Finite Group Databasebeta

← #25164756

Subgroups — #25164756

Order 11008.

860 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138954C211yesmaximal, characteristic, complemented
2#19137637C211yesmaximal, characteristic, complemented
3#19135904C211yesmaximal, characteristic, complemented
4#19135729C211yesmaximal, characteristic, complemented
5#19135591C211yesmaximal, characteristic
6#19135541C211yesmaximal, characteristic, complemented
7#19135279C211yesmaximal, characteristic, complemented
8#19135221C211yesmaximal, characteristic, complemented
9#19135204C211yesmaximal, characteristic, complemented
10#19135182C211yesmaximal, characteristic, complemented
11#19134941C211yesmaximal, characteristic, complemented
12#19134915C211yesmaximal, characteristic, complemented
13#19134687C211yesmaximal, characteristic, complemented
14#102×Dic43C211yesmaximal, characteristic, complemented
15C43×#2034C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×#13063324C2211yescharacteristic
18C2×#13063311—21no—
19C2×#13063299C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22C2×Dic43⋊C8C2211yescharacteristic
23C2×#13063247C2211yescharacteristic
24C2×#13063247C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C8×Dic43C2211yescharacteristic
29#14582814—21no—
30#14582812—21no—
31#14582802—21no—
32#14582802C2211yescharacteristic
33#14582800C2211yescharacteristic
34#14582800C2211yescharacteristic
35#14582798C2211yescharacteristic
36#14582792—21no—
37#14582788—21no—
38#14582779—21no—
39C4⋊C4×Dic43C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C22⋊C4×Dic43—21no—
42C4×C22⋊Dic43C2211yescharacteristic
43#14582662C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#121×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C23×Dic43—21no—
63C2×#10621882—22no—
64C2×#10621882—41no—
65C2×#10621882—41no—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063324—22no—
69#13063324—41no—
70#13063311—44no—
71#13063299—22no—
72#13063299—41no—
73D4×Dic43—22no—
74D4×Dic43—41no—
75#13063284—22no—
76#13063284—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43D411yescharacteristic
87C2×C22⋊Dic43D411yescharacteristic
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98Dic43⋊C8—41no—
99#13063247—22no—
100#13063247—41no—
101#13063246—22no—
102#13063245—22no—
103C22⋊(C43⋊C8)—41no—
104C8×Dic43—41no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95D411yescharacteristic
109C43⋊#95D411yescharacteristic
110C22×D4×C43—21no—
111C22×D4×C43C2311yescharacteristic
112C23×C4×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115#121×C43—22no—
116#121×C43—22no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122#106×C43—22no—
123#102×C43—22no—
124#102×C43—41no—
125C22⋊C8×C43—41no—
126#95×C43—21no—
127C24×C43—21no—
128C24×C43C2×D411yescharacteristic
129C23×D43—21no—
130C2×D4×C43—24no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—81no—
137C2×D4×C43—81no—
138C2×D4×C43#4112yes—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—42no—
151C2×C22⋊D43—42no—
152C2×C22⋊D43—81no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—42no—
157C22×Dic43—42no—
158C22×Dic43—81no—
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D411yescharacteristic
163C2×D172—21no—
164C2×D172—21no—
165C2×D172—21no—
166C2×D172—21no—
167C2×D172—21no—
168C2×D172—21no—
169C2×Dic86—42no—
170C2×Dic86—42no—
171C2×Dic86—81no—
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—
182C4⋊C4×C43—21no—
183C4⋊C4×C43#4112yes—
184C22⋊C4×C43—24no—
185C22⋊C4×C43—42no—
186C22⋊Dic43—22no—
187C22⋊Dic43—22no—
188C22⋊Dic43—42no—
189C22⋊Dic43—42no—
190C22⋊Dic43—42no—
191C22⋊Dic43—81no—
192#10621882—44no—
193(C2×D43)⋊C4—42no—
194(C2×D43)⋊C4—42no—
195(C2×D43)⋊C4—42no—
196(C2×D43)⋊C4—42no—
197(C2×D43)⋊C4—81no—
198C4⋊Dic43—21no—
199C4⋊Dic43—21no—
200C4⋊Dic43—21no—
201C4⋊Dic43—21no—
202C4⋊Dic43—81no—
203C4⋊Dic43#4112yes—
204C4⋊Dic43#4112yes—
205Dic43⋊C4—42no—
206C4×Dic43—21no—
207C4×Dic43—21no—
208C4×Dic43—21no—
209C4×Dic43—21no—
210C4×Dic43—42no—
211C4×Dic43—42no—
212C4×Dic43—81no—
213C2×C43⋊C8—21no—
214C2×C43⋊C8—21no—
215C2×C43⋊C8—21no—
216C2×C43⋊C8—21no—
217C2×C43⋊C8—21no—
218C2×C43⋊C8—21no—
219C23×C43—22no—
220C23×C43—21no—
221C23×C43—21no—
222C23×C43—21no—
223C23×C43—21no—
224C23×C43—21no—
225C23×C43—21no—
226C23×C43—21no—
227C23×C43—41no—
228C23×C43—41no—
229C23×C43—41no—
230C23×C43—41no—
231C23×C43—41no—
232C23×C43—41no—
233C23×C43C22×D411yescharacteristic
234C22×D43—41no—
235C22×D43—41no—
236C22×D43—41no—
237C22×D43—41no—
238C22×D43—41no—
239C22×D43—41no—
240C22×D43—41no—
241D4×C43—22no—
242D4×C43—22no—
243D4×C43—41no—
244D4×C43—41no—
245D4×C43—84no—
246C2×C4×C43—21no—
247C2×C4×C43—22no—
248C2×C4×C43—21no—
249C2×C4×C43—21no—
250C2×C4×C43—41no—
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—41no—
260C2×C4×C43—41no—
261C2×C4×C43—41no—
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43C2×#4111yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43H(5,𝔽2)11yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C22⋊D43—84no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285C2×Dic43—41no—
286C2×Dic43—41no—
287C2×Dic43—41no—
288C2×Dic43—84no—
289C2×Dic43#13512yes—
290C2×Dic43AGL(1,ℤ/8)12yes—
291D172—41no—
292D172—41no—
293D172—41no—
294D172—41no—
295Dic86—84no—
296C8×C43—41no—
297C8×C43—41no—
298C43⋊C8—41no—
299C43⋊C8—41no—
300#26729—431nomaximal, Sylow
301C22×C43—41no—
302C22×C43—42no—
303C22×C43—41no—
304C22×C43—42no—
305C22×C43—41no—
306C22×C43—42no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43—41no—
311C22×C43—81no—
312C22×C43—81no—
313C22×C43—81no—
314C22×C43—81no—
315C22×C43#52511yescharacteristic
316C22×C43#54611yescharacteristic
317C22×C43#54611yescharacteristic
318C22×C43C2×#13511yescharacteristic
319C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C43#57611yescharacteristic
321C22×C43#57711yescharacteristic
322C2×D43—81no—
323C2×D43—81no—
324C2×D43—81no—
325C2×D43—81no—
326C2×D43—81no—
327C2×D43—81no—
328C2×D43—81no—
329C4×C43—42no—
330C4×C43—41no—
331C4×C43—81no—
332C4×C43—81no—
333C4×C43#52911yescharacteristic
334C4×C43#53811yescharacteristic
335C4×C43#55511yescharacteristic
336C4×C43#55911yescharacteristic
337Dic43—22no—
338Dic43—22no—
339Dic43—41no—
340Dic43—42no—
341Dic43—41no—
342Dic43—42no—
343Dic43—81no—
344#2491—431no—
345#2363—431no—
346#2054—431no—
347#2034D4311yescharacteristic, complemented
348#2023—431no—
349#1999—431no—
350#1987—431no—
351#1934—431no—
352#1926—431no—
353#1923—431no—
354#1920—431no—
355#1879—431no—
356#1875—431no—
357#1825—431no—
358C4×#102—431no—
359C2×C43—81no—
360C2×C43—82no—
361C2×C43#245911yescharacteristic
362C2×C43#310611yescharacteristic
363C2×C43#311811yescharacteristic
364C2×C43#330111yescharacteristic
365C2×C43#330511yescharacteristic
366C2×C43#330611yescharacteristic
367C2×C43#332511yescharacteristic
368D43—161no—
369C22×D8—431no—
370C2×C4⋊Q8—431no—
371C2×#124—861no—
372C2×#121—431no—
373C2×#121C2×D4311yescharacteristic
374C2×C4×D4—431no—
375C2×#117—431no—
376C2×#106C2×D4311yescharacteristic
377C2×C4⋊C8—431no—
378C2×#102—431no—
379C2×#102—431no—
380C2×#102—431no—
381C2×#102—431no—
382C2×#102C2×D4311yescharacteristic
383C2×#102C2×D4311yescharacteristic
384C2×C22⋊C8—431no—
385C2×C22⋊C8C2×D4311yescharacteristic
386C2×C4×C8—431no—
387#394—861no—
388#393—861no—
389#390—431no—
390#390—431no—
391#390—431no—
392#390—861no—
393#389—431no—
394#388—861no—
395#388—861no—
396#386—861no—
397#380C2×D4311yescharacteristic
398C4×C4⋊C4—431no—
399C4×C4⋊C4—431no—
400C4×C22⋊C4—431no—
401C4×C22⋊C4—861no—
402#340—431no—
403#340—431no—
404#340—431no—
405#340—431no—
406#340—431no—
407#340—431no—
408#340—431no—
409#340C2×D4311yescharacteristic
410#336—431no—
411#336—431no—
412C43#2672911yescharacteristic, complemented, Sylow
413C22×Q8—861no—
414C22×D4—21no—
415C22×D4—431no—
416C22×D4—861no—
417C22×D4C22×D4311yescharacteristic
418C23×C4—861no—
419C23×C4C22×D4311yescharacteristic
420C2×D8—862no—
421C2×D8—1721no—
422C2×D8—1721no—
423C22×C8—431no—
424C22×C8—431no—
425C22×C8C22×D4311yescharacteristic
426C22×C8C22×D4311yescharacteristic
427C4⋊Q8—862no—
428C4⋊Q8—1721no—
429#124—1724no—
430#121—22no—
431#121—22no—
432#121—862no—
433#121—1721no—
434C4×D4—862no—
435C4×D4—1721no—
436#117—862no—
437#117—1721no—
438C2×C4⋊C4—431no—
439C2×C4⋊C4—431no—
440C2×C4⋊C4—431no—
441C2×C4⋊C4—861no—
442C2×C4⋊C4—861no—
443C2×C4⋊C4C22×D4311yescharacteristic
444C2×C4⋊C4C22×D4311yescharacteristic
445C2×C4⋊C4C22×D4311yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—431no—
449C2×C22⋊C4—431no—
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×C22⋊C4—861no—
459C2×C42—431no—
460C2×C42—431no—
461C2×C42—861no—
462C2×C42—861no—
463C2×C42—861no—
464#106—22no—
465C4⋊C8—1721no—
466#102—22no—
467#102—41no—
468#102—862no—
469#102—862no—
470#102—862no—
471#102—1721no—
472C22⋊C8—41no—
473C22⋊C8—1721no—
474C4×C8—1721no—
475#95—21no—
476#95—431no—
477#95—431no—
478#95—861no—
479#95—861no—
480#95—861no—
481C24—21no—
482C24—861no—
483C24D4×D4311yescharacteristic
484C2×Q8—3441no—
485C2×Q8—1722no—
486C2×Q8—1722no—
487C2×D4—24no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—81no—
494C2×D4—81no—
495C2×D4—861no—
496C2×D4—861no—
497C2×D4—861no—
498C2×D4—861no—
499C2×D4—861no—
500C2×D4—861no—
501C2×D4—3441no—
502C2×D4—1722no—
503C2×D4—1722no—
504C2×D4#1062190012yes—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—431no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—3441no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4D4×D4311yescharacteristic
525C22×C4C23×D4311yescharacteristic
526D8—1724no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—861no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—432no—
545C4⋊C4—432no—
546C4⋊C4—861no—
547C4⋊C4—861no—
548C4⋊C4—861no—
549C4⋊C4—861no—
550C4⋊C4—3441no—
551C4⋊C4—1722no—
552C4⋊C4#1062190012yes—
553C22⋊C4—24no—
554C22⋊C4—42no—
555C22⋊C4—862no—
556C22⋊C4—862no—
557C22⋊C4—3441no—
558C22⋊C4—3441no—
559C22⋊C4—1722no—
560C22⋊C4—1722no—
561C22⋊C4—1722no—
562C22⋊C4—1722no—
563C22⋊C4—1722no—
564C22⋊C4—1722no—
565C22⋊C4—1722no—
566C42—861no—
567C42—861no—
568C42—861no—
569C42—861no—
570C42—3441no—
571C42—1722no—
572C42—1722no—
573C23—22no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—1721no—
588C23—1721no—
589C23—1721no—
590C23—1721no—
591C23—1721no—
592C23—1721no—
593C23—1721no—
594C23C2×D4×D4311yescharacteristic
595Q8—3444no—
596D4—22no—
597D4—22no—
598D4—41no—
599D4—41no—
600D4—84no—
601D4—3444no—
602D4—1721no—
603D4—1721no—
604D4—1721no—
605D4—1721no—
606C2×C4—21no—
607C2×C4—22no—
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—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—432no—
623C2×C4—432no—
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—862no—
634C2×C4—861no—
635C2×C4—862no—
636C2×C4—3444no—
637C2×C4—1721no—
638C2×C4—1721no—
639C2×C4—1721no—
640C2×C4—1721no—
641C2×C4—1721no—
642C2×C4—1721no—
643C2×C4—1721no—
644C2×C4#41×D4311yescharacteristic
645C2×C4#41×D4311yescharacteristic
646C2×C4C2×#1062190011yescharacteristic
647C2×C4C2×#1062190011yescharacteristic
648C2×C4#1306337011yescharacteristic
649C2×C4#1306337111yescharacteristic
650C8—41no—
651C8—41no—
652C8—1721no—
653C8—1721no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22—42no—
658C22—41no—
659C22—41no—
660C22—42no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—3441no—
669C22—3441no—
670C22—3441no—
671C22—3441no—
672C22—3441no—
673C22—3441no—
674C22—3441no—
675C22#1458340511yescharacteristic
676C22#1458353811yescharacteristic
677C22#1458354111yescharacteristic
678C22#135×D4311yescharacteristic
679C22AGL(1,ℤ/8)×D4311yescharacteristic
680C22#1458370311yescharacteristic
681C22#1458370511yescharacteristic
682C4—42no—
683C4—41no—
684C4—81no—
685C4—81no—
686C4—862no—
687C4—862no—
688C4—3441no—
689C4—1721no—
690C4—1722no—
691C4—1721no—
692C4—1722no—
693C4#1458342611yescharacteristic
694C4#1458348611yescharacteristic
695C4#1458361311yescharacteristic
696C4#1458363111yescharacteristic
697C2—81no—
698C2—82no—
699C2—6881no—
700C2#1913852511yescharacteristic
701C2#1914464811yescharacteristic
702C2#1914478011yescharacteristic
703C2#1914649211yescharacteristic
704C2#1914654311yescharacteristic
705C2#1914655911yescharacteristic
706C2#1914683211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2034C2
socleC23×C43C22×D4
prime radical#19135591C2
hypercenter#2034D43
hypocenterC43#26729
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2034

Complements

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

NH ≅ G/Ntype
1. #19138954C2semidirect
2. #19137637C2semidirect
3. #19135904C2semidirect
4. #19135729C2semidirect
6. #19135541C2semidirect
7. #19135279C2semidirect
8. #19135221C2semidirect
9. #19135204C2semidirect
10. #19135182C2semidirect
11. #19134941C2semidirect
12. #19134915C2semidirect
13. #19134687C2semidirect
14. #102×Dic43C2semidirect
15. C43×#2034C2semidirect
347. #2034D43semidirect
412. C43#26729semidirect

Maximal subgroups

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

subgroupindex
#191389542
#191376372
#191359042
#191357292
#191355912
#191355412
#191352792
#191352212
#191352042
#191351822
#191349412
#191349152
#191346872
#102×Dic432
C43×#20342
#2672943