Finite Group Databasebeta

← #25165068

Subgroups — #25165068

Order 11008.

720 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19138934C211yesmaximal, characteristic
2#19137624C211yesmaximal, characteristic
3#19135917C211yesmaximal, characteristic, complemented
4#19135800C211yesmaximal, characteristic
5#19135747C211yesmaximal, characteristic, complemented
6#19135604C211yesmaximal, characteristic
7#19135552C211yesmaximal, characteristic, complemented
8#19135287C211yesmaximal, characteristic, complemented
9#19135209C211yesmaximal, characteristic
10#19135189C211yesmaximal, characteristic, complemented
11#19134933C211yesmaximal, characteristic, complemented
12#19134904C211yesmaximal, characteristic
13#19134688C211yesmaximal, characteristic
14#19134424C211yesmaximal, characteristic, complemented
15C43×#1928C211yesmaximal, characteristic, complemented
16C22×#10621885C2211yescharacteristic
17C2×#13063317C2211yescharacteristic
18C2×#13063305C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×#13063290C2211yescharacteristic
21C2×#13063283C2211yescharacteristic
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×#13063250C2211yescharacteristic
24C2×#13063250C2211yescharacteristic
25C2×#13063249C2211yescharacteristic
26C2×#13063248C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30#14582840—21no—
31#14582828—21no—
32#14582806C2211yescharacteristic
33#14582805C2211yescharacteristic
34#14582798C2211yescharacteristic
35#14582791—21no—
36#14582790—21no—
37#14582788—21no—
38#14582784—21no—
39#14582763—21no—
40#14582756C2211yescharacteristic
41C4⋊C4×Dic43C2211yescharacteristic
42C4×C4⋊Dic43—21no—
43C4×(C2×D43)⋊C4C2211yescharacteristic
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#103×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C43×#391C2211yescharacteristic
56C4×C4⋊C4×C43C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×C4×D43C2311yescharacteristic
61C2×#10621885—22no—
62C2×#10621885—41no—
63C2×#10621885—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063317—22no—
67#13063317—41no—
68#13063305—22no—
69#13063305—22no—
70#13063301—22no—
71#13063301—41no—
72#13063290—22no—
73#13063290—41no—
74#13063283—22no—
75#13063283—41no—
76C2×C4⋊Dic43—21no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×Dic43⋊C4—21no—
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—21no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4—21no—
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×(C2×D43)⋊C4D411yescharacteristic
91C2×C4×Dic43—21no—
92C2×C4×Dic43—21no—
93C2×C4×Dic43—21no—
94C2×C4×Dic43C2311yescharacteristic
95C4⋊(C43⋊C8)—41no—
96#13063250—22no—
97#13063250—41no—
98#13063249—41no—
99#13063248—22no—
100(C2×D43)⋊C8—41no—
101(C2×D43)⋊C8—41no—
102#13063235—41no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95—21no—
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C22×Q8×C43C2311yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C4⋊C4×C43C2311yescharacteristic
118C2×C42×C43—21no—
119C2×C42×C43C2311yescharacteristic
120#107×C43—22no—
121#103×C43—22no—
122#103×C43—22no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43C2×D411yescharacteristic
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C22×C4×C43—21no—
134C22×C4×C43—21no—
135C22×C4×C43—21no—
136C22×C4×C43—21no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2411yescharacteristic
140C22×Dic43—21no—
141C22×Dic43—21no—
142C22×Dic43—21no—
143C22×Dic43—21no—
144C22×Dic43C2×D411yescharacteristic
145C22×Dic43C2×D411yescharacteristic
146C22×Dic43C2×D411yescharacteristic
147C2×C4×D43—21no—
148C2×C4×D43—21no—
149C2×C4×D43—21no—
150C2×C4×D43—21no—
151C2×C4×D43—21no—
152C2×C4×D43—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86#4112yes—
159C2×C8×C43—21no—
160C2×C8×C43—21no—
161C2×C8×C43—21no—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C4⋊C4×C43—21no—
166C4⋊C4×C43—21no—
167C4⋊C4×C43—21no—
168C4⋊C4×C43—21no—
169C4⋊C4×C43#4112yes—
170C4⋊C4×C43#4112yes—
171C42×C43—21no—
172C42×C43—21no—
173C42×C43—42no—
174#10621885—44no—
175(C2×D43)⋊C4—24no—
176(C2×D43)⋊C4—41no—
177(C2×D43)⋊C4—41no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—42no—
181C4⋊Dic43—24no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—21no—
187C4⋊Dic43—42no—
188C4⋊Dic43#4112yes—
189Dic43⋊C4—42no—
190Dic43⋊C4—42no—
191Dic43⋊C4—42no—
192Dic43⋊C4—42no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—42no—
196C4×Dic43—42no—
197C4×Dic43—42no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C23×C43C22×D411yescharacteristic
205C22×D43—21no—
206C22×D43—21no—
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—21no—
210C22×D43—21no—
211C22×D43—21no—
212Q8×C43—41no—
213Q8×C43—41no—
214Q8×C43—41no—
215Q8×C43—41no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—21no—
219C2×C4×C43—21no—
220C2×C4×C43—21no—
221C2×C4×C43—21no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—41no—
225C2×C4×C43—41no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—41no—
231C2×C4×C43—41no—
232C2×C4×C43—41no—
233C2×C4×C43—41no—
234C2×C4×C43C2×#4111yescharacteristic
235C2×C4×C43C2×#4111yescharacteristic
236C2×C4×C43C2×#4111yescharacteristic
237C2×C4×C43C2×#4111yescharacteristic
238C2×C4×C43H(5,𝔽2)11yescharacteristic
239C2×C4×C43H(5,𝔽2)11yescharacteristic
240C2×Dic43—21no—
241C2×Dic43—22no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—22no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257C2×Dic43—41no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C4×D43—41no—
262C4×D43—41no—
263C4×D43—41no—
264C4×D43—41no—
265Dic86—22no—
266Dic86—22no—
267Dic86—41no—
268Dic86—41no—
269C8×C43—41no—
270C8×C43—41no—
271C43⋊C8—41no—
272C43⋊C8—41no—
273#26749—431nomaximal, Sylow
274C22×C43#52511yescharacteristic
275C22×C43#54611yescharacteristic
276C22×C43#54611yescharacteristic
277C22×C43#57511yescharacteristic
278C22×C43#57511yescharacteristic
279C22×C43#57811yescharacteristic
280C22×C43#57811yescharacteristic
281C2×D43—41no—
282C2×D43—41no—
283C2×D43—41no—
284C2×D43—41no—
285C2×D43—41no—
286C2×D43—41no—
287C2×D43—41no—
288C4×C43—42no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—42no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43#52911yescharacteristic
295C4×C43#53811yescharacteristic
296C4×C43#55511yescharacteristic
297C4×C43#55911yescharacteristic
298Dic43—42no—
299Dic43—41no—
300Dic43—41no—
301Dic43—42no—
302Dic43—41no—
303Dic43—81no—
304Dic43—81no—
305#2489—431no—
306#2362—431no—
307#2056—431no—
308#2036—431no—
309#2026—431no—
310#2001—431no—
311#1989—431no—
312#1935—431no—
313#1928D4311yescharacteristic, complemented
314#1924—431no—
315#1921—431no—
316#1878—431no—
317#1873—431no—
318#1825—431no—
319#1763—431no—
320C2×C43#245911yescharacteristic
321C2×C43#311111yescharacteristic
322C2×C43#312711yescharacteristic
323C2×C43#331311yescharacteristic
324C2×C43#331511yescharacteristic
325C2×C43#331511yescharacteristic
326C2×C43#332711yescharacteristic
327D43—81no—
328C22×Q16—431no—
329C2×#125—431no—
330C2×C22⋊Q8—431no—
331C2×C22⋊Q8—431no—
332C2×C4×Q8—431no—
333C2×#117—431no—
334C2×#107C2×D4311yescharacteristic
335C2×C4⋊C8—431no—
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103C2×D4311yescharacteristic
341C2×#103C2×D4311yescharacteristic
342C2×C22⋊C8—431no—
343C2×C22⋊C8—431no—
344C2×#97—431no—
345#400—861no—
346#397—861no—
347#391—431no—
348#391—431no—
349#391C2×D4311yescharacteristic
350#389—431no—
351#388—861no—
352#388—861no—
353#388—861no—
354#387—861no—
355#382—861no—
356#380—431no—
357C4×C4⋊C4—431no—
358C4×C4⋊C4—861no—
359C4×C4⋊C4C2×D4311yescharacteristic
360C4×C22⋊C4—431no—
361#340—431no—
362#340—431no—
363#340—431no—
364#340—431no—
365#340—431no—
366#340—431no—
367#340—431no—
368#340C2×D4311yescharacteristic
369#336—431no—
370#336C2×D4311yescharacteristic
371C43#2674911yescharacteristic, complemented, Sylow
372C22×Q8—431no—
373C22×Q8C22×D4311yescharacteristic
374C23×C4—431no—
375C2×Q16—862no—
376C2×Q16—1721no—
377C2×Q16—1721no—
378C22×C8—431no—
379C22×C8—431no—
380C22×C8C22×D4311yescharacteristic
381C22×C8C22×D4311yescharacteristic
382#125—862no—
383#125—1721no—
384C22⋊Q8—862no—
385C22⋊Q8—862no—
386C22⋊Q8—862no—
387C22⋊Q8—1721no—
388C4×Q8—862no—
389C4×Q8—1721no—
390#117—862no—
391#117—1721no—
392C2×C4⋊C4—431no—
393C2×C4⋊C4—431no—
394C2×C4⋊C4—431no—
395C2×C4⋊C4—861no—
396C2×C4⋊C4—861no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—431no—
405C2×C22⋊C4—431no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C42—21no—
411C2×C42—431no—
412C2×C42—861no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42C22×D4311yescharacteristic
416#107—22no—
417C4⋊C8—1721no—
418#103—22no—
419#103—22no—
420#103—862no—
421#103—862no—
422#103—1721no—
423#103—1721no—
424C22⋊C8—1721no—
425C22⋊C8—1721no—
426#97—1721no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—431no—
431#95—431no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439C24—431no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—432no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—431no—
457C22×C4—431no—
458C22×C4—431no—
459C22×C4—861no—
460C22×C4—861no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4D4×D4311yescharacteristic
470C22×C4D4×D4311yescharacteristic
471C22×C4C23×D4311yescharacteristic
472Q16—1724no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—861no—
480C2×C8—861no—
481C2×C8—861no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—432no—
490C4⋊C4—864no—
491C4⋊C4—861no—
492C4⋊C4—861no—
493C4⋊C4—861no—
494C4⋊C4—861no—
495C4⋊C4—861no—
496C4⋊C4—1722no—
497C4⋊C4—1722no—
498C4⋊C4—1722no—
499C4⋊C4—1722no—
500C4⋊C4—1722no—
501C4⋊C4#1062189812yes—
502C4⋊C4#1062190012yes—
503C22⋊C4—864no—
504C22⋊C4—1721no—
505C22⋊C4—1721no—
506C22⋊C4—1722no—
507C22⋊C4—1722no—
508C22⋊C4—1722no—
509C42—21no—
510C42—21no—
511C42—42no—
512C42—861no—
513C42—861no—
514C42—1722no—
515C42—1722no—
516C42—1722no—
517C23—861no—
518C23—861no—
519C23—861no—
520C23—861no—
521C23—861no—
522C23—861no—
523C23—861no—
524C23C2×D4×D4311yescharacteristic
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—862no—
530Q8—862no—
531Q8—1721no—
532Q8—1721no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—862no—
552C2×C4—861no—
553C2×C4—861no—
554C2×C4—861no—
555C2×C4—861no—
556C2×C4—861no—
557C2×C4—862no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—1721no—
563C2×C4—1721no—
564C2×C4—1721no—
565C2×C4—1721no—
566C2×C4—1721no—
567C2×C4—1721no—
568C2×C4—1721no—
569C2×C4—1721no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4#41×D4311yescharacteristic
577C2×C4#41×D4311yescharacteristic
578C2×C4C2×#1062190011yescharacteristic
579C2×C4C2×#1062189811yescharacteristic
580C2×C4#1306337111yescharacteristic
581C2×C4#1306337111yescharacteristic
582C8—41no—
583C8—41no—
584C8—1721no—
585C8—1721no—
586C22—1721no—
587C22—1721no—
588C22—1721no—
589C22—1721no—
590C22—1721no—
591C22—1721no—
592C22—1721no—
593C22#1458340911yescharacteristic
594C22#1458354111yescharacteristic
595C22#1458354511yescharacteristic
596C22#1458369511yescharacteristic
597C22#1458369611yescharacteristic
598C22#1458371211yescharacteristic
599C22#1458371511yescharacteristic
600C4—41no—
601C4—41no—
602C4—42no—
603C4—42no—
604C4—81no—
605C4—81no—
606C4—3441no—
607C4—3441no—
608C4—1721no—
609C4—1722no—
610C4—1721no—
611C4—1721no—
612C4—1722no—
613C4#1458342711yescharacteristic
614C4#1458348811yescharacteristic
615C4#1458361411yescharacteristic
616C4#1458363111yescharacteristic
617C2—3441no—
618C2#1913853711yescharacteristic
619C2#1914470111yescharacteristic
620C2#1914489311yescharacteristic
621C2#1914665911yescharacteristic
622C2#1914669411yescharacteristic
623C2#1914669611yescharacteristic
624C2#1914686811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1928C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
hypercenter#1928D43
hypocenterC43#26749
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1928

Complements

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

NH ≅ G/Ntype
3. #19135917C2semidirect
5. #19135747C2semidirect
7. #19135552C2semidirect
8. #19135287C2semidirect
10. #19135189C2semidirect
11. #19134933C2semidirect
14. #19134424C2semidirect
15. C43×#1928C2semidirect
313. #1928D43semidirect
371. C43#26749semidirect

Maximal subgroups

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

subgroupindex
#191389342
#191376242
#191359172
#191358002
#191357472
#191356042
#191355522
#191352872
#191352092
#191351892
#191349332
#191349042
#191346882
#191344242
C43×#19282
#2674943