Finite Group Databasebeta

← #25199533

Subgroups — #25199533

Order 11008.

836 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19137286C211yesmaximal, characteristic, complemented
2#19137282C211yesmaximal, characteristic, complemented
3#19136019C211yesmaximal, characteristic, complemented
4#19135787C211yesmaximal, characteristic, complemented
5#19135783C211yesmaximal, characteristic, complemented
6#19135592C211yesmaximal, characteristic
7#19135225C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic, complemented
9#19135179C211yesmaximal, characteristic, complemented
10#19135177C211yesmaximal, characteristic, complemented
11#19134943C211yesmaximal, characteristic, complemented
12#19134940C211yesmaximal, characteristic, complemented
13#19134839C211yesmaximal, characteristic, complemented
14#19134665C211yesmaximal, characteristic, complemented
15C43×#1862C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063300C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×#13063287C2211yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582801C2211yescharacteristic
31#14582800—21no—
32#14582799—21no—
33#14582795C2211yescharacteristic
34#14582793—21no—
35#14582788—21no—
36#14582778—21no—
37#14582777—21no—
38#14582772—21no—
39#14582770—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×C4×D4×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#389C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×D172—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43—21no—
63C22×C4×D43C2311yescharacteristic
64C2×#10621882—22no—
65C2×#10621882—22no—
66C2×#10621882—41no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69#13063300—22no—
70#13063300—22no—
71#13063296—22no—
72#13063296—22no—
73#13063287—41no—
74#13063287—41no—
75#13063282—41no—
76#13063282—41no—
77C2×C4⋊Dic43C2311yescharacteristic
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×(C2×D43)⋊C4D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97#13063257—22no—
98#13063256—22no—
99#13063247—22no—
100#13063247—22no—
101#13063246—22no—
102#13063245—41no—
103(C2×D43)⋊C8—41no—
104(C2×D43)⋊C8—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C4×D4×C43—41no—
115C4×D4×C43—41no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C42×C43C2311yescharacteristic
122#107×C43—41no—
123#102×C43—22no—
124#102×C43—41no—
125#95×C43—21no—
126C24×C43—21no—
127C23×D43—21no—
128C23×D43C2×D411yescharacteristic
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43#4112yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—42no—
139C22×C4×C43—81no—
140C22×C4×C43—81no—
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2411yescharacteristic
144C2×C22⋊D43—24no—
145C2×C22⋊D43—81no—
146C2×C22⋊D43—81no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—24no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—81no—
160C2×D172—81no—
161C2×D172#4112yes—
162C2×C4×D43—21no—
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—42no—
169C2×C4×D43—81no—
170C2×C4×D43—81no—
171C2×C8×C43—21no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C4⋊C4×C43—81no—
183C4⋊C4×C43#4112yes—
184C22⋊C4×C43—42no—
185C42×C43—21no—
186C42×C43—21no—
187C22⋊Dic43—24no—
188C22⋊Dic43—81no—
189C22⋊Dic43—81no—
190#10621882—44no—
191(C2×D43)⋊C4—24no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—81no—
196(C2×D43)⋊C4—81no—
197(C2×D43)⋊C4—81no—
198(C2×D43)⋊C4—81no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—21no—
203C4⋊Dic43—21no—
204C4⋊Dic43#4112yes—
205Dic43⋊C4—41no—
206Dic43⋊C4—41no—
207Dic43⋊C4—81no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—81no—
211C4×Dic43—81no—
212C2×C43⋊C8—21no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C23×C43—22no—
219C23×C43—41no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43C22×D411yescharacteristic
226C22×D43—22no—
227C22×D43—21no—
228C22×D43—21no—
229C22×D43—21no—
230C22×D43—21no—
231C22×D43—21no—
232C22×D43—21no—
233C22×D43—21no—
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—41no—
243D4×C43—41no—
244C2×C4×C43—22no—
245C2×C4×C43—21no—
246C2×C4×C43—21no—
247C2×C4×C43—21no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—84no—
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C22⋊D43—84no—
267C2×Dic43—22no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285D172—22no—
286D172—22no—
287D172—41no—
288D172—41no—
289D172—84no—
290C4×D43—41no—
291C4×D43—41no—
292C4×D43—41no—
293C4×D43—41no—
294C4×D43—84no—
295C8×C43—41no—
296C8×C43—41no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299#29421—431nomaximal, Sylow
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—81no—
304C22×C43—81no—
305C22×C43—81no—
306C22×C43—81no—
307C22×C43#52511yescharacteristic
308C22×C43#52511yescharacteristic
309C22×C43#53411yescharacteristic
310C22×C43#57611yescharacteristic
311C22×C43#57611yescharacteristic
312C22×C43#57711yescharacteristic
313C22×C43#57711yescharacteristic
314C2×D43—41no—
315C2×D43—42no—
316C2×D43—41no—
317C2×D43—41no—
318C2×D43—42no—
319C2×D43—41no—
320C2×D43—41no—
321C2×D43—42no—
322C2×D43—41no—
323C2×D43—41no—
324C2×D43—81no—
325C2×D43—81no—
326C2×D43—81no—
327C2×D43—81no—
328C4×C43—42no—
329C4×C43—41no—
330C4×C43—41no—
331C4×C43—81no—
332C4×C43—81no—
333C4×C43#55111yescharacteristic
334C4×C43#55311yescharacteristic
335C4×C43#55311yescharacteristic
336C4×C43#55911yescharacteristic
337Dic43—41no—
338Dic43—42no—
339Dic43—41no—
340Dic43—41no—
341Dic43—81no—
342Dic43—81no—
343#2324—431no—
344#2324—431no—
345#2075—431no—
346#2034—431no—
347#2034—431no—
348#1999—431no—
349#1926—431no—
350#1926—431no—
351#1920—431no—
352#1920—431no—
353#1879—431no—
354#1879—431no—
355#1862—431no—
356#1862D4311yescharacteristic, complemented
357#1818—431no—
358C2×C43—82no—
359C2×C43#260011yescharacteristic
360C2×C43#311811yescharacteristic
361C2×C43#311811yescharacteristic
362C2×C43#311911yescharacteristic
363C2×C43#311911yescharacteristic
364C2×C43#319911yescharacteristic
365C2×C43#320411yescharacteristic
366D43—81no—
367D43—82no—
368C22×D8—431no—
369C2×#121—431no—
370C2×#121—431no—
371C2×C4×D4—431no—
372C2×C4×D4C2×D4311yescharacteristic
373C2×#117—431no—
374C2×#107C2×D4311yescharacteristic
375C2×#106—431no—
376C2×#106—431no—
377C2×#102—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102C2×D4311yescharacteristic
382C2×#102C2×D4311yescharacteristic
383C2×C22⋊C8—431no—
384C2×C22⋊C8—431no—
385#390—431no—
386#390—431no—
387#390—861no—
388#390—861no—
389#389—431no—
390#389C2×D4311yescharacteristic
391#388—861no—
392#388—861no—
393#386—861no—
394#386—861no—
395#385—861no—
396#385—861no—
397#380—431no—
398#380—431no—
399C4×C4⋊C4—431no—
400C4×C4⋊C4—431no—
401#340—431no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340—431no—
406#340C2×D4311yescharacteristic
407#336—431no—
408#336—431no—
409#336—431no—
410#336C2×D4311yescharacteristic
411C43#2942111yescharacteristic, complemented, Sylow
412C22×D4—431no—
413C22×D4—861no—
414C22×D4—861no—
415C22×D4C22×D4311yescharacteristic
416C23×C4—21no—
417C23×C4—431no—
418C23×C4—861no—
419C2×D8—862no—
420C2×D8—862no—
421C2×D8—1721no—
422C22×C8—431no—
423C22×C8—431no—
424C22×C8C22×D4311yescharacteristic
425C22×C8C22×D4311yescharacteristic
426#121—862no—
427#121—862no—
428#121—862no—
429#121—862no—
430C4×D4—41no—
431C4×D4—41no—
432C4×D4—1721no—
433C4×D4—1721no—
434#117—1721no—
435#117—1721no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—431no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—431no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—431no—
448C2×C22⋊C4—431no—
449C2×C22⋊C4—861no—
450C2×C22⋊C4—861no—
451C2×C22⋊C4—861no—
452C2×C22⋊C4—861no—
453C2×C22⋊C4—861no—
454C2×C22⋊C4—861no—
455C2×C22⋊C4—861no—
456C2×C22⋊C4—861no—
457C2×C22⋊C4—861no—
458C2×C42—431no—
459C2×C42—861no—
460C2×C42—861no—
461C2×C42C22×D4311yescharacteristic
462#107—41no—
463#106—862no—
464#106—862no—
465#102—22no—
466#102—41no—
467#102—862no—
468#102—862no—
469#102—862no—
470#102—1721no—
471C22⋊C8—1721no—
472C22⋊C8—1721no—
473#95—21no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—21no—
480C24—431no—
481C24—861no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—432no—
488C2×D4—864no—
489C2×D4—864no—
490C2×D4—861no—
491C2×D4—861no—
492C2×D4—861no—
493C2×D4—861no—
494C2×D4—861no—
495C2×D4—3441no—
496C2×D4—3441no—
497C2×D4—3441no—
498C2×D4—3441no—
499C2×D4#1062190212yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—81no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—431no—
509C22×C4—861no—
510C22×C4—861no—
511C22×C4—861no—
512C22×C4—861no—
513C22×C4—861no—
514C22×C4—861no—
515C22×C4—861no—
516C22×C4—861no—
517C22×C4—861no—
518C22×C4—3441no—
519C22×C4—3441no—
520C22×C4—1722no—
521C22×C4D4×D4311yescharacteristic
522C22×C4D4×D4311yescharacteristic
523C22×C4C23×D4311yescharacteristic
524D8—1724no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—861no—
532C2×C8—861no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—81no—
543C4⋊C4—432no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—3441no—
550C4⋊C4—1721no—
551C4⋊C4—1721no—
552C4⋊C4#1062189812yes—
553C22⋊C4—42no—
554C22⋊C4—864no—
555C22⋊C4—864no—
556C22⋊C4—3441no—
557C22⋊C4—3441no—
558C22⋊C4—3441no—
559C22⋊C4—3441no—
560C22⋊C4—3441no—
561C22⋊C4—3441no—
562C22⋊C4—1721no—
563C22⋊C4—1721no—
564C22⋊C4—1722no—
565C42—21no—
566C42—21no—
567C42—861no—
568C42—861no—
569C42—3441no—
570C42—3441no—
571C23—22no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—862no—
579C23—861no—
580C23—861no—
581C23—861no—
582C23—861no—
583C23—861no—
584C23—861no—
585C23—861no—
586C23—1721no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23C2×D4×D4311yescharacteristic
593D4—22no—
594D4—22no—
595D4—41no—
596D4—41no—
597D4—862no—
598D4—862no—
599D4—3444no—
600D4—3444no—
601D4—1721no—
602D4—1721no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—84no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—862no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—861no—
628C2×C4—861no—
629C2×C4—3444no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4—1721no—
634C2×C4—1721no—
635C2×C4—1721no—
636C2×C4—1721no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4#41×D4311yescharacteristic
643C2×C4#41×D4311yescharacteristic
644C2×C4C2×#1062189811yescharacteristic
645C2×C4C2×#1062190211yescharacteristic
646C2×C4#1306337011yescharacteristic
647C2×C4#1306337011yescharacteristic
648C8—41no—
649C8—41no—
650C8—1721no—
651C8—1721no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—3441no—
660C22—3441no—
661C22—3441no—
662C22—3441no—
663C22—1721no—
664C22—1721no—
665C22—1722no—
666C22—1721no—
667C22—1721no—
668C22—1722no—
669C22—1721no—
670C22—1722no—
671C22—1721no—
672C22—1721no—
673C22#1458340811yescharacteristic
674C22#1458341211yescharacteristic
675C22#1458345911yescharacteristic
676C22#1458370011yescharacteristic
677C22#1458370311yescharacteristic
678C22#1458370611yescharacteristic
679C22#1458370811yescharacteristic
680C4—41no—
681C4—42no—
682C4—41no—
683C4—81no—
684C4—81no—
685C4—3441no—
686C4—3441no—
687C4—1721no—
688C4—1722no—
689C4—1721no—
690C4—1721no—
691C4#1458357611yescharacteristic
692C4#1458359411yescharacteristic
693C4#1458359711yescharacteristic
694C4#1458363211yescharacteristic
695C2—82no—
696C2—3442no—
697C2—3441no—
698C2#1914018111yescharacteristic
699C2#1914477511yescharacteristic
700C2#1914478611yescharacteristic
701C2#1914479211yescharacteristic
702C2#1914479911yescharacteristic
703C2#1914545811yescharacteristic
704C2#1914550311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1862C2
socleC23×C43C22×D4
prime radical#19135592C2
hypercenter#1862D43
hypocenterC43#29421
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
1. #19137286C2semidirect
2. #19137282C2semidirect
3. #19136019C2semidirect
4. #19135787C2semidirect
5. #19135783C2semidirect
7. #19135225C2semidirect
8. #19135223C2semidirect
9. #19135179C2semidirect
10. #19135177C2semidirect
11. #19134943C2semidirect
12. #19134940C2semidirect
13. #19134839C2semidirect
14. #19134665C2semidirect
15. C43×#1862C2semidirect
356. #1862D43semidirect
411. C43#29421semidirect

Maximal subgroups

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

subgroupindex
#191372862
#191372822
#191360192
#191357872
#191357832
#191355922
#191352252
#191352232
#191351792
#191351772
#191349432
#191349402
#191348392
#191346652
C43×#18622
#2942143