Finite Group Databasebeta

← #25199487

Subgroups — #25199487

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#19137291C211yesmaximal, characteristic, complemented
2#19137282C211yesmaximal, characteristic, complemented
3#19136034C211yesmaximal, characteristic, complemented
4#19135782C211yesmaximal, characteristic, complemented
5#19135776C211yesmaximal, characteristic, complemented
6#19135590C211yesmaximal, characteristic
7#19135219C211yesmaximal, characteristic, complemented
8#19135217C211yesmaximal, characteristic, complemented
9#19135171C211yesmaximal, characteristic, complemented
10#19135167C211yesmaximal, characteristic, complemented
11#19134945C211yesmaximal, characteristic, complemented
12#19134856C211yesmaximal, characteristic, complemented
13#19134854C211yesmaximal, characteristic, complemented
14#19134665C211yesmaximal, characteristic, complemented
15C43×#1879C211yesmaximal, characteristic, complemented
16C2×#13063296C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×D4×Dic43C2211yescharacteristic
19C2×#13063282C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063256C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29#14582802C2211yescharacteristic
30#14582799—21no—
31#14582799—21no—
32#14582797C2211yescharacteristic
33#14582795C2211yescharacteristic
34#14582793—21no—
35#14582787—21no—
36#14582778—21no—
37#14582776—21no—
38#14582772—21no—
39#14582771—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C4×C4⋊Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×D8×C43C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C22×C22⋊D43—21no—
61C23×Dic43—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063296—22no—
66#13063296—22no—
67#13063296—22no—
68#13063296—22no—
69D4×Dic43—41no—
70D4×Dic43—41no—
71#13063282—41no—
72#13063282—41no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
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)⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063259—22no—
94#13063256—22no—
95#13063256—41no—
96#13063246—22no—
97#13063246—22no—
98#13063246—22no—
99#13063246—41no—
100(C2×D43)⋊C8—41no—
101(C2×D43)⋊C8—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×D4×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C2×D8×C43—22no—
112C2×D8×C43—22no—
113C2×D8×C43—41no—
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C4×D4×C43—41no—
117C4×D4×C43—41no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C22⋊C4×C43—21no—
123C2×C42×C43C2311yescharacteristic
124#102×C43—22no—
125#102×C43—41no—
126C24×C43—21no—
127C24×C43—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—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43#4112yes—
140C2×D4×C43#4112yes—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—42no—
144C22×C4×C43—81no—
145C22×C4×C43—81no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2411yescharacteristic
149C2×C22⋊D43—24no—
150C2×C22⋊D43—24no—
151C2×C22⋊D43—81no—
152C2×C22⋊D43—81no—
153C2×C22⋊D43—81no—
154C2×C22⋊D43—81no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—42no—
160C22×Dic43—81no—
161C22×Dic43—81no—
162C22×Dic43C2×D411yescharacteristic
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171D8×C43—44no—
172C2×C8×C43—21no—
173C2×C8×C43—21no—
174C2×C8×C43—21no—
175C2×C8×C43—21no—
176C2×C8×C43—21no—
177C2×C8×C43—21no—
178C4⋊C4×C43—21no—
179C4⋊C4×C43—21no—
180C4⋊C4×C43—21no—
181C4⋊C4×C43—21no—
182C22⋊C4×C43—42no—
183C22⋊C4×C43—81no—
184C22⋊C4×C43—81no—
185C42×C43—21no—
186C42×C43—21no—
187C22⋊Dic43—24no—
188C22⋊Dic43—24no—
189C22⋊Dic43—42no—
190C22⋊Dic43—81no—
191C22⋊Dic43—81no—
192(C2×D43)⋊C4—41no—
193(C2×D43)⋊C4—41no—
194(C2×D43)⋊C4—81no—
195(C2×D43)⋊C4—81no—
196C4⋊Dic43—21no—
197C4⋊Dic43—21no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43#4112yes—
203C4⋊Dic43#4112yes—
204Dic43⋊C4—41no—
205Dic43⋊C4—41no—
206Dic43⋊C4—81no—
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—22no—
220C23×C43—41no—
221C23×C43—41no—
222C23×C43—41no—
223C23×C43—41no—
224C23×C43—41no—
225C23×C43—41no—
226C23×C43—41no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43C22×D411yescharacteristic
233C22×D43—21no—
234C22×D43—21no—
235C22×D43—21no—
236C22×D43—21no—
237C22×D43—21no—
238C22×D43—21no—
239C22×D43—21no—
240D4×C43—22no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—22no—
244D4×C43—41no—
245D4×C43—41no—
246D4×C43—41no—
247D4×C43—41no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—21no—
251C2×C4×C43—21no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43—84no—
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C22⋊D43—84no—
268C22⋊D43—84no—
269C2×Dic43—22no—
270C2×Dic43—22no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—84no—
291C4×D43—41no—
292C4×D43—41no—
293C4×D43—41no—
294C4×D43—41no—
295C8×C43—41no—
296C8×C43—41no—
297C43⋊C8—41no—
298C43⋊C8—41no—
299#29418—431nomaximal, Sylow
300C22×C43—42no—
301C22×C43—42no—
302C22×C43—42no—
303C22×C43—42no—
304C22×C43—42no—
305C22×C43—42no—
306C22×C43—81no—
307C22×C43—81no—
308C22×C43—81no—
309C22×C43—81no—
310C22×C43—81no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43#52511yescharacteristic
315C22×C43#52511yescharacteristic
316C22×C43#53411yescharacteristic
317C22×C43#57611yescharacteristic
318C22×C43#57611yescharacteristic
319C22×C43#57711yescharacteristic
320C22×C43#57711yescharacteristic
321C2×D43—41no—
322C2×D43—41no—
323C2×D43—41no—
324C2×D43—41no—
325C2×D43—41no—
326C2×D43—41no—
327C2×D43—41no—
328C4×C43—41no—
329C4×C43—41no—
330C4×C43—81no—
331C4×C43—81no—
332C4×C43#55111yescharacteristic
333C4×C43#55311yescharacteristic
334C4×C43#55311yescharacteristic
335C4×C43#55911yescharacteristic
336Dic43—41no—
337Dic43—42no—
338Dic43—42no—
339Dic43—41no—
340Dic43—41no—
341Dic43—81no—
342Dic43—81no—
343#2324—431no—
344#2324—431no—
345#2077—431no—
346#2034—431no—
347#2033—431no—
348#1999—431no—
349#1926—431no—
350#1925—431no—
351#1919—431no—
352#1918—431no—
353#1879—431no—
354#1879D4311yescharacteristic, complemented
355#1864—431no—
356#1864—431no—
357#1818—431no—
358C2×C43—82no—
359C2×C43—82no—
360C2×C43#260011yescharacteristic
361C2×C43#311811yescharacteristic
362C2×C43#311911yescharacteristic
363C2×C43#312211yescharacteristic
364C2×C43#312511yescharacteristic
365C2×C43#319811yescharacteristic
366C2×C43#319811yescharacteristic
367D43—81no—
368C22×D8C2×D4311yescharacteristic
369C2×#121—431no—
370C2×#121—431no—
371C2×C4×D4—431no—
372C2×C4×D4C2×D4311yescharacteristic
373C2×#117—431no—
374C2×#107—431no—
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—861no—
387#390—861no—
388#390C2×D4311yescharacteristic
389#389—431no—
390#389—431no—
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#2941811yescharacteristic, complemented, Sylow
412C22×D4—861no—
413C22×D4—861no—
414C22×D4C22×D4311yescharacteristic
415C22×D4C22×D4311yescharacteristic
416C23×C4—21no—
417C23×C4—431no—
418C23×C4—861no—
419C2×D8—22no—
420C2×D8—22no—
421C2×D8—41no—
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—431no—
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⋊C4—861no—
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—431no—
450C2×C22⋊C4—431no—
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—862no—
463#106—862no—
464#106—1721no—
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—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24—21no—
480C24—21no—
481C24—431no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—864no—
493C2×D4—864no—
494C2×D4—3441no—
495C2×D4—3441no—
496C2×D4—3441no—
497C2×D4—3441no—
498C2×D4#1062189812yes—
499C2×D4#1062190012yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4—431no—
506C22×C4—431no—
507C22×C4—431no—
508C22×C4—861no—
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—44no—
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—432no—
542C4⋊C4—432no—
543C4⋊C4—861no—
544C4⋊C4—861no—
545C4⋊C4—861no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—3441no—
550C4⋊C4—3441no—
551C4⋊C4—1721no—
552C4⋊C4—1721no—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C22⋊C4—864no—
557C22⋊C4—864no—
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—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—861no—
586C23—861no—
587C23—861no—
588C23—861no—
589C23—861no—
590C23—861no—
591C23—861no—
592C23C2×D4×D4311yescharacteristic
593D4—22no—
594D4—22no—
595D4—22no—
596D4—22no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—41no—
601D4—3444no—
602D4—3444no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—84no—
616C2×C4—861no—
617C2×C4—862no—
618C2×C4—861no—
619C2×C4—862no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—861no—
625C2×C4—861no—
626C2×C4—861no—
627C2×C4—3444no—
628C2×C4—1721no—
629C2×C4—1721no—
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×#1062190011yescharacteristic
645C2×C4C2×#1062189811yescharacteristic
646C2×C4#1306337011yescharacteristic
647C2×C4#1306337011yescharacteristic
648C8—41no—
649C8—41no—
650C8—1721no—
651C8—1721no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—1721no—
667C22—1721no—
668C22—1721no—
669C22—1721no—
670C22—1721no—
671C22—1721no—
672C22—1721no—
673C22#1458340811yescharacteristic
674C22#1458340911yescharacteristic
675C22#1458345911yescharacteristic
676C22#1458370011yescharacteristic
677C22#1458370111yescharacteristic
678C22#1458370911yescharacteristic
679C22#1458370911yescharacteristic
680C4—41no—
681C4—41no—
682C4—81no—
683C4—81no—
684C4—3441no—
685C4—3441no—
686C4—1722no—
687C4—1721no—
688C4—1722no—
689C4—1721no—
690C4—1721no—
691C4#1458357511yescharacteristic
692C4#1458359211yescharacteristic
693C4#1458359811yescharacteristic
694C4#1458363311yescharacteristic
695C2—82no—
696C2—82no—
697C2—3441no—
698C2#1914017911yescharacteristic
699C2#1914477611yescharacteristic
700C2#1914479111yescharacteristic
701C2#1914483511yescharacteristic
702C2#1914487611yescharacteristic
703C2#1914544311yescharacteristic
704C2#1914544411yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1879C2
socleC23×C43C22×D4
prime radical#19135590C2
hypercenter#1879D43
hypocenterC43#29418
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
1. #19137291C2semidirect
2. #19137282C2semidirect
3. #19136034C2semidirect
4. #19135782C2semidirect
5. #19135776C2semidirect
7. #19135219C2semidirect
8. #19135217C2semidirect
9. #19135171C2semidirect
10. #19135167C2semidirect
11. #19134945C2semidirect
12. #19134856C2semidirect
13. #19134854C2semidirect
14. #19134665C2semidirect
15. C43×#1879C2semidirect
354. #1879D43semidirect
411. C43#29418semidirect

Maximal subgroups

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

subgroupindex
#191372912
#191372822
#191360342
#191357822
#191357762
#191355902
#191352192
#191352172
#191351712
#191351672
#191349452
#191348562
#191348542
#191346652
C43×#18792
#2941843