Finite Group Databasebeta

← #25103852

Subgroups — #25103852

Order 11008.

900 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583216C211yesmaximal, characteristic
2#19137282C211yesmaximal, characteristic
3#19136949C211yesmaximal, characteristic, complemented
4#19135225C211yesmaximal, characteristic, complemented
5#19135217C211yesmaximal, characteristic, complemented
6#19135179C211yesmaximal, characteristic, complemented
7#19135171C211yesmaximal, characteristic, complemented
8#19134914C211yesmaximal, characteristic
9#19134797C211yesmaximal, characteristic, complemented
10#19134680C211yesmaximal, characteristic, complemented
11#19134492C211yesmaximal, characteristic, complemented
12C4×#13063256C211yesmaximal, characteristic, complemented
13C4×#13063246C211yesmaximal, characteristic, complemented
14#19134364C211yesmaximal, characteristic, complemented
15C43×#1762C211yesmaximal, characteristic, complemented
16C2×#13063296C2211yescharacteristic
17C2×#13063283C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19C2×C4⋊C4×D43C2211yescharacteristic
20#14583216C418yescomplemented
21C2×#13063259C2211yescharacteristic
22C2×#13063257C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×#13063246C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×C4×C43⋊C8C2211yescharacteristic
30#14582802C2211yescharacteristic
31#14582799—21no—
32#14582795C2211yescharacteristic
33#14582793—21no—
34#14582778—21no—
35#14582772—21no—
36#14582756C2211yescharacteristic
37C4⋊C4×Dic43C2211yescharacteristic
38C4⋊C4×Dic43C2211yescharacteristic
39C4×Dic43⋊C4—21no—
40C4×C4⋊Dic43C2211yescharacteristic
41C4×C4⋊Dic43C2211yescharacteristic
42#14582750—21no—
43C4×(C2×D43)⋊C4—21no—
44#14582746—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53C2×C4×D4×C43C2211yescharacteristic
54C2×#102×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×#97×C43C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C22⋊D43—21no—
61C22×C4×D43—21no—
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063296—22no—
66#13063296C2×C414yes—
67#13063283—22no—
68#13063283—22no—
69#13063282—22no—
70#13063282—22no—
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4D411yescharacteristic
78C2×Dic43⋊C4D411yescharacteristic
79C4⋊C4×D43—22no—
80C4⋊C4×D43C2×C414yescomplemented
81C2×C22⋊Dic43—21no—
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4D411yescharacteristic
87C2×(C2×D43)⋊C4D411yescharacteristic
88C2×C4×Dic43—21no—
89C2×C4×Dic43—21no—
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43C2311yescharacteristic
94#13063259—22no—
95#13063257C2×C414yescomplemented
96#13063256—22no—
97#13063256C2×C414yescomplemented
98#13063246—22no—
99#13063246C2×C414yes—
100(C2×D43)⋊C8—22no—
101(C2×D43)⋊C8C2×C414yescomplemented
102C4×C43⋊C8—22no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×D4×C43C2311yescharacteristic
110C23×C4×C43—21no—
111C22×C8×C43C2311yescharacteristic
112C22×C8×C43C2311yescharacteristic
113C4×D4×C43—22no—
114C4×D4×C43—22no—
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119C2×C42×C43—21no—
120C2×C42×C43C2311yescharacteristic
121#102×C43—22no—
122#102×C43C2×C414yes—
123#97×C43—22no—
124#95×C43—21no—
125C24×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×D4×C43—21no—
128C2×D4×C43—21no—
129C2×D4×C43—21no—
130C2×D4×C43—21no—
131C2×D4×C43—21no—
132C2×D4×C43C22×C412yes—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—42no—
137C22×C4×C43—81no—
138C22×C4×C43—81no—
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2411yescharacteristic
142C2×C22⋊D43—24no—
143C2×C22⋊D43—81no—
144C2×C22⋊D43—81no—
145C22×Dic43—21no—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C2×C4×D43—21no—
153C2×C4×D43—21no—
154C2×C4×D43—21no—
155C2×C4×D43—21no—
156C2×C4×D43—24no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×C4×D43C22×C412yes—
160C2×C4×D43#4112yes—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43C22×C412yes—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43C22×C412yes—
172C4⋊C4×C43#4112yes—
173C22⋊C4×C43—42no—
174C42×C43—81no—
175C42×C43#4112yes—
176C42×C43#4112yes—
177C22⋊Dic43—24no—
178C22⋊Dic43—81no—
179C22⋊Dic43—81no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—22no—
182(C2×D43)⋊C4—22no—
183(C2×D43)⋊C4—81no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43C22×C412yes—
190C4⋊Dic43C22×C412yes—
191C4⋊Dic43#4112yes—
192Dic43⋊C4—22no—
193Dic43⋊C4—22no—
194Dic43⋊C4—24no—
195Dic43⋊C4—81no—
196C4×Dic43—24no—
197C4×Dic43—21no—
198C4×Dic43—21no—
199C4×Dic43—81no—
200C4×Dic43—81no—
201C4×Dic43—81no—
202C4×Dic43—81no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8C22×C412yes—
209C23×C43—22no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43C22×D411yescharacteristic
217C22×D43—21no—
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43C4×D412yes—
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—22no—
233C2×C4×C43—22no—
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#12312yes—
243C2×C4×C43#12312yes—
244C2×C4×C43C23×C411yescharacteristic
245C2×C4×C43C2×#4111yescharacteristic
246C2×C4×C43C2×#4111yescharacteristic
247C2×C4×C43C2×#4111yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C22⋊D43—84no—
251C2×Dic43—21no—
252C2×Dic43—21no—
253C2×Dic43—22no—
254C2×Dic43—22no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—22no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
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×Dic43C4×D412yes—
272C4×D43—22no—
273C4×D43—22no—
274C4×D43—22no—
275C4×D43—22no—
276C4×D43—84no—
277C8×C43—22no—
278C8×C43—41no—
279C43⋊C8—22no—
280C43⋊C8—41no—
281#21584—431nomaximal, Sylow
282C22×C43—42no—
283C22×C43—42no—
284C22×C43—42no—
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43C2×C4×D411yescharacteristic
290C22×C43C2×#12311yescharacteristic
291C22×C43#52511yescharacteristic
292C22×C43#57611yescharacteristic
293C22×C43#57711yescharacteristic
294C22×C43#57711yescharacteristic
295C22×C43#57711yescharacteristic
296C2×D43—22no—
297C2×D43—22no—
298C2×D43—22no—
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C4×C43—22no—
304C4×C43—22no—
305C4×C43—42no—
306C4×C43—42no—
307C4×C43—81no—
308C4×C43C4×#4111yescharacteristic
309C4×C43C4×#4111yescharacteristic
310C4×C43#52911yescharacteristic
311C4×C43#52911yescharacteristic
312Dic43—22no—
313Dic43—41no—
314Dic43—41no—
315Dic43—42no—
316Dic43—42no—
317Dic43—42no—
318Dic43—81no—
319C2×#481—431no—
320#2324—431no—
321#2274—431no—
322#1926—431no—
323#1925—431no—
324#1920—431no—
325#1919—431no—
326#1875—431no—
327#1854—431no—
328#1823—431no—
329#1776—431no—
330C4×#106—431no—
331#1762D4311yescharacteristic, complemented
332C4×#102—431no—
333#1750—431no—
334C2×C43—82no—
335C2×C43C4×#12311yescharacteristic
336C2×C43#294611yescharacteristic
337C2×C43#294911yescharacteristic
338C2×C43#309611yescharacteristic
339C2×C43#309911yescharacteristic
340C2×C43#311911yescharacteristic
341C2×C43#312511yescharacteristic
342D43—42no—
343C2×#121—431no—
344C2×C4×D4C2×D4311yescharacteristic
345C2×#117—431no—
346C2×#117—431no—
347C22×C4⋊C4—431no—
348#481—438no—
349C2×#107—431no—
350C2×#106—431no—
351C2×#106—431no—
352C2×#106—431no—
353C2×#102—431no—
354C2×#102—431no—
355C2×#102C2×D4311yescharacteristic
356C2×#102C2×D4311yescharacteristic
357C2×C22⋊C8—431no—
358C2×C22⋊C8—431no—
359C2×#97C2×D4311yescharacteristic
360C2×C4×C8—431no—
361#390—431no—
362#390—861no—
363#389—431no—
364#388—861no—
365#386—861no—
366#385—861no—
367#380—431no—
368C4×C4⋊C4—431no—
369C4×C4⋊C4—431no—
370C4×C4⋊C4—431no—
371C4×C4⋊C4—431no—
372C4×C4⋊C4—861no—
373C4×C4⋊C4—861no—
374C4×C4⋊C4C2×D4311yescharacteristic
375C4×C22⋊C4—861no—
376C4×C22⋊C4—861no—
377#340—431no—
378#340—431no—
379#340—431no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340C2×D4311yescharacteristic
384#340C2×D4311yescharacteristic
385#336—431no—
386#336—431no—
387C43#2158411yescharacteristic, complemented, Sylow
388C22×D4—861no—
389C22×D4C22×D4311yescharacteristic
390C23×C4—21no—
391C23×C4—431no—
392C23×C4—861no—
393C22×C8—431no—
394C22×C8—431no—
395C22×C8C22×D4311yescharacteristic
396C22×C8C22×D4311yescharacteristic
397#121—434no—
398#121—862no—
399C4×D4—22no—
400C4×D4—22no—
401#117—862no—
402#117—862no—
403#117—862no—
404#117—862no—
405C2×C4⋊C4—431no—
406C2×C4⋊C4—431no—
407C2×C4⋊C4—431no—
408C2×C4⋊C4—434no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—862no—
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×C42—21no—
427C2×C42—431no—
428C2×C42—861no—
429C2×C42—861no—
430C2×C42—861no—
431C2×C42—861no—
432C2×C42—861no—
433C2×C42C22×D4311yescharacteristic
434#107—862no—
435#106—434no—
436#106—434no—
437#106—862no—
438#102—22no—
439#102—434no—
440#102—862no—
441#102C4×D4314yes—
442C22⋊C8—434no—
443C22⋊C8—862no—
444#97—22no—
445C4×C8—862no—
446#95—21no—
447#95—861no—
448#95—861no—
449#95—861no—
450#95—861no—
451#95—861no—
452#95—861no—
453C24—21no—
454C24—431no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—864no—
461C2×D4—3441no—
462C2×D4—3441no—
463C2×D4C2×C4×D4312yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—81no—
470C22×C4—431no—
471C22×C4—432no—
472C22×C4—432no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—864no—
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—3441no—
485C22×C4—3441no—
486C22×C4D4×D4311yescharacteristic
487C22×C4D4×D4311yescharacteristic
488C22×C4C23×D4311yescharacteristic
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—432no—
495C2×C8—861no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8C2×C4×D4312yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—432no—
506C4⋊C4—432no—
507C4⋊C4—432no—
508C4⋊C4—864no—
509C4⋊C4—862no—
510C4⋊C4—862no—
511C4⋊C4—861no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—3441no—
517C4⋊C4C2×C4×D4312yes—
518C4⋊C4#1062189812yes—
519C22⋊C4—42no—
520C22⋊C4—864no—
521C22⋊C4—864no—
522C22⋊C4—862no—
523C22⋊C4—862no—
524C22⋊C4—3441no—
525C22⋊C4—3441no—
526C22⋊C4—3441no—
527C42—81no—
528C42—864no—
529C42—861no—
530C42—861no—
531C42—3441no—
532C42—3441no—
533C42—3441no—
534C42—3441no—
535C42#1062189812yes—
536C42#1062190012yes—
537C23—22no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—432no—
545C23—861no—
546C23—861no—
547C23—861no—
548C23—861no—
549C23—861no—
550C23—861no—
551C23C2×D4×D4311yescharacteristic
552D4—22no—
553D4—22no—
554D4—41no—
555D4—41no—
556D4—3444no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—84no—
571C2×C4—432no—
572C2×C4—861no—
573C2×C4—861no—
574C2×C4—862no—
575C2×C4—862no—
576C2×C4—862no—
577C2×C4—862no—
578C2×C4—862no—
579C2×C4—862no—
580C2×C4—861no—
581C2×C4—861no—
582C2×C4—862no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—3444no—
588C2×C4—1721no—
589C2×C4—1721no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
593C2×C4—1721no—
594C2×C4—1721no—
595C2×C4—1721no—
596C2×C4—1721no—
597C2×C4#1306330712yes—
598C2×C4#1306330712yes—
599C2×C4C22×C4×D4311yescharacteristic
600C2×C4#41×D4311yescharacteristic
601C2×C4#41×D4311yescharacteristic
602C2×C4C2×#1062190011yescharacteristic
603C2×C4C2×#1062189811yescharacteristic
604C2×C4C2×#1062189811yescharacteristic
605C8—22no—
606C8—41no—
607C8—862no—
608C8—1721no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—862no—
617C22—862no—
618C22—862no—
619C22—1721no—
620C22—1721no—
621C22—1721no—
622C22—1721no—
623C22C4×D4×D4311yescharacteristic
624C22C2×#1306330711yescharacteristic
625C22#1458340811yescharacteristic
626C22#1458370311yescharacteristic
627C22#1458370811yescharacteristic
628C22#1458370911yescharacteristic
629C22#1458370911yescharacteristic
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—81no—
635C4—862no—
636C4—3441no—
637C4—1722no—
638C4—1722no—
639C4—1722no—
640C4—1721no—
641C4—1721no—
642C4C4×#1062190011yescharacteristic
643C4C4×#1062189811yescharacteristic
644C4#1458342711yescharacteristic
645C4#1458343111yescharacteristic
646C2—82no—
647C2—1722no—
648C2C4×#1306330711yescharacteristic
649C2#1914342411yescharacteristic
650C2#1914345111yescharacteristic
651C2#1914455111yescharacteristic
652C2#1914458311yescharacteristic
653C2#1914479211yescharacteristic
654C2#1914487611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1762C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1762D43
hypocenterC43#21584
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1762

Complements

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

NH ≅ G/Ntype
3. #19136949C2semidirect
4. #19135225C2semidirect
5. #19135217C2semidirect
6. #19135179C2semidirect
7. #19135171C2semidirect
9. #19134797C2semidirect
10. #19134680C2semidirect
11. #19134492C2semidirect
12. C4×#13063256C2semidirect
13. C4×#13063246C2semidirect
14. #19134364C2semidirect
15. C43×#1762C2semidirect
20. #14583216C4semidirect
80. C4⋊C4×D43C2×C4semidirect
95. #13063257C2×C4semidirect
97. #13063256C2×C4semidirect
101. (C2×D43)⋊C8C2×C4semidirect
331. #1762D43semidirect
387. C43#21584semidirect

Maximal subgroups

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

subgroupindex
C2×#145832162
#191372822
#191369492
#191352252
#191352172
#191351792
#191351712
#191349142
#191347972
#191346802
#191344922
C4×#130632562
C4×#130632462
#191343642
C43×#17622
#2158443