Finite Group Databasebeta

← #25117252

Subgroups — #25117252

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×#14583057C211yesmaximal, characteristic
2C2×#14582993C211yesmaximal, characteristic, complemented
3C2×#14582907C211yesmaximal, characteristic
4#19137622C211yesmaximal, characteristic
5#19137427C211yesmaximal, characteristic
6#19135464C211yesmaximal, characteristic, complemented
7#19135269C211yesmaximal, characteristic, complemented
8#19135235C211yesmaximal, characteristic, complemented
9#19135026C211yesmaximal, characteristic
10#19134937C211yesmaximal, characteristic, complemented
11#19134937C211yesmaximal, characteristic, complemented
12#19134860C211yesmaximal, characteristic, complemented
13#19134424C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic
15C43×#1854C211yesmaximal, characteristic
16C23×Dic86C2211yescharacteristic
17C22×Dic172C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621877C2211yescharacteristic
20C2×#13063304C2211yescharacteristic
21C2×#13063290C2211yescharacteristic
22C2×#13063290C2211yescharacteristic
23C2×#13063290C2211yescharacteristic
24#14583057C418yescomplemented
25#14582993—24no—
26#14582907—24no—
27C2×#13063250C2211yescharacteristic
28C2×#13063250C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×#13063248C2211yescharacteristic
33C2×#13063248C2211yescharacteristic
34C2×#13063248C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582804C2211yescharacteristic
40#14582803—21no—
41#14582803—21no—
42#14582795C2211yescharacteristic
43#14582793—21no—
44#14582787—21no—
45#14582783—21no—
46#14582757—21no—
47C4⋊C4×Dic43C2211yescharacteristic
48C4×Dic43⋊C4—21no—
49C22⋊C4×Dic43—21no—
50C4×C22⋊Dic43C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C2×#117×C43C2211yescharacteristic
56C2×#107×C43C2211yescharacteristic
57C2×#106×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#380C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#340C2211yescharacteristic
62C22×Dic86—22no—
63C22×Dic86—22no—
64C22×Dic86—21no—
65C22×Dic86—22no—
66C22×Dic86—41no—
67C22×Dic86—41no—
68C22×Dic86C2×C414yes—
69C22×Dic86C2311yescharacteristic
70C22×Dic86C2311yescharacteristic
71C22×Dic86C2311yescharacteristic
72C23×Dic43—21no—
73C2×Dic172—22no—
74C2×Dic172—22no—
75C2×Dic172—41no—
76C2×Dic172—41no—
77C2×Dic172C2×C414yes—
78C2×Dic172C2×C414yes—
79C2×#10621877—22no—
80C2×#10621877—22no—
81C2×#10621877—41no—
82C22×C43⋊C8C2311yescharacteristic
83C22×C43⋊C8C2311yescharacteristic
84#13063304—22no—
85#13063304C2×C414yes—
86#13063290—22no—
87#13063290—22no—
88#13063290—22no—
89#13063290—41no—
90#13063290—41no—
91#13063290—41no—
92C2×C4⋊Dic43C2311yescharacteristic
93C2×Dic43⋊C4—21no—
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C2×Dic43⋊C4—21no—
97C2×Dic43⋊C4—21no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43D411yescharacteristic
100C2×C22⋊Dic43D411yescharacteristic
101C2×C4×Dic43—21no—
102C2×C4×Dic43—21no—
103C2×C4×Dic43—21no—
104C2×C4×Dic43—21no—
105C2×C4×Dic43C2311yescharacteristic
106C2×C4×Dic43C2311yescharacteristic
107#13063250C2×C414yes—
108#13063250C2×C414yes—
109#13063248—22no—
110#13063248—22no—
111#13063248—22no—
112#13063248—22no—
113#13063248—41no—
114#13063248D414yes—
115#13063235—41no—
116C8×Dic43—22no—
117C43⋊#95—21no—
118C43⋊#95—21no—
119C43⋊#95—21no—
120C43⋊#95—21no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95—21no—
125C43⋊#95D411yescharacteristic
126C43⋊#95D411yescharacteristic
127C23×C4×C43C2311yescharacteristic
128C22×C8×C43C2311yescharacteristic
129C22×C8×C43C2311yescharacteristic
130#117×C43—22no—
131#117×C43—41no—
132C2×C4⋊C4×C43C2311yescharacteristic
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C4⋊C4×C43C2311yescharacteristic
136C2×C22⋊C4×C43—21no—
137C2×C22⋊C4×C43—21no—
138C2×C42×C43—21no—
139#107×C43—22no—
140#106×C43—41no—
141C22⋊C8×C43C2×C414yes—
142#95×C43—21no—
143C24×C43C2×D411yescharacteristic
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43—21no—
149C22×C4×C43—21no—
150C22×C4×C43—21no—
151C22×C4×C43—21no—
152C22×C4×C43C22×C412yes—
153C22×C4×C43C2×D411yescharacteristic
154C22×C4×C43#4112yes—
155C22×C4×C43C2411yescharacteristic
156C22×Dic43—24no—
157C22×Dic43—21no—
158C22×Dic43—21no—
159C22×Dic43—21no—
160C22×Dic43—21no—
161C22×Dic43—42no—
162C22×Dic43—42no—
163C22×Dic43C2×D411yescharacteristic
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166C22×Dic43C2×D411yescharacteristic
167C2×Dic86—21no—
168C2×Dic86—21no—
169C2×Dic86—21no—
170C2×Dic86—21no—
171C2×Dic86—21no—
172C2×Dic86—21no—
173C2×Dic86—21no—
174C2×Dic86—21no—
175C2×Dic86—21no—
176C2×Dic86—21no—
177C2×Dic86—21no—
178C2×Dic86—28no—
179C2×Dic86—24no—
180C2×Dic86—21no—
181C2×Dic86—21no—
182C2×Dic86—44no—
183C2×Dic86—44no—
184C2×Dic86—44no—
185C2×Dic86—42no—
186C2×Dic86—42no—
187C2×Dic86C22×C412yes—
188C2×Dic86C22×C412yes—
189C2×Dic86C22×C412yes—
190C2×Dic86C2×D412yes—
191C2×Dic86#4112yes—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43C22×C412yes—
197C2×C8×C43C22×C412yes—
198C4⋊C4×C43—21no—
199C4⋊C4×C43—21no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43—21no—
204C4⋊C4×C43—21no—
205C4⋊C4×C43C2×D412yes—
206C22⋊C4×C43—42no—
207C22⋊C4×C43—42no—
208C42×C43—42no—
209C22⋊Dic43—22no—
210C22⋊Dic43—24no—
211C22⋊Dic43—41no—
212C4⋊Dic43—21no—
213C4⋊Dic43C22×C412yes—
214Dic43⋊C4—24no—
215Dic43⋊C4—42no—
216Dic43⋊C4—42no—
217Dic43⋊C4—42no—
218Dic43⋊C4—42no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—42no—
224C4×Dic43—42no—
225C4×Dic43—42no—
226C4×Dic43—42no—
227#10621877—44no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8C2×D412yes—
234Dic172—28no—
235Dic172—44no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43—21no—
240C23×C43—21no—
241C23×C43—21no—
242C23×C43C4×D412yes—
243C23×C43C22×D411yescharacteristic
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—22no—
247C2×C4×C43—22no—
248C2×C4×C43—22no—
249C2×C4×C43—22no—
250C2×C4×C43—22no—
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×C43C4×D412yes—
263C2×C4×C43C23×C411yescharacteristic
264C2×C4×C43C22×D411yescharacteristic
265C2×C4×C43C2×#4111yescharacteristic
266C2×C4×C43C2×#4111yescharacteristic
267C2×C4×C43H(5,𝔽2)11yescharacteristic
268C2×C4×C43H(5,𝔽2)11yescharacteristic
269C2×Dic43—22no—
270C2×Dic43—21no—
271C2×Dic43—22no—
272C2×Dic43—22no—
273C2×Dic43—21no—
274C2×Dic43—22no—
275C2×Dic43—22no—
276C2×Dic43—22no—
277C2×Dic43—21no—
278C2×Dic43—21no—
279C2×Dic43—21no—
280C2×Dic43—21no—
281C2×Dic43—21no—
282C2×Dic43—21no—
283C2×Dic43—21no—
284C2×Dic43—21no—
285C2×Dic43—21no—
286C2×Dic43—48no—
287C2×Dic43—41no—
288C2×Dic43—41no—
289C2×Dic43—41no—
290C2×Dic43—41no—
291C2×Dic43—41no—
292C2×Dic43—41no—
293C2×Dic43#13712yes—
294Dic86—22no—
295Dic86—22no—
296Dic86—22no—
297Dic86—22no—
298Dic86—22no—
299Dic86—22no—
300Dic86—22no—
301Dic86—48no—
302Dic86—41no—
303Dic86—41no—
304Dic86—41no—
305Dic86—41no—
306Dic86C4×D414yes—
307C8×C43—22no—
308C8×C43—22no—
309C43⋊C8—22no—
310C43⋊C8—41no—
311#22881—431nomaximal, Sylow
312C22×C43—22no—
313C22×C43—22no—
314C22×C43—22no—
315C22×C43—41no—
316C22×C43—41no—
317C22×C43—41no—
318C22×C43—41no—
319C22×C43C2×C4×D411yescharacteristic
320C22×C43D4211yescharacteristic
321C22×C43#54611yescharacteristic
322C22×C43C2×#13711yescharacteristic
323C22×C43#57511yescharacteristic
324C22×C43#57811yescharacteristic
325C22×C43#57811yescharacteristic
326C4×C43—22no—
327C4×C43—42no—
328C4×C43—81no—
329C4×C43—81no—
330C4×C43—81no—
331C4×C43C2×C4×D411yescharacteristic
332C4×C43#51811yescharacteristic
333C4×C43#54611yescharacteristic
334C4×C43#55111yescharacteristic
335Dic43—24no—
336Dic43—22no—
337Dic43—41no—
338Dic43—42no—
339Dic43—42no—
340Dic43—42no—
341Dic43—41no—
342Dic43—41no—
343C2×#451—431no—
344C2×C4×Q16—431no—
345C2×#419—431no—
346#2362—431no—
347Q8×C22⋊C4—431no—
348#1971—431no—
349#1933—431no—
350#1928—431no—
351#1894—431no—
352#1878—431no—
353#1878—431no—
354#1865—431no—
355#1854D4311yescharacteristic
356#1763—431no—
357#1753—431no—
358C2×C43—42no—
359C2×C43#235811yescharacteristic
360C2×C43C4×#13711yescharacteristic
361C2×C43#295011yescharacteristic
362C2×C43#326911yescharacteristic
363C2×C43#327011yescharacteristic
364C2×C43#332711yescharacteristic
365C2×C43#332811yescharacteristic
366C23×Q8—431no—
367C22×Q16—431no—
368C22×Q16—431no—
369C22×M16—431no—
370C2×C22⋊Q8—431no—
371C2×C4×Q8—431no—
372C2×C4×Q8—431no—
373C2×C4×Q8—431no—
374C2×#117C2×D4311yescharacteristic
375#451—438no—
376C4×Q16—864no—
377C2×#107C2×D4311yescharacteristic
378C2×#106C2×D4311yescharacteristic
379#419—864no—
380C2×#103—431no—
381C2×#103—431no—
382C2×#103—431no—
383C2×#103—431no—
384C2×#103—431no—
385C2×#103—431no—
386C2×#103—431no—
387C2×#103—431no—
388C2×C22⋊C8C2×D4311yescharacteristic
389C2×#97—431no—
390C2×C4×C8—431no—
391#391—431no—
392#391—431no—
393#391—431no—
394#391—861no—
395#391—861no—
396#389—431no—
397#388—861no—
398#388—861no—
399#387—861no—
400#380—861no—
401#380C2×D4311yescharacteristic
402C4×C4⋊C4—431no—
403C4×C4⋊C4—861no—
404C4×C22⋊C4—431no—
405C4×C22⋊C4—861no—
406#340—431no—
407#340—431no—
408#340C2×D4311yescharacteristic
409#340C2×D4311yescharacteristic
410#336—431no—
411#336—431no—
412C43#2288111yescharacteristic, complemented, Sylow
413C22×Q8—434no—
414C22×Q8—431no—
415C22×Q8—431no—
416C22×Q8—431no—
417C22×Q8—862no—
418C22×Q8—862no—
419C22×Q8—861no—
420C22×Q8—862no—
421C22×Q8—1721no—
422C22×Q8—1721no—
423C23×C4—861no—
424C23×C4C22×D4311yescharacteristic
425C2×Q16—434no—
426C2×Q16—434no—
427C2×Q16—862no—
428C2×Q16—862no—
429C2×Q16—1721no—
430C2×Q16—1721no—
431C2×M16—862no—
432C2×M16—862no—
433C2×M16—1721no—
434C22×C8—431no—
435C22×C8—431no—
436C22×C8C22×D4311yescharacteristic
437C22×C8C22×D4311yescharacteristic
438C22⋊Q8—434no—
439C22⋊Q8—862no—
440C4×Q8—862no—
441C4×Q8—862no—
442C4×Q8—862no—
443C4×Q8—1721no—
444C4×Q8—1721no—
445C4×Q8—1721no—
446#117—22no—
447#117—41no—
448C2×C4⋊C4—431no—
449C2×C4⋊C4—861no—
450C2×C4⋊C4—861no—
451C2×C4⋊C4—861no—
452C2×C4⋊C4—861no—
453C2×C4⋊C4—861no—
454C2×C4⋊C4C22×D4311yescharacteristic
455C2×C4⋊C4C22×D4311yescharacteristic
456C2×C4⋊C4C22×D4311yescharacteristic
457C2×C4⋊C4C22×D4311yescharacteristic
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—431no—
461C2×C22⋊C4—431no—
462C2×C22⋊C4—861no—
463C2×C42—21no—
464C2×C42—431no—
465C2×C42—431no—
466C2×C42—861no—
467C2×C42—861no—
468C2×C42—861no—
469C2×C42—861no—
470#107—22no—
471#106—41no—
472#103—434no—
473#103—434no—
474#103—434no—
475#103—862no—
476#103—862no—
477#103—862no—
478#103—862no—
479#103—1721no—
480C22⋊C8C4×D4314yes—
481#97—1721no—
482C4×C8—862no—
483#95—21no—
484#95—431no—
485#95—431no—
486#95—861no—
487#95—861no—
488#95—861no—
489#95—861no—
490#95—861no—
491#95—861no—
492#95—861no—
493#95—861no—
494C24D4×D4311yescharacteristic
495C2×Q8—432no—
496C2×Q8—432no—
497C2×Q8—432no—
498C2×Q8—432no—
499C2×Q8—432no—
500C2×Q8—868no—
501C2×Q8—864no—
502C2×Q8—861no—
503C2×Q8—861no—
504C2×Q8—861no—
505C2×Q8—861no—
506C2×Q8—861no—
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—1722no—
516C2×Q8—1722no—
517C2×Q8—1724no—
518C2×Q8—1724no—
519C2×Q8—1724no—
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—864no—
534C22×C4—861no—
535C22×C4—861no—
536C22×C4—861no—
537C22×C4—1722no—
538C22×C4—1722no—
539C22×C4C2×C4×D4312yes—
540C22×C4D4×D4311yescharacteristic
541C22×C4#1062190212yes—
542C22×C4C23×D4311yescharacteristic
543Q16—868no—
544Q16—1724no—
545M16—1724no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—432no—
551C2×C8—861no—
552C2×C8—861no—
553C2×C8—861no—
554C2×C8—861no—
555C2×C8—861no—
556C2×C8C2×C4×D4312yes—
557C2×C8C2×C4×D4312yes—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—432no—
566C4⋊C4—864no—
567C4⋊C4—861no—
568C4⋊C4—1722no—
569C4⋊C4—1722no—
570C4⋊C4—1722no—
571C4⋊C4—1722no—
572C4⋊C4D4×D4312yes—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C22⋊C4—862no—
576C22⋊C4—864no—
577C22⋊C4—1721no—
578C42—42no—
579C42—861no—
580C42—861no—
581C42—861no—
582C42—861no—
583C42—1722no—
584C42—1722no—
585C42—1722no—
586C42—1722no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23#1306328712yes—
594C23C2×D4×D4311yescharacteristic
595Q8—434no—
596Q8—862no—
597Q8—862no—
598Q8—862no—
599Q8—862no—
600Q8—862no—
601Q8—862no—
602Q8—862no—
603Q8—1728no—
604Q8—1721no—
605Q8—1721no—
606Q8—1721no—
607Q8—1721no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
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—432no—
627C2×C4—862no—
628C2×C4—861no—
629C2×C4—861no—
630C2×C4—862no—
631C2×C4—862no—
632C2×C4—862no—
633C2×C4—862no—
634C2×C4—862no—
635C2×C4—861no—
636C2×C4—861no—
637C2×C4—861no—
638C2×C4—861no—
639C2×C4—861no—
640C2×C4—861no—
641C2×C4—861no—
642C2×C4—861no—
643C2×C4—861no—
644C2×C4—1728no—
645C2×C4—1721no—
646C2×C4—1721no—
647C2×C4—1721no—
648C2×C4—1721no—
649C2×C4—1721no—
650C2×C4—1721no—
651C2×C4#1306328712yes—
652C2×C4C22×C4×D4311yescharacteristic
653C2×C4C2×D4×D4311yescharacteristic
654C2×C4#41×D4311yescharacteristic
655C2×C4C2×#1062190211yescharacteristic
656C2×C4#1306337011yescharacteristic
657C2×C4#1306337111yescharacteristic
658C8—22no—
659C8—22no—
660C8—862no—
661C8—1721no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22C2×#1306328711yescharacteristic
670C22#1458353111yescharacteristic
671C22#1458354111yescharacteristic
672C22#137×D4311yescharacteristic
673C22#1458369511yescharacteristic
674C22#1458371311yescharacteristic
675C22#1458371311yescharacteristic
676C4—22no—
677C4—42no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—864no—
682C4—862no—
683C4—1722no—
684C4—1722no—
685C4—1721no—
686C4—1721no—
687C4—1721no—
688C4—1722no—
689C4C4×D4×D4311yescharacteristic
690C4#1458337111yescharacteristic
691C4#1458354011yescharacteristic
692C4#1458357611yescharacteristic
693C2—42no—
694C2#1913757111yescharacteristic
695C2#1914341311yescharacteristic
696C2#1914346211yescharacteristic
697C2#1914614811yescharacteristic
698C2#1914616311yescharacteristic
699C2#1914686111yescharacteristic
700C2#1914687611yescharacteristic
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#22881
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
2. C2×#14582993C2semidirect
6. #19135464C2semidirect
7. #19135269C2semidirect
8. #19135235C2semidirect
10. #19134937C2semidirect
11. #19134937C2semidirect
12. #19134860C2semidirect
13. #19134424C2semidirect
24. #14583057C4semidirect
412. C43#22881semidirect

Maximal subgroups

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

subgroupindex
C2×#145830572
C2×#145829932
C2×#145829072
#191376222
#191374272
#191354642
#191352692
#191352352
#191350262
#191349372
#191348602
#191344242
#191343812
C43×#18542
#2288143