Finite Group Databasebeta

← #25107906

Subgroups — #25107906

Order 11008.

920 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583057C211yesmaximal, characteristic
2#19137273C211yesmaximal, characteristic
3#19137179C211yesmaximal, characteristic
4#19135464C211yesmaximal, characteristic, complemented
5#19135454C211yesmaximal, characteristic, complemented
6#19135283C211yesmaximal, characteristic, complemented
7#19135269C211yesmaximal, characteristic, complemented
8#19135235C211yesmaximal, characteristic, complemented
9#19135228C211yesmaximal, characteristic, complemented
10#19134937C211yesmaximal, characteristic, complemented
11#19134937C211yesmaximal, characteristic, complemented
12#19134907C211yesmaximal, characteristic
13#19134529C211yesmaximal, characteristic
14#19134363C211yesmaximal, characteristic
15C43×#1854C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C2×#13063304C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063284C2211yescharacteristic
22#14583057C418yescomplemented
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×#13063248C2211yescharacteristic
28C2×#13063248C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582805—21no—
35#14582805—21no—
36#14582804C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582804C2211yescharacteristic
40#14582804C2211yescharacteristic
41#14582796—21no—
42#14582795C2211yescharacteristic
43#14582793—21no—
44#14582787—21no—
45#14582786—21no—
46#14582760—21no—
47#14582760—21no—
48C4⋊C4×Dic43C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×Dic86—21no—
61C22×Dic86—22no—
62C22×Dic86—41no—
63C22×Dic86—41no—
64C22×Dic86—41no—
65C22×Dic86—41no—
66C22×Dic86C2×C414yes—
67C22×Dic86C2311yescharacteristic
68C22×Dic86C2311yescharacteristic
69C22×Dic86C2311yescharacteristic
70C23×Dic43—21no—
71C2×Dic172—41no—
72C2×Dic172—41no—
73C2×Dic172—41no—
74C2×Dic172—41no—
75C2×Dic172C2×C414yes—
76C2×Dic172C2×C414yes—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063304—22no—
80#13063304C2×C414yes—
81#13063290—41no—
82#13063290—41no—
83#13063284—41no—
84#13063284—41no—
85C2×C4⋊Dic43D411yescharacteristic
86C2×C4⋊Dic43D411yescharacteristic
87C2×C4⋊Dic43C2311yescharacteristic
88C2×Dic43⋊C4—21no—
89C2×Dic43⋊C4—21no—
90C2×Dic43⋊C4—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43D411yescharacteristic
93C2×C22⋊Dic43D411yescharacteristic
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97C2×C4×Dic43C2311yescharacteristic
98#13063250C2×C414yes—
99#13063250C2×C414yes—
100#13063248—41no—
101#13063248—41no—
102#13063248—41no—
103#13063248—41no—
104#13063248—41no—
105#13063248—41no—
106C22⋊(C43⋊C8)—22no—
107#13063235—41no—
108C8×Dic43—41no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95—21no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C23×C4×C43C2311yescharacteristic
122C22×C8×C43C2311yescharacteristic
123C22×C8×C43C2311yescharacteristic
124#117×C43—41no—
125#117×C43—41no—
126C2×C4⋊C4×C43C2311yescharacteristic
127C2×C4⋊C4×C43C2311yescharacteristic
128C2×C4⋊C4×C43C2311yescharacteristic
129C2×C4⋊C4×C43C2311yescharacteristic
130C2×C22⋊C4×C43—21no—
131C2×C22⋊C4×C43—21no—
132C2×C42×C43—21no—
133#107×C43—41no—
134#106×C43—41no—
135C22⋊C8×C43C2×C414yes—
136#95×C43—21no—
137C24×C43C2×D411yescharacteristic
138C22×C4×C43—21no—
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×C43C22×C412yes—
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43#4112yes—
149C22×C4×C43C2411yescharacteristic
150C22×Dic43—24no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—42no—
156C22×Dic43—42no—
157C22×Dic43C2×D411yescharacteristic
158C22×Dic43C2×D411yescharacteristic
159C22×Dic43C2×D411yescharacteristic
160C22×Dic43C2×D411yescharacteristic
161C2×Dic86—21no—
162C2×Dic86—21no—
163C2×Dic86—21no—
164C2×Dic86—21no—
165C2×Dic86—21no—
166C2×Dic86—21no—
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—24no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—44no—
178C2×Dic86—44no—
179C2×Dic86—42no—
180C2×Dic86—42no—
181C2×Dic86—44no—
182C2×Dic86—44no—
183C2×Dic86C22×C412yes—
184C2×Dic86C22×C412yes—
185C2×Dic86C22×C412yes—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43C22×C412yes—
191C2×C8×C43C22×C412yes—
192C4⋊C4×C43—21no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43—21no—
196C4⋊C4×C43—21no—
197C4⋊C4×C43—21no—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C22⋊C4×C43—42no—
201C22⋊C4×C43—81no—
202C42×C43—42no—
203C22⋊Dic43—24no—
204C22⋊Dic43—41no—
205C22⋊Dic43—41no—
206C4⋊Dic43—21no—
207C4⋊Dic43—41no—
208C4⋊Dic43—41no—
209C4⋊Dic43C22×C412yes—
210Dic43⋊C4—24no—
211Dic43⋊C4—42no—
212Dic43⋊C4—81no—
213C4×Dic43—21no—
214C4×Dic43—21no—
215C4×Dic43—21no—
216C4×Dic43—21no—
217C4×Dic43—42no—
218C4×Dic43—81no—
219C2×C43⋊C8—21no—
220C2×C43⋊C8—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225Dic172—44no—
226Dic172—44no—
227C23×C43—21no—
228C23×C43—21no—
229C23×C43—21no—
230C23×C43—21no—
231C23×C43—21no—
232C23×C43—21no—
233C23×C43C4×D412yes—
234C23×C43C22×D411yescharacteristic
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—22no—
238C2×C4×C43—22no—
239C2×C4×C43—22no—
240C2×C4×C43—22no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43C4×D412yes—
254C2×C4×C43C23×C411yescharacteristic
255C2×C4×C43C2×#4111yescharacteristic
256C2×C4×C43H(5,𝔽2)11yescharacteristic
257C2×C4×C43H(5,𝔽2)11yescharacteristic
258C2×C4×C43H(5,𝔽2)11yescharacteristic
259C2×C4×C43H(5,𝔽2)11yescharacteristic
260C2×Dic43—22no—
261C2×Dic43—22no—
262C2×Dic43—22no—
263C2×Dic43—22no—
264C2×Dic43—21no—
265C2×Dic43—21no—
266C2×Dic43—21no—
267C2×Dic43—21no—
268C2×Dic43—21no—
269C2×Dic43—21no—
270C2×Dic43—21no—
271C2×Dic43—21no—
272C2×Dic43—21no—
273C2×Dic43—21no—
274C2×Dic43—21no—
275C2×Dic43—21no—
276C2×Dic43—48no—
277C2×Dic43—41no—
278C2×Dic43—41no—
279C2×Dic43—41no—
280C2×Dic43—41no—
281C2×Dic43—41no—
282C2×Dic43—41no—
283C2×Dic43—41no—
284C2×Dic43—41no—
285Dic86—22no—
286Dic86—22no—
287Dic86—22no—
288Dic86—22no—
289Dic86—22no—
290Dic86—22no—
291Dic86—48no—
292Dic86—41no—
293Dic86—41no—
294Dic86—41no—
295Dic86—41no—
296Dic86—41no—
297Dic86—41no—
298C8×C43—22no—
299C8×C43—22no—
300C43⋊C8—41no—
301C43⋊C8—41no—
302#22054—431nomaximal, Sylow
303C22×C43—22no—
304C22×C43—22no—
305C22×C43—22no—
306C22×C43—41no—
307C22×C43—41no—
308C22×C43—41no—
309C22×C43—41no—
310C22×C43C2×C4×D411yescharacteristic
311C22×C43#53411yescharacteristic
312C22×C43#53511yescharacteristic
313C22×C43#57711yescharacteristic
314C22×C43#57811yescharacteristic
315C22×C43#57811yescharacteristic
316C22×C43#57811yescharacteristic
317C4×C43—22no—
318C4×C43—81no—
319C4×C43—81no—
320C4×C43—81no—
321C4×C43—81no—
322C4×C43#51811yescharacteristic
323C4×C43#51811yescharacteristic
324C4×C43#53811yescharacteristic
325C4×C43#53811yescharacteristic
326Dic43—42no—
327Dic43—42no—
328Dic43—42no—
329Dic43—41no—
330Dic43—41no—
331Dic43—41no—
332Dic43—41no—
333Dic43—42no—
334C2×#451—431no—
335#2323—431no—
336#2310—431no—
337#1971—431no—
338#1969—431no—
339#1935—431no—
340#1933—431no—
341#1928—431no—
342#1927—431no—
343#1878—431no—
344#1878—431no—
345#1873—431no—
346#1854D4311yescharacteristic
347#1787—431no—
348#1750—431no—
349C2×C43—42no—
350C2×C43#232111yescharacteristic
351C2×C43#294711yescharacteristic
352C2×C43#295011yescharacteristic
353C2×C43#320111yescharacteristic
354C2×C43#320211yescharacteristic
355C2×C43#322311yescharacteristic
356C2×C43#322511yescharacteristic
357C23×Q8—431no—
358C22×Q16—431no—
359C22×Q16—431no—
360C2×C22⋊Q8—431no—
361C2×C4×Q8—431no—
362C2×#117—431no—
363C2×#117C2×D4311yescharacteristic
364#451—438no—
365C2×#107C2×D4311yescharacteristic
366C2×#106C2×D4311yescharacteristic
367C2×#103—431no—
368C2×#103—431no—
369C2×#103—431no—
370C2×#103—431no—
371C2×#103—431no—
372C2×#103—431no—
373C2×#103—431no—
374C2×#103—431no—
375C2×C22⋊C8—431no—
376C2×C22⋊C8C2×D4311yescharacteristic
377C2×#97—431no—
378C2×C4×C8—431no—
379#391—431no—
380#391—431no—
381#391—431no—
382#391—431no—
383#391—431no—
384#391—861no—
385#391—861no—
386#389—431no—
387#389—861no—
388#388—861no—
389#388—861no—
390#387—861no—
391#381—861no—
392#381—861no—
393#380C2×D4311yescharacteristic
394C4×C4⋊C4—431no—
395#340—431no—
396#340—431no—
397#340C2×D4311yescharacteristic
398#340C2×D4311yescharacteristic
399#336—431no—
400#336—431no—
401C43#2205411yescharacteristic, complemented, Sylow
402C22×Q8—434no—
403C22×Q8—431no—
404C22×Q8—431no—
405C22×Q8—431no—
406C22×Q8—861no—
407C22×Q8—862no—
408C22×Q8—1721no—
409C22×Q8—1721no—
410C22×Q8—1721no—
411C22×Q8—1721no—
412C23×C4—861no—
413C23×C4C22×D4311yescharacteristic
414C2×Q16—434no—
415C2×Q16—434no—
416C2×Q16—1721no—
417C2×Q16—1721no—
418C2×Q16—1721no—
419C2×Q16—1721no—
420C22×C8—431no—
421C22×C8—431no—
422C22×C8C22×D4311yescharacteristic
423C22×C8C22×D4311yescharacteristic
424C22⋊Q8—434no—
425C22⋊Q8—862no—
426C4×Q8—1721no—
427C4×Q8—1721no—
428#117—41no—
429#117—41no—
430#117—1721no—
431#117—1721no—
432C2×C4⋊C4—431no—
433C2×C4⋊C4—431no—
434C2×C4⋊C4—431no—
435C2×C4⋊C4—861no—
436C2×C4⋊C4—861no—
437C2×C4⋊C4—861no—
438C2×C4⋊C4C22×D4311yescharacteristic
439C2×C4⋊C4C22×D4311yescharacteristic
440C2×C4⋊C4C22×D4311yescharacteristic
441C2×C4⋊C4C22×D4311yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—431no—
445C2×C22⋊C4—431no—
446C2×C22⋊C4—861no—
447C2×C42—21no—
448C2×C42—431no—
449C2×C42—431no—
450C2×C42—861no—
451C2×C42—861no—
452#107—41no—
453#106—41no—
454#103—434no—
455#103—434no—
456#103—1721no—
457#103—1721no—
458#103—1721no—
459#103—1721no—
460#103—1721no—
461#103—1721no—
462C22⋊C8—862no—
463C22⋊C8C4×D4314yes—
464#97—1721no—
465C4×C8—1721no—
466#95—21no—
467#95—861no—
468#95—861no—
469#95—861no—
470#95—861no—
471#95—861no—
472#95—861no—
473#95—861no—
474#95—861no—
475#95—861no—
476#95—861no—
477#95—861no—
478#95—861no—
479C24D4×D4311yescharacteristic
480C2×Q8—432no—
481C2×Q8—432no—
482C2×Q8—432no—
483C2×Q8—864no—
484C2×Q8—861no—
485C2×Q8—861no—
486C2×Q8—861no—
487C2×Q8—861no—
488C2×Q8—861no—
489C2×Q8—861no—
490C2×Q8—861no—
491C2×Q8—861no—
492C2×Q8—861no—
493C2×Q8—861no—
494C2×Q8—861no—
495C2×Q8—861no—
496C2×Q8—861no—
497C2×Q8—861no—
498C2×Q8—861no—
499C2×Q8—1724no—
500C2×Q8—1724no—
501C2×Q8—1722no—
502C2×Q8—1722no—
503C2×Q8—1724no—
504C2×Q8—1724no—
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—431no—
514C22×C4—431no—
515C22×C4—431no—
516C22×C4—431no—
517C22×C4—864no—
518C22×C4—861no—
519C22×C4—861no—
520C22×C4—861no—
521C22×C4—861no—
522C22×C4—1722no—
523C22×C4—1722no—
524C22×C4C2×C4×D4312yes—
525C22×C4D4×D4311yescharacteristic
526C22×C4#1062190212yes—
527C22×C4C23×D4311yescharacteristic
528Q16—1724no—
529Q16—1724no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—861no—
535C2×C8—861no—
536C2×C8—861no—
537C2×C8—861no—
538C2×C8—861no—
539C2×C8—861no—
540C2×C8C2×C4×D4312yes—
541C2×C8C2×C4×D4312yes—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—432no—
551C4⋊C4—864no—
552C4⋊C4—861no—
553C4⋊C4—3441no—
554C4⋊C4—1721no—
555C4⋊C4—1721no—
556C4⋊C4—1722no—
557C22⋊C4—42no—
558C22⋊C4—81no—
559C22⋊C4—864no—
560C22⋊C4—1721no—
561C22⋊C4—1721no—
562C42—42no—
563C42—861no—
564C42—861no—
565C42—861no—
566C42—861no—
567C42—3441no—
568C42—1722no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23#1306328712yes—
576C23C2×D4×D4311yescharacteristic
577Q8—862no—
578Q8—862no—
579Q8—862no—
580Q8—862no—
581Q8—862no—
582Q8—862no—
583Q8—1728no—
584Q8—1721no—
585Q8—1721no—
586Q8—1721no—
587Q8—1721no—
588Q8—1721no—
589Q8—1721no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—862no—
609C2×C4—862no—
610C2×C4—862no—
611C2×C4—862no—
612C2×C4—861no—
613C2×C4—861no—
614C2×C4—861no—
615C2×C4—861no—
616C2×C4—861no—
617C2×C4—861no—
618C2×C4—861no—
619C2×C4—861no—
620C2×C4—861no—
621C2×C4—861no—
622C2×C4—861no—
623C2×C4—861no—
624C2×C4—1728no—
625C2×C4—1721no—
626C2×C4—1721no—
627C2×C4—1721no—
628C2×C4—1721no—
629C2×C4—1721no—
630C2×C4—1721no—
631C2×C4—1721no—
632C2×C4—1721no—
633C2×C4#1306328712yes—
634C2×C4C22×C4×D4311yescharacteristic
635C2×C4C2×#1062190211yescharacteristic
636C2×C4#1306337011yescharacteristic
637C2×C4#1306337011yescharacteristic
638C2×C4#1306337111yescharacteristic
639C2×C4#1306337111yescharacteristic
640C8—22no—
641C8—22no—
642C8—1721no—
643C8—1721no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—41no—
651C22C2×#1306328711yescharacteristic
652C22#1458346011yescharacteristic
653C22#1458346411yescharacteristic
654C22#1458370911yescharacteristic
655C22#1458371311yescharacteristic
656C22#1458371311yescharacteristic
657C22#1458371511yescharacteristic
658C4—22no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—1721no—
664C4—1721no—
665C4—1722no—
666C4—1721no—
667C4—1721no—
668C4—1722no—
669C4—1722no—
670C4—1722no—
671C4#1458337111yescharacteristic
672C4#1458337111yescharacteristic
673C4#1458348911yescharacteristic
674C4#1458348911yescharacteristic
675C2—42no—
676C2#1913725211yescharacteristic
677C2#1914343611yescharacteristic
678C2#1914346211yescharacteristic
679C2#1914547511yescharacteristic
680C2#1914548911yescharacteristic
681C2#1914567611yescharacteristic
682C2#1914570011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#22054
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #19135464C2semidirect
5. #19135454C2semidirect
6. #19135283C2semidirect
7. #19135269C2semidirect
8. #19135235C2semidirect
9. #19135228C2semidirect
10. #19134937C2semidirect
11. #19134937C2semidirect
22. #14583057C4semidirect
401. C43#22054semidirect

Maximal subgroups

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

subgroupindex
C2×#145830572
#191372732
#191371792
#191354642
#191354542
#191352832
#191352692
#191352352
#191352282
#191349372
#191349072
#191345292
#191343632
C43×#18542
#2205443