Finite Group Databasebeta

← #25100913

Subgroups — #25100913

Order 11008.

950 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583008C211yesmaximal, characteristic
2#19137057C211yesmaximal, characteristic, complemented
3#19137053C211yesmaximal, characteristic, complemented
4#19135470C211yesmaximal, characteristic
5#19135458C211yesmaximal, characteristic
6#19135335C211yesmaximal, characteristic, complemented
7#19135322C211yesmaximal, characteristic, complemented
8#19135292C211yesmaximal, characteristic, complemented
9#19135280C211yesmaximal, characteristic, complemented
10#19135276C211yesmaximal, characteristic, complemented
11#19134491C211yesmaximal, characteristic, complemented
12#19134422C211yesmaximal, characteristic, complemented
13#19134419C211yesmaximal, characteristic, complemented
14#97×Dic43C211yesmaximal, characteristic, complemented
15C43×#1936C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063283—21no—
20C2×#13063281—21no—
21#14583008C418yescomplemented
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063246C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31C2×#13063235C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582798C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582793—21no—
41#14582791—21no—
42#14582789—21no—
43#14582787—21no—
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C22⋊C4×Dic43—21no—
47#14582746—21no—
48C42×Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582662C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#102×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#97×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C43×#389C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×D172C2311yescharacteristic
61C23×Dic43—21no—
62C22×C4×D43—21no—
63C2×#10621882—22no—
64C2×#10621882—22no—
65C2×#10621882C2×C414yes—
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68D4×Dic43—22no—
69D4×Dic43C2×C414yes—
70#13063287—22no—
71#13063287C2×C414yes—
72#13063283—44no—
73#13063281—44no—
74C2×C4⋊Dic43—21no—
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×C4⋊Dic43C2311yescharacteristic
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×C22⋊Dic43—21no—
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43D411yescharacteristic
91C2×C4×Dic43D411yescharacteristic
92C2×C4×Dic43D411yescharacteristic
93C2×C4×Dic43D411yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063258—22no—
97#13063256—22no—
98#13063256C2×C414yes—
99#13063247—22no—
100#13063247C2×C414yes—
101#13063246—22no—
102#13063245—22no—
103#13063236—22no—
104#13063235—22no—
105#13063235C2×C414yes—
106C8×Dic43—22no—
107C8×Dic43—22no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C22×D4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C22⋊C4×C43—21no—
121C2×C22⋊C4×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#102×C43—22no—
124#102×C43C2×C414yes—
125#97×C43—22no—
126#95×C43—21no—
127C24×C43—21no—
128C23×D43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43—21no—
133C2×D4×C43—21no—
134C2×D4×C43C22×C412yes—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2411yescharacteristic
141C22×Dic43—24no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—42no—
146C22×Dic43—42no—
147C22×Dic43C2×D411yescharacteristic
148C22×Dic43C2×D411yescharacteristic
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C2×D172—21no—
152C2×D172—21no—
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172C22×C412yes—
157C2×C4×D43—24no—
158C2×C4×D43—42no—
159C2×C4×D43—42no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43C22×C412yes—
165C2×C8×C43#4112yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—42no—
172C4⋊C4×C43C22×C412yes—
173C22⋊C4×C43—42no—
174C22⋊C4×C43—42no—
175C42×C43—21no—
176C42×C43—21no—
177C22⋊Dic43—24no—
178C22⋊Dic43—42no—
179C22⋊Dic43—42no—
180#10621882—28no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—42no—
192C4⋊Dic43C22×C412yes—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—22no—
198C4×Dic43—22no—
199C4×Dic43—41no—
200C4×Dic43—41no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C4×Dic43C22×C412yes—
204C4×Dic43#4112yes—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8C22×C412yes—
208C2×C43⋊C8#4112yes—
209C2×C43⋊C8#4112yes—
210C2×C43⋊C8#4112yes—
211C23×C43—22no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43—41no—
218C23×C43C22×D411yescharacteristic
219C22×D43—22no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225C22×D43—41no—
226D4×C43—22no—
227D4×C43—22no—
228D4×C43—41no—
229D4×C43—41no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43—41no—
240C2×C4×C43—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—48no—
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×Dic43C4×D412yes—
270C2×Dic43C4×D412yes—
271C2×Dic43AGL(1,ℤ/8)12yes—
272C2×Dic43AGL(1,ℤ/8)12yes—
273D172—22no—
274D172—22no—
275D172—41no—
276D172—41no—
277C4×D43—48no—
278C8×C43—22no—
279C8×C43—22no—
280C43⋊C8—22no—
281C43⋊C8#11714yescomplemented
282#21286—431nomaximal, Sylow
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—42no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43C2×C4×D411yescharacteristic
291C22×C43#53211yescharacteristic
292C22×C43#53211yescharacteristic
293C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
294C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
295C22×C43#57511yescharacteristic
296C22×C43#57511yescharacteristic
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C4×C43—41no—
305C4×C43—41no—
306C4×C43—42no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C2×#11711yescharacteristic
310C4×C43C4×#4111yescharacteristic
311C4×C43#52911yescharacteristic
312C4×C43#52911yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—22no—
316Dic43—22no—
317Dic43—42no—
318Dic43—81no—
319Dic43—81no—
320C2×#442—431no—
321#2293—431no—
322#2293—431no—
323#1972—431no—
324#1970—431no—
325#1944—431no—
326#1941—431no—
327#1936—431no—
328#1936D4311yescharacteristic, complemented
329#1934—431no—
330#1934—431no—
331#1776—431no—
332#1762—431no—
333#1762—431no—
334C4×#97—431no—
335C2×C43—82no—
336C2×C43#229311yescharacteristic
337C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
338C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
339C2×C43#318011yescharacteristic
340C2×C43#318011yescharacteristic
341C2×C43#318311yescharacteristic
342C2×C43#318411yescharacteristic
343D43—82no—
344C22×D8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C2×#117—861no—
348C2×#117—861no—
349#442—438no—
350C2×#107—431no—
351C2×#106—431no—
352C2×#106—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102—431no—
356C2×#102—431no—
357C2×#102C2×D4311yescharacteristic
358C2×#102C2×D4311yescharacteristic
359C2×#97—431no—
360C2×#97—431no—
361C2×#97—431no—
362C2×#97C2×D4311yescharacteristic
363C2×C4×C8—431no—
364C2×C4×C8—431no—
365#390—431no—
366#390—431no—
367#390—431no—
368#390C2×D4311yescharacteristic
369#389—431no—
370#389—431no—
371#389—431no—
372#389C2×D4311yescharacteristic
373#388—861no—
374#388—861no—
375#388—861no—
376#388—861no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4—431no—
379C4×C22⋊C4—861no—
380C4×C22⋊C4—861no—
381C43—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340C2×D4311yescharacteristic
387#340C2×D4311yescharacteristic
388C43#2128611yescharacteristic, complemented, Sylow
389C22×D4—431no—
390C22×D4C22×D4311yescharacteristic
391C23×C4—861no—
392C23×C4—861no—
393C2×D8—434no—
394C2×D8—862no—
395C2×D8—862no—
396C22×C8—431no—
397C22×C8—431no—
398C22×C8C22×D4311yescharacteristic
399C22×C8C22×D4311yescharacteristic
400C4×D4—434no—
401C4×D4—434no—
402C4×D4—862no—
403C4×D4—862no—
404#117—1724no—
405#117—1724no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—431no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—861no—
411C2×C4⋊C4—861no—
412C2×C4⋊C4—861no—
413C2×C4⋊C4C22×D4311yescharacteristic
414C2×C4⋊C4C22×D4311yescharacteristic
415C2×C4⋊C4C22×D4311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—861no—
419C2×C22⋊C4—861no—
420C2×C22⋊C4—861no—
421C2×C22⋊C4—861no—
422C2×C22⋊C4—861no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C42—431no—
427C2×C42—431no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—431no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42C22×D4311yescharacteristic
435#107—862no—
436#106—434no—
437#106—862no—
438#102—22no—
439#102—434no—
440#102—862no—
441#102—862no—
442#102—862no—
443#102C4×D4314yes—
444#97—22no—
445#97—434no—
446#97—862no—
447#97—862no—
448C4×C8—862no—
449C4×C8—862no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456C24—21no—
457C24—861no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—432no—
464C2×D4—861no—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4C2×C4×D4312yes—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—431no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—1722no—
483C22×C4—1722no—
484C22×C4—1722no—
485C22×C4—1722no—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489D8—868no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—432no—
495C2×C8—432no—
496C2×C8—432no—
497C2×C8—432no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8C2×C4×D4312yes—
501C2×C8#1062190012yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—432no—
509C4⋊C4—861no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—1722no—
515C4⋊C4—1722no—
516C4⋊C4—1722no—
517C4⋊C4C2×C4×D4312yes—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—864no—
521C22⋊C4—864no—
522C22⋊C4—1722no—
523C22⋊C4—1722no—
524C22⋊C4—1722no—
525C22⋊C4—1722no—
526C22⋊C4—1722no—
527C22⋊C4—1722no—
528C42—21no—
529C42—21no—
530C42—432no—
531C42—432no—
532C42—862no—
533C42—862no—
534C42—861no—
535C42—861no—
536C42—1721no—
537C42—1721no—
538C42—1722no—
539C42—1722no—
540C23—22no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—862no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23C2×D4×D4311yescharacteristic
555D4—22no—
556D4—22no—
557D4—41no—
558D4—41no—
559D4—862no—
560D4—862no—
561D4—1721no—
562D4—1721no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—432no—
579C2×C4—432no—
580C2×C4—432no—
581C2×C4—432no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—862no—
591C2×C4—1728no—
592C2×C4—1728no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4—1721no—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4#41×D4311yescharacteristic
606C2×C4C2×#1062190011yescharacteristic
607C8—22no—
608C8—22no—
609C8—434no—
610C8—862no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—3441no—
619C22—3441no—
620C22—3441no—
621C22—3441no—
622C22—1722no—
623C22—1722no—
624C22—1722no—
625C22C4×D4×D4311yescharacteristic
626C22#1458344411yescharacteristic
627C22#1458344811yescharacteristic
628C22AGL(1,ℤ/8)×D4311yescharacteristic
629C22AGL(1,ℤ/8)×D4311yescharacteristic
630C22#1458369511yescharacteristic
631C22#1458369811yescharacteristic
632C4—41no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—862no—
638C4—862no—
639C4—862no—
640C4—862no—
641C4—3441no—
642C4—3441no—
643C4—1722no—
644C4#117×D4311yescharacteristic
645C4C4×#1062190011yescharacteristic
646C4#1458342611yescharacteristic
647C4#1458343211yescharacteristic
648C2—82no—
649C2—3442no—
650C2#1913705511yescharacteristic
651C2#1914340011yescharacteristic
652C2#1914340611yescharacteristic
653C2#1914529211yescharacteristic
654C2#1914529611yescharacteristic
655C2#1914531711yescharacteristic
656C2#1914532811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1936C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenter#1936D43
hypocenterC43#21286
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. #19137057C2semidirect
3. #19137053C2semidirect
6. #19135335C2semidirect
7. #19135322C2semidirect
8. #19135292C2semidirect
9. #19135280C2semidirect
10. #19135276C2semidirect
11. #19134491C2semidirect
12. #19134422C2semidirect
13. #19134419C2semidirect
14. #97×Dic43C2semidirect
15. C43×#1936C2semidirect
21. #14583008C4semidirect
281. C43⋊C8#117semidirect
328. #1936D43semidirect
388. C43#21286semidirect

Maximal subgroups

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

subgroupindex
C2×#145830082
#191370572
#191370532
#191354702
#191354582
#191353352
#191353222
#191352922
#191352802
#191352762
#191344912
#191344222
#191344192
#97×Dic432
C43×#19362
#2128643