Finite Group Databasebeta

← #25169375

Subgroups — #25169375

Order 11008.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139009C211yesmaximal, characteristic, complemented
2#19137638C211yesmaximal, characteristic
3#19135983C211yesmaximal, characteristic, complemented
4#19135782C211yesmaximal, characteristic
5#19135775C211yesmaximal, characteristic
6#19135361C211yesmaximal, characteristic, complemented
7#19135327C211yesmaximal, characteristic, complemented
8#19135202C211yesmaximal, characteristic, complemented
9#19135181C211yesmaximal, characteristic, complemented
10#19135178C211yesmaximal, characteristic, complemented
11#19134858C211yesmaximal, characteristic, complemented
12#19134795C211yesmaximal, characteristic, complemented
13#19134689C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2073C211yesmaximal, characteristic, complemented
16C2×#13063296C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063283C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063257C2211yescharacteristic
22C2×#13063256C2211yescharacteristic
23C2×C4⋊(C43⋊C8)C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582841—21no—
30#14582826—21no—
31#14582799—21no—
32#14582798C2211yescharacteristic
33#14582797C2211yescharacteristic
34#14582795C2211yescharacteristic
35#14582793—21no—
36#14582788—21no—
37#14582776—21no—
38#14582766—21no—
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44C4×(C2×D43)⋊C4C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#102×C43C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C43×#390C2211yescharacteristic
55C43×#382C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×C22⋊D43—21no—
60C23×Dic43—21no—
61C22×C4×D43C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64#13063296—22no—
65#13063296—22no—
66D4×Dic43—22no—
67D4×Dic43—41no—
68#13063283—22no—
69#13063283—41no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4D411yescharacteristic
83C2×(C2×D43)⋊C4D411yescharacteristic
84C2×C4×Dic43—21no—
85C2×C4×Dic43—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88#13063258—22no—
89#13063258—41no—
90#13063257—22no—
91#13063256—22no—
92C4⋊(C43⋊C8)—22no—
93#13063246—22no—
94#13063246—41no—
95(C2×D43)⋊C8—22no—
96(C2×D43)⋊C8—41no—
97C8×Dic43—41no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95D411yescharacteristic
106C43⋊#95D411yescharacteristic
107C22×D4×C43C2311yescharacteristic
108C22×C8×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C42×C43C2311yescharacteristic
116#102×C43—22no—
117#102×C43—22no—
118#95×C43—21no—
119#95×C43—21no—
120C24×C43—21no—
121C23×D43C2×D411yescharacteristic
122C2×D4×C43—21no—
123C2×D4×C43—21no—
124C2×D4×C43—21no—
125C2×D4×C43—21no—
126C2×D4×C43—21no—
127C2×D4×C43#4112yes—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C2×C22⋊D43—24no—
135C2×C22⋊D43—81no—
136C2×C22⋊D43—81no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—42no—
142C22×Dic43—42no—
143C22×Dic43—81no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43—21no—
158C2×C8×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C22⋊C4×C43—42no—
166C22⋊C4×C43—81no—
167C42×C43—21no—
168C42×C43—21no—
169C22⋊Dic43—24no—
170C22⋊Dic43—42no—
171(C2×D43)⋊C4—22no—
172(C2×D43)⋊C4—41no—
173(C2×D43)⋊C4—42no—
174(C2×D43)⋊C4—42no—
175(C2×D43)⋊C4—81no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179C4⋊Dic43—21no—
180C4⋊Dic43—21no—
181C4⋊Dic43—21no—
182C4⋊Dic43—81no—
183C4⋊Dic43#4112yes—
184C4⋊Dic43#4112yes—
185Dic43⋊C4—81no—
186Dic43⋊C4—81no—
187C4×Dic43—21no—
188C4×Dic43—21no—
189C4×Dic43—42no—
190C4×Dic43—42no—
191C4×Dic43—81no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8—21no—
195C2×C43⋊C8—21no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8#4112yes—
198C23×C43—22no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43—41no—
203C23×C43—41no—
204C23×C43—41no—
205C23×C43C22×D411yescharacteristic
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212C22×D43—21no—
213D4×C43—22no—
214D4×C43—22no—
215D4×C43—41no—
216D4×C43—41no—
217C2×C4×C43—21no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43H(5,𝔽2)11yescharacteristic
237C2×C4×C432−1+411yescharacteristic
238C22⋊D43—84no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—84no—
260C2×Dic43#13512yes—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265C8×C43—41no—
266C8×C43—41no—
267C43⋊C8—22no—
268C43⋊C8—41no—
269#27038—431nomaximal, Sylow
270C22×C43—42no—
271C22×C43—42no—
272C22×C43—42no—
273C22×C43—81no—
274C22×C43—81no—
275C22×C43—81no—
276C22×C43—81no—
277C22×C43#52511yescharacteristic
278C22×C43#54611yescharacteristic
279C22×C43#54711yescharacteristic
280C22×C43C2×#13511yescharacteristic
281C22×C43#57511yescharacteristic
282C22×C43#57611yescharacteristic
283C22×C43#57711yescharacteristic
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C2×D43—41no—
289C2×D43—41no—
290C2×D43—41no—
291C4×C43—41no—
292C4×C43—41no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43#52911yescharacteristic
297C4×C43#53911yescharacteristic
298C4×C43#55311yescharacteristic
299C4×C43#55611yescharacteristic
300Dic43—22no—
301Dic43—42no—
302Dic43—41no—
303Dic43—42no—
304Dic43—41no—
305Dic43—81no—
306Dic43—81no—
307#2495—431no—
308#2363—431no—
309#2073D4311yescharacteristic, complemented
310#2067—431no—
311#2034—431no—
312#2033—431no—
313#1949—431no—
314#1942—431no—
315#1923—431no—
316#1920—431no—
317#1920—431no—
318#1864—431no—
319#1854—431no—
320#1825—431no—
321C4×#102—431no—
322C2×C43—82no—
323C2×C43#246611yescharacteristic
324C2×C43#310211yescharacteristic
325C2×C43#311811yescharacteristic
326C2×C43#329611yescharacteristic
327C2×C43#330911yescharacteristic
328C2×C43#334111yescharacteristic
329C2×C43#335111yescharacteristic
330D43—81no—
331C2×#121—431no—
332C2×C4×D4—431no—
333C2×#117—431no—
334C2×#107—431no—
335C2×#107—431no—
336C2×#106—431no—
337C2×#106—431no—
338C2×C4⋊C8—431no—
339C2×#102—431no—
340C2×#102—431no—
341C2×#102C2×D4311yescharacteristic
342C2×#102C2×D4311yescharacteristic
343C2×C22⋊C8—431no—
344C2×C22⋊C8—431no—
345C2×C4×C8—431no—
346#400—861no—
347#397—861no—
348#390—861no—
349#390C2×D4311yescharacteristic
350#389—431no—
351#389—431no—
352#389—431no—
353#388—861no—
354#388—861no—
355#386—861no—
356#383—861no—
357#382C2×D4311yescharacteristic
358#380—431no—
359#380—431no—
360C4×C4⋊C4—431no—
361C4×C4⋊C4—431no—
362C4×C22⋊C4—431no—
363C4×C22⋊C4—861no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#340C2×D4311yescharacteristic
371#340C2×D4311yescharacteristic
372#336—431no—
373#336C2×D4311yescharacteristic
374C43#2703811yescharacteristic, complemented, Sylow
375C22×D4—861no—
376C22×D4C22×D4311yescharacteristic
377C23×C4—431no—
378C23×C4—861no—
379C22×C8—431no—
380C22×C8—431no—
381C22×C8C22×D4311yescharacteristic
382C22×C8C22×D4311yescharacteristic
383#121—862no—
384#121—862no—
385C4×D4—862no—
386C4×D4—1721no—
387#117—862no—
388#117—1721no—
389C2×C4⋊C4—431no—
390C2×C4⋊C4—431no—
391C2×C4⋊C4—431no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—861no—
394C2×C4⋊C4—861no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4C22×D4311yescharacteristic
397C2×C4⋊C4C22×D4311yescharacteristic
398C2×C4⋊C4C22×D4311yescharacteristic
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—431no—
402C2×C22⋊C4—431no—
403C2×C22⋊C4—861no—
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C42—431no—
409C2×C42—861no—
410C2×C42—861no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#107—862no—
414#107—1721no—
415#106—862no—
416#106—862no—
417C4⋊C8—862no—
418#102—22no—
419#102—22no—
420#102—862no—
421#102—1721no—
422C22⋊C8—862no—
423C22⋊C8—1721no—
424C4×C8—1721no—
425#95—21no—
426#95—21no—
427#95—431no—
428#95—431no—
429#95—861no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436C24—21no—
437C24—431no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—864no—
444C2×D4—3441no—
445C2×D4—3441no—
446C2×D4#1062190012yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—431no—
451C22×C4—431no—
452C22×C4—431no—
453C22×C4—861no—
454C22×C4—861no—
455C22×C4—861no—
456C22×C4—861no—
457C22×C4—861no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—3441no—
464C22×C4—1722no—
465C22×C4—1722no—
466C22×C4D4×D4311yescharacteristic
467C22×C4D4×D4311yescharacteristic
468C22×C4C23×D4311yescharacteristic
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—432no—
476C2×C8—861no—
477C2×C8—861no—
478C2×C8—861no—
479C2×C8—861no—
480C2×C8—861no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—432no—
488C4⋊C4—432no—
489C4⋊C4—861no—
490C4⋊C4—861no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—3441no—
496C4⋊C4—3441no—
497C4⋊C4—3441no—
498C22⋊C4—42no—
499C22⋊C4—81no—
500C22⋊C4—862no—
501C22⋊C4—864no—
502C22⋊C4—3441no—
503C22⋊C4—1721no—
504C22⋊C4—1722no—
505C22⋊C4—1722no—
506C22⋊C4—1722no—
507C42—21no—
508C42—21no—
509C42—861no—
510C42—861no—
511C42—3441no—
512C42—1722no—
513C42—1722no—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23—861no—
525C23—861no—
526C23—861no—
527C23—861no—
528C23C2×D4×D4311yescharacteristic
529D4—22no—
530D4—22no—
531D4—41no—
532D4—41no—
533D4—3444no—
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—432no—
550C2×C4—861no—
551C2×C4—861no—
552C2×C4—861no—
553C2×C4—862no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—861no—
558C2×C4—862no—
559C2×C4—861no—
560C2×C4—3444no—
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#41×D4311yescharacteristic
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4#1306337111yescharacteristic
580C2×C4#1306337211yescharacteristic
581C8—41no—
582C8—41no—
583C8—862no—
584C8—1721no—
585C22—42no—
586C22—42no—
587C22—42no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22—1721no—
593C22—1721no—
594C22—1721no—
595C22—1721no—
596C22—1721no—
597C22—1721no—
598C22—1721no—
599C22#1458340911yescharacteristic
600C22#1458354211yescharacteristic
601C22#1458354711yescharacteristic
602C22#135×D4311yescharacteristic
603C22#1458369511yescharacteristic
604C22#1458370311yescharacteristic
605C22#1458370611yescharacteristic
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—862no—
612C4—3441no—
613C4—3441no—
614C4—1721no—
615C4—1722no—
616C4—1721no—
617C4—1722no—
618C4#1458342611yescharacteristic
619C4#1458349311yescharacteristic
620C4#1458360011yescharacteristic
621C4#1458361611yescharacteristic
622C2—82no—
623C2—3441no—
624C2#1913863211yescharacteristic
625C2#1914461011yescharacteristic
626C2#1914477811yescharacteristic
627C2#1914642911yescharacteristic
628C2#1914660011yescharacteristic
629C2#1914701211yescharacteristic
630C2#1914714811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2073C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#2073D43
hypocenterC43#27038
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2073

Complements

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

NH ≅ G/Ntype
1. #19139009C2semidirect
3. #19135983C2semidirect
6. #19135361C2semidirect
7. #19135327C2semidirect
8. #19135202C2semidirect
9. #19135181C2semidirect
10. #19135178C2semidirect
11. #19134858C2semidirect
12. #19134795C2semidirect
13. #19134689C2semidirect
14. #102×Dic43C2semidirect
15. C43×#2073C2semidirect
309. #2073D43semidirect
374. C43#27038semidirect

Maximal subgroups

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

subgroupindex
#191390092
#191376382
#191359832
#191357822
#191357752
#191353612
#191353272
#191352022
#191351812
#191351782
#191348582
#191347952
#191346892
#102×Dic432
C43×#20732
#2703843