Finite Group Databasebeta

← #25116340

Subgroups — #25116340

Order 11008.

934 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×#14582979C211yesmaximal, characteristic
2#19137543C211yesmaximal, characteristic, complemented
3#19137540C211yesmaximal, characteristic, complemented
4#19135460C211yesmaximal, characteristic
5#19135458C211yesmaximal, characteristic
6#19135217C211yesmaximal, characteristic, complemented
7#19135216C211yesmaximal, characteristic, complemented
8#19135214C211yesmaximal, characteristic, complemented
9#19134753C211yesmaximal, characteristic, complemented
10#19134594C211yesmaximal, characteristic, complemented
11#19134593C211yesmaximal, characteristic, complemented
12C4×#13063258C211yesmaximal, characteristic, complemented
13#19134487C211yesmaximal, characteristic, complemented
14#19134456C211yesmaximal, characteristic, complemented
15C43×#1925C211yesmaximal, characteristic, complemented
16C22×#10621882C2211yescharacteristic
17C2×D4×Dic43C2211yescharacteristic
18C2×#13063287C2211yescharacteristic
19C2×#13063282—21no—
20C2×#13063281—21no—
21#14582979C418yescomplemented
22C2×#13063259C2211yescharacteristic
23C2×#13063258C2211yescharacteristic
24C2×#13063258C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×#13063247C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063246C2211yescharacteristic
30C2×#13063245C2211yescharacteristic
31C2×C4×C43⋊C8C2211yescharacteristic
32C2×C8×Dic43C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582802C2211yescharacteristic
35#14582801C2211yescharacteristic
36#14582800C2211yescharacteristic
37#14582793—21no—
38#14582790—21no—
39#14582788—21no—
40#14582787—21no—
41#14582768C2211yescharacteristic
42#14582768C2211yescharacteristic
43#14582758—21no—
44#14582757—21no—
45C4⋊C4×Dic43C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47C4×Dic43⋊C4C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C43×#390C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#336C2211yescharacteristic
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#13063282—44no—
73#13063281—44no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×Dic43⋊C4D411yescharacteristic
82C2×Dic43⋊C4D411yescharacteristic
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×C22⋊Dic43—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C2×C4×Dic43C2311yescharacteristic
96#13063259—41no—
97#13063258—22no—
98#13063258—22no—
99#13063258C2×C414yes—
100Dic43⋊C8—22no—
101#13063247—41no—
102#13063247C2×C414yes—
103#13063246—41no—
104#13063245—41no—
105C4×C43⋊C8—22no—
106C8×Dic43—22no—
107C8×Dic43C2×C414yes—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×D4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C22⋊C4×C43—21no—
120C2×C22⋊C4×C43—21no—
121C2×C42×C43—21no—
122C2×C42×C43C2311yescharacteristic
123#107×C43—41no—
124#102×C43—41no—
125#102×C43C2×C414yes—
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×C43—21no—
165C2×C8×C43C22×C412yes—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C22×C412yes—
172C22⋊C4×C43—42no—
173C22⋊C4×C43—81no—
174C42×C43—21no—
175C42×C43—21no—
176C42×C43—42no—
177C22⋊Dic43—24no—
178C22⋊Dic43—42no—
179C22⋊Dic43—81no—
180#10621882—28no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—42no—
183(C2×D43)⋊C4—42no—
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⋊Dic43C22×C412yes—
192Dic43⋊C4—22no—
193Dic43⋊C4—42no—
194Dic43⋊C4—42no—
195Dic43⋊C4—81no—
196Dic43⋊C4—81no—
197Dic43⋊C4D814yescomplemented
198C4×Dic43—21no—
199C4×Dic43—21no—
200C4×Dic43—42no—
201C4×Dic43—42no—
202C4×Dic43—42no—
203C4×Dic43C22×C412yes—
204C4×Dic43#4112yes—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C22×C412yes—
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—21no—
231C2×C4×C43—21no—
232C2×C4×C43—22no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—41no—
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×C43C2×D812yes—
245C2×C4×C43C23×C411yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43H(5,𝔽2)11yescharacteristic
250C2×C4×C432−1+411yescharacteristic
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—22no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—48no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43—41no—
267C2×Dic43—41no—
268C2×Dic43C4×D412yes—
269C2×Dic43C4×D412yes—
270C2×Dic43C2×D812yes—
271C2×Dic43C2×D812yes—
272C2×Dic43#13512yes—
273D172—22no—
274D172—22no—
275D172—41no—
276D172—41no—
277C4×D43—48no—
278C8×C43—22no—
279C8×C43—41no—
280C43⋊C8—41no—
281C43⋊C8#11714yescomplemented
282#22807—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#54711yescharacteristic
292C22×C43#55011yescharacteristic
293C22×C43C22×D811yescharacteristic
294C22×C43C2×#13511yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57811yescharacteristic
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—42no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C4×C43—22no—
305C4×C43—41no—
306C4×C43—42no—
307C4×C43—81no—
308C4×C43—81no—
309C4×C43C2×#11711yescharacteristic
310C4×C43#52011yescharacteristic
311C4×C43#55511yescharacteristic
312C4×C43#55611yescharacteristic
313Dic43—22no—
314Dic43—22no—
315Dic43—41no—
316Dic43—42no—
317Dic43—81no—
318Dic43—81no—
319Dic43C4×D814yes—
320C2×C4×D8—431no—
321#2354—431no—
322#2354—431no—
323#1970—431no—
324#1970—431no—
325#1925—431no—
326#1925—431no—
327#1925—431no—
328#1925D4311yescharacteristic, complemented
329#1845—431no—
330#1802—431no—
331#1802—431no—
332C4×#107—431no—
333C4×#107—431no—
334C8×C4⋊C4—431no—
335C2×C43—82no—
336C2×C43#235411yescharacteristic
337C2×C43C2×C4×D811yescharacteristic
338C2×C43#295111yescharacteristic
339C2×C43#333411yescharacteristic
340C2×C43#334111yescharacteristic
341C2×C43#339111yescharacteristic
342C2×C43#339311yescharacteristic
343D43—82no—
344C22×D8—431no—
345C2×C4×D4—431no—
346C2×C4×D4—431no—
347C2×#117—861no—
348C2×#117—861no—
349C4×D8—438no—
350C2×#107—431no—
351C2×#107—431no—
352C2×#107—431no—
353C2×#107—431no—
354C2×#107C2×D4311yescharacteristic
355C2×C4⋊C8—431no—
356C2×#102—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×#102C2×D4311yescharacteristic
361C2×#102C2×D4311yescharacteristic
362C2×C4×C8—431no—
363C2×C4×C8—431no—
364C2×C4×C8—431no—
365#390—431no—
366#390—431no—
367#390—431no—
368#390C2×D4311yescharacteristic
369#388—861no—
370#388—861no—
371#388—861no—
372#388—861no—
373#384—431no—
374#384—431no—
375#380—861no—
376#380—861no—
377C4×C4⋊C4—431no—
378C4×C4⋊C4—431no—
379C4×C4⋊C4—431no—
380C4×C4⋊C4—431no—
381C4×C4⋊C4C2×D4311yescharacteristic
382#340—431no—
383#340—431no—
384#340—431no—
385#340C2×D4311yescharacteristic
386#336—431no—
387#336C2×D4311yescharacteristic
388C43#2280711yescharacteristic, 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—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⋊C4C22×D4311yescharacteristic
416C2×C4⋊C4C22×D4311yescharacteristic
417C2×C4⋊C4C22×D4311yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
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×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C42—21no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42—861no—
434C2×C42C22×D4311yescharacteristic
435#107—41no—
436#107—434no—
437#107—862no—
438#107—862no—
439#107—1721no—
440C4⋊C8—862no—
441#102—41no—
442#102—434no—
443#102—1721no—
444#102—1721no—
445#102—1721no—
446#102C4×D4314yes—
447C4×C8—434no—
448C4×C8—862no—
449C4×C8—862no—
450#95—21no—
451#95—431no—
452#95—431no—
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—21no—
495C2×C8—432no—
496C2×C8—432no—
497C2×C8—432no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8C2×C4×D4312yes—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—434no—
508C4⋊C4—432no—
509C4⋊C4—862no—
510C4⋊C4—861no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—3441no—
516C4⋊C4—3441no—
517C4⋊C4—1722no—
518C4⋊C4—1722no—
519C4⋊C4C2×C4×D4312yes—
520C22⋊C4—42no—
521C22⋊C4—81no—
522C22⋊C4—864no—
523C22⋊C4—864no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C22⋊C4—1722no—
528C22⋊C4—1722no—
529C22⋊C4—1722no—
530C42—21no—
531C42—21no—
532C42—42no—
533C42—432no—
534C42—432no—
535C42—861no—
536C42—861no—
537C42—1722no—
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—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—432no—
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—862no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—1728no—
591C2×C4—1728no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4—1721no—
598C2×C4—1721no—
599C2×C4—1721no—
600C2×C4D8×D4312yes—
601C2×C4C22×C4×D4311yescharacteristic
602C2×C4#41×D4311yescharacteristic
603C2×C4#41×D4311yescharacteristic
604C2×C4#41×D4311yescharacteristic
605C2×C4#1306337011yescharacteristic
606C2×C4#1306337211yescharacteristic
607C8—22no—
608C8—41no—
609C8—434no—
610C8—1721no—
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#1458354711yescharacteristic
627C22#1458356711yescharacteristic
628C22C2×D8×D4311yescharacteristic
629C22#135×D4311yescharacteristic
630C22#1458370311yescharacteristic
631C22#1458371511yescharacteristic
632C4—22no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—434no—
638C4—862no—
639C4—862no—
640C4—3441no—
641C4—3441no—
642C4—1721no—
643C4—1722no—
644C4#117×D4311yescharacteristic
645C4#1458337811yescharacteristic
646C4#1458361111yescharacteristic
647C4#1458361611yescharacteristic
648C2—82no—
649C2—3442no—
650C2#1913754111yescharacteristic
651C2C4×D8×D4311yescharacteristic
652C2#1914346711yescharacteristic
653C2#1914693711yescharacteristic
654C2#1914701211yescharacteristic
655C2#1914756611yescharacteristic
656C2#1914757811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1925C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
cosocleC22×C4×C43C24
hypercenter#1925D43
hypocenterC43#22807
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1925

Complements

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

NH ≅ G/Ntype
2. #19137543C2semidirect
3. #19137540C2semidirect
6. #19135217C2semidirect
7. #19135216C2semidirect
8. #19135214C2semidirect
9. #19134753C2semidirect
10. #19134594C2semidirect
11. #19134593C2semidirect
12. C4×#13063258C2semidirect
13. #19134487C2semidirect
14. #19134456C2semidirect
15. C43×#1925C2semidirect
21. #14582979C4semidirect
197. Dic43⋊C4D8semidirect
281. C43⋊C8#117semidirect
328. #1925D43semidirect
388. C43#22807semidirect

Maximal subgroups

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

subgroupindex
C2×#145829792
#191375432
#191375402
#191354602
#191354582
#191352172
#191352162
#191352142
#191347532
#191345942
#191345932
C4×#130632582
#191344872
#191344562
C43×#19252
#2280743