Finite Group Databasebeta

← #25200318

Subgroups — #25200318

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#19140387C211yesmaximal, characteristic
2#19137280C211yesmaximal, characteristic, complemented
3#19136029C211yesmaximal, characteristic, complemented
4#19135797C211yesmaximal, characteristic, complemented
5#19135776C211yesmaximal, characteristic
6#19135595C211yesmaximal, characteristic
7#19135328C211yesmaximal, characteristic, complemented
8#19135295C211yesmaximal, characteristic, complemented
9#19135288C211yesmaximal, characteristic, complemented
10#19135217C211yesmaximal, characteristic, complemented
11#19135175C211yesmaximal, characteristic, complemented
12#19134952C211yesmaximal, characteristic, complemented
13#19134851C211yesmaximal, characteristic, complemented
14#19134362C211yesmaximal, characteristic, complemented
15C43×#1968C211yesmaximal, characteristic, complemented
16C2×#13063301C2211yescharacteristic
17C2×#13063296C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×#13063282C2211yescharacteristic
20C2×#13063259C2211yescharacteristic
21C2×#13063259C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063246C2211yescharacteristic
25C2×#13063246C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×#13063236C2211yescharacteristic
29#14582835—21no—
30#14582827—21no—
31#14582815—21no—
32#14582814—21no—
33#14582802C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582797C2211yescharacteristic
36#14582797C2211yescharacteristic
37#14582796—21no—
38#14582791—21no—
39#14582788—21no—
40#14582781—21no—
41#14582756C2211yescharacteristic
42#14582756C2211yescharacteristic
43C4⋊C4×Dic43C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×SD16×C43C2211yescharacteristic
53C2×#106×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#102×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#390C2211yescharacteristic
59C22×C22⋊D43—21no—
60C22×C4×D43C2311yescharacteristic
61C22×C43⋊C8C2311yescharacteristic
62C22×C43⋊C8C2311yescharacteristic
63#13063301—22no—
64#13063301—22no—
65#13063296—41no—
66#13063296—41no—
67Q8×Dic43—41no—
68Q8×Dic43—41no—
69#13063282—41no—
70#13063282—41no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4D411yescharacteristic
81C2×Dic43⋊C4D411yescharacteristic
82C2×C22⋊Dic43—21no—
83C2×C22⋊Dic43—21no—
84C2×C22⋊Dic43—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92C2×C4×Dic43C2311yescharacteristic
93#13063259—22no—
94#13063259—41no—
95#13063249—22no—
96#13063249—41no—
97#13063246—22no—
98#13063246—41no—
99(C2×D43)⋊C8—22no—
100(C2×D43)⋊C8—22no—
101#13063236—41no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C22×Q8×C43C2311yescharacteristic
109C22×D4×C43C2311yescharacteristic
110C2×SD16×C43—22no—
111C2×SD16×C43—22no—
112C2×SD16×C43—41no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C22⋊C4×C43—21no—
118C2×C22⋊C4×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#106×C43—22no—
121#103×C43—22no—
122#102×C43—22no—
123C4×C8×C43—41no—
124#95×C43—21no—
125#95×C43—21no—
126C24×C43—21no—
127C23×D43C2×D411yescharacteristic
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43#4112yes—
134C2×D4×C43—21no—
135C2×D4×C43—21no—
136C2×D4×C43—21no—
137C2×D4×C43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—21no—
140C22×C4×C43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2×D411yescharacteristic
145C22×C4×C43C2411yescharacteristic
146C2×C22⋊D43—42no—
147C2×C22⋊D43—81no—
148C2×C22⋊D43—81no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
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—21no—
161C2×C4×D43—21no—
162SD16×C43—44no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43#4112yes—
168C2×C8×C43#4112yes—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C22⋊C4×C43—81no—
174C22⋊C4×C43—81no—
175C42×C43—21no—
176C42×C43—21no—
177C22⋊Dic43—42no—
178C22⋊Dic43—81no—
179C22⋊Dic43—81no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—41no—
182(C2×D43)⋊C4—41no—
183(C2×D43)⋊C4—81no—
184(C2×D43)⋊C4—81no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—21no—
189C4⋊Dic43—21no—
190C4⋊Dic43—21no—
191C4⋊Dic43—21no—
192C4⋊Dic43—42no—
193C4⋊Dic43—81no—
194C4⋊Dic43#4112yes—
195Dic43⋊C4—24no—
196Dic43⋊C4—41no—
197Dic43⋊C4—41no—
198Dic43⋊C4—81no—
199Dic43⋊C4—81no—
200C4×Dic43—21no—
201C4×Dic43—21no—
202C4×Dic43—42no—
203C4×Dic43—81no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C2×C43⋊C8—21no—
207C2×C43⋊C8—21no—
208C2×C43⋊C8—21no—
209C2×C43⋊C8—21no—
210C23×C43—41no—
211C23×C43—41no—
212C23×C43—41no—
213C23×C43—41no—
214C23×C43—41no—
215C23×C43—41no—
216C23×C43—41no—
217C23×C43C22×D411yescharacteristic
218C22×D43—21no—
219C22×D43—21no—
220C22×D43—21no—
221C22×D43—21no—
222C22×D43—21no—
223C22×D43—21no—
224C22×D43—21no—
225Q8×C43—22no—
226Q8×C43—22no—
227Q8×C43—41no—
228Q8×C43—41no—
229D4×C43—41no—
230D4×C43—41no—
231D4×C43—41no—
232D4×C43—41no—
233C2×C4×C43—22no—
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—41no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43—41no—
244C2×C4×C43—41no—
245C2×C4×C43—41no—
246C2×C4×C43—41no—
247C2×C4×C43—41no—
248C2×C4×C43C2×#4111yescharacteristic
249C2×C4×C43C2×#4111yescharacteristic
250C2×C4×C43C2×#4111yescharacteristic
251C2×C4×C43C2×#4111yescharacteristic
252C2×C4×C43H(5,𝔽2)11yescharacteristic
253C2×C4×C43H(5,𝔽2)11yescharacteristic
254C22⋊D43—84no—
255C2×Dic43—21no—
256C2×Dic43—22no—
257C2×Dic43—21no—
258C2×Dic43—21no—
259C2×Dic43—21no—
260C2×Dic43—21no—
261C2×Dic43—21no—
262C2×Dic43—21no—
263C2×Dic43—21no—
264C2×Dic43—21no—
265C2×Dic43—41no—
266C2×Dic43—41no—
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—
276C4×D43—41no—
277C4×D43—41no—
278C4×D43—41no—
279C4×D43—41no—
280C8×C43—22no—
281C8×C43—22no—
282C43⋊C8—41no—
283C43⋊C8—41no—
284#29475—431nomaximal, Sylow
285C22×C43—81no—
286C22×C43—81no—
287C22×C43—81no—
288C22×C43—81no—
289C22×C43—81no—
290C22×C43—81no—
291C22×C43—81no—
292C22×C43#52511yescharacteristic
293C22×C43#53211yescharacteristic
294C22×C43#53411yescharacteristic
295C22×C43#57611yescharacteristic
296C22×C43#57711yescharacteristic
297C22×C43#57711yescharacteristic
298C22×C43#57811yescharacteristic
299C2×D43—41no—
300C2×D43—41no—
301C2×D43—41no—
302C2×D43—41no—
303C2×D43—41no—
304C2×D43—41no—
305C2×D43—41no—
306C4×C43—42no—
307C4×C43—41no—
308C4×C43—41no—
309C4×C43—81no—
310C4×C43—81no—
311C4×C43#55111yescharacteristic
312C4×C43#55311yescharacteristic
313C4×C43#55311yescharacteristic
314C4×C43#55911yescharacteristic
315Dic43—41no—
316Dic43—42no—
317Dic43—41no—
318Dic43—41no—
319Dic43—81no—
320Dic43—81no—
321Dic43—81no—
322#2624—431no—
323#2323—431no—
324#2077—431no—
325#2036—431no—
326#2033—431no—
327#2000—431no—
328#1968D4311yescharacteristic, complemented
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—161no—
338C2×C43#260211yescharacteristic
339C2×C43#311911yescharacteristic
340C2×C43#312111yescharacteristic
341C2×C43#317411yescharacteristic
342C2×C43#317511yescharacteristic
343C2×C43#319811yescharacteristic
344C2×C43#320111yescharacteristic
345D43—81no—
346C22×SD16C2×D4311yescharacteristic
347C2×C22⋊Q8—431no—
348C2×#121—431no—
349C2×C4×Q8—431no—
350C2×#117—431no—
351C2×#107—431no—
352C2×#107—431no—
353C2×#106C2×D4311yescharacteristic
354C2×#103—431no—
355C2×#103—431no—
356C2×#103C2×D4311yescharacteristic
357C2×#102—431no—
358C2×#102—431no—
359C2×#102C2×D4311yescharacteristic
360C2×C22⋊C8—431no—
361C2×C22⋊C8—431no—
362C2×#97—431no—
363C2×C4×C8C2×D4311yescharacteristic
364#399—861no—
365#397—861no—
366#394—861no—
367#394—861no—
368#391C2×D4311yescharacteristic
369#390—431no—
370#390C2×D4311yescharacteristic
371#389—431no—
372#389—431no—
373#389—431no—
374#389—861no—
375#388—861no—
376#388—861no—
377#387—861no—
378#380—431no—
379#380—431no—
380C4×C4⋊C4—431no—
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—861no—
392C22×D4C22×D4311yescharacteristic
393C23×C4—431no—
394C2×SD16—22no—
395C2×SD16—22no—
396C2×SD16—41no—
397C22×C8—431no—
398C22×C8—431no—
399C22×C8C22×D4311yescharacteristic
400C22×C8C22×D4311yescharacteristic
401C22⋊Q8—862no—
402C22⋊Q8—862no—
403#121—1721no—
404#121—1721no—
405C4×Q8—1721no—
406C4×Q8—1721no—
407#117—1721no—
408#117—1721no—
409C2×C4⋊C4—431no—
410C2×C4⋊C4—431no—
411C2×C4⋊C4—431no—
412C2×C4⋊C4—431no—
413C2×C4⋊C4—431no—
414C2×C4⋊C4—431no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—861no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4—861no—
419C2×C4⋊C4—861no—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—431no—
425C2×C22⋊C4—431no—
426C2×C22⋊C4—861no—
427C2×C22⋊C4—861no—
428C2×C22⋊C4—861no—
429C2×C22⋊C4—861no—
430C2×C22⋊C4—861no—
431C2×C22⋊C4—861no—
432C2×C42—431no—
433C2×C42—861no—
434C2×C42—861no—
435C2×C42C22×D4311yescharacteristic
436#107—862no—
437#107—1721no—
438#106—22no—
439#103—22no—
440#103—862no—
441#103—1721no—
442#102—22no—
443#102—862no—
444#102—1721no—
445C22⋊C8—862no—
446C22⋊C8—862no—
447#97—1721no—
448C4×C8—41no—
449#95—21no—
450#95—21no—
451#95—861no—
452#95—861no—
453#95—861no—
454#95—861no—
455#95—861no—
456#95—861no—
457C24—21no—
458C24—431no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8#1062189812yes—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—3441no—
472C2×D4—3441no—
473C2×D4—1722no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—431no—
478C22×C4—431no—
479C22×C4—431no—
480C22×C4—861no—
481C22×C4—861no—
482C22×C4—861no—
483C22×C4—861no—
484C22×C4—861no—
485C22×C4—861no—
486C22×C4—861no—
487C22×C4—861no—
488C22×C4—861no—
489C22×C4—861no—
490C22×C4D4×D4311yescharacteristic
491C22×C4D4×D4311yescharacteristic
492C22×C4C23×D4311yescharacteristic
493SD16—44no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—861no—
499C2×C8—861no—
500C2×C8—861no—
501C2×C8—861no—
502C2×C8—861no—
503C2×C8—861no—
504C2×C8#1062190012yes—
505C2×C8#1062190012yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—432no—
511C4⋊C4—864no—
512C4⋊C4—861no—
513C4⋊C4—861no—
514C4⋊C4—861no—
515C4⋊C4—861no—
516C4⋊C4—861no—
517C4⋊C4—861no—
518C4⋊C4—861no—
519C4⋊C4—3441no—
520C4⋊C4—3441no—
521C4⋊C4—3441no—
522C4⋊C4—1721no—
523C4⋊C4—1721no—
524C4⋊C4—1722no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C22⋊C4—864no—
528C22⋊C4—3441no—
529C22⋊C4—3441no—
530C22⋊C4—3441no—
531C22⋊C4—3441no—
532C22⋊C4—1721no—
533C22⋊C4—1721no—
534C22⋊C4—1722no—
535C42—21no—
536C42—21no—
537C42—861no—
538C42—861no—
539C42—3441no—
540C42—1722no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—861no—
549C23—861no—
550C23—861no—
551C23—861no—
552C23—861no—
553C23—861no—
554C23—861no—
555C23C2×D4×D4311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—3444no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—862no—
581C2×C4—861no—
582C2×C4—861no—
583C2×C4—861no—
584C2×C4—861no—
585C2×C4—861no—
586C2×C4—861no—
587C2×C4—861no—
588C2×C4—861no—
589C2×C4—861no—
590C2×C4—1721no—
591C2×C4—1721no—
592C2×C4—1721no—
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×C4—1721no—
605C2×C4#41×D4311yescharacteristic
606C2×C4C2×#1062190011yescharacteristic
607C2×C4C2×#1062190011yescharacteristic
608C2×C4C2×#1062189811yescharacteristic
609C2×C4#1306337011yescharacteristic
610C2×C4#1306337111yescharacteristic
611C8—22no—
612C8—22no—
613C8—1721no—
614C8—1721no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—1721no—
623C22—1721no—
624C22—1721no—
625C22—1721no—
626C22—1721no—
627C22—1721no—
628C22—1721no—
629C22#1458340811yescharacteristic
630C22#1458344711yescharacteristic
631C22#1458345711yescharacteristic
632C22#1458370111yescharacteristic
633C22#1458370511yescharacteristic
634C22#1458370511yescharacteristic
635C22#1458371311yescharacteristic
636C4—42no—
637C4—41no—
638C4—41no—
639C4—81no—
640C4—81no—
641C4—3441no—
642C4—3441no—
643C4—3441no—
644C4—1722no—
645C4—1721no—
646C4—1721no—
647C4—1721no—
648C4#1458357511yescharacteristic
649C4#1458359211yescharacteristic
650C4#1458359511yescharacteristic
651C4#1458363111yescharacteristic
652C2—161no—
653C2—3441no—
654C2#1914020411yescharacteristic
655C2#1914480011yescharacteristic
656C2#1914482011yescharacteristic
657C2#1914522011yescharacteristic
658C2#1914523111yescharacteristic
659C2#1914545011yescharacteristic
660C2#1914547011yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1968C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
hypercenter#1968D43
hypocenterC43#29475
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1968

Complements

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

NH ≅ G/Ntype
2. #19137280C2semidirect
3. #19136029C2semidirect
4. #19135797C2semidirect
7. #19135328C2semidirect
8. #19135295C2semidirect
9. #19135288C2semidirect
10. #19135217C2semidirect
11. #19135175C2semidirect
12. #19134952C2semidirect
13. #19134851C2semidirect
14. #19134362C2semidirect
15. C43×#1968C2semidirect
328. #1968D43semidirect
389. C43#29475semidirect

Maximal subgroups

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

subgroupindex
#191403872
#191372802
#191360292
#191357972
#191357762
#191355952
#191353282
#191352952
#191352882
#191352172
#191351752
#191349522
#191348512
#191343622
C43×#19682
#2947543