Finite Group Databasebeta

← #25115358

Subgroups — #25115358

Order 11008.

906 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582974C211yesmaximal, characteristic
2#19137526C211yesmaximal, characteristic
3#19137525C211yesmaximal, characteristic
4#19135366C211yesmaximal, characteristic, complemented
5#19135364C211yesmaximal, characteristic, complemented
6#19134797C211yesmaximal, characteristic, complemented
7#19134785C211yesmaximal, characteristic, complemented
8#19134781C211yesmaximal, characteristic, complemented
9#19134724C211yesmaximal, characteristic, complemented
10#19134626C211yesmaximal, characteristic, complemented
11#19134625C211yesmaximal, characteristic, complemented
12#107×Dic43C211yesmaximal, characteristic, complemented
13#19134316C211yesmaximal, characteristic, complemented
14#19134313C211yesmaximal, characteristic, complemented
15C43×#1854C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C2×C4×C22⋊D43C2211yescharacteristic
19C2×#13063283C2211yescharacteristic
20C22×C4⋊Dic43C2211yescharacteristic
21C2×C4⋊C4×D43C2211yescharacteristic
22#14582974C418yescomplemented
23C2×#13063259C2211yescharacteristic
24C2×#13063259C2211yescharacteristic
25C2×#13063258C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×Dic43⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×C8×Dic43C2211yescharacteristic
30#14582793—21no—
31#14582791—21no—
32#14582786—21no—
33#14582783—21no—
34#14582776—21no—
35#14582775—21no—
36#14582764C2211yescharacteristic
37#14582764C2211yescharacteristic
38#14582759C2211yescharacteristic
39#14582756C2211yescharacteristic
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4⋊C4×Dic43C2211yescharacteristic
43C22⋊C4×Dic43—21no—
44C4×(C2×D43)⋊C4—21no—
45#14582662C2211yescharacteristic
46#14582662C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582661C2211yescharacteristic
53C2×#117×C43C2211yescharacteristic
54C2×#107×C43C2211yescharacteristic
55C2×#106×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C43×#380C2211yescharacteristic
58C43×#340C2211yescharacteristic
59C43×#340C2211yescharacteristic
60C22×C22⋊D43D411yescharacteristic
61C23×Dic43—21no—
62C22×C4×D43—21no—
63C22×C4×D43C2311yescharacteristic
64C2×#10621877—41no—
65C2×#10621877—41no—
66C2×#10621877C2×C414yescomplemented
67C2×#10621872—41no—
68C2×#10621872—41no—
69C2×#10621872C2×C414yescomplemented
70C22×C43⋊C8C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C4×C22⋊D43C2×C414yes—
73C4×C22⋊D43Q814yes—
74#13063283—22no—
75#13063283—41no—
76C2×C4⋊Dic43—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—41no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×C4⋊Dic43C2311yescharacteristic
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4D411yescharacteristic
85C4⋊C4×D43—22no—
86C4⋊C4×D43—41no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43D411yescharacteristic
89C2×(C2×D43)⋊C4—21no—
90C2×(C2×D43)⋊C4—21no—
91C2×(C2×D43)⋊C4—21no—
92C2×(C2×D43)⋊C4D411yescharacteristic
93C2×C4×Dic43—21no—
94C2×C4×Dic43—21no—
95C2×C4×Dic43—21no—
96C2×C4×Dic43C2311yescharacteristic
97#13063259—22no—
98#13063259—41no—
99#13063258—41no—
100#13063256—41no—
101Dic43⋊C8C2×C414yescomplemented
102(C2×D43)⋊C8C2×C414yescomplemented
103C8×Dic43C2×C414yescomplemented
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95—21no—
111C43⋊#95—21no—
112C43⋊#95—21no—
113C23×C4×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C22×C8×C43C2311yescharacteristic
116#117×C43—22no—
117#117×C43—41no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C22⋊C4×C43—21no—
123C2×C22⋊C4×C43—21no—
124C2×C42×C43—21no—
125#107×C43—22no—
126#106×C43—41no—
127C22⋊C8×C43C2×C414yescomplemented
128#95×C43—21no—
129C24×C43C2×D411yescharacteristic
130C23×D43C2×D411yescharacteristic
131C22×C4×C43—21no—
132C22×C4×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43C22×C412yes—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×Q812yes—
142C22×C4×C43C2411yescharacteristic
143C2×C22⋊D43—41no—
144C2×C22⋊D43—41no—
145C2×C22⋊D43C4⋊C414yes—
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—42no—
151C22×Dic43—42no—
152C22×Dic43—81no—
153C22×Dic43C2×D411yescharacteristic
154C22×Dic43C2×D411yescharacteristic
155C22×Dic43C2×D411yescharacteristic
156C2×C4×D43—21no—
157C2×C4×D43—21no—
158C2×C4×D43—21no—
159C2×C4×D43—21no—
160C2×C4×D43—42no—
161C2×C4×D43—42no—
162C2×C4×D43—81no—
163C2×C4×D43C22×C412yes—
164C2×C4×D43C2×Q812yes—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43—21no—
169C2×C8×C43C22×C412yes—
170C2×C8×C43C22×C412yes—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—21no—
177C4⋊C4×C43—21no—
178C4⋊C4×C43#4112yes—
179C22⋊C4×C43—42no—
180C22⋊C4×C43—42no—
181C42×C43—42no—
182C22⋊Dic43—81no—
183C22⋊Dic43C4⋊C414yes—
184(C2×D43)⋊C4—42no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4C4⋊C414yes—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—42no—
196C4⋊Dic43#4112yes—
197Dic43⋊C4—42no—
198Dic43⋊C4C4⋊C414yes—
199C4×Dic43—42no—
200C4×Dic43—81no—
201C4×Dic43—81no—
202C4×Dic43C22×C412yes—
203C4×Dic43C2×Q812yes—
204#10621877—44no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8C22×C412yes—
210C2×C43⋊C8C22×C412yes—
211#10621872—44no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43—21no—
218C23×C43C2×C4⋊C412yes—
219C23×C43C22×D411yescharacteristic
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225C22×D43—21no—
226C22×D43C2×C4⋊C412yes—
227C2×C4×C43—21no—
228C2×C4×C43—21no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—22no—
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—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43C2×C4⋊C412yes—
246C2×C4×C43C23×C411yescharacteristic
247C2×C4×C43C22×Q811yescharacteristic
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43H(5,𝔽2)11yescharacteristic
251C2×C4×C43H(5,𝔽2)11yescharacteristic
252C22⋊D43—44no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—22no—
260C2×Dic43—41no—
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×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—84no—
272C2×Dic43C2×C4⋊C412yes—
273C2×Dic43C2×C4⋊C412yes—
274C2×Dic43C2×C4⋊C412yes—
275C4×D43—22no—
276C4×D43—22no—
277C4×D43—22no—
278C4×D43—22no—
279C4×D43—84no—
280C8×C43—22no—
281C8×C43—22no—
282C43⋊C8—22no—
283C43⋊C8—22no—
284#22716—431nomaximal, Sylow
285C22×C43—22no—
286C22×C43—22no—
287C22×C43—22no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43C22×C4⋊C411yescharacteristic
293C22×C43#54611yescharacteristic
294C22×C43#54611yescharacteristic
295C22×C43#57511yescharacteristic
296C22×C43#57511yescharacteristic
297C22×C43#57611yescharacteristic
298C22×C43#57811yescharacteristic
299C2×D43—22no—
300C2×D43—22no—
301C2×D43—22no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C4×C43—22no—
307C4×C43—42no—
308C4×C43—81no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43C4×#4111yescharacteristic
312C4×C43#51811yescharacteristic
313C4×C43#55411yescharacteristic
314C4×C43#55411yescharacteristic
315Dic43—22no—
316Dic43—22no—
317Dic43—22no—
318Dic43—42no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322C2×#436—431no—
323#2352—431no—
324#2352—431no—
325#1949—431no—
326#1949—431no—
327#1854—431no—
328#1854D4311yescharacteristic, complemented
329#1852—431no—
330#1852—431no—
331#1835—431no—
332#1809—431no—
333#1809—431no—
334C4×#107—431no—
335#1736—431no—
336#1736—431no—
337C2×C43—42no—
338C2×C43#234911yescharacteristic
339C2×C43#291111yescharacteristic
340C2×C43#291311yescharacteristic
341C2×C43#332211yescharacteristic
342C2×C43#332211yescharacteristic
343C2×C43#332711yescharacteristic
344C2×C43#332711yescharacteristic
345D43—42no—
346C22×M16—431no—
347C22×M16—431no—
348C2×C4×D4—431no—
349C2×#117—431no—
350C2×#117C2×D4311yescharacteristic
351C22×C4⋊C4—431no—
352C22×C4⋊C4—431no—
353#436—438no—
354C2×#107—431no—
355C2×#107—431no—
356C2×#107—431no—
357C2×#107C2×D4311yescharacteristic
358C2×#106—431no—
359C2×#106C2×D4311yescharacteristic
360C2×C4⋊C8—431no—
361C2×C22⋊C8—431no—
362C2×C22⋊C8C2×D4311yescharacteristic
363C2×C4×C8—431no—
364#388—861no—
365#388—861no—
366#387—861no—
367#387—861no—
368#386—861no—
369#386—861no—
370#382—431no—
371#382—431no—
372#380—431no—
373#380—431no—
374#380—431no—
375#380C2×D4311yescharacteristic
376C4×C4⋊C4—431no—
377C4×C4⋊C4—431no—
378C4×C22⋊C4—861no—
379C4×C22⋊C4—861no—
380#340—431no—
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#340—431no—
388#340C2×D4311yescharacteristic
389#340C2×D4311yescharacteristic
390C43#2271611yescharacteristic, complemented, Sylow
391C22×D4—431no—
392C23×C4—431no—
393C23×C4—861no—
394C23×C4—861no—
395C23×C4C22×D4311yescharacteristic
396C2×M16—434no—
397C2×M16—434no—
398C2×M16—1721no—
399C2×M16—1721no—
400C2×M16—1721no—
401C2×M16—1721no—
402C22×C8—431no—
403C22×C8—431no—
404C22×C8C22×D4311yescharacteristic
405C22×C8C22×D4311yescharacteristic
406C4×D4—434no—
407C4×D4—434no—
408#117—22no—
409#117—41no—
410#117—862no—
411#117—1721no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—431no—
416C2×C4⋊C4—431no—
417C2×C4⋊C4—862no—
418C2×C4⋊C4—862no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4—861no—
421C2×C4⋊C4—1721no—
422C2×C4⋊C4—1721no—
423C2×C4⋊C4C22×D4311yescharacteristic
424C2×C4⋊C4C22×D4311yescharacteristic
425C2×C4⋊C4C22×D4311yescharacteristic
426C2×C4⋊C4C22×D4311yescharacteristic
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—431no—
430C2×C22⋊C4—431no—
431C2×C22⋊C4—861no—
432C2×C22⋊C4—861no—
433C2×C22⋊C4—861no—
434C2×C22⋊C4—861no—
435C2×C42—21no—
436C2×C42—431no—
437C2×C42—861no—
438C2×C42—861no—
439C2×C42—861no—
440#107—22no—
441#107—862no—
442#107—1721no—
443#107—1721no—
444#106—41no—
445#106—1721no—
446C4⋊C8—434no—
447C22⋊C8—434no—
448C22⋊C8C4×D4314yescomplemented
449C4×C8—434no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457#95—861no—
458#95—861no—
459#95—861no—
460C24—431no—
461C24D4×D4311yescharacteristic
462C2×D4—434no—
463C2×D4—1721no—
464C2×D4—1721no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—431no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—432no—
477C22×C4—432no—
478C22×C4—861no—
479C22×C4—861no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—3441no—
487C22×C4—3441no—
488C22×C4—1722no—
489C22×C4—1722no—
490C22×C4—1722no—
491C22×C4—1722no—
492C22×C4C2×C4×D4312yes—
493C22×C4D4×D4311yescharacteristic
494C22×C4Q8×D4312yes—
495C22×C4C23×D4311yescharacteristic
496M16—1724no—
497M16—1724no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—432no—
503C2×C8—432no—
504C2×C8—861no—
505C2×C8—861no—
506C2×C8—861no—
507C2×C8—861no—
508C2×C8C2×C4×D4312yes—
509C2×C8C2×C4×D4312yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—434no—
518C4⋊C4—432no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—861no—
523C4⋊C4—861no—
524C4⋊C4—861no—
525C4⋊C4—861no—
526C4⋊C4—1722no—
527C4⋊C4—1722no—
528C4⋊C4#1062190012yes—
529C22⋊C4—42no—
530C22⋊C4—42no—
531C22⋊C4—434no—
532C22⋊C4—434no—
533C22⋊C4—3441no—
534C22⋊C4—3441no—
535C22⋊C4—1722no—
536C22⋊C4—1722no—
537C42—42no—
538C42—432no—
539C42—432no—
540C42—3441no—
541C42—3441no—
542C42—1722no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—432no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23—861no—
556C23C4⋊C4×D4312yes—
557C23C2×D4×D4311yescharacteristic
558D4—1724no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
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—861no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—862no—
587C2×C4—862no—
588C2×C4—862no—
589C2×C4—862no—
590C2×C4—862no—
591C2×C4—3444no—
592C2×C4—3444no—
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×C4—1721no—
602C2×C4—1721no—
603C2×C4—1721no—
604C2×C4C4⋊C4×D4312yes—
605C2×C4C22×C4×D4311yescharacteristic
606C2×C4C2×Q8×D4311yescharacteristic
607C2×C4#41×D4311yescharacteristic
608C2×C4C2×#1062190011yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337111yescharacteristic
611C8—22no—
612C8—22no—
613C8—862no—
614C8—862no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—862no—
623C22—862no—
624C22—862no—
625C22—1721no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22C2×C4⋊C4×D4311yescharacteristic
630C22#1458353611yescharacteristic
631C22#1458354111yescharacteristic
632C22#1458369511yescharacteristic
633C22#1458369811yescharacteristic
634C22#1458370111yescharacteristic
635C22#1458371311yescharacteristic
636C4—22no—
637C4—42no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4—862no—
642C4—862no—
643C4—862no—
644C4—3441no—
645C4—3441no—
646C4—3441no—
647C4—1722no—
648C4C4×#1062190011yescharacteristic
649C4#1458337111yescharacteristic
650C4#1458360311yescharacteristic
651C4#1458360711yescharacteristic
652C2—42no—
653C2—1722no—
654C2#1913750111yescharacteristic
655C2#1914318211yescharacteristic
656C2#1914319211yescharacteristic
657C2#1914678911yescharacteristic
658C2#1914679411yescharacteristic
659C2#1914685611yescharacteristic
660C2#1914686111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1854C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
cosocleC22×C4×C43C24
hypercenter#1854D43
hypocenterC43#22716
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #19135366C2semidirect
5. #19135364C2semidirect
6. #19134797C2semidirect
7. #19134785C2semidirect
8. #19134781C2semidirect
9. #19134724C2semidirect
10. #19134626C2semidirect
11. #19134625C2semidirect
12. #107×Dic43C2semidirect
13. #19134316C2semidirect
14. #19134313C2semidirect
15. C43×#1854C2semidirect
22. #14582974C4semidirect
66. C2×#10621877C2×C4semidirect
69. C2×#10621872C2×C4semidirect
101. Dic43⋊C8C2×C4semidirect
102. (C2×D43)⋊C8C2×C4semidirect
103. C8×Dic43C2×C4semidirect
127. C22⋊C8×C43C2×C4semidirect
328. #1854D43semidirect
390. C43#22716semidirect
448. C22⋊C8C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145829742
#191375262
#191375252
#191353662
#191353642
#191347972
#191347852
#191347812
#191347242
#191346262
#191346252
#107×Dic432
#191343162
#191343132
C43×#18542
#2271643