Finite Group Databasebeta

← #25200830

Subgroups — #25200830

Order 11008.

724 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140563C211yesmaximal, characteristic, complemented
2#19137303C211yesmaximal, characteristic
3#19136004C211yesmaximal, characteristic, complemented
4#19135836C211yesmaximal, characteristic
5#19135692C211yesmaximal, characteristic
6#19135474C211yesmaximal, characteristic
7#19135454C211yesmaximal, characteristic, complemented
8#19135286C211yesmaximal, characteristic, complemented
9#19135279C211yesmaximal, characteristic
10#19134937C211yesmaximal, characteristic, complemented
11#19134930C211yesmaximal, characteristic
12#19134846C211yesmaximal, characteristic, complemented
13#19134839C211yesmaximal, characteristic
14#19134345C211yesmaximal, characteristic, complemented
15C43×#2083C211yesmaximal, characteristic, complemented
16C22×Dic172C2211yescharacteristic
17C22×#10621873C2211yescharacteristic
18C2×#13063313C2211yescharacteristic
19C2×#13063290C2211yescharacteristic
20C2×#13063287C2211yescharacteristic
21C2×#13063250C2211yescharacteristic
22C2×#13063248C2211yescharacteristic
23C2×#13063248C2211yescharacteristic
24C2×#13063248C2211yescharacteristic
25C2×#13063248C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28C2×#13063245C2211yescharacteristic
29C2×#13063235C2211yescharacteristic
30C2×C8×Dic43C2211yescharacteristic
31C43⋊#401—21no—
32#14582841—21no—
33#14582838—21no—
34#14582837—21no—
35#14582805C2211yescharacteristic
36#14582804C2211yescharacteristic
37#14582804C2211yescharacteristic
38#14582804C2211yescharacteristic
39#14582800C2211yescharacteristic
40#14582798C2211yescharacteristic
41#14582795C2211yescharacteristic
42#14582789—21no—
43#14582789—21no—
44#14582770—21no—
45#14582770—21no—
46#14582745C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C2×#107×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C43×#389C2211yescharacteristic
55C43×#384C2211yescharacteristic
56C43×#340C2211yescharacteristic
57C43×#340C2211yescharacteristic
58C43×#336C2211yescharacteristic
59C22×Dic86C2311yescharacteristic
60C22×Dic86C2311yescharacteristic
61C22×D172C2311yescharacteristic
62C22×C4×D43—21no—
63C2×Dic172—22no—
64C2×Dic172—22no—
65C2×Dic172—41no—
66C2×#10621873—22no—
67C2×#10621873—22no—
68C2×#10621873—41no—
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063313—22no—
72#13063313—22no—
73#13063290—41no—
74#13063290—41no—
75#13063287—41no—
76#13063287—41no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43C2311yescharacteristic
79C2×Dic43⋊C4—21no—
80C2×Dic43⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×C4×Dic43—21no—
87C2×C4×Dic43C2311yescharacteristic
88C2×C4×Dic43C2311yescharacteristic
89#13063250—22no—
90#13063248—22no—
91#13063248—41no—
92#13063248—41no—
93#13063248—41no—
94#13063247—22no—
95#13063245—22no—
96#13063245—41no—
97#13063235—22no—
98C8×Dic43—22no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C43⋊#95—21no—
108C43⋊#95—21no—
109C43⋊#95D411yescharacteristic
110C43⋊#95D411yescharacteristic
111C43⋊#95D411yescharacteristic
112C43⋊#95D411yescharacteristic
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43—21no—
116C2×C4⋊C4×C43—21no—
117C2×C4⋊C4×C43—21no—
118C2×C4⋊C4×C43C2311yescharacteristic
119C2×C4⋊C4×C43C2311yescharacteristic
120C2×C4⋊C4×C43C2311yescharacteristic
121C2×C4⋊C4×C43C2311yescharacteristic
122C2×C42×C43C2311yescharacteristic
123#107×C43—41no—
124#107×C43—41no—
125#95×C43—21no—
126C23×D43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2411yescharacteristic
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—21no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C22×Dic43C2×D411yescharacteristic
141C2×D172—21no—
142C2×D172—21no—
143C2×D172—21no—
144C2×D172—21no—
145C2×D172—21no—
146C2×D172#4112yes—
147C2×C4×D43—42no—
148C2×C4×D43—81no—
149C2×C4×D43—81no—
150C2×Dic86—21no—
151C2×Dic86—21no—
152C2×Dic86—21no—
153C2×Dic86—21no—
154C2×Dic86—21no—
155C2×Dic86—21no—
156C2×Dic86—21no—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—21no—
160C2×Dic86—21no—
161C2×Dic86#4112yes—
162C2×C8×C43—21no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43#4112yes—
167C2×C8×C43#4112yes—
168C4⋊C4×C43—21no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—21no—
175C4⋊C4×C43—21no—
176C4⋊C4×C43—81no—
177C4⋊C4×C43—81no—
178C4⋊C4×C43—81no—
179C42×C43—21no—
180C42×C43—21no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—42no—
184(C2×D43)⋊C4—81no—
185(C2×D43)⋊C4—81no—
186C4⋊Dic43—21no—
187C4⋊Dic43—21no—
188C4⋊Dic43—81no—
189Dic43⋊C4—42no—
190Dic43⋊C4—81no—
191C4×Dic43—21no—
192C4×Dic43—21no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—42no—
196C2×C43⋊C8—21no—
197C2×C43⋊C8—21no—
198C2×C43⋊C8—21no—
199C2×C43⋊C8—21no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202Dic172—44no—
203#10621873—44no—
204C23×C43C22×D411yescharacteristic
205C22×D43—22no—
206C22×D43—41no—
207C22×D43—41no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
217C2×C4×C43—21no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
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×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43C2×#4111yescharacteristic
233C2×C4×C43C2×#4111yescharacteristic
234C2×C4×C43H(5,𝔽2)11yescharacteristic
235C2×C4×C43H(5,𝔽2)11yescharacteristic
236C2×Dic43—22no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—21no—
244C2×Dic43—21no—
245C2×Dic43—21no—
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—41no—
250C2×Dic43—41no—
251C2×Dic43—41no—
252C2×Dic43—41no—
253C2×Dic43—41no—
254C2×Dic43—41no—
255C2×Dic43—41no—
256C2×Dic43—41no—
257D172—22no—
258D172—22no—
259D172—41no—
260D172—41no—
261C4×D43—84no—
262Dic86—22no—
263Dic86—22no—
264Dic86—41no—
265Dic86—41no—
266Dic86—41no—
267Dic86—41no—
268Dic86—41no—
269Dic86—41no—
270C8×C43—22no—
271C8×C43—22no—
272C43⋊C8—41no—
273C43⋊C8—41no—
274#29511—431nomaximal, Sylow
275C22×C43#52511yescharacteristic
276C22×C43#53211yescharacteristic
277C22×C43#53511yescharacteristic
278C22×C43#57611yescharacteristic
279C22×C43#57711yescharacteristic
280C22×C43#57811yescharacteristic
281C22×C43#57811yescharacteristic
282C2×D43—42no—
283C2×D43—42no—
284C2×D43—42no—
285C2×D43—81no—
286C2×D43—81no—
287C2×D43—81no—
288C2×D43—81no—
289C4×C43—41no—
290C4×C43—41no—
291C4×C43—81no—
292C4×C43—81no—
293C4×C43—81no—
294C4×C43—81no—
295C4×C43#55111yescharacteristic
296C4×C43#55111yescharacteristic
297C4×C43#55311yescharacteristic
298C4×C43#55311yescharacteristic
299Dic43—42no—
300Dic43—41no—
301Dic43—41no—
302Dic43—41no—
303Dic43—41no—
304Dic43—81no—
305Dic43—81no—
306#2645—431no—
307#2326—431no—
308#2083D4311yescharacteristic, complemented
309#2072—431no—
310#2042—431no—
311#2015—431no—
312#1973—431no—
313#1969—431no—
314#1935—431no—
315#1934—431no—
316#1878—431no—
317#1877—431no—
318#1863—431no—
319#1862—431no—
320#1746—431no—
321C2×C43#260311yescharacteristic
322C2×C43#312011yescharacteristic
323C2×C43#312411yescharacteristic
324C2×C43#317511yescharacteristic
325C2×C43#317811yescharacteristic
326C2×C43#322311yescharacteristic
327C2×C43#322411yescharacteristic
328D43—82no—
329C22×Q16—431no—
330C22×SD16—431no—
331C2×#124—431no—
332C2×C4×Q8—431no—
333C2×C4×D4—431no—
334C2×#107C2×D4311yescharacteristic
335C2×#107C2×D4311yescharacteristic
336C2×#103—431no—
337C2×#103—431no—
338C2×#103—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#102—431no—
342C2×#102—431no—
343C2×#102—431no—
344C2×#97—431no—
345C2×C4×C8—431no—
346#401—861no—
347#400—861no—
348#400—861no—
349#400—861no—
350#391—431no—
351#391—431no—
352#391—431no—
353#391—431no—
354#390—431no—
355#389—431no—
356#389—431no—
357#389C2×D4311yescharacteristic
358#388—861no—
359#388—861no—
360#385—861no—
361#385—861no—
362#384C2×D4311yescharacteristic
363#376—431no—
364#340—431no—
365#340—431no—
366#340C2×D4311yescharacteristic
367#340C2×D4311yescharacteristic
368#336—431no—
369#336—431no—
370#336—431no—
371#336C2×D4311yescharacteristic
372C43#2951111yescharacteristic, complemented, Sylow
373C22×Q8—431no—
374C22×Q8—431no—
375C22×D4—431no—
376C23×C4—861no—
377C2×Q16—862no—
378C2×Q16—862no—
379C2×Q16—1721no—
380C2×SD16—862no—
381C2×SD16—862no—
382C2×SD16—1721no—
383C22×C8—431no—
384C22×C8—431no—
385C22×C8C22×D4311yescharacteristic
386C22×C8C22×D4311yescharacteristic
387#124—862no—
388#124—862no—
389C4×Q8—1721no—
390C4×Q8—1721no—
391C4×D4—1721no—
392C4×D4—1721no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4C22×D4311yescharacteristic
401C2×C4⋊C4C22×D4311yescharacteristic
402C2×C4⋊C4C22×D4311yescharacteristic
403C2×C4⋊C4C22×D4311yescharacteristic
404C2×C22⋊C4—861no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C42—431no—
410C2×C42—431no—
411C2×C42—861no—
412C2×C42C22×D4311yescharacteristic
413#107—41no—
414#107—41no—
415#103—862no—
416#103—862no—
417#103—1721no—
418#103—1721no—
419#103—1721no—
420#102—862no—
421#102—862no—
422#102—1721no—
423#97—862no—
424C4×C8—862no—
425#95—21no—
426#95—431no—
427#95—431no—
428#95—431no—
429#95—431no—
430#95—861no—
431#95—861no—
432#95—861no—
433#95—861no—
434#95—861no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440C24—861no—
441C2×Q8—432no—
442C2×Q8—861no—
443C2×Q8—861no—
444C2×Q8—861no—
445C2×Q8—861no—
446C2×Q8—861no—
447C2×Q8—861no—
448C2×Q8—861no—
449C2×Q8—861no—
450C2×Q8—861no—
451C2×Q8—861no—
452C2×Q8—861no—
453C2×D4—432no—
454C2×D4—861no—
455C2×D4—861no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—431no—
464C22×C4—431no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—861no—
468C22×C4—861no—
469C22×C4—861no—
470C22×C4—3441no—
471C22×C4—3441no—
472C22×C4—1722no—
473C22×C4D4×D4311yescharacteristic
474C22×C4D4×D4311yescharacteristic
475C22×C4C23×D4311yescharacteristic
476Q16—1724no—
477SD16—1724no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—861no—
483C2×C8—861no—
484C2×C8—861no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8#1062190212yes—
489C2×C8#1062190212yes—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—81no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—3441no—
504C4⋊C4—3441no—
505C4⋊C4—1722no—
506C22⋊C4—864no—
507C22⋊C4—864no—
508C22⋊C4—3441no—
509C22⋊C4—3441no—
510C22⋊C4—1722no—
511C42—21no—
512C42—21no—
513C42—861no—
514C42—861no—
515C42—861no—
516C42—861no—
517C42—1722no—
518C23—862no—
519C23—1721no—
520C23—1721no—
521C23—1721no—
522C23—1721no—
523C23—1721no—
524C23—1721no—
525C23C2×D4×D4311yescharacteristic
526Q8—862no—
527Q8—862no—
528Q8—1721no—
529Q8—1721no—
530Q8—1721no—
531Q8—1721no—
532Q8—1721no—
533Q8—1721no—
534D4—862no—
535D4—862no—
536D4—1721no—
537D4—1721no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—862no—
557C2×C4—861no—
558C2×C4—861no—
559C2×C4—861no—
560C2×C4—861no—
561C2×C4—861no—
562C2×C4—861no—
563C2×C4—861no—
564C2×C4—861no—
565C2×C4—861no—
566C2×C4—861no—
567C2×C4—861no—
568C2×C4—861no—
569C2×C4—3444no—
570C2×C4—1721no—
571C2×C4—1721no—
572C2×C4—1721no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4#41×D4311yescharacteristic
579C2×C4#41×D4311yescharacteristic
580C2×C4C2×#1062190211yescharacteristic
581C2×C4C2×#1062190211yescharacteristic
582C2×C4#1306337011yescharacteristic
583C2×C4#1306337111yescharacteristic
584C8—22no—
585C8—22no—
586C8—1721no—
587C8—1721no—
588C22—3441no—
589C22—3441no—
590C22—3441no—
591C22—3441no—
592C22—1722no—
593C22—1722no—
594C22—1722no—
595C22#1458340711yescharacteristic
596C22#1458345011yescharacteristic
597C22#1458346511yescharacteristic
598C22#1458370011yescharacteristic
599C22#1458370911yescharacteristic
600C22#1458371211yescharacteristic
601C22#1458371511yescharacteristic
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4—3441no—
609C4—3441no—
610C4—1721no—
611C4—1721no—
612C4—1722no—
613C4—1721no—
614C4—1721no—
615C4#1458357611yescharacteristic
616C4#1458357611yescharacteristic
617C4#1458360211yescharacteristic
618C4#1458360211yescharacteristic
619C2—3442no—
620C2#1914022311yescharacteristic
621C2#1914480411yescharacteristic
622C2#1914485211yescharacteristic
623C2#1914523711yescharacteristic
624C2#1914526811yescharacteristic
625C2#1914567711yescharacteristic
626C2#1914568611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#2083C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#2083D43
hypocenterC43#29511
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2083

Complements

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

NH ≅ G/Ntype
1. #19140563C2semidirect
3. #19136004C2semidirect
7. #19135454C2semidirect
8. #19135286C2semidirect
10. #19134937C2semidirect
12. #19134846C2semidirect
14. #19134345C2semidirect
15. C43×#2083C2semidirect
308. #2083D43semidirect
372. C43#29511semidirect

Maximal subgroups

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

subgroupindex
#191405632
#191373032
#191360042
#191358362
#191356922
#191354742
#191354542
#191352862
#191352792
#191349372
#191349302
#191348462
#191348392
#191343452
C43×#20832
#2951143