Finite Group Databasebeta

← #25107201

Subgroups — #25107201

Order 11008.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582957C211yesmaximal, characteristic
2#19137219C211yesmaximal, characteristic
3#19137202C211yesmaximal, characteristic
4#19135364C211yesmaximal, characteristic, complemented
5#19135362C211yesmaximal, characteristic, complemented
6#19135355C211yesmaximal, characteristic, complemented
7#19135352C211yesmaximal, characteristic, complemented
8#19134796C211yesmaximal, characteristic
9#19134792C211yesmaximal, characteristic
10#19134783C211yesmaximal, characteristic
11#19134760C211yesmaximal, characteristic, complemented
12#19134756C211yesmaximal, characteristic, complemented
13#19134727C211yesmaximal, characteristic, complemented
14#19134721C211yesmaximal, characteristic, complemented
15C43×#1853C211yesmaximal, characteristic
16C2×#13063284C2211yescharacteristic
17C2×#13063284C2211yescharacteristic
18#14582957C418yescomplemented
19C2×#13063259C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×#13063258C2211yescharacteristic
22C2×#13063258C2211yescharacteristic
23C2×#13063257C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×Dic43⋊C8C2211yescharacteristic
26C2×Dic43⋊C8C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×#13063235C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582795—21no—
31#14582795—21no—
32#14582793—21no—
33#14582787—21no—
34#14582784—21no—
35#14582782—21no—
36#14582772—21no—
37#14582772—21no—
38#14582768C2211yescharacteristic
39#14582768C2211yescharacteristic
40#14582768C2211yescharacteristic
41#14582764C2211yescharacteristic
42#14582764C2211yescharacteristic
43#14582764C2211yescharacteristic
44#14582759C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4⋊C4×Dic43C2211yescharacteristic
47#14582662C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C2×#106×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C43⋊C8C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62#13063284—41no—
63#13063284—41no—
64#13063284C2×C414yes—
65#13063284Q814yes—
66C2×C4⋊Dic43D411yescharacteristic
67C2×C4⋊Dic43D411yescharacteristic
68C2×C4⋊Dic43C2311yescharacteristic
69C2×C4⋊Dic43C2311yescharacteristic
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×C22⋊Dic43—21no—
79C2×C22⋊Dic43—21no—
80C2×C22⋊Dic43D411yescharacteristic
81C2×C22⋊Dic43D411yescharacteristic
82C2×C4×Dic43—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—21no—
85C2×C4×Dic43C2311yescharacteristic
86C2×C4×Dic43C2311yescharacteristic
87#13063259—41no—
88#13063258—41no—
89#13063258—41no—
90#13063258—41no—
91#13063257—41no—
92#13063256—41no—
93Dic43⋊C8C2×C414yescomplemented
94Dic43⋊C8C2×C414yescomplemented
95C22⋊(C43⋊C8)C2×C414yes—
96#13063235C2×C414yescomplemented
97C8×Dic43C2×C414yescomplemented
98C43⋊#95—21no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C23×C4×C43—21no—
108C23×C4×C43C2311yescharacteristic
109C22×C8×C43C2311yescharacteristic
110C22×C8×C43C2311yescharacteristic
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43—41no—
113C2×C4⋊C4×C43—41no—
114C2×C4⋊C4×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C22⋊C4×C43—21no—
119#106×C43—41no—
120#106×C43—41no—
121C22⋊C8×C43C2×C414yes—
122#95×C43—21no—
123C24×C43C2×D411yescharacteristic
124C22×C4×C43—21no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—42no—
133C22×C4×C43—81no—
134C22×C4×C43—81no—
135C22×C4×C43C22×C412yes—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×Q812yes—
138C22×C4×C43C2411yescharacteristic
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43C2×D411yescharacteristic
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C8×C43—21no—
148C2×C8×C43—21no—
149C2×C8×C43—21no—
150C2×C8×C43—21no—
151C2×C8×C43C22×C412yes—
152C2×C8×C43C22×C412yes—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—21no—
157C4⋊C4×C43—21no—
158C4⋊C4×C43—21no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—21no—
161C4⋊C4×C43—42no—
162C22⋊C4×C43—81no—
163C22⋊Dic43—42no—
164C22⋊Dic43—81no—
165C22⋊Dic43C4⋊C414yes—
166C22⋊Dic43C4⋊C414yes—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—21no—
170C4⋊Dic43—21no—
171C4⋊Dic43—21no—
172C4⋊Dic43—21no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43C4⋊C414yes—
176C4⋊Dic43C4⋊C414yes—
177Dic43⋊C4—81no—
178Dic43⋊C4—81no—
179Dic43⋊C4—81no—
180Dic43⋊C4—81no—
181Dic43⋊C4—81no—
182Dic43⋊C4—81no—
183C4×Dic43—42no—
184C4×Dic43—81no—
185C4×Dic43—81no—
186C4×Dic43C22×C412yes—
187C4×Dic43C22×C412yes—
188C4×Dic43C2×Q812yes—
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×C43—21no—
197C23×C43—21no—
198C23×C43—21no—
199C23×C43—21no—
200C23×C43—21no—
201C23×C43—21no—
202C23×C43C2×C4⋊C412yes—
203C23×C43C22×D411yescharacteristic
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—22no—
207C2×C4×C43—22no—
208C2×C4×C43—22no—
209C2×C4×C43—22no—
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×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—84no—
223C2×C4×C43C2×C4⋊C412yes—
224C2×C4×C43C23×C411yescharacteristic
225C2×C4×C43C22×Q811yescharacteristic
226C2×C4×C43H(5,𝔽2)11yescharacteristic
227C2×C4×C43H(5,𝔽2)11yescharacteristic
228C2×C4×C432−1+411yescharacteristic
229C2×C4×C432−1+411yescharacteristic
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
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×Dic43—41no—
247C2×Dic43—41no—
248C2×Dic43—41no—
249C2×Dic43—41no—
250C2×Dic43C2×C4⋊C412yes—
251C2×Dic43C2×C4⋊C412yes—
252C2×Dic43C2×C4⋊C412yes—
253C2×Dic43C2×C4⋊C412yes—
254C8×C43—22no—
255C8×C43—22no—
256C43⋊C8—22no—
257C43⋊C8—22no—
258#21992—431nomaximal, Sylow
259C22×C43—22no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—41no—
263C22×C43—41no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C22×C4⋊C411yescharacteristic
267C22×C43#53511yescharacteristic
268C22×C43#53611yescharacteristic
269C22×C43#57611yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57711yescharacteristic
272C22×C43#57811yescharacteristic
273C4×C43—22no—
274C4×C43—81no—
275C4×C43—81no—
276C4×C43—81no—
277C4×C43—81no—
278C4×C43#52011yescharacteristic
279C4×C43#52011yescharacteristic
280C4×C43#54411yescharacteristic
281C4×C43#54411yescharacteristic
282Dic43—22no—
283Dic43—22no—
284Dic43—22no—
285Dic43—22no—
286Dic43—81no—
287Dic43—81no—
288Dic43—81no—
289Dic43—81no—
290C2×#433—431no—
291#2317—431no—
292#2314—431no—
293#1949—431no—
294#1949—431no—
295#1948—431no—
296#1947—431no—
297#1854—431no—
298#1854—431no—
299#1853D4311yescharacteristic
300#1852—431no—
301#1847—431no—
302#1846—431no—
303#1836—431no—
304#1834—431no—
305C2×C43—42no—
306C2×C43#231711yescharacteristic
307C2×C43#291211yescharacteristic
308C2×C43#291311yescharacteristic
309C2×C43#322411yescharacteristic
310C2×C43#322511yescharacteristic
311C2×C43#324111yescharacteristic
312C2×C43#324211yescharacteristic
313C2×#117—431no—
314C2×#117—431no—
315C22×C4⋊C4C2×D4311yescharacteristic
316#433—438no—
317C2×#107—431no—
318C2×#107—431no—
319C2×#107—431no—
320C2×#107—431no—
321C2×#106—431no—
322C2×#106—431no—
323C2×#106C2×D4311yescharacteristic
324C2×#106C2×D4311yescharacteristic
325C2×C4⋊C8—431no—
326C2×C4⋊C8—431no—
327C2×C22⋊C8—431no—
328C2×C22⋊C8C2×D4311yescharacteristic
329C2×#97—431no—
330C2×C4×C8—431no—
331#389—861no—
332#389—861no—
333#388—861no—
334#388—861no—
335#387—861no—
336#387—861no—
337#385—861no—
338#385—861no—
339#384—431no—
340#384—431no—
341#384—431no—
342#382—431no—
343#382—431no—
344#382—431no—
345#380—431no—
346#380C2×D4311yescharacteristic
347C4×C4⋊C4—431no—
348C4×C4⋊C4—431no—
349#340—431no—
350#340—431no—
351#340—431no—
352#340—431no—
353#340—431no—
354#340—431no—
355#340C2×D4311yescharacteristic
356#340C2×D4311yescharacteristic
357C43#2199211yescharacteristic, complemented, Sylow
358C23×C4—21no—
359C23×C4C22×D4311yescharacteristic
360C22×C8—431no—
361C22×C8—431no—
362C22×C8C22×D4311yescharacteristic
363C22×C8C22×D4311yescharacteristic
364#117—434no—
365#117—434no—
366#117—1721no—
367#117—1721no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4—41no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4—861no—
381C2×C4⋊C4—861no—
382C2×C4⋊C4—861no—
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C4⋊C4C22×D4311yescharacteristic
385C2×C4⋊C4C22×D4311yescharacteristic
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C22⋊C4—21no—
388C2×C22⋊C4—431no—
389C2×C22⋊C4—431no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42—861no—
395C2×C42—861no—
396C2×C42—861no—
397#107—1721no—
398#107—1721no—
399#107—1721no—
400#107—1721no—
401#106—41no—
402#106—41no—
403#106—1721no—
404#106—1721no—
405C4⋊C8—434no—
406C4⋊C8—434no—
407C22⋊C8—434no—
408C22⋊C8C4×D4314yes—
409#97—434no—
410C4×C8—434no—
411#95—21no—
412#95—861no—
413#95—861no—
414#95—861no—
415#95—861no—
416#95—861no—
417#95—861no—
418#95—861no—
419#95—861no—
420#95—861no—
421C24D4×D4311yescharacteristic
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—81no—
432C22×C4—81no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—861no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—861no—
441C22×C4C2×C4×D4312yes—
442C22×C4D4×D4311yescharacteristic
443C22×C4Q8×D4312yes—
444C22×C4C23×D4311yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—432no—
450C2×C8—432no—
451C2×C8—861no—
452C2×C8—861no—
453C2×C8—861no—
454C2×C8—861no—
455C2×C8C2×C4×D4312yes—
456C2×C8C2×C4×D4312yes—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—42no—
466C4⋊C4—434no—
467C4⋊C4—434no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—861no—
472C4⋊C4—861no—
473C4⋊C4—861no—
474C4⋊C4—861no—
475C4⋊C4—861no—
476C4⋊C4—3441no—
477C4⋊C4—3441no—
478C4⋊C4—3441no—
479C4⋊C4—3441no—
480C4⋊C4—3441no—
481C4⋊C4—3441no—
482C22⋊C4—81no—
483C22⋊C4—434no—
484C22⋊C4—434no—
485C22⋊C4—3441no—
486C22⋊C4—1722no—
487C42—432no—
488C42—432no—
489C42—432no—
490C42—432no—
491C42—3441no—
492C42—3441no—
493C42—1722no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23C4⋊C4×D4312yes—
501C23C2×D4×D4311yescharacteristic
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
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—41no—
520C2×C4—84no—
521C2×C4—432no—
522C2×C4—432no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—861no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—1721no—
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×C4C4⋊C4×D4312yes—
546C2×C4C22×C4×D4311yescharacteristic
547C2×C4C2×Q8×D4311yescharacteristic
548C2×C4#1306337011yescharacteristic
549C2×C4#1306337011yescharacteristic
550C2×C4#1306337211yescharacteristic
551C2×C4#1306337211yescharacteristic
552C8—22no—
553C8—22no—
554C8—862no—
555C8—862no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22C2×C4⋊C4×D4311yescharacteristic
564C22#1458346411yescharacteristic
565C22#1458347111yescharacteristic
566C22#1458370311yescharacteristic
567C22#1458370511yescharacteristic
568C22#1458370511yescharacteristic
569C22#1458371511yescharacteristic
570C4—22no—
571C4—81no—
572C4—81no—
573C4—81no—
574C4—81no—
575C4—862no—
576C4—862no—
577C4—862no—
578C4—862no—
579C4—3441no—
580C4—3441no—
581C4—3441no—
582C4—3441no—
583C4#1458337811yescharacteristic
584C4#1458337811yescharacteristic
585C4#1458352811yescharacteristic
586C4#1458352811yescharacteristic
587C2—42no—
588C2#1913721411yescharacteristic
589C2#1914318611yescharacteristic
590C2#1914319411yescharacteristic
591C2#1914569311yescharacteristic
592C2#1914570211yescharacteristic
593C2#1914585211yescharacteristic
594C2#1914585911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1853C2
socleC23×C43C22×D4
prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenter#1853D43
hypocenterC43#21992
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1853

Complements

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

NH ≅ G/Ntype
4. #19135364C2semidirect
5. #19135362C2semidirect
6. #19135355C2semidirect
7. #19135352C2semidirect
11. #19134760C2semidirect
12. #19134756C2semidirect
13. #19134727C2semidirect
14. #19134721C2semidirect
18. #14582957C4semidirect
93. Dic43⋊C8C2×C4semidirect
94. Dic43⋊C8C2×C4semidirect
96. #13063235C2×C4semidirect
97. C8×Dic43C2×C4semidirect
357. C43#21992semidirect

Maximal subgroups

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

subgroupindex
C2×#145829572
#191372192
#191372022
#191353642
#191353622
#191353552
#191353522
#191347962
#191347922
#191347832
#191347602
#191347562
#191347272
#191347212
C43×#18532
#2199243