Finite Group Databasebeta

← #25137953

Subgroups — #25137953

Order 11008.

794 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583199C211yesmaximal, characteristic, complemented
2C2×#14582959C211yesmaximal, characteristic, complemented
3#19140428C211yesmaximal, characteristic, complemented
4#19137282C211yesmaximal, characteristic
5#19136033C211yesmaximal, characteristic, complemented
6#19136027C211yesmaximal, characteristic, complemented
7#19135775C211yesmaximal, characteristic
8#19135775C211yesmaximal, characteristic
9#19135550C211yesmaximal, characteristic, complemented
10#19135351C211yesmaximal, characteristic, complemented
11#19135332C211yesmaximal, characteristic, complemented
12#19135327C211yesmaximal, characteristic, complemented
13#19135294C211yesmaximal, characteristic, complemented
14#19135280C211yesmaximal, characteristic, complemented
15C43×#1802C211yesmaximal, characteristic, complemented
16C2×#13063317C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19#14583199—24no—
20#14582959—24no—
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×C8×Dic43C2211yescharacteristic
32#14582829—21no—
33#14582829—21no—
34#14582821—21no—
35#14582821—21no—
36#14582802C2211yescharacteristic
37#14582799—21no—
38#14582798C2211yescharacteristic
39#14582798C2211yescharacteristic
40#14582795C2211yescharacteristic
41#14582793—21no—
42#14582778—21no—
43#14582772—21no—
44#14582756C2211yescharacteristic
45#14582756C2211yescharacteristic
46#14582756C2211yescharacteristic
47C4×C4⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54C2×C4×D4×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C2×#102×C43C2211yescharacteristic
57C2×#102×C43C2211yescharacteristic
58C43×#384C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C22×C22⋊D43—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063317—22no—
66#13063317—22no—
67#13063296—22no—
68#13063296—22no—
69#13063282—22no—
70#13063282—22no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43C2311yescharacteristic
92#13063258—22no—
93#13063258—22no—
94#13063258—22no—
95#13063256—22no—
96C4⋊(C43⋊C8)D414yescomplemented
97#13063246—22no—
98#13063246—22no—
99(C2×D43)⋊C8—22no—
100(C2×D43)⋊C8—22no—
101#13063235—22no—
102C8×Dic43—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C22×D4×C43C2311yescharacteristic
111C23×C4×C43—21no—
112C22×C8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C4×D4×C43—22no—
115C4×D4×C43—22no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123C4⋊C8×C43—22no—
124#102×C43—22no—
125#102×C43—22no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43#4112yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—42no—
138C22×C4×C43—81no—
139C22×C4×C43—81no—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C2×C22⋊D43—24no—
144C2×C22⋊D43—81no—
145C2×C22⋊D43—81no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43—81no—
173C22⋊C4×C43—42no—
174C42×C43C2×D412yes—
175C42×C43#4112yes—
176C22⋊Dic43—24no—
177C22⋊Dic43—81no—
178C22⋊Dic43—81no—
179(C2×D43)⋊C4—22no—
180(C2×D43)⋊C4—22no—
181(C2×D43)⋊C4—81no—
182(C2×D43)⋊C4—81no—
183(C2×D43)⋊C4—81no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—81no—
192C4⋊Dic43—81no—
193C4⋊Dic43#4112yes—
194Dic43⋊C4—22no—
195Dic43⋊C4—22no—
196Dic43⋊C4—42no—
197Dic43⋊C4—42no—
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⋊C8C2×D412yes—
207C2×C43⋊C8C2×D412yes—
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—
223D4×C43—22no—
224D4×C43—22no—
225D4×C43—41no—
226D4×C43—41no—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—21no—
230C2×C4×C43—21no—
231C2×C4×C43—41no—
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—84no—
241C2×C4×C43#12112yes—
242C2×C4×C43#12112yes—
243C2×C4×C43C22×D411yescharacteristic
244C2×C4×C43C2×#4111yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C432−1+411yescharacteristic
248C2×C4×C432−1+411yescharacteristic
249C22⋊D43—84no—
250C2×Dic43—21no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—22no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—41no—
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—
271C4×D43—41no—
272C4×D43—41no—
273C4×D43—41no—
274C4×D43—41no—
275C8×C43—41no—
276C8×C43—41no—
277C43⋊C8—22no—
278C43⋊C8—22no—
279#24713—431nomaximal, Sylow
280C22×C43—42no—
281C22×C43—42no—
282C22×C43—42no—
283C22×C43—81no—
284C22×C43—81no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43C2×#12111yescharacteristic
288C22×C43#52511yescharacteristic
289C22×C43#53611yescharacteristic
290C22×C43#57611yescharacteristic
291C22×C43#57611yescharacteristic
292C22×C43#57711yescharacteristic
293C22×C43#57811yescharacteristic
294C2×D43—41no—
295C2×D43—41no—
296C2×D43—41no—
297C2×D43—41no—
298C2×D43—41no—
299C2×D43—41no—
300C2×D43—41no—
301C4×C43—22no—
302C4×C43—22no—
303C4×C43—81no—
304C4×C43—81no—
305C4×C43—81no—
306C4×C43#54711yescharacteristic
307C4×C43#54811yescharacteristic
308C4×C43#55211yescharacteristic
309C4×C43#55611yescharacteristic
310Dic43—42no—
311Dic43—41no—
312Dic43—41no—
313Dic43—41no—
314Dic43—81no—
315Dic43—81no—
316Dic43—81no—
317C2×#478—431no—
318C2×#433—431no—
319#2629—431no—
320#2324—431no—
321#2077—431no—
322#2076—431no—
323#2033—431no—
324#2033—431no—
325#1989—431no—
326#1947—431no—
327#1943—431no—
328#1942—431no—
329#1936—431no—
330#1934—431no—
331#1802D4311yescharacteristic, complemented
332C2×C43—82no—
333C2×C43#241511yescharacteristic
334C2×C43#306111yescharacteristic
335C2×C43#306211yescharacteristic
336C2×C43#312011yescharacteristic
337C2×C43#312211yescharacteristic
338C2×C43#324111yescharacteristic
339C2×C43#324311yescharacteristic
340D43—81no—
341C2×#125—431no—
342C2×#121—431no—
343C2×C4×D4C2×D4311yescharacteristic
344C2×#117—431no—
345#478—864no—
346#433—864no—
347C2×#107—431no—
348C2×#107—431no—
349C2×#107—431no—
350C2×#106—431no—
351C2×C4⋊C8—431no—
352C2×C4⋊C8C2×D4311yescharacteristic
353C2×#102—431no—
354C2×#102—431no—
355C2×#102C2×D4311yescharacteristic
356C2×#102C2×D4311yescharacteristic
357C2×C22⋊C8—431no—
358C2×C22⋊C8—431no—
359C2×#97—431no—
360C2×C4×C8—431no—
361#398—861no—
362#398—861no—
363#396—861no—
364#396—861no—
365#390—431no—
366#390—861no—
367#389—431no—
368#389—431no—
369#389—431no—
370#388—861no—
371#386—861no—
372#385—861no—
373#384C2×D4311yescharacteristic
374#380—431no—
375#380—431no—
376#380—431no—
377C4×C4⋊C4—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340C2×D4311yescharacteristic
385#340C2×D4311yescharacteristic
386C43#2471311yescharacteristic, complemented, Sylow
387C22×D4—861no—
388C22×D4C22×D4311yescharacteristic
389C23×C4—21no—
390C23×C4—431no—
391C22×C8—431no—
392C22×C8—431no—
393C22×C8C22×D4311yescharacteristic
394C22×C8C22×D4311yescharacteristic
395#125—862no—
396#125—862no—
397#121—862no—
398#121—862no—
399C4×D4—22no—
400C4×D4—22no—
401#117—862no—
402#117—862no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4—861no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C4⋊C4C22×D4311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—431no—
421C2×C22⋊C4—431no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C42—431no—
429C2×C42—861no—
430C2×C42C22×D4311yescharacteristic
431#107—862no—
432#107—862no—
433#107—862no—
434#106—862no—
435C4⋊C8—22no—
436C4⋊C8—434no—
437#102—22no—
438#102—22no—
439#102—862no—
440#102—862no—
441C22⋊C8—862no—
442C22⋊C8—862no—
443#97—862no—
444C4×C8—862no—
445#95—861no—
446#95—861no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452C24—21no—
453C24—431no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—864no—
460C2×D4—3441no—
461C2×D4—3441no—
462C2×D4#1062190012yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—81no—
468C22×C4—81no—
469C22×C4—431no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—861no—
473C22×C4—861no—
474C22×C4—861no—
475C22×C4—861no—
476C22×C4—861no—
477C22×C4—861no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4D4×D4311yescharacteristic
483C22×C4D4×D4311yescharacteristic
484C22×C4C23×D4311yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—432no—
492C2×C8—432no—
493C2×C8—861no—
494C2×C8—861no—
495C2×C8—861no—
496C2×C8—861no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—81no—
504C4⋊C4—81no—
505C4⋊C4—432no—
506C4⋊C4—862no—
507C4⋊C4—862no—
508C4⋊C4—861no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—3441no—
516C4⋊C4—3441no—
517C4⋊C4—3441no—
518C4⋊C4—1722no—
519C4⋊C4—1722no—
520C22⋊C4—42no—
521C22⋊C4—864no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—3441no—
528C22⋊C4—3441no—
529C42—861no—
530C42—861no—
531C42—3441no—
532C42#1062189812yes—
533C42D4×D4312yes—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—861no—
542C23—861no—
543C23—861no—
544C23—861no—
545C23—861no—
546C23—861no—
547C23—861no—
548C23C2×D4×D4311yescharacteristic
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—3444no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—84no—
568C2×C4—861no—
569C2×C4—861no—
570C2×C4—861no—
571C2×C4—861no—
572C2×C4—862no—
573C2×C4—861no—
574C2×C4—861no—
575C2×C4—861no—
576C2×C4—861no—
577C2×C4—861no—
578C2×C4—1721no—
579C2×C4—1721no—
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#1306329812yes—
594C2×C4#1306329812yes—
595C2×C4C2×D4×D4311yescharacteristic
596C2×C4#41×D4311yescharacteristic
597C2×C4C2×#1062190011yescharacteristic
598C2×C4C2×#1062189811yescharacteristic
599C2×C4#1306337211yescharacteristic
600C2×C4#1306337311yescharacteristic
601C8—41no—
602C8—41no—
603C8—862no—
604C8—862no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—1721no—
613C22—1721no—
614C22—1721no—
615C22—1721no—
616C22—1721no—
617C22—1721no—
618C22—1721no—
619C22C2×#1306329811yescharacteristic
620C22#1458340911yescharacteristic
621C22#1458347211yescharacteristic
622C22#1458370011yescharacteristic
623C22#1458370311yescharacteristic
624C22#1458370511yescharacteristic
625C22#1458371511yescharacteristic
626C4—22no—
627C4—22no—
628C4—81no—
629C4—81no—
630C4—81no—
631C4—3441no—
632C4—3441no—
633C4—3441no—
634C4—1721no—
635C4—1721no—
636C4—1722no—
637C4—1721no—
638C4#1458355111yescharacteristic
639C4#1458355511yescharacteristic
640C4#1458358411yescharacteristic
641C4#1458361711yescharacteristic
642C2—82no—
643C2—3441no—
644C2#1913802611yescharacteristic
645C2#1914426411yescharacteristic
646C2#1914427311yescharacteristic
647C2#1914480611yescharacteristic
648C2#1914483611yescharacteristic
649C2#1914584711yescharacteristic
650C2#1914587511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1802C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1802D43
hypocenterC43#24713
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1802

Complements

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

NH ≅ G/Ntype
1. C2×#14583199C2semidirect
2. C2×#14582959C2semidirect
3. #19140428C2semidirect
5. #19136033C2semidirect
6. #19136027C2semidirect
9. #19135550C2semidirect
10. #19135351C2semidirect
11. #19135332C2semidirect
12. #19135327C2semidirect
13. #19135294C2semidirect
14. #19135280C2semidirect
15. C43×#1802C2semidirect
96. C4⋊(C43⋊C8)D4semidirect
331. #1802D43semidirect
386. C43#24713semidirect

Maximal subgroups

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

subgroupindex
C2×#145831992
C2×#145829592
#191404282
#191372822
#191360332
#191360272
#191357752
#191355502
#191353512
#191353322
#191353272
#191352942
#191352802
C43×#18022
#2471343