Finite Group Databasebeta

← #25137930

Subgroups — #25137930

Order 11008.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582959C211yesmaximal, characteristic, complemented
2#19140417C211yesmaximal, characteristic, complemented
3#19137282C211yesmaximal, characteristic
4#19136024C211yesmaximal, characteristic, complemented
5#19136019C211yesmaximal, characteristic, complemented
6#19135783C211yesmaximal, characteristic
7#19135776C211yesmaximal, characteristic
8#19135544C211yesmaximal, characteristic, complemented
9#19135365C211yesmaximal, characteristic, complemented
10#19135336C211yesmaximal, characteristic, complemented
11#19135326C211yesmaximal, characteristic, complemented
12#19135289C211yesmaximal, characteristic, complemented
13#19135275C211yesmaximal, characteristic, complemented
14#19134605C211yesmaximal, characteristic, complemented
15C2×C43×#474C211yesmaximal, characteristic, complemented
16C2×#13063296C2211yescharacteristic
17C2×#13063282C2211yescharacteristic
18#14582959—24no—
19C2×#13063259C2211yescharacteristic
20C2×#13063257C2211yescharacteristic
21C2×C4⋊(C43⋊C8)C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2211yescharacteristic
24C2×(C2×D43)⋊C8C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×#13063235C2211yescharacteristic
27C2×C8×Dic43C2211yescharacteristic
28#14582837—21no—
29#14582834—21no—
30#14582818—21no—
31#14582810—21no—
32#14582802C2211yescharacteristic
33#14582799—21no—
34#14582795C2211yescharacteristic
35#14582795C2211yescharacteristic
36#14582795C2211yescharacteristic
37#14582793—21no—
38#14582778—21no—
39#14582772—21no—
40#14582765C2211yescharacteristic
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43#14582756C2211yescharacteristic
44C4×C4⋊Dic43C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×C4⋊Q8×C43C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C43×#474—24no—
56C2×#107×C43C2211yescharacteristic
57C2×#107×C43C2211yescharacteristic
58C2×C4⋊C8×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063296—22no—
66#13063296—22no—
67#13063282—22no—
68#13063282—22no—
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4D411yescharacteristic
77C2×Dic43⋊C4D411yescharacteristic
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4D411yescharacteristic
85C2×(C2×D43)⋊C4D411yescharacteristic
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88#13063259—22no—
89#13063257—22no—
90C4⋊(C43⋊C8)—22no—
91#13063246—22no—
92#13063246—22no—
93(C2×D43)⋊C8—22no—
94(C2×D43)⋊C8—22no—
95#13063235—22no—
96C8×Dic43—22no—
97C43⋊#95—21no—
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C22×Q8×C43—21no—
107C22×D4×C43C2311yescharacteristic
108C23×C4×C43—21no—
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C4⋊Q8×C43—22no—
112C4⋊Q8×C43—22no—
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#107×C43—22no—
122#107×C43—22no—
123C4⋊C8×C43D414yescomplemented
124#102×C43—22no—
125#102×C43—22no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×Q8×C43—42no—
129C2×Q8×C43—81no—
130C2×Q8×C43—81no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43#4112yes—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—42no—
141C22×C4×C43—81no—
142C22×C4×C43—81no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—24no—
147C2×C22⋊D43—81no—
148C2×C22⋊D43—81no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—21no—
161C2×C4×D43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43C2×D412yes—
167C2×C8×C43C2×D412yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—42no—
175C22⋊C4×C43—42no—
176C42×C43C2×D412yes—
177C42×C43#4112yes—
178C22⋊Dic43—24no—
179C22⋊Dic43—81no—
180C22⋊Dic43—81no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185(C2×D43)⋊C4—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—81no—
197Dic43⋊C4—81no—
198Dic43⋊C4—81no—
199C4×Dic43—21no—
200C4×Dic43—21no—
201C4×Dic43—81no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C23×C43—22no—
209C23×C43—41no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43C22×D411yescharacteristic
216C22×D43—21no—
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223Q8×C43—84no—
224D4×C43—22no—
225D4×C43—22no—
226D4×C43—41no—
227D4×C43—41no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—21no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—84no—
242C2×C4×C43#12112yes—
243C2×C4×C43#12112yes—
244C2×C4×C43C22×D411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C2×C4×C432−1+411yescharacteristic
250C22⋊D43—84no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C4×D43—41no—
276C8×C43—22no—
277C8×C43—22no—
278C43⋊C8—41no—
279C43⋊C8—41no—
280#24712—431nomaximal, Sylow
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43C2×#12111yescharacteristic
289C22×C43#52511yescharacteristic
290C22×C43#53611yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57611yescharacteristic
293C22×C43#57711yescharacteristic
294C22×C43#57811yescharacteristic
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C4×C43—22no—
303C4×C43—22no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43—81no—
307C4×C43#54711yescharacteristic
308C4×C43#54811yescharacteristic
309C4×C43#55211yescharacteristic
310C4×C43#55611yescharacteristic
311Dic43—42no—
312Dic43—41no—
313Dic43—41no—
314Dic43—41no—
315Dic43—81no—
316Dic43—81no—
317Dic43—81no—
318C2×#474D4311yescharacteristic, complemented
319C2×#433—431no—
320#2628—431no—
321#2324—431no—
322#2076—431no—
323#2075—431no—
324#2034—431no—
325#2033—431no—
326#1987—431no—
327#1949—431no—
328#1944—431no—
329#1942—431no—
330#1936—431no—
331#1934—431no—
332#1804—431no—
333C2×C43—82no—
334C2×C43#241511yescharacteristic
335C2×C43#305811yescharacteristic
336C2×C43#306311yescharacteristic
337C2×C43#311811yescharacteristic
338C2×C43#312411yescharacteristic
339C2×C43#324111yescharacteristic
340C2×C43#324311yescharacteristic
341D43—81no—
342C2×C4⋊Q8C2×D4311yescharacteristic
343C2×#121—431no—
344C2×C4×D4C2×D4311yescharacteristic
345C2×#117—431no—
346#474—24no—
347#433—864no—
348C2×#107—431no—
349C2×#107C2×D4311yescharacteristic
350C2×#107C2×D4311yescharacteristic
351C2×#106—431no—
352C2×C4⋊C8—431no—
353C2×C4⋊C8C2×D4311yescharacteristic
354C2×#102—431no—
355C2×#102—431no—
356C2×#102C2×D4311yescharacteristic
357C2×#102C2×D4311yescharacteristic
358C2×C22⋊C8—431no—
359C2×C22⋊C8—431no—
360C2×#97—431no—
361C2×C4×C8—431no—
362#400—861no—
363#399—861no—
364#395—861no—
365#393—861no—
366#390—431no—
367#390—861no—
368#389—431no—
369#389—431no—
370#389—431no—
371#388—861no—
372#386—861no—
373#385—861no—
374#382—431no—
375#380—431no—
376#380—431no—
377#380—431no—
378C4×C4⋊C4—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387C43#2471211yescharacteristic, complemented, Sylow
388C22×Q8—21no—
389C22×D4—861no—
390C22×D4C22×D4311yescharacteristic
391C23×C4—21no—
392C23×C4—431no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397C4⋊Q8—22no—
398C4⋊Q8—22no—
399#121—862no—
400#121—862no—
401C4×D4—22no—
402C4×D4—22no—
403#117—862no—
404#117—862no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—431no—
420C2×C22⋊C4—431no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42C22×D4311yescharacteristic
430#107—22no—
431#107—22no—
432#107—862no—
433#106—862no—
434C4⋊C8—862no—
435C4⋊C8C22⋊D4314yescomplemented
436#102—22no—
437#102—22no—
438#102—862no—
439#102—862no—
440C22⋊C8—862no—
441C22⋊C8—862no—
442#97—862no—
443C4×C8—862no—
444#95—861no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453C24—21no—
454C24—431no—
455C2×Q8—42no—
456C2×Q8—81no—
457C2×Q8—81no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—864no—
464C2×D4—3441no—
465C2×D4—3441no—
466C2×D4#1062190212yes—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—81no—
472C22×C4—81no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8C2×C22⋊D4312yes—
500C2×C8C2×C22⋊D4312yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—432no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—3441no—
519C4⋊C4—3441no—
520C4⋊C4—3441no—
521C22⋊C4—42no—
522C22⋊C4—864no—
523C22⋊C4—862no—
524C22⋊C4—862no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—3441no—
529C22⋊C4—3441no—
530C42—861no—
531C42—861no—
532C42—3441no—
533C42#1062190012yes—
534C42C2×C22⋊D4312yes—
535C23—22no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—861no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—861no—
547C23—861no—
548C23—861no—
549C23C2×D4×D4311yescharacteristic
550Q8—84no—
551D4—22no—
552D4—22no—
553D4—41no—
554D4—41no—
555D4—3444no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—84no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—862no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—861no—
579C2×C4—861no—
580C2×C4—1721no—
581C2×C4—1721no—
582C2×C4—1721no—
583C2×C4—1721no—
584C2×C4—1721no—
585C2×C4—1721no—
586C2×C4—1721no—
587C2×C4—1721no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4#1306329612yes—
596C2×C4#1306329612yes—
597C2×C4C22×C22⋊D4311yescharacteristic
598C2×C4#41×D4311yescharacteristic
599C2×C4C2×#1062190011yescharacteristic
600C2×C4C2×#1062190211yescharacteristic
601C2×C4#1306337211yescharacteristic
602C2×C4#1306337311yescharacteristic
603C8—22no—
604C8—22no—
605C8—1721no—
606C8—1721no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—1721no—
615C22—1721no—
616C22—1721no—
617C22—1721no—
618C22—1721no—
619C22—1721no—
620C22—1721no—
621C22C2×#1306329611yescharacteristic
622C22#1458341211yescharacteristic
623C22#1458347211yescharacteristic
624C22#1458370011yescharacteristic
625C22#1458370011yescharacteristic
626C22#1458370811yescharacteristic
627C22#1458371511yescharacteristic
628C4—22no—
629C4—22no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—3441no—
634C4—3441no—
635C4—3441no—
636C4—1721no—
637C4—1722no—
638C4—1721no—
639C4—1721no—
640C4#1458354811yescharacteristic
641C4#1458356011yescharacteristic
642C4#1458359111yescharacteristic
643C4#1458362011yescharacteristic
644C2—82no—
645C2—3441no—
646C2#1913802011yescharacteristic
647C2#1914423911yescharacteristic
648C2#1914428011yescharacteristic
649C2#1914478611yescharacteristic
650C2#1914486211yescharacteristic
651C2#1914585511yescharacteristic
652C2#1914587511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#474C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenterC2×#474D43
hypocenterC43#24712
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#14582959C2semidirect
2. #19140417C2semidirect
4. #19136024C2semidirect
5. #19136019C2semidirect
8. #19135544C2semidirect
9. #19135365C2semidirect
10. #19135336C2semidirect
11. #19135326C2semidirect
12. #19135289C2semidirect
13. #19135275C2semidirect
14. #19134605C2semidirect
15. C2×C43×#474C2semidirect
123. C4⋊C8×C43D4semidirect
318. C2×#474D43semidirect
387. C43#24712semidirect
435. C4⋊C8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829592
#191404172
#191372822
#191360242
#191360192
#191357832
#191357762
#191355442
#191353652
#191353362
#191353262
#191352892
#191352752
#191346052
C2×C43×#4742
#2471243