Finite Group Databasebeta

← #25200321

Subgroups — #25200321

Order 11008.

742 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
1#19140384C211yesmaximal, characteristic
2#19136032C211yesmaximal, characteristic, complemented
3#19135795C211yesmaximal, characteristic, complemented
4#19135777C211yesmaximal, characteristic
5#19135596C211yesmaximal, characteristic
6#19135452C211yesmaximal, characteristic, complemented
7#19135325C211yesmaximal, characteristic, complemented
8#19135291C211yesmaximal, characteristic, complemented
9#19135288C211yesmaximal, characteristic, complemented
10#19135215C211yesmaximal, characteristic, complemented
11#19135173C211yesmaximal, characteristic, complemented
12#19134950C211yesmaximal, characteristic, complemented
13#19134849C211yesmaximal, characteristic, complemented
14#19134361C211yesmaximal, characteristic, complemented
15C43×#2323C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063299C2211yescharacteristic
18C2×#13063258C2211yescharacteristic
19C2×#13063258C2211yescharacteristic
20C2×#13063256C2211yescharacteristic
21C2×#13063249C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063245C2211yescharacteristic
25C2×#13063245C2211yescharacteristic
26C2×#13063245C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063236C2211yescharacteristic
30C2×C4×C43⋊C8C2211yescharacteristic
31#14582834—21no—
32#14582825—21no—
33#14582814—21no—
34#14582814—21no—
35#14582801C2211yescharacteristic
36#14582801C2211yescharacteristic
37#14582797C2211yescharacteristic
38#14582797C2211yescharacteristic
39#14582759C2211yescharacteristic
40#14582661C2211yescharacteristic
41#14582661C2211yescharacteristic
42#14582661C2211yescharacteristic
43#14582661C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48C2×C22⋊Q8×C43C2211yescharacteristic
49C2×C4×Q8×C43C2211yescharacteristic
50C2×#117×C43C2211yescharacteristic
51C43×#391C2211yescharacteristic
52C43×#389—21no—
53C43×#389C2211yescharacteristic
54C43×#388—21no—
55C43×#388—21no—
56C43×#387—21no—
57C43×#380C2211yescharacteristic
58C4×C4⋊C4×C43C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C22⋊D43—21no—
61C2×#10621884—22no—
62C2×#10621884—22no—
63C2×#10621884—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66C22×C43⋊C8C2311yescharacteristic
67C22×C43⋊C8C2311yescharacteristic
68#13063299—41no—
69#13063299—41no—
70C2×C4⋊Dic43C2311yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×C22⋊Dic43—21no—
76C2×(C2×D43)⋊C4—21no—
77C2×(C2×D43)⋊C4—21no—
78C2×(C2×D43)⋊C4—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81#13063258—22no—
82#13063258—41no—
83#13063256—22no—
84#13063249—22no—
85#13063249—22no—
86#13063249—41no—
87#13063245—22no—
88#13063245—22no—
89#13063245—41no—
90C22⋊(C43⋊C8)—22no—
91C22⋊(C43⋊C8)—22no—
92#13063236—41no—
93C4×C43⋊C8—41no—
94C43⋊#95—21no—
95C43⋊#95—21no—
96C43⋊#95—21no—
97C22×Q8×C43C2311yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C22⋊Q8×C43—22no—
100C22⋊Q8×C43—22no—
101C4×Q8×C43—41no—
102C4×Q8×C43—41no—
103#117×C43—41no—
104#117×C43—41no—
105C2×C4⋊C4×C43—21no—
106C2×C4⋊C4×C43—21no—
107C2×C4⋊C4×C43—21no—
108C2×C4⋊C4×C43D411yescharacteristic
109C2×C4⋊C4×C43D411yescharacteristic
110C2×C4⋊C4×C43C2311yescharacteristic
111C2×C4⋊C4×C43C2311yescharacteristic
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C22⋊C4×C43—21no—
114C2×C22⋊C4×C43—21no—
115C2×C22⋊C4×C43D411yescharacteristic
116C2×C22⋊C4×C43D411yescharacteristic
117C2×C42×C43—21no—
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120C2×C42×C43C2311yescharacteristic
121#95×C43—21no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43C2×D411yescharacteristic
127C23×D43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43#4112yes—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43—21no—
138C22×C4×C43—21no—
139C22×C4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2×D411yescharacteristic
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D411yescharacteristic
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2411yescharacteristic
150C2×C22⋊D43—42no—
151C2×C22⋊D43—81no—
152C2×C22⋊D43—81no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172—21no—
159C2×D172—21no—
160C2×D172—21no—
161C2×D172—21no—
162C4⋊C4×C43—24no—
163C4⋊C4×C43—21no—
164C4⋊C4×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—41no—
169C4⋊C4×C43—41no—
170C4⋊C4×C43—42no—
171C4⋊C4×C43—81no—
172C4⋊C4×C43#4112yes—
173C22⋊C4×C43—24no—
174C22⋊C4×C43—41no—
175C22⋊C4×C43—41no—
176C22⋊C4×C43—81no—
177C42×C43—21no—
178C42×C43—21no—
179C42×C43—21no—
180C42×C43—21no—
181C42×C43—42no—
182C42×C43—81no—
183C22⋊Dic43—81no—
184#10621884—44no—
185(C2×D43)⋊C4—42no—
186(C2×D43)⋊C4—81no—
187(C2×D43)⋊C4—81no—
188(C2×D43)⋊C4—81no—
189(C2×D43)⋊C4—81no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—21no—
193C4⋊Dic43—21no—
194C4⋊Dic43—21no—
195C4⋊Dic43—21no—
196Dic43⋊C4—81no—
197Dic43⋊C4—81no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8#4112yes—
209C2×C43⋊C8#4112yes—
210C23×C43—21no—
211C23×C43—21no—
212C23×C43—21no—
213C23×C43—21no—
214C23×C43—21no—
215C23×C43—21no—
216C23×C43—21no—
217C23×C43C22×D411yescharacteristic
218C22×D43—41no—
219C22×D43—41no—
220C22×D43—41no—
221C22×D43—41no—
222C22×D43—41no—
223C22×D43—41no—
224C22×D43—41no—
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43—41no—
228Q8×C43—41no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—21no—
232C2×C4×C43—21no—
233C2×C4×C43—21no—
234C2×C4×C43—21no—
235C2×C4×C43—21no—
236C2×C4×C43—21no—
237C2×C4×C43—21no—
238C2×C4×C43—21no—
239C2×C4×C43—21no—
240C2×C4×C43—21no—
241C2×C4×C43—21no—
242C2×C4×C43—21no—
243C2×C4×C43—21no—
244C2×C4×C43—21no—
245C2×C4×C43—21no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43—41no—
249C2×C4×C43—41no—
250C2×C4×C43—41no—
251C2×C4×C43—41no—
252C2×C4×C43—41no—
253C2×C4×C43—41no—
254C2×C4×C43—41no—
255C2×C4×C43—41no—
256C2×C4×C43—41no—
257C2×C4×C43—41no—
258C2×C4×C43—41no—
259C2×C4×C43—41no—
260C2×C4×C43C2×#4111yescharacteristic
261C2×C4×C43C2×#4111yescharacteristic
262C2×C4×C43C2×#4111yescharacteristic
263C2×C4×C43C2×#4111yescharacteristic
264C2×C4×C43H(5,𝔽2)11yescharacteristic
265C2×C4×C43H(5,𝔽2)11yescharacteristic
266C22⋊D43—84no—
267C2×Dic43—41no—
268C2×Dic43—41no—
269C2×Dic43—41no—
270C2×Dic43—41no—
271C2×Dic43—41no—
272C2×Dic43—41no—
273C2×Dic43—41no—
274C2×Dic43—41no—
275C2×Dic43—41no—
276D172—41no—
277D172—41no—
278D172—41no—
279D172—41no—
280C43⋊C8—22no—
281C43⋊C8—22no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#29475—431nomaximal, Sylow
285C22×C43—41no—
286C22×C43—41no—
287C22×C43—41no—
288C22×C43—41no—
289C22×C43—41no—
290C22×C43—41no—
291C22×C43—41no—
292C22×C43#52511yescharacteristic
293C22×C43#53211yescharacteristic
294C22×C43#53411yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57711yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57811yescharacteristic
299C2×D43—81no—
300C2×D43—81no—
301C2×D43—81no—
302C2×D43—81no—
303C2×D43—81no—
304C2×D43—81no—
305C2×D43—81no—
306C4×C43—41no—
307C4×C43—42no—
308C4×C43—42no—
309C4×C43—41no—
310C4×C43—41no—
311C4×C43—41no—
312C4×C43—41no—
313C4×C43—81no—
314C4×C43—81no—
315C4×C43#55111yescharacteristic
316C4×C43#55311yescharacteristic
317C4×C43#55311yescharacteristic
318C4×C43#55911yescharacteristic
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322#2624—431no—
323#2323D4311yescharacteristic, complemented
324#2077—431no—
325#2036—431no—
326#2033—431no—
327#2000—431no—
328#1968—431no—
329#1942—431no—
330#1936—431no—
331#1935—431no—
332#1925—431no—
333#1919—431no—
334#1880—431no—
335#1863—431no—
336#1750—431no—
337C2×C43—81no—
338C2×C43#260211yescharacteristic
339C2×C43#311911yescharacteristic
340C2×C43#312111yescharacteristic
341C2×C43#317411yescharacteristic
342C2×C43#317511yescharacteristic
343C2×C43#319811yescharacteristic
344C2×C43#320111yescharacteristic
345D43—161no—
346C22×SD16—431no—
347C2×C22⋊Q8C2×D4311yescharacteristic
348C2×#121—431no—
349C2×C4×Q8C2×D4311yescharacteristic
350C2×#117C2×D4311yescharacteristic
351C2×#107—431no—
352C2×#107—431no—
353C2×#106—431no—
354C2×#103—431no—
355C2×#103—431no—
356C2×#103—431no—
357C2×#102—431no—
358C2×#102—431no—
359C2×#102—431no—
360C2×C22⋊C8—431no—
361C2×C22⋊C8—431no—
362C2×#97—431no—
363C2×C4×C8—431no—
364#399—861no—
365#397—861no—
366#394—861no—
367#394—861no—
368#391C2×D4311yescharacteristic
369#390—431no—
370#390—431no—
371#389—21no—
372#389—431no—
373#389—431no—
374#389C2×D4311yescharacteristic
375#388—21no—
376#388—21no—
377#387—21no—
378#380—431no—
379#380C2×D4311yescharacteristic
380C4×C4⋊C4C2×D4311yescharacteristic
381#340—431no—
382#340—431no—
383#340—431no—
384#340—431no—
385#340—431no—
386#340—431no—
387#336—431no—
388#336—431no—
389C43#2947511yescharacteristic, complemented, Sylow
390C22×Q8C22×D4311yescharacteristic
391C22×D4—431no—
392C22×D4—861no—
393C23×C4C22×D4311yescharacteristic
394C2×SD16—862no—
395C2×SD16—862no—
396C2×SD16—1721no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8—431no—
400C22×C8—431no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403#121—1721no—
404#121—1721no—
405C4×Q8—41no—
406C4×Q8—41no—
407#117—41no—
408#117—41no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4C22⋊D4311yescharacteristic
418C2×C4⋊C4C22⋊D4311yescharacteristic
419C2×C4⋊C4C22×D4311yescharacteristic
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—861no—
425C2×C22⋊C4—861no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4C22⋊D4311yescharacteristic
431C2×C22⋊C4C22⋊D4311yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C22×D4311yescharacteristic
435C2×C42C22×D4311yescharacteristic
436#107—862no—
437#107—1721no—
438#106—862no—
439#103—862no—
440#103—862no—
441#103—1721no—
442#102—862no—
443#102—862no—
444#102—1721no—
445C22⋊C8—862no—
446C22⋊C8—862no—
447#97—1721no—
448C4×C8—1721no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—861no—
455#95—861no—
456#95—861no—
457C24—861no—
458C24C2×C22⋊D4311yescharacteristic
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8#1062189812yes—
465C2×D4—861no—
466C2×D4—861no—
467C2×D4—861no—
468C2×D4—861no—
469C2×D4—861no—
470C2×D4—861no—
471C2×D4—3441no—
472C2×D4—3441no—
473C2×D4—1722no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4C2×C22⋊D4311yescharacteristic
488C22×C4C2×C22⋊D4311yescharacteristic
489C22×C4C2×C22⋊D4311yescharacteristic
490C22×C4C2×C22⋊D4311yescharacteristic
491C22×C4C2×C22⋊D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493SD16—1724no—
494C2×C8—432no—
495C2×C8—432no—
496C2×C8—861no—
497C2×C8—861no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8—861no—
505C2×C8—861no—
506C4⋊C4—24no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—42no—
515C4⋊C4—81no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—861no—
520C4⋊C4—861no—
521C4⋊C4—861no—
522C4⋊C4—3441no—
523C4⋊C4—3441no—
524C4⋊C4#1062189812yes—
525C22⋊C4—24no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C22⋊C4—81no—
529C22⋊C4—3441no—
530C22⋊C4—3441no—
531C22⋊C4—3441no—
532C22⋊C4—3441no—
533C22⋊C4—3441no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—42no—
540C42—81no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—1721no—
549C23—1721no—
550C23—1721no—
551C23—1721no—
552C23—1721no—
553C23—1721no—
554C23—1721no—
555C23C22×C22⋊D4311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560D4—3444no—
561D4—1721no—
562D4—1721no—
563D4—1721no—
564D4—1721no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
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×C4—1721no—
605C2×C4#41×D4311yescharacteristic
606C2×C4#41×D4311yescharacteristic
607C2×C4C2×#1062189811yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337011yescharacteristic
611C8—862no—
612C8—862no—
613C8—1721no—
614C8—1721no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—3441no—
623C22—3441no—
624C22—3441no—
625C22—3441no—
626C22—3441no—
627C22—3441no—
628C22—3441no—
629C22#1458341011yescharacteristic
630C22#1458344511yescharacteristic
631C22#1458345811yescharacteristic
632C22#1458370211yescharacteristic
633C22#1458370711yescharacteristic
634C22#1458370711yescharacteristic
635C22#1458371411yescharacteristic
636C4—41no—
637C4—41no—
638C4—42no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—41no—
643C4—81no—
644C4—81no—
645C4—3441no—
646C4—3441no—
647C4—3441no—
648C4#1458357811yescharacteristic
649C4#1458359811yescharacteristic
650C4#1458359911yescharacteristic
651C4#1458363211yescharacteristic
652C2—81no—
653C2—6881no—
654C2#1914020711yescharacteristic
655C2#1914479411yescharacteristic
656C2#1914482411yescharacteristic
657C2#1914522411yescharacteristic
658C2#1914522811yescharacteristic
659C2#1914544111yescharacteristic
660C2#1914547711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2323C2
socleC23×C43C22×D4
prime radicalC2×#13063299C22
hypercenter#2323D43
hypocenterC43#29475
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
2. #19136032C2semidirect
3. #19135795C2semidirect
6. #19135452C2semidirect
7. #19135325C2semidirect
8. #19135291C2semidirect
9. #19135288C2semidirect
10. #19135215C2semidirect
11. #19135173C2semidirect
12. #19134950C2semidirect
13. #19134849C2semidirect
14. #19134361C2semidirect
15. C43×#2323C2semidirect
323. #2323D43semidirect
389. C43#29475semidirect

Maximal subgroups

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

subgroupindex
#191403842
#191360322
#191357952
#191357772
#191355962
#191354522
#191353252
#191352912
#191352882
#191352152
#191351732
#191349502
#191348492
#191343612
C43×#23232
#2947543