Finite Group Databasebeta

← #25125004

Subgroups — #25125004

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583509C211yesmaximal, characteristic
2C2×#14583003C211yesmaximal, characteristic, complemented
3C2×#14582993C211yesmaximal, characteristic, complemented
4#19137273C211yesmaximal, characteristic
5#19135931C211yesmaximal, characteristic, complemented
6#19135839C211yesmaximal, characteristic, complemented
7#19135791C211yesmaximal, characteristic
8#19135745C211yesmaximal, characteristic, complemented
9#19135696C211yesmaximal, characteristic, complemented
10#19135605C211yesmaximal, characteristic
11#19135603C211yesmaximal, characteristic
12#19134424C211yesmaximal, characteristic, complemented
13#103×Dic43C211yesmaximal, characteristic, complemented
14#19134363C211yesmaximal, characteristic
15C43×#2036C211yesmaximal, characteristic
16C22×Dic172C2211yescharacteristic
17C22×#10621885C2211yescharacteristic
18#14583509—24no—
19#14583509—24no—
20C2×#13063323C2211yescharacteristic
21C2×#13063318—21no—
22C2×#13063318—21no—
23C2×#13063316—21no—
24C2×#13063316C2211yescharacteristic
25C2×#13063315—21no—
26C2×#13063304C2211yescharacteristic
27C2×#13063304C2211yescharacteristic
28C2×Q8×Dic43C2211yescharacteristic
29C2×#13063290C2211yescharacteristic
30C2×#13063290C2211yescharacteristic
31C2×#13063284C2211yescharacteristic
32#14583003—24no—
33#14582993—24no—
34C2×#13063256C2211yescharacteristic
35C2×#13063250C2211yescharacteristic
36C2×#13063250C2211yescharacteristic
37C2×#13063249C2211yescharacteristic
38C2×#13063248C2211yescharacteristic
39C2×#13063248C2211yescharacteristic
40C2×#13063248C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44#14582804C2211yescharacteristic
45#14582796—21no—
46#14582795C2211yescharacteristic
47#14582793—21no—
48#14582787—21no—
49#14582786—21no—
50C4⋊C4×Dic43C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#380C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C22×Dic86C2311yescharacteristic
65C2×Dic172—22no—
66C2×Dic172—22no—
67C2×Dic172—22no—
68C2×#10621885—22no—
69C2×#10621885—22no—
70C2×#10621885—22no—
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063323—22no—
74#13063323—22no—
75#13063318—28no—
76#13063318—28no—
77#13063316—28no—
78#13063316—22no—
79#13063316—22no—
80#13063315—28no—
81#13063304—22no—
82#13063304—22no—
83#13063304—22no—
84#13063304—22no—
85Q8×Dic43—22no—
86Q8×Dic43D414yes—
87#13063290—22no—
88#13063290—22no—
89#13063290—22no—
90#13063290D414yes—
91#13063284—22no—
92#13063284—22no—
93C2×C4⋊Dic43—21no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43D411yescharacteristic
96C2×C4⋊Dic43D411yescharacteristic
97C2×C4⋊Dic43C2311yescharacteristic
98C2×C4⋊Dic43C2311yescharacteristic
99C2×Dic43⋊C4—21no—
100C2×Dic43⋊C4—21no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
106C2×Dic43⋊C4—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43D411yescharacteristic
110C2×C22⋊Dic43D411yescharacteristic
111C2×C4×Dic43—21no—
112C2×C4×Dic43—21no—
113C2×C4×Dic43—21no—
114C2×C4×Dic43—21no—
115C2×C4×Dic43C2311yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117#13063256—22no—
118#13063250—22no—
119#13063250—22no—
120#13063249—22no—
121#13063248—22no—
122#13063248—22no—
123#13063248—22no—
124C22⋊(C43⋊C8)—22no—
125#13063235—22no—
126C8×Dic43—22no—
127C43⋊#95—21no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C22×Q8×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C22⋊Q8×C43—22no—
136C22⋊Q8×C43—22no—
137C2×C4⋊C4×C43—21no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C4⋊C4×C43C2311yescharacteristic
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143#107×C43—22no—
144#103×C43—22no—
145#103×C43—22no—
146C22⋊C8×C43—22no—
147#95×C43—21no—
148C24×C43C2×D411yescharacteristic
149C2×Q8×C43—21no—
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C2×D412yes—
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43C2×D411yescharacteristic
166C22×C4×C43C2411yescharacteristic
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43C2×D411yescharacteristic
172C22×Dic43C2×D411yescharacteristic
173C22×Dic43C2×D411yescharacteristic
174C22×Dic43C2×D411yescharacteristic
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—21no—
179C2×Dic86—21no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—21no—
183C2×Dic86—21no—
184C2×Dic86—21no—
185C2×Dic86C2×D412yes—
186C2×Dic86#4112yes—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43#4112yes—
193C4⋊C4×C43—24no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43C2×D412yes—
200C22⋊C4×C43—24no—
201C22⋊C4×C43—81no—
202C22⋊Dic43—24no—
203C22⋊Dic43—24no—
204C22⋊Dic43—22no—
205C22⋊Dic43—22no—
206#10621885—28no—
207C4⋊Dic43—24no—
208C4⋊Dic43—21no—
209C4⋊Dic43—21no—
210C4⋊Dic43—24no—
211C4⋊Dic43—22no—
212C4⋊Dic43—22no—
213C4⋊Dic43C2×D412yes—
214C4⋊Dic43#4112yes—
215Dic43⋊C4—24no—
216Dic43⋊C4—24no—
217Dic43⋊C4—24no—
218Dic43⋊C4—24no—
219Dic43⋊C4—24no—
220Dic43⋊C4—24no—
221Dic43⋊C4—42no—
222Dic43⋊C4—81no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—24no—
226C4×Dic43—24no—
227C4×Dic43—42no—
228C4×Dic43—81no—
229C4×Dic43C2×D412yes—
230C4×Dic43C2×D412yes—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8#4112yes—
237Dic172—28no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43C22×D411yescharacteristic
246Q8×C43—22no—
247Q8×C43—22no—
248Q8×C43—41no—
249Q8×C43—41no—
250C2×C4×C43—22no—
251C2×C4×C43—22no—
252C2×C4×C43—21no—
253C2×C4×C43—21no—
254C2×C4×C43—21no—
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×C43—41no—
263C2×C4×C43—41no—
264C2×C4×C43—41no—
265C2×C4×C43—41no—
266C2×C4×C43—41no—
267C2×C4×C43—41no—
268C2×C4×C43—41no—
269C2×C4×C43C22×D411yescharacteristic
270C2×C4×C43C22×D411yescharacteristic
271C2×C4×C43C2×#4111yescharacteristic
272C2×C4×C43C2×#4111yescharacteristic
273C2×C4×C43C2×#4111yescharacteristic
274C2×C4×C43C2×#4111yescharacteristic
275C2×Dic43—21no—
276C2×Dic43—21no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—22no—
281C2×Dic43—21no—
282C2×Dic43—22no—
283C2×Dic43—22no—
284C2×Dic43—22no—
285C2×Dic43—21no—
286C2×Dic43—21no—
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43—41no—
294C2×Dic43—41no—
295C2×Dic43—41no—
296C2×Dic43—41no—
297C2×Dic43#12012yes—
298C2×Dic43#12012yes—
299Dic86—22no—
300Dic86—22no—
301Dic86—22no—
302Dic86—22no—
303Dic86—41no—
304Dic86—41no—
305Dic86—41no—
306Dic86—41no—
307C8×C43—22no—
308C8×C43—41no—
309C43⋊C8—22no—
310C43⋊C8—41no—
311#23586—431nomaximal, Sylow
312C22×C43—41no—
313C22×C43—41no—
314C22×C43—41no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43C2×#12011yescharacteristic
320C22×C43#52511yescharacteristic
321C22×C43#53211yescharacteristic
322C22×C43#57711yescharacteristic
323C22×C43#57811yescharacteristic
324C22×C43#57811yescharacteristic
325C22×C43#57811yescharacteristic
326C4×C43—41no—
327C4×C43—42no—
328C4×C43—42no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43#52511yescharacteristic
332C4×C43#52511yescharacteristic
333C4×C43#53211yescharacteristic
334C4×C43#53211yescharacteristic
335Dic43—22no—
336Dic43—22no—
337Dic43—42no—
338Dic43—42no—
339Dic43—42no—
340Dic43—41no—
341Dic43—42no—
342Dic43—41no—
343C2×#541—431no—
344C2×#441—431no—
345C2×C4×Q16—431no—
346#2323—431no—
347#2059—431no—
348#2043—431no—
349#2036D4311yescharacteristic
350#2035—431no—
351#2026—431no—
352#2016—431no—
353#2001—431no—
354#2001—431no—
355#1763—431no—
356C4×#103—431no—
357#1750—431no—
358C2×C43—81no—
359C2×C43#238811yescharacteristic
360C2×C43#301111yescharacteristic
361C2×C43#301311yescharacteristic
362C2×C43#312011yescharacteristic
363C2×C43#312711yescharacteristic
364C2×C43#317711yescharacteristic
365C2×C43#317811yescharacteristic
366C22×Q16—431no—
367C22×Q16—431no—
368#541—864no—
369#541—864no—
370C2×C4⋊Q8—431no—
371C2×#126—861no—
372C2×#126—861no—
373C2×#125—431no—
374C2×#125—861no—
375C2×#125—861no—
376C2×C22⋊Q8—431no—
377C2×C22⋊Q8—431no—
378C2×C22⋊Q8C2×D4311yescharacteristic
379C2×C4×Q8—431no—
380C2×C4×Q8—431no—
381C2×C4×Q8—431no—
382C2×#117—431no—
383#441—864no—
384C4×Q16—864no—
385C2×#107C2×D4311yescharacteristic
386C2×#106—431no—
387C2×#103—431no—
388C2×#103—431no—
389C2×#103—431no—
390C2×#103—431no—
391C2×#103—431no—
392C2×#103—431no—
393C2×#103C2×D4311yescharacteristic
394C2×#103C2×D4311yescharacteristic
395C2×C22⋊C8—431no—
396C2×C22⋊C8C2×D4311yescharacteristic
397C2×#97—431no—
398C2×C4×C8—431no—
399#391—431no—
400#389—431no—
401#389—861no—
402#388—861no—
403#388—861no—
404#387—861no—
405#380C2×D4311yescharacteristic
406C4×C4⋊C4—431no—
407#340—431no—
408#340—431no—
409#340—431no—
410#340C2×D4311yescharacteristic
411#336—431no—
412#336—431no—
413C43#2358611yescharacteristic, complemented, Sylow
414C22×Q8—431no—
415C22×Q8—431no—
416C22×Q8C22×D4311yescharacteristic
417C23×C4C22×D4311yescharacteristic
418C2×Q16—862no—
419C2×Q16—862no—
420C2×Q16—862no—
421C2×Q16—862no—
422C2×Q16—862no—
423C2×Q16—862no—
424C22×C8—431no—
425C22×C8—431no—
426C22×C8C22×D4311yescharacteristic
427C22×C8C22×D4311yescharacteristic
428C4⋊Q8—862no—
429C4⋊Q8—862no—
430#126—868no—
431#126—868no—
432#125—862no—
433#125—868no—
434#125—868no—
435#125—862no—
436C22⋊Q8—22no—
437C22⋊Q8—22no—
438C22⋊Q8—862no—
439C22⋊Q8—862no—
440C22⋊Q8—862no—
441C22⋊Q8—862no—
442C4×Q8—434no—
443C4×Q8—434no—
444C4×Q8—862no—
445C4×Q8—862no—
446C4×Q8—862no—
447C4×Q8—862no—
448#117—862no—
449#117—862no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—431no—
452C2×C4⋊C4—431no—
453C2×C4⋊C4—431no—
454C2×C4⋊C4—431no—
455C2×C4⋊C4—861no—
456C2×C4⋊C4—861no—
457C2×C4⋊C4—861no—
458C2×C4⋊C4—861no—
459C2×C4⋊C4—861no—
460C2×C4⋊C4—861no—
461C2×C4⋊C4—861no—
462C2×C4⋊C4—861no—
463C2×C4⋊C4—861no—
464C2×C4⋊C4—861no—
465C2×C4⋊C4C22×D4311yescharacteristic
466C2×C4⋊C4C22×D4311yescharacteristic
467C2×C4⋊C4C22×D4311yescharacteristic
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—431no—
471C2×C22⋊C4—431no—
472C2×C22⋊C4—861no—
473C2×C22⋊C4—861no—
474C2×C42—431no—
475C2×C42—431no—
476C2×C42—861no—
477C2×C42—861no—
478C2×C42—861no—
479C2×C42—861no—
480#107—22no—
481#106—862no—
482#103—22no—
483#103—22no—
484#103—862no—
485#103—862no—
486#103—862no—
487#103—862no—
488#103—862no—
489#103—862no—
490C22⋊C8—22no—
491C22⋊C8—862no—
492#97—862no—
493C4×C8—862no—
494#95—21no—
495#95—861no—
496#95—861no—
497#95—861no—
498#95—861no—
499C24D4×D4311yescharacteristic
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—432no—
506C2×Q8—432no—
507C2×Q8—861no—
508C2×Q8—861no—
509C2×Q8—861no—
510C2×Q8—861no—
511C2×Q8—861no—
512C2×Q8—861no—
513C2×Q8—861no—
514C2×Q8—861no—
515C2×Q8—861no—
516C2×Q8—861no—
517C2×Q8D4×D4312yes—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—431no—
529C22×C4—431no—
530C22×C4—431no—
531C22×C4—431no—
532C22×C4—861no—
533C22×C4—861no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4D4×D4311yescharacteristic
537C22×C4C23×D4311yescharacteristic
538Q16—868no—
539Q16—868no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—432no—
546C2×C8—861no—
547C2×C8—861no—
548C2×C8—861no—
549C2×C8—861no—
550C2×C8—861no—
551C2×C8#1062190012yes—
552C4⋊C4—24no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—432no—
559C4⋊C4—432no—
560C4⋊C4—862no—
561C4⋊C4—862no—
562C4⋊C4—864no—
563C4⋊C4—864no—
564C4⋊C4—864no—
565C4⋊C4—864no—
566C4⋊C4—864no—
567C4⋊C4—864no—
568C4⋊C4—864no—
569C4⋊C4—864no—
570C4⋊C4—861no—
571C4⋊C4—861no—
572C4⋊C4—3441no—
573C4⋊C4—1722no—
574C4⋊C4D4×D4312yes—
575C22⋊C4—24no—
576C22⋊C4—81no—
577C22⋊C4—862no—
578C22⋊C4—862no—
579C22⋊C4—864no—
580C22⋊C4—864no—
581C42—432no—
582C42—432no—
583C42—864no—
584C42—864no—
585C42—861no—
586C42—861no—
587C42—3441no—
588C42—1722no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C2×D4×D4311yescharacteristic
597Q8—22no—
598Q8—22no—
599Q8—41no—
600Q8—41no—
601Q8—862no—
602Q8—862no—
603Q8—862no—
604Q8—862no—
605Q8—1721no—
606Q8—1721no—
607Q8—1721no—
608Q8—1721no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
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—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—432no—
629C2×C4—432no—
630C2×C4—861no—
631C2×C4—861no—
632C2×C4—861no—
633C2×C4—861no—
634C2×C4—862no—
635C2×C4—861no—
636C2×C4—861no—
637C2×C4—862no—
638C2×C4—862no—
639C2×C4—862no—
640C2×C4—861no—
641C2×C4—861no—
642C2×C4—861no—
643C2×C4—861no—
644C2×C4—1721no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4—1721no—
652C2×C4C2×D4×D4311yescharacteristic
653C2×C4C2×D4×D4311yescharacteristic
654C2×C4#41×D4311yescharacteristic
655C2×C4#41×D4311yescharacteristic
656C2×C4#41×D4311yescharacteristic
657C2×C4C2×#1062190011yescharacteristic
658C8—22no—
659C8—41no—
660C8—862no—
661C8—1721no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22#120×D4311yescharacteristic
670C22#1458340711yescharacteristic
671C22#1458344411yescharacteristic
672C22#1458370911yescharacteristic
673C22#1458371211yescharacteristic
674C22#1458371311yescharacteristic
675C22#1458371511yescharacteristic
676C4—41no—
677C4—42no—
678C4—42no—
679C4—81no—
680C4—81no—
681C4—862no—
682C4—862no—
683C4—1722no—
684C4—1722no—
685C4—1722no—
686C4—1721no—
687C4—1722no—
688C4—1721no—
689C4#1458340711yescharacteristic
690C4#1458340911yescharacteristic
691C4#1458344411yescharacteristic
692C4#1458344811yescharacteristic
693C2—81no—
694C2#1913780911yescharacteristic
695C2#1914388511yescharacteristic
696C2#1914390811yescharacteristic
697C2#1914480411yescharacteristic
698C2#1914489111yescharacteristic
699C2#1914524711yescharacteristic
700C2#1914525611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2036C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
hypercenter#2036D43
hypocenterC43#23586
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2036

Complements

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

NH ≅ G/Ntype
2. C2×#14583003C2semidirect
3. C2×#14582993C2semidirect
5. #19135931C2semidirect
6. #19135839C2semidirect
8. #19135745C2semidirect
9. #19135696C2semidirect
12. #19134424C2semidirect
13. #103×Dic43C2semidirect
413. C43#23586semidirect

Maximal subgroups

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

subgroupindex
C2×#145835092
C2×#145830032
C2×#145829932
#191372732
#191359312
#191358392
#191357912
#191357452
#191356962
#191356052
#191356032
#191344242
#103×Dic432
#191343632
C43×#20362
#2358643