Finite Group Databasebeta

← #25104002

Subgroups — #25104002

Order 11008.

768 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144512C211yesmaximal, characteristic
2#19143300C211yesmaximal, characteristic
3#19143011C211yesmaximal, characteristic, complemented
4#19135242C211yesmaximal, characteristic, complemented
5#19135241C211yesmaximal, characteristic, complemented
6#19135197C211yesmaximal, characteristic, complemented
7#19135196C211yesmaximal, characteristic, complemented
8#19134896C211yesmaximal, characteristic
9#19134798C211yesmaximal, characteristic, complemented
10#19134693C211yesmaximal, characteristic, complemented
11#19134480C211yesmaximal, characteristic, complemented
12#19134441C211yesmaximal, characteristic, complemented
13#19134432C211yesmaximal, characteristic, complemented
14#19134378C211yesmaximal, characteristic, complemented
15C43×#1772C211yesmaximal, characteristic, complemented
16C2×#13063331C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×M16×D43C2211yescharacteristic
19#14583411C2211yescharacteristic
20#117×D43C2211yescharacteristic
21#14583243C411yescharacteristic, complemented
22#14583242C411yescharacteristic, complemented
23#14583236C411yescharacteristic, complemented
24#14583231C411yescharacteristic, complemented
25#14583226C411yescharacteristic, complemented
26#14583225C411yescharacteristic, complemented
27#14583219C411yescharacteristic, complemented
28#14583214C411yescharacteristic, complemented
29#14582978—21no—
30#14582978—21no—
31#14582972—21no—
32#14582972—21no—
33C2×#13063260C2211yescharacteristic
34#14582935C2211yescharacteristic
35#14582926C2211yescharacteristic
36C2×#13063253C2211yescharacteristic
37C2×#13063251C2211yescharacteristic
38#14582896C2211yescharacteristic
39#14582893C2211yescharacteristic
40#14582867C2211yescharacteristic
41#14582862C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43#14582857C2211yescharacteristic
44#14582856—21no—
45#14582855C2211yescharacteristic
46#14582854C2211yescharacteristic
47#14582853—21no—
48#14582851—21no—
49C4×#10621872—21no—
50C2×#13063235C2211yescharacteristic
51C4×(C2×D43)⋊C4C2211yescharacteristic
52#14582664C2211yescharacteristic
53#14582663C2211yescharacteristic
54#14582660C2211yescharacteristic
55#14582659C2211yescharacteristic
56#14582658C2211yescharacteristic
57#14582658C2211yescharacteristic
58#14582654C2211yescharacteristic
59#14582653C2211yescharacteristic
60C2×#108×C43C2211yescharacteristic
61C43×#427C2211yescharacteristic
62C43×#405C2211yescharacteristic
63C43×#405C2211yescharacteristic
64C2×C4×C8×C43C2211yescharacteristic
65C43×#339C2211yescharacteristic
66C43×#339C2211yescharacteristic
67C2×#10621898C2311yescharacteristic
68C22×C4×D43C2311yescharacteristic
69#13063331—22no—
70#13063331—22no—
71C2×#10621877C2311yescharacteristic
72C2×#10621877C2311yescharacteristic
73C2×#10621872—21no—
74C2×#10621872—22no—
75C2×#10621872—22no—
76C2×#10621872—21no—
77C2×#10621872D411yescharacteristic
78C2×#10621872D411yescharacteristic
79C2×#10621872D411yescharacteristic
80C2×#10621872D411yescharacteristic
81M16×D43—22no—
82M16×D43—22no—
83C22×C43⋊C8C2311yescharacteristic
84C22×C43⋊C8C2311yescharacteristic
85C2×C8×D43—21no—
86C2×C8×D43—21no—
87#13063309—21no—
88#13063305C2×C411yescharacteristic
89#13063305C2×C411yescharacteristic
90#13063300C2×C411yescharacteristic
91#13063300C2×C411yescharacteristic
92#13063295—21no—
93C4×D172—21no—
94C4×D172—21no—
95#13063284C2311yescharacteristic
96#13063283C2×C411yescharacteristic
97#13063283C2×C411yescharacteristic
98#13063282—21no—
99#13063281—21no—
100C4⋊C4×D43C2×C411yescharacteristic
101C4⋊C4×D43C2×C411yescharacteristic
102C2×(C2×D43)⋊C4—21no—
103C22⋊C4×D43—21no—
104C2×C4×Dic43C2311yescharacteristic
105C42×D43—21no—
106#13063260—22no—
107#13063258C2×C411yescharacteristic
108#13063258C2×C411yescharacteristic
109#13063256C2×C411yescharacteristic
110#13063256C2×C411yescharacteristic
111C4⋊(C43⋊C8)—21no—
112C4⋊(C43⋊C8)—21no—
113#13063253—22no—
114#13063251—22no—
115#13063250C2×C411yescharacteristic
116#13063250C2×C411yescharacteristic
117#13063248C2×C411yescharacteristic
118#13063248C2×C411yescharacteristic
119#13063247C2×C411yescharacteristic
120#13063247C2×C411yescharacteristic
121#13063245C2×C411yescharacteristic
122#13063245C2×C411yescharacteristic
123(C2×D43)⋊C8—21no—
124(C2×D43)⋊C8—21no—
125(C2×D43)⋊C8—21no—
126(C2×D43)⋊C8—21no—
127(C2×D43)⋊C8C2×C411yescharacteristic
128(C2×D43)⋊C8C2×C411yescharacteristic
129(C2×D43)⋊C8C2×C411yescharacteristic
130(C2×D43)⋊C8C2×C411yescharacteristic
131#13063236—21no—
132#13063235—21no—
133#13063235—22no—
134#13063235—21no—
135C4×C43⋊C8—21no—
136C8×Dic43—21no—
137C8×Dic43—21no—
138C43⋊#95—21no—
139C2×M16×C43C2311yescharacteristic
140C2×M16×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143#117×C43C2311yescharacteristic
144#117×C43C2311yescharacteristic
145C2×C42×C43C2311yescharacteristic
146#108×C43—22no—
147#107×C43C2×C411yescharacteristic
148#107×C43C2×C411yescharacteristic
149#106×C43C2×C411yescharacteristic
150#106×C43C2×C411yescharacteristic
151#97×C43—21no—
152#97×C43—21no—
153C4×C8×C43—21no—
154C4×C8×C43—21no—
155C4×C8×C43—22no—
156C23×D43#4111yescharacteristic
157C22×C4×C43—21no—
158C22×C4×C43C2411yescharacteristic
159C2×C22⋊D43—21no—
160C22×Dic43—21no—
161C22×Dic43#4111yescharacteristic
162#10621898—21no—
163#10621898—21no—
164#10621898—21no—
165#10621898—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172C22×C411yescharacteristic
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43C22×C411yescharacteristic
177C2×C4×D43C22×C411yescharacteristic
178C2×C4×D43C2×D411yescharacteristic
179C2×C4×D43C2×D411yescharacteristic
180C2×Dic86C22×C411yescharacteristic
181M16×C43—21no—
182M16×C43—21no—
183M16×C43—21no—
184M16×C43#4112yes—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43C22×C411yescharacteristic
190C2×C8×C43C22×C411yescharacteristic
191C2×C8×C43C2×D411yescharacteristic
192C2×C8×C43C2×D411yescharacteristic
193C2×C8×C43#4112yes—
194C2×C8×C43#4112yes—
195C4⋊C4×C43C22×C411yescharacteristic
196C4⋊C4×C43C22×C411yescharacteristic
197C4⋊C4×C43C22×C411yescharacteristic
198C4⋊C4×C43C22×C411yescharacteristic
199C22⋊C4×C43—21no—
200C22⋊C4×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C42×C43—21no—
204C42×C43—21no—
205C22⋊Dic43—21no—
206(C2×D43)⋊C4—21no—
207(C2×D43)⋊C4—21no—
208(C2×D43)⋊C4—21no—
209(C2×D43)⋊C4—21no—
210(C2×D43)⋊C4—21no—
211(C2×D43)⋊C4—21no—
212(C2×D43)⋊C4—42no—
213C4⋊Dic43—21no—
214C4⋊Dic43—21no—
215C4⋊Dic43C22×C411yescharacteristic
216C4⋊Dic43C22×C411yescharacteristic
217Dic43⋊C4—21no—
218Dic43⋊C4—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224#10621877—21no—
225#10621877—21no—
226#10621877—21no—
227#10621877#4112yes—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8C22×C411yescharacteristic
235C2×C43⋊C8C22×C411yescharacteristic
236C2×C43⋊C8C2×D411yescharacteristic
237C2×C43⋊C8C2×D411yescharacteristic
238#10621872—24no—
239#10621872—22no—
240#10621872—22no—
241#10621872—22no—
242#10621872—22no—
243#10621872—42no—
244C8×D43—24no—
245C8×D43—42no—
246C23×C43C2×#4111yescharacteristic
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—41no—
251C22×D43—41no—
252C22×D43C4×D411yescharacteristic
253C22×D43C4×D411yescharacteristic
254C2×C4×C43—22no—
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×C43C23×C411yescharacteristic
262C2×C4×C43C22×D411yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C22⋊D43—41no—
268C22⋊D43—41no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276C2×Dic43—41no—
277C2×Dic43C4×D411yescharacteristic
278C2×Dic43C4×D411yescharacteristic
279D172—21no—
280D172—21no—
281D172—81no—
282D172—81no—
283C4×D43—21no—
284C4×D43—21no—
285C4×D43—21no—
286C4×D43—21no—
287C4×D43—21no—
288C4×D43—21no—
289C4×D43—21no—
290C4×D43—21no—
291C4×D43—41no—
292C4×D43—41no—
293C4×D43—81no—
294C4×D43—81no—
295Dic86—21no—
296Dic86—21no—
297C8×C43—21no—
298C8×C43—21no—
299C8×C43—22no—
300C8×C43—41no—
301C8×C43#12312yes—
302C8×C43#12312yes—
303C43⋊C8—21no—
304C43⋊C8—21no—
305C43⋊C8—21no—
306C43⋊C8—21no—
307C43⋊C8—22no—
308C43⋊C8—41no—
309#21594—431nomaximal, Sylow
310C22×C43—21no—
311C22×C43—21no—
312C22×C43C2×C4×D411yescharacteristic
313C22×C43#52911yescharacteristic
314C22×C43#52911yescharacteristic
315C2×D43—21no—
316C2×D43—21no—
317C2×D43—21no—
318C2×D43—21no—
319C2×D43—21no—
320C2×D43—21no—
321C2×D43—41no—
322C2×D43—41no—
323C2×D43—41no—
324C2×D43—81no—
325C2×D43—81no—
326C4×C43—42no—
327C4×C43—41no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43C4×#4111yescharacteristic
332C4×C43C4×#4111yescharacteristic
333C4×C43C2×#12311yescharacteristic
334C4×C43#52511yescharacteristic
335Dic43—21no—
336Dic43—21no—
337Dic43—41no—
338Dic43—41no—
339Dic43—41no—
340Dic43—81no—
341#3091—431no—
342#2930—431no—
343#2873—431no—
344#1929—431no—
345#1929—431no—
346#1922—431no—
347#1922—431no—
348#1871—431no—
349#1855—431no—
350#1826—431no—
351#1773—431no—
352#1772D4311yescharacteristic, complemented
353#1765—431no—
354#1764—431no—
355#1753—431no—
356C2×C43—21no—
357C2×C43—21no—
358C2×C43C4×#12311yescharacteristic
359C2×C43#295611yescharacteristic
360C2×C43#295711yescharacteristic
361D43—41no—
362D43—41no—
363D43—81no—
364C2×#131—431no—
365C22×M16—431no—
366C22×M16—431no—
367#525—431no—
368C2×#117—431no—
369#485—431no—
370#485—431no—
371#484—431no—
372#483—431no—
373#482—431no—
374#482—431no—
375#481—431no—
376#480—431no—
377#436—861no—
378#436—861no—
379#435—861no—
380#435—861no—
381C2×#108—431no—
382C2×#108C2×D4311yescharacteristic
383#427—431no—
384#427C2×D4311yescharacteristic
385#424—431no—
386C2×#104—431no—
387C2×#104—431no—
388#416—431no—
389#416—431no—
390#408—431no—
391#407—431no—
392C2×C22⋊C8—431no—
393#405—431no—
394#405—431no—
395#405—431no—
396#405—861no—
397#405—861no—
398#405C2×D4311yescharacteristic
399#405C2×D4311yescharacteristic
400C4×M16—861no—
401C4×M16—861no—
402C2×#97—431no—
403C2×C4×C8C2×D4311yescharacteristic
404C4×C22⋊C4—431no—
405#341—431no—
406#341—431no—
407#339—431no—
408#339—431no—
409#339—431no—
410#339—431no—
411#339C2×D4311yescharacteristic
412#339C2×D4311yescharacteristic
413#336—431no—
414#336—431no—
415C43#2159411yescharacteristic, complemented, Sylow
416C2×#41—431no—
417C23×C4—431no—
418#131—862no—
419#131—862no—
420C2×M16—431no—
421C2×M16—431no—
422C2×M16—431no—
423C2×M16—431no—
424C2×M16—431no—
425C2×M16—431no—
426C2×M16—861no—
427C2×M16—862no—
428C2×M16—862no—
429C2×M16—862no—
430C2×M16—861no—
431C2×M16—862no—
432C2×M16C22×D4311yescharacteristic
433C2×M16C22×D4311yescharacteristic
434C22×C8—431no—
435C22×C8—431no—
436C22×C8—861no—
437C22×C8—861no—
438C22×C8C22×D4311yescharacteristic
439C22×C8C22×D4311yescharacteristic
440#123—861no—
441C22⋊Q8—431no—
442C22⋊Q8—431no—
443#121—431no—
444#121—431no—
445#120—861no—
446C4×D4—861no—
447C4×D4—861no—
448#117—431no—
449#117—431no—
450#117—431no—
451#117—861no—
452#117—861no—
453#117C22×D4311yescharacteristic
454#117C22×D4311yescharacteristic
455C2×C4⋊C4—431no—
456C2×C4⋊C4—431no—
457C2×C22⋊C4—861no—
458C2×C22⋊C4—861no—
459C2×C42—431no—
460C2×C42—861no—
461C2×C42C22×D4311yescharacteristic
462#108—22no—
463#108—862no—
464#107—431no—
465#107—431no—
466#107C4×D4311yescharacteristic
467#107C4×D4311yescharacteristic
468#106—431no—
469#106—431no—
470#106C4×D4311yescharacteristic
471#106C4×D4311yescharacteristic
472C4⋊C8—861no—
473C4⋊C8—861no—
474#104—862no—
475#104—862no—
476#103—431no—
477#103—431no—
478#103—431no—
479#103—431no—
480#102—431no—
481#102—431no—
482#102—431no—
483#102—431no—
484C22⋊C8—431no—
485C22⋊C8—431no—
486C22⋊C8—431no—
487C22⋊C8—431no—
488C22⋊C8—861no—
489C22⋊C8—861no—
490C22⋊C8—861no—
491C22⋊C8—861no—
492#97—21no—
493#97—21no—
494#97—861no—
495#97—861no—
496#97—861no—
497#97—862no—
498C4×C8—22no—
499C4×C8—21no—
500C4×C8—21no—
501C4×C8—861no—
502C4×C8—861no—
503C4×C8—861no—
504#95—861no—
505C24—431no—
506#41—861no—
507#41—861no—
508#41—861no—
509#41—861no—
510C2×Q8—431no—
511C2×D4—431no—
512C2×D4—861no—
513C2×D4—861no—
514C2×D4—861no—
515C22×C4—21no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—431no—
519C22×C4—431no—
520C22×C4—431no—
521C22×C4—861no—
522C22×C4—861no—
523C22×C4—861no—
524C22×C4—861no—
525C22×C4—861no—
526C22×C4—861no—
527C22×C4—861no—
528C22×C4—861no—
529C22×C4C23×D4311yescharacteristic
530M16—21no—
531M16—21no—
532M16—21no—
533M16—432no—
534M16—864no—
535M16—861no—
536M16—862no—
537M16—862no—
538M16—862no—
539M16—862no—
540M16—861no—
541M16—861no—
542M16—1722no—
543M16#1062189812yes—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—431no—
549C2×C8—431no—
550C2×C8—431no—
551C2×C8—431no—
552C2×C8—864no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8—861no—
557C2×C8—861no—
558C2×C8—861no—
559C2×C8—1722no—
560C2×C8C2×C4×D4311yescharacteristic
561C2×C8C2×C4×D4311yescharacteristic
562C2×C8#1062189812yes—
563C2×C8D4×D4311yescharacteristic
564C2×C8D4×D4311yescharacteristic
565C2×C8#1062190212yes—
566C4⋊C4—431no—
567C4⋊C4—431no—
568C4⋊C4—861no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4—861no—
572C4⋊C4C2×C4×D4311yescharacteristic
573C4⋊C4C2×C4×D4311yescharacteristic
574C4⋊C4C2×C4×D4311yescharacteristic
575C4⋊C4C2×C4×D4311yescharacteristic
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—861no—
579C22⋊C4—861no—
580C22⋊C4—861no—
581C22⋊C4—861no—
582C22⋊C4—861no—
583C22⋊C4—861no—
584C22⋊C4—861no—
585C22⋊C4—1722no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—861no—
591C42—861no—
592C42—861no—
593C42—861no—
594C42—861no—
595C23—431no—
596C23—431no—
597C23—861no—
598C23—861no—
599C23—861no—
600C23—1721no—
601C23—1721no—
602C23#41×D4311yescharacteristic
603Q8—861no—
604Q8—861no—
605D4—861no—
606D4—861no—
607D4—3441no—
608D4—3441no—
609D4—1721no—
610D4—1721no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—431no—
619C2×C4—431no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—3441no—
634C2×C4—3441no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4C22×C4×D4311yescharacteristic
641C2×C4C2×D4×D4311yescharacteristic
642C2×C4#41×D4311yescharacteristic
643C2×C4C2×#1062189811yescharacteristic
644C2×C4C2×#1062189811yescharacteristic
645C2×C4C2×#1062190211yescharacteristic
646C8—21no—
647C8—21no—
648C8—22no—
649C8—41no—
650C8—861no—
651C8—861no—
652C8—861no—
653C8—861no—
654C8—862no—
655C8—1721no—
656C8#1306331012yes—
657C8#1306331012yes—
658C22—21no—
659C22—21no—
660C22—861no—
661C22—861no—
662C22—861no—
663C22—861no—
664C22—861no—
665C22—861no—
666C22—3441no—
667C22—3441no—
668C22—1721no—
669C22—1721no—
670C22—1721no—
671C22C4×D4×D4311yescharacteristic
672C22#1458342711yescharacteristic
673C22#1458343611yescharacteristic
674C4—42no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—861no—
680C4—861no—
681C4—3441no—
682C4—1721no—
683C4—1721no—
684C4—1721no—
685C4C4×#1062189811yescharacteristic
686C4C4×#1062190211yescharacteristic
687C4C2×#1306331011yescharacteristic
688C4#1458340811yescharacteristic
689C2—21no—
690C2—21no—
691C2—3441no—
692C2—1721no—
693C2—1721no—
694C2C4×#1306331011yescharacteristic
695C2#1914350011yescharacteristic
696C2#1914350711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1772C2
socleC22×C43C2×C4×D4
prime radical#14583411C22
cosocleC22×C4×C43C24
hypercenter#1772D43
hypocenterC43#21594
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1772

Complements

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

NH ≅ G/Ntype
3. #19143011C2semidirect
4. #19135242C2semidirect
5. #19135241C2semidirect
6. #19135197C2semidirect
7. #19135196C2semidirect
9. #19134798C2semidirect
10. #19134693C2semidirect
11. #19134480C2semidirect
12. #19134441C2semidirect
13. #19134432C2semidirect
14. #19134378C2semidirect
15. C43×#1772C2semidirect
21. #14583243C4semidirect
22. #14583242C4semidirect
23. #14583236C4semidirect
24. #14583231C4semidirect
25. #14583226C4semidirect
26. #14583225C4semidirect
27. #14583219C4semidirect
28. #14583214C4semidirect
352. #1772D43semidirect
415. C43#21594semidirect

Maximal subgroups

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

subgroupindex
#191445122
#191433002
#191430112
#191352422
#191352412
#191351972
#191351962
#191348962
#191347982
#191346932
#191344802
#191344412
#191344322
#191343782
C43×#17722
#2159443