Finite Group Databasebeta

← #25107175

Subgroups — #25107175

Order 11008.

786 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582955C211yesmaximal, characteristic
2#19137001C211yesmaximal, characteristic
3#19136991C211yesmaximal, characteristic
4#19135365C211yesmaximal, characteristic, complemented
5#19135363C211yesmaximal, characteristic, complemented
6#19135361C211yesmaximal, characteristic, complemented
7#19134797C211yesmaximal, characteristic
8#19134795C211yesmaximal, characteristic
9#19134793C211yesmaximal, characteristic
10#19134791C211yesmaximal, characteristic
11#19134762C211yesmaximal, characteristic, complemented
12#19134760C211yesmaximal, characteristic, complemented
13#19134727C211yesmaximal, characteristic, complemented
14#19134727C211yesmaximal, characteristic, complemented
15C43×#1949C211yesmaximal, characteristic, complemented
16C2×#13063283C2211yescharacteristic
17C2×#13063283C2211yescharacteristic
18C2×C42×D43C2211yescharacteristic
19#14582955C418yescomplemented
20C2×#13063259C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×#13063256C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×#13063235C2211yescharacteristic
31#14582768C2211yescharacteristic
32#14582768C2211yescharacteristic
33#14582766—21no—
34#14582765C2211yescharacteristic
35#14582764C2211yescharacteristic
36#14582764C2211yescharacteristic
37#14582761—21no—
38#14582758—21no—
39#14582758—21no—
40#14582756C2211yescharacteristic
41#14582756C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582750—21no—
44#14582750—21no—
45C4×(C2×D43)⋊C4—21no—
46#14582745—21no—
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×C4⋊C8×C43C2211yescharacteristic
56C43×#382C2211yescharacteristic
57C4×C4⋊C4×C43C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C4×D43D411yescharacteristic
61C22×C4×D43D411yescharacteristic
62C22×C4×D43C2311yescharacteristic
63C22×C43⋊C8C2311yescharacteristic
64C22×C43⋊C8C2311yescharacteristic
65#13063283—41no—
66#13063283—41no—
67#13063283—41no—
68#13063283—41no—
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⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87C42×D43C2×C414yes—
88C42×D43Q814yes—
89#13063259—41no—
90#13063258—41no—
91#13063258—41no—
92#13063257—41no—
93#13063256—41no—
94#13063256—41no—
95C4⋊(C43⋊C8)C2×C414yes—
96(C2×D43)⋊C8C2×C414yes—
97(C2×D43)⋊C8C2×C414yes—
98#13063235C2×C414yes—
99#13063235C2×C414yes—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C4⋊C4×C43C2311yescharacteristic
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C42×C43—21no—
116C2×C42×C43C2311yescharacteristic
117#107×C43—41no—
118#106×C43—41no—
119C4⋊C8×C43C2×C414yes—
120#95×C43—21no—
121#95×C43—21no—
122#95×C43—21no—
123C23×D43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2411yescharacteristic
131C22×Dic43—21no—
132C22×Dic43—21no—
133C22×Dic43—21no—
134C22×Dic43—21no—
135C22×Dic43C2×D411yescharacteristic
136C22×Dic43C2×D411yescharacteristic
137C22×Dic43C2×D411yescharacteristic
138C2×C4×D43—21no—
139C2×C4×D43—21no—
140C2×C4×D43—21no—
141C2×C4×D43—21no—
142C2×C4×D43—41no—
143C2×C4×D43—41no—
144C2×C4×D43—41no—
145C2×C4×D43—41no—
146C2×C4×D43C4⋊C414yes—
147C2×C4×D43C4⋊C414yes—
148C2×C4×D43C22×C412yes—
149C2×C4×D43C2×Q812yes—
150C2×C8×C43—21no—
151C2×C8×C43—21no—
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43C22×C412yes—
155C2×C8×C43C22×C412yes—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—21no—
162C4⋊C4×C43—21no—
163C4⋊C4×C43—21no—
164C42×C43—42no—
165C42×C43C22×C412yes—
166C42×C43C2×Q812yes—
167(C2×D43)⋊C4—42no—
168(C2×D43)⋊C4—42no—
169(C2×D43)⋊C4—42no—
170(C2×D43)⋊C4—42no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—21no—
177C4⋊Dic43—21no—
178C4⋊Dic43—21no—
179Dic43⋊C4—42no—
180Dic43⋊C4—42no—
181Dic43⋊C4—42no—
182Dic43⋊C4—42no—
183C4×Dic43—42no—
184C4×Dic43—42no—
185C4×Dic43—42no—
186C4×Dic43C4⋊C414yes—
187C4×Dic43C4⋊C414yes—
188C4×Dic43C22×C412yes—
189C4×Dic43C2×Q812yes—
190C2×C43⋊C8—21no—
191C2×C43⋊C8—21no—
192C2×C43⋊C8—21no—
193C2×C43⋊C8—21no—
194C2×C43⋊C8C22×C412yes—
195C2×C43⋊C8C22×C412yes—
196C23×C43C22×D411yescharacteristic
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—21no—
203C22×D43C2×C4⋊C412yes—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—41no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—41no—
213C2×C4×C43—41no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43C2×C4⋊C412yes—
221C2×C4×C43C2×C4⋊C412yes—
222C2×C4×C43C23×C411yescharacteristic
223C2×C4×C43C22×Q811yescharacteristic
224C2×C4×C43H(5,𝔽2)11yescharacteristic
225C2×C4×C43H(5,𝔽2)11yescharacteristic
226C2×C4×C432−1+411yescharacteristic
227C2×C4×C432−1+411yescharacteristic
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43C2×C4⋊C412yes—
247C2×Dic43C2×C4⋊C412yes—
248C2×Dic43C2×C4⋊C412yes—
249C4×D43—22no—
250C4×D43—22no—
251C4×D43—22no—
252C4×D43—22no—
253C4×D43—44no—
254C4×D43—44no—
255C8×C43—22no—
256C8×C43—22no—
257C43⋊C8—22no—
258C43⋊C8—22no—
259#21989—431nomaximal, Sylow
260C22×C43C22×C4⋊C411yescharacteristic
261C22×C43#53511yescharacteristic
262C22×C43#53611yescharacteristic
263C22×C43#57511yescharacteristic
264C22×C43#57511yescharacteristic
265C22×C43#57511yescharacteristic
266C22×C43#57511yescharacteristic
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C4×C43—22no—
275C4×C43—22no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43—81no—
279C4×C43—81no—
280C4×C43#52011yescharacteristic
281C4×C43#52011yescharacteristic
282C4×C43#54411yescharacteristic
283C4×C43#54411yescharacteristic
284Dic43—22no—
285Dic43—22no—
286Dic43—22no—
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290Dic43—81no—
291C2×#432—431no—
292#2285—431no—
293#2283—431no—
294#1949—431no—
295#1949—431no—
296#1949—431no—
297#1949D4311yescharacteristic, complemented
298#1854—431no—
299#1854—431no—
300#1854—431no—
301#1854—431no—
302#1847—431no—
303#1847—431no—
304#1836—431no—
305#1836—431no—
306C2×C43#231711yescharacteristic
307C2×C43#291111yescharacteristic
308C2×C43#291111yescharacteristic
309C2×C43#321911yescharacteristic
310C2×C43#321911yescharacteristic
311C2×C43#324011yescharacteristic
312C2×C43#324011yescharacteristic
313D43—42no—
314C2×#117—431no—
315C2×#117—431no—
316C22×C42—431no—
317#432—438no—
318C2×#107—431no—
319C2×#107—431no—
320C2×#107—431no—
321C2×#107C2×D4311yescharacteristic
322C2×#106—431no—
323C2×#106—431no—
324C2×#106—431no—
325C2×#106C2×D4311yescharacteristic
326C2×C4⋊C8—431no—
327C2×C4⋊C8C2×D4311yescharacteristic
328C2×C22⋊C8—431no—
329C2×C22⋊C8—431no—
330C2×#97—431no—
331C2×#97—431no—
332#384—431no—
333#384—431no—
334#383—861no—
335#382—431no—
336#382—431no—
337#382—431no—
338#382C2×D4311yescharacteristic
339#381—861no—
340#380—431no—
341#380—431no—
342#380—861no—
343#380—861no—
344C4×C4⋊C4—431no—
345C4×C4⋊C4—861no—
346C4×C4⋊C4—861no—
347C4×C4⋊C4C2×D4311yescharacteristic
348C4×C22⋊C4—861no—
349#376—861no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340—431no—
356#340C2×D4311yescharacteristic
357#340C2×D4311yescharacteristic
358C43#2198911yescharacteristic, complemented, Sylow
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—431no—
362C22×C8—431no—
363C22×C8—431no—
364C22×C8C22×D4311yescharacteristic
365C22×C8C22×D4311yescharacteristic
366#117—1721no—
367#117—1721no—
368#117—1721no—
369#117—1721no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C4⋊C4C22×D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C22⋊C4—861no—
383C2×C22⋊C4—861no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C42—21no—
387C2×C42—431no—
388C2×C42—431no—
389C2×C42—431no—
390C2×C42—434no—
391C2×C42—434no—
392C2×C42—861no—
393C2×C42—861no—
394C2×C42—861no—
395C2×C42C22×D4311yescharacteristic
396#107—41no—
397#107—1721no—
398#107—1721no—
399#107—1721no—
400#106—41no—
401#106—1721no—
402#106—1721no—
403#106—1721no—
404C4⋊C8—434no—
405C4⋊C8C4×D4314yes—
406C22⋊C8—434no—
407C22⋊C8—434no—
408#97—434no—
409#97—434no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421#95—861no—
422C24—431no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—432no—
431C22×C4—432no—
432C22×C4—434no—
433C22×C4—434no—
434C22×C4—861no—
435C22×C4—861no—
436C22×C4—861no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4—861no—
442C22×C4—1721no—
443C22×C4—1721no—
444C22×C4—1721no—
445C22×C4—1721no—
446C22×C4D4×D4311yescharacteristic
447C22×C4D4×D4311yescharacteristic
448C22×C4C23×D4311yescharacteristic
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—432no—
454C2×C8—432no—
455C2×C8—861no—
456C2×C8—861no—
457C2×C8—861no—
458C2×C8—861no—
459C2×C8C2×C4×D4312yes—
460C2×C8C2×C4×D4312yes—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—1722no—
478C4⋊C4—1722no—
479C4⋊C4—1722no—
480C4⋊C4—1722no—
481C22⋊C4—1722no—
482C22⋊C4—1722no—
483C22⋊C4—1722no—
484C22⋊C4—1722no—
485C42—42no—
486C42—434no—
487C42—434no—
488C42—432no—
489C42—432no—
490C42—1722no—
491C42—1722no—
492C42—1722no—
493C42C2×C4×D4312yes—
494C42Q8×D4312yes—
495C23—432no—
496C23—861no—
497C23—861no—
498C23—861no—
499C23—861no—
500C23—861no—
501C23—861no—
502C23C2×D4×D4311yescharacteristic
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—432no—
520C2×C4—432no—
521C2×C4—432no—
522C2×C4—861no—
523C2×C4—861no—
524C2×C4—861no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—1724no—
533C2×C4—1724no—
534C2×C4—1721no—
535C2×C4—1721no—
536C2×C4—1721no—
537C2×C4—1721no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4—1721no—
544C2×C4—1721no—
545C2×C4—1721no—
546C2×C4C4⋊C4×D4312yes—
547C2×C4C4⋊C4×D4312yes—
548C2×C4C22×C4×D4311yescharacteristic
549C2×C4C2×Q8×D4311yescharacteristic
550C2×C4#1306337011yescharacteristic
551C2×C4#1306337111yescharacteristic
552C2×C4#1306337211yescharacteristic
553C2×C4#1306337311yescharacteristic
554C8—22no—
555C8—22no—
556C8—862no—
557C8—862no—
558C22—862no—
559C22—862no—
560C22—862no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22—1721no—
565C22C2×C4⋊C4×D4311yescharacteristic
566C22#1458346511yescharacteristic
567C22#1458347211yescharacteristic
568C22#1458369511yescharacteristic
569C22#1458369611yescharacteristic
570C22#1458369611yescharacteristic
571C22#1458369811yescharacteristic
572C4—22no—
573C4—22no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—862no—
579C4—862no—
580C4—862no—
581C4—3441no—
582C4—3441no—
583C4—3441no—
584C4—3441no—
585C4#1458337811yescharacteristic
586C4#1458338111yescharacteristic
587C4#1458352611yescharacteristic
588C4#1458352911yescharacteristic
589C2—1722no—
590C2#1913721711yescharacteristic
591C2#1914318211yescharacteristic
592C2#1914318311yescharacteristic
593C2#1914563111yescharacteristic
594C2#1914563711yescharacteristic
595C2#1914583411yescharacteristic
596C2#1914584011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1949C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1949D43
hypocenterC43#21989
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #19135365C2semidirect
5. #19135363C2semidirect
6. #19135361C2semidirect
11. #19134762C2semidirect
12. #19134760C2semidirect
13. #19134727C2semidirect
14. #19134727C2semidirect
15. C43×#1949C2semidirect
19. #14582955C4semidirect
297. #1949D43semidirect
358. C43#21989semidirect

Maximal subgroups

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

subgroupindex
C2×#145829552
#191370012
#191369912
#191353652
#191353632
#191353612
#191347972
#191347952
#191347932
#191347912
#191347622
#191347602
#191347272
C43×#19492
#2198943