Finite Group Databasebeta

← #25981355

Subgroups — #25981355

Order 11008.

2142 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148449C211yesmaximal, characteristic, complemented
2C2×#14583552C211yesmaximal, characteristic, complemented
3#19146522C214yesmaximal, complemented
4#19146515C214yesmaximal, complemented
5#19146320C214yesmaximal, complemented
6#19146315C214yesmaximal, complemented
7#19145520C211yesmaximal, characteristic, complemented
8#19145379C214yesmaximal, complemented
9#19144599C211yesmaximal, characteristic, complemented
10#19144596C211yesmaximal, characteristic, complemented
11#19143818C214yesmaximal, complemented
12#19143618C211yesmaximal, characteristic, complemented
13C43×#3209C211yesmaximal, characteristic, complemented
14C22×#10621902C2212yes—
15C2×#13063348C2218yescomplemented
16#14583634—22no—
17#14583622C2212yescomplemented
18#14583615C2212yescomplemented
19#14583602—22no—
20#14583571C2212yescomplemented
21#14583552—22no—
22#14583552—22no—
23#14583552C2214yes—
24#14583552C2214yes—
25#14583552C2212yescomplemented
26#14583489—22no—
27#14583468—21no—
28#14583449C2211yescharacteristic
29#14583412C2214yes—
30C2×#13063310—22no—
31C2×#13063301C2212yes—
32C2×#13063300—21no—
33#14583379—21no—
34C2×C4×D172C2211yescharacteristic
35C2×C4×D172C2211yescharacteristic
36C2×C4⋊C4×D43—21no—
37#14583273C2212yescomplemented
38#14583249C2212yescomplemented
39#14583239C2218yescomplemented
40#14583227C2212yes—
41#14583213C2212yes—
42#14583186C2212yescomplemented
43#14583180C2212yescomplemented
44#14583137C2218yescomplemented
45#14583131C2218yescomplemented
46#14583101C2214yescomplemented
47#14583101C2212yescomplemented
48#14583095C2212yescomplemented
49#14583060C2218yescomplemented
50#14583060C2218yescomplemented
51#14583049C2212yes—
52#14583047C2218yescomplemented
53#14583038C2214yes—
54#14583035C2212yes—
55C4×#10621884C2214yescomplemented
56C4×D344C2214yescomplemented
57C8×D172C2214yescomplemented
58#14582964C2214yescomplemented
59#14582952C2211yescharacteristic
60#14582894C2218yescomplemented
61C22⋊C8×D43C2214yes—
62C43×#533C2211yescharacteristic
63C2×C4⋊Q8×C43C2211yescharacteristic
64C43×#494C2212yescomplemented
65C43×#487C2212yescomplemented
66C43×#462C2214yescomplemented
67C43×#451C2214yes—
68C43×#431C2211yescharacteristic
69C2×#10621902—24no—
70C2×#10621902—48no—
71C2×#10621902C2318yes—
72C2×#10621902C2314yes—
73C2×#10621898—21no—
74C22×D172—22no—
75C22×D172D411yescharacteristic
76C22×D172C2311yescharacteristic
77C22×C4×D43—21no—
78C22×C4×D43—22no—
79C22×C4×D43C2312yes—
80#13063348—416no—
81C2×#10621884C2314yes—
82C2×#10621884C2318yes—
83C2×D344C2314yes—
84C2×C8×D43C2318yes—
85#13063325C2311yescharacteristic
86#13063322—22no—
87#13063322C2311yescharacteristic
88#13063320—24no—
89#13063314—24no—
90#13063313—22no—
91#13063313—21no—
92#13063310—24no—
93#13063310—28no—
94#13063310—28no—
95#13063310—24no—
96#13063301—24no—
97#13063301C2318yes—
98#13063301C2314yes—
99#13063300—24no—
100#13063300—24no—
101#13063300—22no—
102#13063300—22no—
103#13063300—24no—
104#13063300C2314yes—
105#13063299—21no—
106#13063299C2312yes—
107#13063295—24no—
108C4×Dic86—22no—
109C4×D172—21no—
110C4×D172—21no—
111C4×D172—21no—
112C4×D172—22no—
113C4×D172D412yes—
114C4×D172D412yes—
115C4×D172C2312yes—
116C4×D172C2312yes—
117C4×D172C2312yes—
118C4×D172C2312yes—
119C4×D172C2312yes—
120#13063287—24no—
121(C22⋊D43)⋊C4—24no—
122#13063283—22no—
123#13063283C2314yes—
124C2×C4⋊Dic43D411yescharacteristic
125C2×C4⋊Dic43C2311yescharacteristic
126C2×Dic43⋊C4—22no—
127C4⋊C4×D43—24no—
128C4⋊C4×D43—24no—
129C4⋊C4×D43—22no—
130C2×(C2×D43)⋊C4—22no—
131C2×(C2×D43)⋊C4—21no—
132C2×(C2×D43)⋊C4D412yes—
133#13063259C2314yes—
134#13063256C2314yes—
135C4⋊(C43⋊C8)C2312yes—
136#13063249C2314yes—
137#13063249C2318yes—
138#13063247C2314yes—
139#13063247C2314yes—
140#13063245C2314yes—
141C22⋊(C43⋊C8)C2312yes—
142(C2×D43)⋊C8C2318yes—
143C4×C43⋊C8C2312yes—
144C22×Q8×C43C2312yes—
145C2×Q16×C43C2318yes—
146C4⋊Q8×C43—21no—
147C4⋊Q8×C43—21no—
148C4⋊Q8×C43C2312yes—
149C4⋊Q8×C43C2312yes—
150C4⋊Q8×C43C2311yescharacteristic
151C4⋊Q8×C43C2311yescharacteristic
152#125×C43—21no—
153C22⋊Q8×C43—21no—
154C22⋊Q8×C43C2312yes—
155C4×Q8×C43—21no—
156C4×Q8×C43C2312yes—
157#117×C43—21no—
158C2×C4⋊C4×C43—21no—
159C2×C4⋊C4×C43—21no—
160C2×C42×C43C2311yescharacteristic
161C4⋊C8×C43C2312yes—
162#103×C43C2318yes—
163C22⋊C8×C43C2312yes—
164C4×C8×C43C2312yes—
165C23×D43—21no—
166C23×D43C2×D412yes—
167C2×Q8×C43—22no—
168C2×Q8×C43—21no—
169C2×Q8×C43—44no—
170C2×Q8×C43C2414yes—
171C2×Q8×C43C2412yes—
172C22×C4×C43—22no—
173C22×C4×C43C2×D411yescharacteristic
174C22×C4×C43C2×D411yescharacteristic
175C22×C4×C43C2411yescharacteristic
176C2×C22⋊D43—22no—
177C22×Dic43—21no—
178C22×Dic43C2×D412yes—
179#10621902—216no—
180#10621902—48no—
181#10621902—48no—
182#10621902—416no—
183#10621898—44no—
184C2×D172—24no—
185C2×D172—21no—
186C2×D172—24no—
187C2×D172—21no—
188C2×D172—21no—
189C2×D172—28no—
190C2×D172—24no—
191C2×D172—24no—
192C2×D172—48no—
193C2×D172C2×D412yes—
194C2×D172C2×D412yes—
195C2×D172C2412yes—
196C2×D172C2412yes—
197C2×C4×D43—22no—
198C2×C4×D43—22no—
199C2×C4×D43—22no—
200C2×C4×D43—28no—
201C2×C4×D43—24no—
202C2×C4×D43—48no—
203C2×C4×D43—44no—
204C2×C4×D43—44no—
205C2×C4×D43C2×D414yes—
206C2×C4×D43C2414yes—
207C2×Dic86—21no—
208Q16×C43—48no—
209C2×C8×C43C2414yes—
210C4⋊C4×C43—22no—
211C4⋊C4×C43—22no—
212C4⋊C4×C43—22no—
213C4⋊C4×C43—22no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43—21no—
217C4⋊C4×C43—22no—
218C4⋊C4×C43—22no—
219C4⋊C4×C43C2412yes—
220C22⋊C4×C43—22no—
221C42×C43—22no—
222C42×C43C2×D411yescharacteristic
223C42×C43C2×D411yescharacteristic
224C42×C43C2411yescharacteristic
225C42×C43C2411yescharacteristic
226#10621884—28no—
227#10621884—48no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4—24no—
233(C2×D43)⋊C4—28no—
234(C2×D43)⋊C4—24no—
235(C2×D43)⋊C4—24no—
236(C2×D43)⋊C4C2×D414yes—
237(C2×D43)⋊C4C2×D414yes—
238C4⋊Dic43—21no—
239C4⋊Dic43—21no—
240C4⋊Dic43C2×D412yes—
241C4⋊Dic43C2×D412yes—
242C4⋊Dic43C2412yes—
243C4⋊Dic43C2412yes—
244Dic43⋊C4—28no—
245Dic43⋊C4—24no—
246C4×Dic43—24no—
247C2×C43⋊C8C2414yes—
248D344—28no—
249C8×D43—48no—
250C23×C43C22×D411yescharacteristic
251C22×D43—24no—
252C22×D43—22no—
253C22×D43—24no—
254C22×D43—22no—
255C22×D43—42no—
256C22×D43—42no—
257C22×D43—42no—
258C22×D43—42no—
259C22×D43C22×D414yes—
260Q8×C43—24no—
261Q8×C43—28no—
262Q8×C43—44no—
263Q8×C43—81no—
264C2×C4×C43—22no—
265C2×C4×C43—22no—
266C2×C4×C43—22no—
267C2×C4×C43—24no—
268C2×C4×C43—41no—
269C2×C4×C43—44no—
270C2×C4×C43#13514yescomplemented
271C2×C4×C43C22×D411yescharacteristic
272C2×C4×C43C22×D411yescharacteristic
273C2×C4×C43C22×D411yescharacteristic
274C2×C4×C43C22×D411yescharacteristic
275C2×C4×C43C22×D411yescharacteristic
276C2×C4×C43C2511yescharacteristic
277C22⋊D43—44no—
278C2×Dic43—22no—
279C2×Dic43—22no—
280C2×Dic43—42no—
281C2×Dic43—42no—
282C2×Dic43C22×D414yes—
283D172—24no—
284D172—24no—
285D172—24no—
286D172—22no—
287D172—24no—
288D172—416no—
289D172—42no—
290D172—81no—
291D172—84no—
292D172—84no—
293D172H(5,𝔽2)14yes—
294C4×D43—28no—
295C4×D43—44no—
296C4×D43—416no—
297C4×D43—44no—
298C4×D43—44no—
299C4×D43—44no—
300C4×D43—84no—
301Dic86—42no—
302C8×C43—24no—
303C43⋊C8—24no—
304#61565—431nomaximal, Sylow
305C22×C43—21no—
306C22×C43—21no—
307C22×C43C2×#13512yes—
308C22×C43C23×D411yescharacteristic
309C2×D43—24no—
310C2×D43—24no—
311C2×D43—24no—
312C2×D43—24no—
313C2×D43—48no—
314C2×D43—42no—
315C2×D43—42no—
316C2×D43—42no—
317C2×D43—42no—
318C2×D43—42no—
319C2×D43—84no—
320C4×C43—21no—
321C4×C43—21no—
322C4×C43—21no—
323C4×C43—42no—
324C4×C43—44no—
325C4×C43—42no—
326C4×C43C2×#13512yes—
327C4×C43C2×#13512yes—
328C4×C43C2×H(5,𝔽2)12yes—
329Dic43—24no—
330Dic43—42no—
331Dic43—42no—
332#3506—431no—
333C2×#547—431no—
334#3303—434no—
335#3302—434no—
336#3284—434no—
337#3283—434no—
338#3209D4311yescharacteristic, complemented
339#3206—431no—
340#3190—434no—
341#3101—431no—
342#3100—431no—
343#3002—434no—
344#2972—431no—
345C2×C43—22no—
346C2×C43#348411yescharacteristic
347C2×C43C22×#13511yescharacteristic
348C2×C43#358611yescharacteristic
349D43—44no—
350D43—44no—
351D43—82no—
352C22×#41—432no—
353C2×#135—438no—
354#559—862no—
355#556—432no—
356#555—432no—
357#553—862no—
358#550—432no—
359#547—434no—
360#547—434no—
361#547—432no—
362#547—862no—
363#547—862no—
364#538—862no—
365#535—861no—
366#533C2×D4311yescharacteristic
367#532—431no—
368C2×C4⋊Q8C2×D4311yescharacteristic
369#525—434no—
370C2×#123—862no—
371C2×C22⋊Q8—432no—
372C2×#121—861no—
373#520—861no—
374C2×C4×D4—431no—
375C2×C4×D4—431no—
376C22×C4⋊C4—861no—
377#494C2×D4312yescomplemented
378#492—432no—
379#487—432no—
380#487C2×D4312yescomplemented
381#485—438no—
382#483—432no—
383#480—432no—
384#476—432no—
385#474—432no—
386#467—438no—
387#465—438no—
388#462C2×D4314yescomplemented
389#461—432no—
390#461—434no—
391#459—432no—
392#452—438no—
393#452—438no—
394#451C2×D4314yes—
395#450—432no—
396#449—438no—
397#448—434no—
398#447—432no—
399C4×SD16—434no—
400C4×D8—434no—
401C8×D4—434no—
402C8×D4—434no—
403#431—431no—
404#431C2×D4311yescharacteristic
405#416—438no—
406C2×C22⋊C8—434no—
407C43#6156511yescharacteristic, complemented, Sylow
408C2×#41—438no—
409C2×#41—434no—
410C2×#41—864no—
411C2×#41—861no—
412C2×#41—1728no—
413C22×Q8C22×D4312yes—
414C22×D4—431no—
415C22×D4—431no—
416C22×D4—862no—
417C23×C4—432no—
418C23×C4—862no—
419C23×C4—861no—
420#135—17216no—
421C2×Q16C22×D4318yes—
422C2×SD16—434no—
423C2×SD16—438no—
424C2×D8—434no—
425C22×C8—438no—
426C4⋊Q8—21no—
427C4⋊Q8—21no—
428C4⋊Q8—431no—
429C4⋊Q8C22×D4312yes—
430C4⋊Q8C22×D4312yes—
431C4⋊Q8C22×D4311yescharacteristic
432C4⋊Q8C22×D4311yescharacteristic
433#127—431no—
434#127—862no—
435#126—864no—
436#125—21no—
437#124—862no—
438#124—864no—
439#124—861no—
440#123—868no—
441#123—868no—
442#123—864no—
443#123—864no—
444C22⋊Q8—21no—
445C22⋊Q8—438no—
446C22⋊Q8—434no—
447C22⋊Q8—864no—
448C22⋊Q8C22×D4312yes—
449#121—432no—
450#121—434no—
451#121—864no—
452#121—864no—
453#121—864no—
454#121—862no—
455#121—862no—
456#121—861no—
457#120—864no—
458C4×Q8—21no—
459C4×Q8—862no—
460C4×Q8C22×D4312yes—
461C4×D4—432no—
462C4×D4—432no—
463C4×D4—432no—
464C4×D4—432no—
465C4×D4—432no—
466C4×D4—432no—
467C4×D4—432no—
468C4×D4—862no—
469C4×D4—864no—
470C4×D4—864no—
471C4×D4—861no—
472C4×D4—861no—
473C4×D4—861no—
474#117—21no—
475#117—434no—
476#117—862no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—431no—
480C2×C4⋊C4—431no—
481C2×C4⋊C4—864no—
482C2×C4⋊C4—864no—
483C2×C4⋊C4—862no—
484C2×C4⋊C4—862no—
485C2×C22⋊C4—432no—
486C2×C22⋊C4—862no—
487C2×C22⋊C4—861no—
488C2×C42C22×D4311yescharacteristic
489#107—434no—
490#106—434no—
491C4⋊C8—432no—
492C4⋊C8C22×D4312yes—
493#103—438no—
494#103—434no—
495#103C22×D4318yes—
496#102—434no—
497#102—434no—
498#102—434no—
499C22⋊C8—432no—
500C22⋊C8—438no—
501C22⋊C8C22×D4312yes—
502C4×C8—432no—
503C4×C8C22×D4312yes—
504C24—432no—
505C24—861no—
506#41—8616no—
507#41—1728no—
508#41—1728no—
509#41—17216no—
510#41—1724no—
511C2×Q8—22no—
512C2×Q8—21no—
513C2×Q8—44no—
514C2×Q8—861no—
515C2×Q8C23×D4314yes—
516C2×Q8C23×D4312yes—
517C2×D4—432no—
518C2×D4—432no—
519C2×D4—432no—
520C2×D4—432no—
521C2×D4—864no—
522C2×D4—864no—
523C2×D4—864no—
524C2×D4—868no—
525C2×D4—862no—
526C2×D4—864no—
527C2×D4—861no—
528C2×D4—861no—
529C2×D4—861no—
530C2×D4—1728no—
531C22×C4—22no—
532C22×C4—432no—
533C22×C4—434no—
534C22×C4—434no—
535C22×C4—864no—
536C22×C4—868no—
537C22×C4—861no—
538C22×C4—862no—
539C22×C4—862no—
540C22×C4—862no—
541C22×C4—1724no—
542C22×C4—1728no—
543C22×C4—1724no—
544C22×C4D4×D4311yescharacteristic
545C22×C4D4×D4311yescharacteristic
546C22×C4C23×D4311yescharacteristic
547Q16—48no—
548SD16—868no—
549SD16—1728no—
550D8—868no—
551C2×C8—434no—
552C2×C8—1728no—
553C2×C8C23×D4314yes—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—22no—
563C4⋊C4—432no—
564C4⋊C4—432no—
565C4⋊C4—432no—
566C4⋊C4—432no—
567C4⋊C4—868no—
568C4⋊C4—864no—
569C4⋊C4—861no—
570C4⋊C4—861no—
571C4⋊C4C23×D4312yes—
572C22⋊C4—22no—
573C22⋊C4—434no—
574C22⋊C4—434no—
575C22⋊C4—864no—
576C22⋊C4—868no—
577C22⋊C4—864no—
578C22⋊C4—864no—
579C22⋊C4—862no—
580C22⋊C4—862no—
581C22⋊C4—862no—
582C22⋊C4—862no—
583C42—22no—
584C42—864no—
585C42D4×D4311yescharacteristic
586C42D4×D4311yescharacteristic
587C42C23×D4311yescharacteristic
588C42C23×D4311yescharacteristic
589C23—434no—
590C23—864no—
591C23—864no—
592C23—862no—
593C23—862no—
594C23—1722no—
595C23—1722no—
596C23—1722no—
597C23—1722no—
598C23C2×D4×D4311yescharacteristic
599Q8—24no—
600Q8—28no—
601Q8—44no—
602Q8—81no—
603Q8—1722no—
604D4—434no—
605D4—864no—
606D4—864no—
607D4—864no—
608D4—862no—
609D4—864no—
610D4—3441no—
611D4—3444no—
612D4—3444no—
613D4—17216no—
614D4—1724no—
615D4—1722no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—41no—
621C2×C4—44no—
622C2×C4—434no—
623C2×C4—868no—
624C2×C4—862no—
625C2×C4—862no—
626C2×C4—3444no—
627C2×C4—1724no—
628C2×C4—17216no—
629C2×C4—1722no—
630C2×C4—1722no—
631C2×C4—1724no—
632C2×C4—1724no—
633C2×C4—1724no—
634C2×C4#1306334814yescomplemented
635C2×C4C2×D4×D4311yescharacteristic
636C2×C4C2×D4×D4311yescharacteristic
637C2×C4C2×D4×D4311yescharacteristic
638C2×C4C2×D4×D4311yescharacteristic
639C2×C4C2×D4×D4311yescharacteristic
640C2×C4C24×D4311yescharacteristic
641C8—24no—
642C8—864no—
643C22—21no—
644C22—21no—
645C22—864no—
646C22—864no—
647C22—864no—
648C22—864no—
649C22—3444no—
650C22—1728no—
651C22—1722no—
652C22—1722no—
653C22—1722no—
654C22—1722no—
655C22—1722no—
656C22C2×#1306334812yes—
657C22C22×D4×D4311yescharacteristic
658C4—21no—
659C4—21no—
660C4—21no—
661C4—42no—
662C4—44no—
663C4—42no—
664C4—864no—
665C4—1722no—
666C4—1722no—
667C4C2×#1306334812yes—
668C4C2×#1306334812yes—
669C4H(5,𝔽2)×D4312yes—
670C2—22no—
671C2—3442no—
672C2—1724no—
673C2—1724no—
674C2#1914822911yescharacteristic
675C2C22×#1306334811yescharacteristic
676C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3209C2
socleC22×C43C23×D4
hypercenter#3209D43
hypocenterC43#61565
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3209

Complements

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

NH ≅ G/Ntype
1. #19148449C2semidirect
2. C2×#14583552C2semidirect
3. #19146522C2semidirect
4. #19146515C2semidirect
5. #19146320C2semidirect
6. #19146315C2semidirect
7. #19145520C2semidirect
8. #19145379C2semidirect
9. #19144599C2semidirect
10. #19144596C2semidirect
11. #19143818C2semidirect
12. #19143618C2semidirect
13. C43×#3209C2semidirect
15. C2×#13063348C22semidirect
17. #14583622C22semidirect
18. #14583615C22semidirect
20. #14583571C22semidirect
25. #14583552C22semidirect
37. #14583273C22semidirect
38. #14583249C22semidirect
39. #14583239C22semidirect
42. #14583186C22semidirect
43. #14583180C22semidirect
44. #14583137C22semidirect
45. #14583131C22semidirect
46. #14583101C22semidirect
47. #14583101C22semidirect
48. #14583095C22semidirect
49. #14583060C22semidirect
50. #14583060C22semidirect
52. #14583047C22semidirect
55. C4×#10621884C22semidirect
56. C4×D344C22semidirect
57. C8×D172C22semidirect
58. #14582964C22semidirect
60. #14582894C22semidirect
64. C43×#494C22semidirect
65. C43×#487C22semidirect
66. C43×#462C22semidirect
270. C2×C4×C43#135semidirect
338. #3209D43semidirect
377. #494C2×D43semidirect
380. #487C2×D43semidirect
388. #462C2×D43semidirect
407. C43#61565semidirect
634. C2×C4#13063348semidirect

Maximal subgroups

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

subgroupindex
#191484492
C2×#145835522
#191465222
#191465152
#191463202
#191463152
#191455202
#191453792
#191445992
#191445962
#191438182
#191436182
C43×#32092
#6156543