Finite Group Databasebeta

← #25169905

Subgroups — #25169905

Order 11008.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19139171C211yesmaximal, characteristic, complemented
2#19137671C211yesmaximal, characteristic
3#19136120C211yesmaximal, characteristic
4#19135909C211yesmaximal, characteristic
5#19135833C211yesmaximal, characteristic
6#19135686C211yesmaximal, characteristic
7#19135239C211yesmaximal, characteristic, complemented
8#19135233C211yesmaximal, characteristic, complemented
9#19135168C211yesmaximal, characteristic, complemented
10#19135152C211yesmaximal, characteristic, complemented
11#19134938C211yesmaximal, characteristic, complemented
12#19134932C211yesmaximal, characteristic
13#19134598C211yesmaximal, characteristic, complemented
14C4×#13063247C211yesmaximal, characteristic
15C43×#1969C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C2×#13063314C2211yescharacteristic
18C2×Q8×Dic43C2211yescharacteristic
19C2×C4×D172C2211yescharacteristic
20C2×#13063258C2211yescharacteristic
21C2×Dic43⋊C8C2211yescharacteristic
22C2×#13063249C2211yescharacteristic
23C2×#13063249C2211yescharacteristic
24C2×#13063249C2211yescharacteristic
25C2×#13063247C2211yescharacteristic
26C2×#13063247C2211yescharacteristic
27C2×#13063245C2211yescharacteristic
28#14582840—21no—
29#14582839—21no—
30#14582806C2211yescharacteristic
31#14582806C2211yescharacteristic
32#14582800C2211yescharacteristic
33#14582798C2211yescharacteristic
34#14582791—21no—
35#14582788—21no—
36#14582786—21no—
37#14582781—21no—
38#14582773—21no—
39#14582768C2211yescharacteristic
40C4⋊C4×Dic43C2211yescharacteristic
41C4×Dic43⋊C4C2211yescharacteristic
42C4×C4⋊Dic43C2211yescharacteristic
43#14582746—21no—
44#14582662C2211yescharacteristic
45#14582662C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52C22×Q16×C43C2211yescharacteristic
53C2×#107×C43C2211yescharacteristic
54C2×#103×C43C2211yescharacteristic
55C2×#103×C43C2211yescharacteristic
56C2×C4×C8×C43C2211yescharacteristic
57C43×#391C2211yescharacteristic
58C43×#391C2211yescharacteristic
59C22×D172C2311yescharacteristic
60C22×C4×D43—21no—
61C2×#10621884—22no—
62C2×#10621884—41no—
63C2×#10621884—41no—
64C22×C43⋊C8C2311yescharacteristic
65C22×C43⋊C8C2311yescharacteristic
66#13063314—22no—
67#13063314—22no—
68Q8×Dic43—22no—
69Q8×Dic43—41no—
70C4×D172—22no—
71C4×D172—41no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43—21no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2311yescharacteristic
76C2×C4⋊Dic43C2311yescharacteristic
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4D411yescharacteristic
80C2×Dic43⋊C4D411yescharacteristic
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×Dic43—21no—
88C2×C4×Dic43—21no—
89C2×C4×Dic43C2311yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91#13063258—41no—
92Dic43⋊C8—41no—
93#13063249—22no—
94#13063249—22no—
95#13063249—41no—
96#13063247—22no—
97#13063247—22no—
98#13063245—41no—
99C43⋊#95—21no—
100C43⋊#95—21no—
101C43⋊#95—21no—
102C43⋊#95—21no—
103C43⋊#95—21no—
104C43⋊#95—21no—
105C43⋊#95—21no—
106C43⋊#95D411yescharacteristic
107C43⋊#95D411yescharacteristic
108C22×Q8×C43C2311yescharacteristic
109C22×Q8×C43C2311yescharacteristic
110C2×Q16×C43—22no—
111C2×Q16×C43—22no—
112C2×Q16×C43—41no—
113C22×C8×C43C2311yescharacteristic
114C22×C8×C43C2311yescharacteristic
115C2×C4⋊C4×C43C2311yescharacteristic
116C2×C4⋊C4×C43C2311yescharacteristic
117C2×C42×C43C2311yescharacteristic
118#107×C43—22no—
119#103×C43—41no—
120#103×C43—41no—
121C4×C8×C43—41no—
122#95×C43—21no—
123#95×C43—21no—
124#95×C43—21no—
125#95×C43—21no—
126C23×D43—21no—
127C2×Q8×C43—21no—
128C2×Q8×C43—21no—
129C2×Q8×C43—21no—
130C2×Q8×C43—21no—
131C2×Q8×C43—21no—
132C2×Q8×C43—21no—
133C2×Q8×C43—21no—
134C2×Q8×C43—21no—
135C2×Q8×C43—21no—
136C2×Q8×C43—21no—
137C2×Q8×C43—21no—
138C2×Q8×C43#4112yes—
139C22×C4×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
146C22×Dic43—21no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43C2×D411yescharacteristic
150C22×Dic43C2×D411yescharacteristic
151C22×Dic43C2×D411yescharacteristic
152C22×Dic43C2×D411yescharacteristic
153C2×D172—21no—
154C2×D172—21no—
155C2×D172—21no—
156C2×D172—21no—
157C2×D172—21no—
158C2×D172#4112yes—
159C2×C4×D43—42no—
160C2×C4×D43—42no—
161C2×C4×D43—81no—
162Q16×C43—44no—
163C2×C8×C43—21no—
164C2×C8×C43—21no—
165C2×C8×C43—21no—
166C2×C8×C43—21no—
167C2×C8×C43—21no—
168C2×C8×C43#4112yes—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—21no—
171C4⋊C4×C43—21no—
172C4⋊C4×C43—21no—
173C42×C43—21no—
174C42×C43—21no—
175#10621884—44no—
176(C2×D43)⋊C4—24no—
177(C2×D43)⋊C4—24no—
178(C2×D43)⋊C4—42no—
179(C2×D43)⋊C4—42no—
180(C2×D43)⋊C4—81no—
181C4⋊Dic43—21no—
182C4⋊Dic43—21no—
183C4⋊Dic43—21no—
184C4⋊Dic43—21no—
185C4⋊Dic43—21no—
186C4⋊Dic43—42no—
187C4⋊Dic43—81no—
188C4⋊Dic43#4112yes—
189Dic43⋊C4—22no—
190Dic43⋊C4—22no—
191Dic43⋊C4—42no—
192Dic43⋊C4—81no—
193C4×Dic43—21no—
194C4×Dic43—21no—
195C4×Dic43—21no—
196C4×Dic43—21no—
197C4×Dic43—42no—
198C4×Dic43—81no—
199C4×Dic43—81no—
200C2×C43⋊C8—21no—
201C2×C43⋊C8—21no—
202C2×C43⋊C8—21no—
203C2×C43⋊C8—21no—
204C2×C43⋊C8—21no—
205C2×C43⋊C8—21no—
206C23×C43C22×D411yescharacteristic
207C22×D43—22no—
208C22×D43—41no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43—41no—
212C22×D43—41no—
213C22×D43—41no—
214Q8×C43—22no—
215Q8×C43—22no—
216Q8×C43—41no—
217Q8×C43—41no—
218Q8×C43—41no—
219Q8×C43—41no—
220Q8×C43—41no—
221Q8×C43—41no—
222C2×C4×C43—21no—
223C2×C4×C43—21no—
224C2×C4×C43—22no—
225C2×C4×C43—21no—
226C2×C4×C43—21no—
227C2×C4×C43—21no—
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×C43—41no—
235C2×C4×C43—41no—
236C2×C4×C43—41no—
237C2×C4×C43—41no—
238C2×C4×C43—41no—
239C2×C4×C43#13712yes—
240C2×C4×C43C2×#4111yescharacteristic
241C2×C4×C43C2×#4111yescharacteristic
242C2×C4×C43C2×#4111yescharacteristic
243C2×C4×C43C2×#4111yescharacteristic
244C2×C4×C43H(5,𝔽2)11yescharacteristic
245C2×C4×C43H(5,𝔽2)11yescharacteristic
246C2×Dic43—21no—
247C2×Dic43—21no—
248C2×Dic43—21no—
249C2×Dic43—21no—
250C2×Dic43—21no—
251C2×Dic43—22no—
252C2×Dic43—21no—
253C2×Dic43—21no—
254C2×Dic43—21no—
255C2×Dic43—21no—
256C2×Dic43—21no—
257C2×Dic43—21no—
258C2×Dic43—41no—
259C2×Dic43—41no—
260C2×Dic43—41no—
261C2×Dic43—41no—
262C2×Dic43—41no—
263C2×Dic43—41no—
264C2×Dic43—41no—
265C2×Dic43—41no—
266C2×Dic43#13512yes—
267D172—22no—
268D172—22no—
269D172—41no—
270D172—41no—
271C4×D43—84no—
272C8×C43—22no—
273C8×C43—41no—
274C43⋊C8—41no—
275C43⋊C8—41no—
276#27073—431nomaximal, Sylow
277C22×C43#52511yescharacteristic
278C22×C43#54611yescharacteristic
279C22×C43#55011yescharacteristic
280C22×C43C2×#13511yescharacteristic
281C22×C43C2×#13711yescharacteristic
282C22×C43#57611yescharacteristic
283C22×C43#57811yescharacteristic
284C2×D43—42no—
285C2×D43—42no—
286C2×D43—42no—
287C2×D43—81no—
288C2×D43—81no—
289C2×D43—81no—
290C2×D43—81no—
291C4×C43—22no—
292C4×C43—42no—
293C4×C43—41no—
294C4×C43—81no—
295C4×C43—81no—
296C4×C43—81no—
297C4×C43#52911yescharacteristic
298C4×C43#53811yescharacteristic
299C4×C43#55111yescharacteristic
300C4×C43#55311yescharacteristic
301Dic43—22no—
302Dic43—41no—
303Dic43—41no—
304Dic43—42no—
305Dic43—41no—
306Dic43—81no—
307Dic43—81no—
308#2511—431no—
309#2367—431no—
310#2093—431no—
311#2055—431no—
312#2042—431no—
313#2015—431no—
314#1969D4311yescharacteristic, complemented
315#1928—431no—
316#1928—431no—
317#1918—431no—
318#1916—431no—
319#1878—431no—
320#1877—431no—
321#1803—431no—
322C4×#102—431no—
323C2×C43#246711yescharacteristic
324C2×C43#310711yescharacteristic
325C2×C43#312411yescharacteristic
326C2×C43#330011yescharacteristic
327C2×C43#331411yescharacteristic
328C2×C43#339611yescharacteristic
329C2×C43#339811yescharacteristic
330D43—82no—
331C22×Q16C2×D4311yescharacteristic
332C22×SD16—431no—
333C2×#124—431no—
334C2×C4×Q8—431no—
335C2×C4×D4—431no—
336C2×#107—431no—
337C2×#107C2×D4311yescharacteristic
338C2×C4⋊C8—431no—
339C2×#103—431no—
340C2×#103—431no—
341C2×#103—431no—
342C2×#103C2×D4311yescharacteristic
343C2×#103C2×D4311yescharacteristic
344C2×#102—431no—
345C2×#102—431no—
346C2×#102—431no—
347C2×C4×C8C2×D4311yescharacteristic
348#400—861no—
349#400—861no—
350#391—431no—
351#391—431no—
352#391C2×D4311yescharacteristic
353#391C2×D4311yescharacteristic
354#390—431no—
355#389—431no—
356#388—861no—
357#388—861no—
358#387—861no—
359#387—861no—
360#385—861no—
361#384—431no—
362C4×C4⋊C4—431no—
363C4×C4⋊C4—431no—
364C4×C4⋊C4—431no—
365C4×C22⋊C4—861no—
366#340—431no—
367#340—431no—
368#340—431no—
369#340—431no—
370#336—431no—
371#336—431no—
372#336—431no—
373#336—431no—
374C43#2707311yescharacteristic, complemented, Sylow
375C22×Q8C22×D4311yescharacteristic
376C22×Q8C22×D4311yescharacteristic
377C22×D4—431no—
378C23×C4—861no—
379C2×Q16—22no—
380C2×Q16—22no—
381C2×Q16—41no—
382C2×SD16—862no—
383C2×SD16—1721no—
384C2×SD16—1721no—
385C22×C8—431no—
386C22×C8—431no—
387C22×C8C22×D4311yescharacteristic
388C22×C8C22×D4311yescharacteristic
389#124—862no—
390#124—862no—
391C4×Q8—862no—
392C4×Q8—1721no—
393C4×D4—862no—
394C4×D4—1721no—
395C2×C4⋊C4—431no—
396C2×C4⋊C4—431no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—431no—
399C2×C4⋊C4—431no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4—861no—
404C2×C4⋊C4C22×D4311yescharacteristic
405C2×C4⋊C4C22×D4311yescharacteristic
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—431no—
412C2×C42—431no—
413C2×C42—861no—
414C2×C42—861no—
415C2×C42—861no—
416C2×C42C22×D4311yescharacteristic
417#107—22no—
418#107—1721no—
419C4⋊C8—1721no—
420#103—41no—
421#103—41no—
422#103—862no—
423#103—862no—
424#103—1721no—
425#102—862no—
426#102—862no—
427#102—1721no—
428C4×C8—41no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—431no—
434#95—431no—
435#95—861no—
436#95—861no—
437#95—861no—
438#95—861no—
439#95—861no—
440#95—861no—
441#95—861no—
442C24—861no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8#1062189812yes—
455C2×D4—432no—
456C2×D4—861no—
457C2×D4—861no—
458C2×D4—861no—
459C2×D4—861no—
460C2×D4—861no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—431no—
466C22×C4—431no—
467C22×C4—431no—
468C22×C4—431no—
469C22×C4—861no—
470C22×C4—861no—
471C22×C4—861no—
472C22×C4—3441no—
473C22×C4—1722no—
474C22×C4—1722no—
475C22×C4D4×D4311yescharacteristic
476C22×C4D4×D4311yescharacteristic
477C22×C4C23×D4311yescharacteristic
478Q16—44no—
479SD16—1724no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—861no—
486C2×C8—861no—
487C2×C8—861no—
488C2×C8—861no—
489C2×C8—861no—
490C2×C8—861no—
491C2×C8#1062190012yes—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—432no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—861no—
500C4⋊C4—861no—
501C4⋊C4—861no—
502C4⋊C4—861no—
503C4⋊C4—861no—
504C4⋊C4—3441no—
505C4⋊C4—3441no—
506C4⋊C4—1722no—
507C4⋊C4—1722no—
508C22⋊C4—864no—
509C22⋊C4—864no—
510C22⋊C4—3441no—
511C22⋊C4—1722no—
512C22⋊C4—1722no—
513C42—21no—
514C42—21no—
515C42—861no—
516C42—861no—
517C42—861no—
518C42—861no—
519C42—3441no—
520C42—3441no—
521C42—1722no—
522C23—862no—
523C23—1721no—
524C23—1721no—
525C23—1721no—
526C23—1721no—
527C23—1721no—
528C23—1721no—
529C23C2×D4×D4311yescharacteristic
530Q8—22no—
531Q8—22no—
532Q8—41no—
533Q8—41no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538D4—862no—
539D4—862no—
540D4—1721no—
541D4—1721no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
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—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—432no—
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—861no—
570C2×C4—861no—
571C2×C4—862no—
572C2×C4—3444no—
573C2×C4—1721no—
574C2×C4—1721no—
575C2×C4—1721no—
576C2×C4—1721no—
577C2×C4—1721no—
578C2×C4—1721no—
579C2×C4—1721no—
580C2×C4—1721no—
581C2×C4#1306335712yes—
582C2×C4#41×D4311yescharacteristic
583C2×C4#41×D4311yescharacteristic
584C2×C4C2×#1062190011yescharacteristic
585C2×C4C2×#1062189811yescharacteristic
586C2×C4#1306337011yescharacteristic
587C2×C4#1306337011yescharacteristic
588C8—22no—
589C8—41no—
590C8—1721no—
591C8—1721no—
592C22—3441no—
593C22—3441no—
594C22—3441no—
595C22—3441no—
596C22—1722no—
597C22—1722no—
598C22—1722no—
599C22#1458340811yescharacteristic
600C22#1458353811yescharacteristic
601C22#1458356911yescharacteristic
602C22#135×D4311yescharacteristic
603C22C2×#1306335711yescharacteristic
604C22#1458370111yescharacteristic
605C22#1458371211yescharacteristic
606C4—22no—
607C4—42no—
608C4—41no—
609C4—81no—
610C4—81no—
611C4—81no—
612C4—862no—
613C4—3441no—
614C4—3441no—
615C4—1721no—
616C4—1721no—
617C4—1722no—
618C4—1721no—
619C4#1458342811yescharacteristic
620C4#1458348111yescharacteristic
621C4#1458357511yescharacteristic
622C4#1458359811yescharacteristic
623C2—3442no—
624C2#1913865211yescharacteristic
625C2#1914466411yescharacteristic
626C2#1914486311yescharacteristic
627C2#1914647711yescharacteristic
628C2#1914668211yescharacteristic
629C2#1914760411yescharacteristic
630C2#1914763111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1969C2
socleC23×C43C22×D4
prime radicalC22×D172C23
hypercenter#1969D43
hypocenterC43#27073
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1969

Complements

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

NH ≅ G/Ntype
1. #19139171C2semidirect
7. #19135239C2semidirect
8. #19135233C2semidirect
9. #19135168C2semidirect
10. #19135152C2semidirect
11. #19134938C2semidirect
13. #19134598C2semidirect
15. C43×#1969C2semidirect
314. #1969D43semidirect
374. C43#27073semidirect

Maximal subgroups

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

subgroupindex
#191391712
#191376712
#191361202
#191359092
#191358332
#191356862
#191352392
#191352332
#191351682
#191351522
#191349382
#191349322
#191345982
C4×#130632472
C43×#19692
#2707343