Finite Group Databasebeta

← #25200243

Subgroups — #25200243

Order 11008.

700 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140395C211yesmaximal, characteristic
2#19137280C211yesmaximal, characteristic
3#19136019C211yesmaximal, characteristic
4#19135797C211yesmaximal, characteristic
5#19135797C211yesmaximal, characteristic
6#19135602C211yesmaximal, characteristic
7#19135328C211yesmaximal, characteristic, complemented
8#19135288C211yesmaximal, characteristic, complemented
9#19135288C211yesmaximal, characteristic, complemented
10#19135238C211yesmaximal, characteristic, complemented
11#19135168C211yesmaximal, characteristic, complemented
12#19134938C211yesmaximal, characteristic, complemented
13#19134851C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic
15C43×#1969C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×#13063301C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063282C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29#14582840—21no—
30#14582833—21no—
31#14582828—21no—
32#14582826—21no—
33#14582806C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582796—21no—
38#14582791—21no—
39#14582788—21no—
40#14582781—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063301—22no—
63#13063301—22no—
64#13063301—41no—
65#13063301—41no—
66Q8×Dic43—41no—
67Q8×Dic43—41no—
68#13063282—41no—
69#13063282—41no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×(C2×D43)⋊C4D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43C2311yescharacteristic
91#13063259—22no—
92#13063259—41no—
93#13063249—22no—
94#13063249—22no—
95#13063249—41no—
96#13063249—41no—
97(C2×D43)⋊C8—22no—
98(C2×D43)⋊C8—22no—
99#13063236—41no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C2×Q16×C43—22no—
111C2×Q16×C43—22no—
112C2×Q16×C43—41no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#107×C43—22no—
119#103×C43—22no—
120#103×C43—22no—
121C4×C8×C43—41no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159Q16×C43—44no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43#4112yes—
165C2×C8×C43#4112yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C42×C43—21no—
171C42×C43—21no—
172(C2×D43)⋊C4—24no—
173(C2×D43)⋊C4—41no—
174(C2×D43)⋊C4—41no—
175(C2×D43)⋊C4—42no—
176(C2×D43)⋊C4—81no—
177(C2×D43)⋊C4—81no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—42no—
186C4⋊Dic43—81no—
187C4⋊Dic43#4112yes—
188Dic43⋊C4—24no—
189Dic43⋊C4—41no—
190Dic43⋊C4—41no—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193Dic43⋊C4—81no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—42no—
197C4×Dic43—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43C22×D411yescharacteristic
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212Q8×C43—22no—
213Q8×C43—22no—
214Q8×C43—41no—
215Q8×C43—41no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220C2×C4×C43—22no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—21no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43C2×#4111yescharacteristic
239C2×C4×C43C2×#4111yescharacteristic
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43H(5,𝔽2)11yescharacteristic
243C2×C4×C43H(5,𝔽2)11yescharacteristic
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C4×D43—41no—
266C4×D43—41no—
267C4×D43—41no—
268C4×D43—41no—
269C8×C43—22no—
270C8×C43—22no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#29470—431nomaximal, Sylow
274C22×C43#52511yescharacteristic
275C22×C43#53211yescharacteristic
276C22×C43#53411yescharacteristic
277C22×C43#57611yescharacteristic
278C22×C43#57811yescharacteristic
279C22×C43#57811yescharacteristic
280C22×C43#57811yescharacteristic
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43#55111yescharacteristic
295C4×C43#55311yescharacteristic
296C4×C43#55311yescharacteristic
297C4×C43#55911yescharacteristic
298Dic43—41no—
299Dic43—42no—
300Dic43—41no—
301Dic43—41no—
302Dic43—81no—
303Dic43—81no—
304Dic43—81no—
305#2625—431no—
306#2323—431no—
307#2075—431no—
308#2036—431no—
309#2036—431no—
310#2001—431no—
311#1969D4311yescharacteristic, complemented
312#1942—431no—
313#1935—431no—
314#1935—431no—
315#1928—431no—
316#1918—431no—
317#1878—431no—
318#1863—431no—
319#1750—431no—
320C2×C43#260211yescharacteristic
321C2×C43#312411yescharacteristic
322C2×C43#312711yescharacteristic
323C2×C43#317511yescharacteristic
324C2×C43#317711yescharacteristic
325C2×C43#320211yescharacteristic
326C2×C43#320311yescharacteristic
327D43—81no—
328C22×Q16C2×D4311yescharacteristic
329C2×C22⋊Q8—431no—
330C2×C22⋊Q8—431no—
331C2×C4×Q8—431no—
332C2×#117—431no—
333C2×#107—431no—
334C2×#107—431no—
335C2×#107C2×D4311yescharacteristic
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103C2×D4311yescharacteristic
341C2×#103C2×D4311yescharacteristic
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×#97—431no—
345C2×C4×C8C2×D4311yescharacteristic
346#400—861no—
347#398—861no—
348#397—861no—
349#397—861no—
350#391—431no—
351#391C2×D4311yescharacteristic
352#391C2×D4311yescharacteristic
353#389—431no—
354#389—431no—
355#389—431no—
356#389—861no—
357#388—861no—
358#388—861no—
359#387—861no—
360#380—431no—
361#380—431no—
362C4×C4⋊C4—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#336—431no—
370#336—431no—
371C43#2947011yescharacteristic, complemented, Sylow
372C22×Q8C22×D4311yescharacteristic
373C22×Q8C22×D4311yescharacteristic
374C23×C4—431no—
375C2×Q16—22no—
376C2×Q16—22no—
377C2×Q16—41no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382C22⋊Q8—862no—
383C22⋊Q8—862no—
384C22⋊Q8—1721no—
385C22⋊Q8—1721no—
386C4×Q8—1721no—
387C4×Q8—1721no—
388#117—1721no—
389#117—1721no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—431no—
405C2×C22⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—431no—
411C2×C42—861no—
412C2×C42—861no—
413C2×C42C22×D4311yescharacteristic
414#107—22no—
415#107—862no—
416#107—1721no—
417#103—22no—
418#103—22no—
419#103—862no—
420#103—862no—
421#103—1721no—
422#103—1721no—
423C22⋊C8—862no—
424C22⋊C8—862no—
425#97—1721no—
426C4×C8—41no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439C24—431no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8#1062189812yes—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472Q16—44no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8#1062190012yes—
484C2×C8#1062190012yes—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—432no—
490C4⋊C4—864no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—861no—
497C4⋊C4—861no—
498C4⋊C4—3441no—
499C4⋊C4—3441no—
500C4⋊C4—3441no—
501C4⋊C4—1721no—
502C4⋊C4—1721no—
503C4⋊C4—1722no—
504C4⋊C4—1722no—
505C22⋊C4—864no—
506C22⋊C4—3441no—
507C22⋊C4—3441no—
508C22⋊C4—1721no—
509C22⋊C4—1721no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—861no—
514C42—861no—
515C42—3441no—
516C42—1722no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23C2×D4×D4311yescharacteristic
525Q8—22no—
526Q8—22no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—862no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—1721no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4#41×D4311yescharacteristic
577C2×C4C2×#1062190011yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C2×C4#1306337011yescharacteristic
581C2×C4#1306337111yescharacteristic
582C8—22no—
583C8—22no—
584C8—1721no—
585C8—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22#1458340811yescharacteristic
594C22#1458344711yescharacteristic
595C22#1458345711yescharacteristic
596C22#1458370111yescharacteristic
597C22#1458371211yescharacteristic
598C22#1458371211yescharacteristic
599C22#1458371311yescharacteristic
600C4—41no—
601C4—41no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—3441no—
607C4—3441no—
608C4—3441no—
609C4—1721no—
610C4—1721no—
611C4—1721no—
612C4—1722no—
613C4#1458357511yescharacteristic
614C4#1458359211yescharacteristic
615C4#1458359511yescharacteristic
616C4#1458363111yescharacteristic
617C2—3441no—
618C2#1914020411yescharacteristic
619C2#1914486311yescharacteristic
620C2#1914489211yescharacteristic
621C2#1914523111yescharacteristic
622C2#1914525111yescharacteristic
623C2#1914548511yescharacteristic
624C2#1914549811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1969C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1969D43
hypocenterC43#29470
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
7. #19135328C2semidirect
8. #19135288C2semidirect
9. #19135288C2semidirect
10. #19135238C2semidirect
11. #19135168C2semidirect
12. #19134938C2semidirect
13. #19134851C2semidirect
15. C43×#1969C2semidirect
311. #1969D43semidirect
371. C43#29470semidirect

Maximal subgroups

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

subgroupindex
#191403952
#191372802
#191360192
#191357972
#191356022
#191353282
#191352882
#191352382
#191351682
#191349382
#191348512
#191343622
C43×#19692
#2947043