×C4#1306329711yescharacteristic
619C2×C4#1306329711yescharacteristic
620C2×C4#1306329711yescharacteristic
621C2×C4C2×D4×D4311yescharacteristic
622C2×C4C22×C22⋊D4311yescharacteristic
623C2×C4#41×D4311yescharacteristic
624C2×C4C2×#1062190211yescharacteristic
625C2×C4#1306337111yescharacteristic
626C2×C4#1306337311yescharacteristic
627C8—41no—
628C8—41no—
629C8—862no—
630C8—861no—
631C8—861no—
632C8—861no—
633C8—861no—
634C8—1721no—
635C8—1721no—
636C8—1721no—
637C22—21no—
638C22—21no—
639C22—42no—
640C22—82no—
641C22—82no—
642C22—81no—
643C22—81no—
644C22—3441no—
645C22—3441no—
646C22—3441no—
647C22—6881no—
648C22—6881no—
649C22C2×#1306329711yescharacteristic
650C22#1458343511yescharacteristic
651C22#1458352211yescharacteristic
652C4—21no—
653C4—21no—
654C4—21no—
655C4—21no—
656C4—41no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—81no—
661C4—3441no—
662C4#1458354011yescharacteristic
663C4#1458355911yescharacteristic
664C4#1458356011yescharacteristic
665C4#1458356811yescharacteristic
666C2—21no—
667C2—21no—
668C2—82no—
669C2—6881no—
670C2#1913816311yescharacteristic
671C2#1914431211yescharacteristic
672C2#1914432011yescharacteristic
subgroupG/H
centerC22C2×#13063297
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#3077C2
socleC22×C43C2×#121
prime radicalC22×#10621882C22
hypercenter#3077D43
hypocenterC43#25316
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #19144984C2semidirect
3. #19143544C2semidirect
4. #19135959C2semidirect
5. #19135952C2semidirect
6. #19135857C2semidirect
9. #19135501C2semidirect
10. #19135442C2semidirect
11. #19135368C2semidirect
12. #19135256C2semidirect
13. #19135249C2semidirect
14. C4×#13063242C2semidirect
15. C43×#3077C2semidirect
331. #3077D43semidirect
403. C43#25316semidirect

Maximal subgroups

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

subgroupindex
#191449842
C2×#145831142
#191435442
#191359592
#191359522
#191358572
#191358502
#191355042
#191355012
#191354422
#191353682
#191352562
#191352492
C4×#130632422
C43×#30772
#2531643