Finite Group Databasebeta

← #25975912

Subgroups — #25975912

Order 11008.

1860 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148508C211yesmaximal, characteristic, complemented
2#19148449C211yesmaximal, characteristic, complemented
3#19147220C212yesmaximal, complemented
4#19147189C212yesmaximal, complemented
5#19147139C214yesmaximal, complemented
6#19147064C214yesmaximal, complemented
7#19147017C212yesmaximal, complemented
8#19146951C212yesmaximal, complemented
9#19144588C212yesmaximal, complemented
10#19144555C212yesmaximal, complemented
11#19144377C211yesmaximal, characteristic, complemented
12C2×#14583186C211yesmaximal, characteristic, complemented
13#19144276C212yesmaximal, complemented
14C4×#13063353C211yesmaximal, characteristic, complemented
15#19143341C211yesmaximal, characteristic, complemented
16#19143189C212yesmaximal, complemented
17C43×#3165C211yesmaximal, characteristic, complemented
18C2×#13063353C2211yescharacteristic
19C2×#13063333C2212yes—
20#14583634—22no—
21#14583623C2212yescomplemented
22#14583622—21no—
23#14583615C2212yes—
24#14583615C2212yescomplemented
25#14583610C2212yescomplemented
26#14583602C2214yes—
27#14583597—22no—
28#14583571—21no—
29#14583560—22no—
30#14583552C2212yes—
31#14583552C2212yescomplemented
32#14583523—22no—
33#14583489—22no—
34#14583480C2212yes—
35#14583468C2212yes—
36#14583454—21no—
37#14583450—21no—
38#14583449C2211yescharacteristic
39#14583412—22no—
40#14583380C2212yes—
41#14583379C2212yes—
42C4×#10621898C2211yescharacteristic
43C2×C4×D172C2211yescharacteristic
44#14583242C2214yescomplemented
45#14583231C2214yescomplemented
46#14583226C2214yes—
47#14583226C2214yescomplemented
48#14583225C2214yes—
49#14583219C2214yes—
50#14583219C2214yescomplemented
51#14583214C2214yes—
52#14583203C2212yescomplemented
53#14583196C2212yescomplemented
54#14583191C2211yescharacteristic, complemented
55#14583186C2212yes—
56#14583186C2214yes—
57#14583186C2212yes—
58#14583186C2211yescharacteristic, complemented
59#14583181C2211yescharacteristic, complemented
60#14583176C2211yescharacteristic, complemented
61#14583153C2214yes—
62#14583146C2214yes—
63#14583136C2214yes—
64#14583129C2214yes—
65#14583012C2212yes—
66#14583001C2212yes—
67C4×#10621873C2212yes—
68C4×D344C2212yes—
69#14582978C2212yescomplemented
70#14582972C2214yescomplemented
71C8×D172C2212yescomplemented
72#14582941C2211yescharacteristic
73#14582940C2214yescomplemented
74#14582938C2214yescomplemented
75#14582936C2214yescomplemented
76#14582935C2212yes—
77C2×#13063256C2212yes—
78#106×D43C2214yescomplemented
79C2×C4⋊(C43⋊C8)C2211yescharacteristic
80#14582905C2211yescharacteristic
81#14582901C2211yescharacteristic
82#14582893C2212yes—
83C2×#13063245C2212yes—
84#14582867C2212yes—
85C43×#533C2211yescharacteristic
86C2×C4⋊Q8×C43C2211yescharacteristic
87C43×#501C2214yescomplemented
88C43×#500C2212yescomplemented
89C43×#498C2212yescomplemented
90C43×#428C2212yes—
91C43×#428C2212yes—
92C4×M16×C43C2211yescharacteristic
93C2×#10621902—22no—
94C2×#10621902—22no—
95C2×#10621898C2312yes—
96C2×#10621898C2311yescharacteristic
97C22×D172C2311yescharacteristic
98C22×C4×D43—21no—
99#13063353—24no—
100C2×#10621873C2312yes—
101C2×D344C2312yes—
102#13063333—28no—
103C2×#10621872C2314yes—
104C22×C43⋊C8C2312yes—
105C2×C8×D43C2314yes—
106#13063325D411yescharacteristic
107#13063322—22no—
108#13063322D411yescharacteristic
109#13063320—24no—
110#13063320—24no—
111#13063316—22no—
112#13063314—22no—
113#13063314—24no—
114#13063314—24no—
115#13063313—22no—
116#13063313D412yes—
117#13063310—24no—
118#13063310—24no—
119#13063310—24no—
120#13063305—22no—
121#13063305C2314yes—
122#13063301—24no—
123#13063301—22no—
124#13063301—22no—
125#13063300—24no—
126#13063300—22no—
127#13063300—22no—
128#13063300—22no—
129#13063300C2314yes—
130#13063300C2314yes—
131#13063300C2314yes—
132#13063299—24no—
133#13063299D412yes—
134#13063299D412yes—
135#13063295—24no—
136Q8×Dic43—22no—
137C4×Dic86—22no—
138C4×Dic86C2311yescharacteristic
139C4×Dic86C2311yescharacteristic
140#13063290—22no—
141C4×D172—22no—
142C4×D172—21no—
143C4×D172—21no—
144C4×D172C2312yes—
145C4×D172C2312yes—
146C4×D172C2312yes—
147C4×D172C2311yescharacteristic
148C4×D172C2312yes—
149C4×D172C2311yescharacteristic
150#13063287—22no—
151#13063287—22no—
152#13063287—24no—
153C4×C22⋊D43—21no—
154C4×C22⋊D43—21no—
155C4×C22⋊D43—24no—
156(C22⋊D43)⋊C4—24no—
157#13063284C2311yescharacteristic
158#13063283—22no—
159#13063283—22no—
160#13063283C2314yes—
161#13063283C2314yes—
162#13063282—21no—
163C2×C4⋊Dic43C2311yescharacteristic
164C4⋊C4×D43C2314yes—
165C4⋊C4×D43C2314yes—
166C2×(C2×D43)⋊C4—21no—
167C42×D43—21no—
168#13063259C2312yes—
169#13063258C2312yes—
170#13063258C2312yes—
171#13063257C2312yes—
172#13063256C2312yes—
173#13063256C2314yes—
174#13063256C2314yes—
175#13063256C2312yes—
176C4⋊(C43⋊C8)C2311yescharacteristic
177C4⋊(C43⋊C8)C2311yescharacteristic
178C4⋊(C43⋊C8)C2312yes—
179#13063250C2312yes—
180#13063248C2312yes—
181#13063248C2312yes—
182#13063247C2312yes—
183#13063247C2312yes—
184#13063247C2312yes—
185#13063245C2314yes—
186#13063245C2312yes—
187#13063245C2314yes—
188#13063245C2312yes—
189(C2×D43)⋊C8C2314yes—
190(C2×D43)⋊C8C2314yes—
191C22×Q8×C43—21no—
192C2×M16×C43C2311yescharacteristic
193C2×M16×C43C2311yescharacteristic
194C4⋊Q8×C43—21no—
195C4⋊Q8×C43—21no—
196C4⋊Q8×C43C2311yescharacteristic
197C4⋊Q8×C43C2312yes—
198C4⋊Q8×C43C2312yes—
199C4⋊Q8×C43C2311yescharacteristic
200#125×C43C2312yes—
201C22⋊Q8×C43—21no—
202C22⋊Q8×C43—21no—
203C4×Q8×C43—21no—
204C4×Q8×C43—21no—
205#117×C43C2312yes—
206C2×C4⋊C4×C43—21no—
207C2×C4⋊C4×C43C2312yes—
208C2×C42×C43C2311yescharacteristic
209#107×C43C2314yes—
210#107×C43C2314yes—
211#106×C43C2314yes—
212#106×C43C2314yes—
213#97×C43C2312yes—
214C4×C8×C43C2312yes—
215C23×D43—21no—
216C2×Q8×C43—21no—
217C2×Q8×C43—22no—
218C2×Q8×C43—21no—
219C2×Q8×C43—22no—
220C2×Q8×C43—82no—
221C22×C4×C43—22no—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43C2×D414yes—
227C22×Dic43—21no—
228#10621902—84no—
229#10621902—84no—
230#10621898—24no—
231#10621898—24no—
232#10621898—22no—
233#10621898—22no—
234C2×D172—21no—
235C2×D172—24no—
236C2×D172—24no—
237C2×D172—24no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172C2×D412yes—
241C2×D172C2×D412yes—
242C2×D172C2×D412yes—
243C2×D172C2411yescharacteristic
244C2×D172C2412yes—
245C2×C4×D43—21no—
246C2×C4×D43—21no—
247C2×C4×D43—21no—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—24no—
251C2×C4×D43—24no—
252C2×C4×D43—82no—
253C2×C4×D43C2414yes—
254C2×Dic86C2×D412yes—
255C2×Dic86C2411yescharacteristic
256M16×C43—22no—
257M16×C43#4114yescomplemented
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C4⋊C4×C43—22no—
261C4⋊C4×C43—22no—
262C4⋊C4×C43—22no—
263C4⋊C4×C43—22no—
264C4⋊C4×C43—22no—
265C4⋊C4×C43—21no—
266C4⋊C4×C43—21no—
267C4⋊C4×C43C2412yes—
268C4⋊C4×C43C2414yes—
269C4⋊C4×C43C2412yes—
270C22⋊C4×C43—22no—
271C42×C43—22no—
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2411yescharacteristic
275C42×C43C2411yescharacteristic
276C22⋊Dic43—21no—
277(C2×D43)⋊C4—22no—
278(C2×D43)⋊C4—22no—
279(C2×D43)⋊C4—21no—
280(C2×D43)⋊C4—21no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4C2×D414yes—
288(C2×D43)⋊C4C2×D414yes—
289C4⋊Dic43—21no—
290C4⋊Dic43—24no—
291C4⋊Dic43C2×D412yes—
292C4⋊Dic43C2×D412yes—
293C4⋊Dic43C2411yescharacteristic
294C4⋊Dic43C2411yescharacteristic
295C4⋊Dic43C2412yes—
296Dic43⋊C4—21no—
297Dic43⋊C4—21no—
298Dic43⋊C4—24no—
299Dic43⋊C4—24no—
300C4×Dic43—21no—
301C4×Dic43—21no—
302C4×Dic43—21no—
303C4×Dic43—24no—
304C4×Dic43—24no—
305C2×C43⋊C8—24no—
306C2×C43⋊C8C2412yes—
307C2×C43⋊C8C2412yes—
308D344—24no—
309#10621873—24no—
310#10621872—28no—
311C8×D43—28no—
312C23×C43C22×D411yescharacteristic
313C22×D43—21no—
314C22×D43—22no—
315C22×D43—42no—
316C22×D43—81no—
317C22×D43—81no—
318C22×D43C22×D414yes—
319Q8×C43—44no—
320Q8×C43—42no—
321Q8×C43—81no—
322Q8×C43—82no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—24no—
326C2×C4×C43—22no—
327C2×C4×C43—41no—
328C2×C4×C43—82no—
329C2×C4×C43C22×D411yescharacteristic
330C2×C4×C43C22×D411yescharacteristic
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C22×D411yescharacteristic
333C2×C4×C43C22×D411yescharacteristic
334C2×C4×C43C2×#4112yes—
335C2×C4×C432−1+412yes—
336C2×C4×C43C2511yescharacteristic
337C22⋊D43—28no—
338C22⋊D43—42no—
339C2×Dic43—21no—
340C2×Dic43—21no—
341C2×Dic43—21no—
342C2×Dic43—22no—
343C2×Dic43—81no—
344C2×Dic43C22×D414yes—
345D172—24no—
346D172—24no—
347D172—22no—
348D172—21no—
349D172—22no—
350D172—21no—
351D172—42no—
352D172—42no—
353D172—84no—
354D172—84no—
355D172—84no—
356C4×D43—24no—
357C4×D43—24no—
358C4×D43—42no—
359C4×D43—42no—
360C4×D43—42no—
361C4×D43—44no—
362C4×D43—82no—
363C4×D43—84no—
364C4×D43—84no—
365Dic86—24no—
366Dic86—21no—
367Dic86—21no—
368C8×C43—22no—
369C8×C43C2×#4114yes—
370C43⋊C8—22no—
371C43⋊C8—22no—
372#61279—431nomaximal, Sylow
373C22×C43—21no—
374C22×C43—21no—
375C22×C43#54712yes—
376C22×C43C23×D411yescharacteristic
377C2×D43—24no—
378C2×D43—24no—
379C2×D43—24no—
380C2×D43—42no—
381C2×D43—41no—
382C2×D43—42no—
383C2×D43—41no—
384C2×D43—42no—
385C2×D43—41no—
386C2×D43—84no—
387C4×C43—21no—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—44no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43#54712yes—
394C4×C43#57712yes—
395C4×C43C22×#4111yescharacteristic
396C4×C43C2×2−1+411yescharacteristic
397Dic43—24no—
398Dic43—41no—
399Dic43—41no—
400Dic43—42no—
401Dic43—41no—
402#3511—431no—
403#3506—431no—
404#3357—432no—
405#3354—432no—
406#3350—434no—
407#3345—434no—
408#3341—432no—
409#3335—432no—
410#3165D4311yescharacteristic, complemented
411#3099—432no—
412#3096—432no—
413#3076—431no—
414C2×#476—431no—
415#3062—432no—
416C4×AGL(1,ℤ/8)—431no—
417#2935—431no—
418#2912—432no—
419C2×C43—22no—
420C2×C43C2×#54711yescharacteristic
421C2×C43C2×#57711yescharacteristic
422C2×C43#358511yescharacteristic
423D43—44no—
424D43—81no—
425D43—82no—
426C2×AGL(1,ℤ/8)—431no—
427C2×#131—432no—
428#559—862no—
429#556—432no—
430#556—861no—
431#555—432no—
432#555—432no—
433#554—432no—
434#553—434no—
435#553—862no—
436#550—861no—
437#548—862no—
438#547—432no—
439#547—432no—
440#542—862no—
441#538—862no—
442#537—432no—
443#535—432no—
444#533—861no—
445#533C2×D4311yescharacteristic
446#532—431no—
447#532—861no—
448C2×C4⋊Q8C2×D4311yescharacteristic
449#525—862no—
450#520—432no—
451#520—432no—
452C4×#41—431no—
453C2×C4×D4—431no—
454#501C2×D4314yescomplemented
455#500C2×D4312yescomplemented
456#498C2×D4312yescomplemented
457#485—434no—
458#483—434no—
459#482—434no—
460#482—434no—
461#482—434no—
462#481—434no—
463#481—434no—
464#480—434no—
465#479—432no—
466#478—432no—
467#477—431no—
468#476—431no—
469#476—432no—
470#476—434no—
471#476—432no—
472#475—431no—
473#474—431no—
474#469—434no—
475#468—434no—
476#466—434no—
477#465—434no—
478#442—432no—
479#440—432no—
480C4×SD16—432no—
481C4×D8—432no—
482#436—432no—
483#435—434no—
484C8×D4—432no—
485#428—431no—
486#428—434no—
487#428—434no—
488#428C2×D4312yes—
489#428C2×D4312yes—
490#427—432no—
491#427—434no—
492C2×#106—432no—
493C2×#106—434no—
494C2×C4⋊C8—431no—
495#418—431no—
496#417—431no—
497#416—432no—
498C2×#102—432no—
499#408—432no—
500C4×M16C2×D4311yescharacteristic
501C43#6127911yescharacteristic, complemented, Sylow
502C2×#41—432no—
503C2×#41—431no—
504C2×#41—862no—
505C2×#41—862no—
506C22×Q8—21no—
507C22×D4—431no—
508C23×C4—861no—
509AGL(1,ℤ/8)—864no—
510C2×SD16—432no—
511C2×D8—432no—
512#131—868no—
513C2×M16—434no—
514C2×M16C22×D4311yescharacteristic
515C2×M16C22×D4311yescharacteristic
516C22×C8—432no—
517C22×C8—434no—
518C4⋊Q8—21no—
519C4⋊Q8—21no—
520C4⋊Q8—431no—
521C4⋊Q8C22×D4312yes—
522C4⋊Q8C22×D4312yes—
523C4⋊Q8C22×D4311yescharacteristic
524C4⋊Q8C22×D4311yescharacteristic
525#127—431no—
526#127—862no—
527#126—864no—
528#126—864no—
529#125—862no—
530#125C22×D4312yes—
531#124—432no—
532#124—862no—
533#124—864no—
534#124—864no—
535#124—862no—
536#123—864no—
537#123—864no—
538#123—864no—
539C22⋊Q8—21no—
540C22⋊Q8—21no—
541C22⋊Q8—434no—
542C22⋊Q8—864no—
543C22⋊Q8—862no—
544C22⋊Q8—862no—
545C22⋊Q8—862no—
546#121—432no—
547#121—432no—
548#121—434no—
549#121—434no—
550#121—434no—
551#121—862no—
552#121—862no—
553#121—862no—
554#121—864no—
555#121—864no—
556#120—864no—
557C4×Q8—21no—
558C4×Q8—21no—
559C4×Q8—431no—
560C4×Q8—431no—
561C4×Q8—862no—
562C4×Q8—862no—
563C4×Q8—862no—
564C4×D4—432no—
565C4×D4—432no—
566C4×D4—432no—
567C4×D4—432no—
568C4×D4—431no—
569C4×D4—431no—
570C4×D4—862no—
571C4×D4—864no—
572C4×D4—864no—
573C4×D4—862no—
574C4×D4—862no—
575C4×D4—864no—
576C4×D4—861no—
577C4×D4—861no—
578C4×D4—861no—
579C4×D4—861no—
580#117—431no—
581#117—434no—
582#117—434no—
583#117—862no—
584#117—862no—
585#117—861no—
586#117C22×D4312yes—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—434no—
590C2×C4⋊C4—434no—
591C2×C4⋊C4C22×D4312yes—
592C2×C22⋊C4—861no—
593C2×C42—861no—
594C2×C42C22×D4311yescharacteristic
595#107—432no—
596#107—432no—
597#107—432no—
598#107C22×D4314yes—
599#107C22×D4314yes—
600#106—432no—
601#106—432no—
602#106—434no—
603#106—434no—
604#106—432no—
605#106C22×D4314yes—
606#106C22×D4314yes—
607C4⋊C8—431no—
608C4⋊C8—432no—
609C4⋊C8—431no—
610#103—432no—
611#103—432no—
612#103—432no—
613#102—432no—
614#102—432no—
615#102—432no—
616#102—434no—
617#102—434no—
618#102—432no—
619#102—432no—
620C22⋊C8—434no—
621C22⋊C8—434no—
622#97C22×D4312yes—
623C4×C8C22×D4312yes—
624C24—861no—
625#41—864no—
626#41—864no—
627#41—862no—
628#41—862no—
629#41—3444no—
630#41—3444no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—21no—
634C2×Q8—22no—
635C2×Q8—82no—
636C2×Q8—432no—
637C2×Q8—431no—
638C2×D4—434no—
639C2×D4—432no—
640C2×D4—432no—
641C2×D4—432no—
642C2×D4—431no—
643C2×D4—432no—
644C2×D4—864no—
645C2×D4—864no—
646C2×D4—864no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—862no—
650C2×D4—862no—
651C22×C4—22no—
652C22×C4—434no—
653C22×C4—864no—
654C22×C4—864no—
655C22×C4—861no—
656C22×C4—862no—
657C22×C4—861no—
658C22×C4—861no—
659C22×C4—861no—
660C22×C4—862no—
661C22×C4—3442no—
662C22×C4D4×D4311yescharacteristic
663C22×C4D4×D4311yescharacteristic
664C22×C4C23×D4311yescharacteristic
665SD16—864no—
666D8—864no—
667M16—22no—
668M16—868no—
669M16#1062190214yescomplemented
670C2×C8—432no—
671C2×C8—432no—
672C2×C8—864no—
673C2×C8—868no—
674C2×C8C23×D4312yes—
675C2×C8C23×D4312yes—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—21no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—21no—
683C4⋊C4—432no—
684C4⋊C4—432no—
685C4⋊C4—431no—
686C4⋊C4—431no—
687C4⋊C4—432no—
688C4⋊C4—864no—
689C4⋊C4—864no—
690C4⋊C4—864no—
691C4⋊C4—861no—
692C4⋊C4—861no—
693C4⋊C4—861no—
694C4⋊C4C23×D4314yes—
695C4⋊C4C23×D4312yes—
696C4⋊C4C23×D4312yes—
697C22⋊C4—22no—
698C22⋊C4—434no—
699C22⋊C4—434no—
700C22⋊C4—864no—
701C22⋊C4—864no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—861no—
707C22⋊C4—862no—
708C22⋊C4—862no—
709C22⋊C4—861no—
710C22⋊C4—861no—
711C42—22no—
712C42—864no—
713C42—864no—
714C42—861no—
715C42—861no—
716C42—861no—
717C42D4×D4311yescharacteristic
718C42D4×D4311yescharacteristic
719C42C23×D4311yescharacteristic
720C42C23×D4311yescharacteristic
721C23—434no—
722C23—861no—
723C23—862no—
724C23—3441no—
725C23—3441no—
726C23—1722no—
727C23C2×D4×D4311yescharacteristic
728Q8—44no—
729Q8—42no—
730Q8—82no—
731Q8—81no—
732Q8—864no—
733Q8—861no—
734Q8—861no—
735D4—868no—
736D4—864no—
737D4—864no—
738D4—861no—
739D4—862no—
740D4—862no—
741D4—861no—
742D4—3444no—
743D4—3444no—
744D4—3444no—
745D4—1722no—
746D4—1722no—
747D4—1722no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—41no—
753C2×C4—82no—
754C2×C4—434no—
755C2×C4—864no—
756C2×C4—864no—
757C2×C4—861no—
758C2×C4—862no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—3442no—
762C2×C4—3444no—
763C2×C4—3444no—
764C2×C4—3441no—
765C2×C4—1722no—
766C2×C4—1722no—
767C2×C4—1724no—
768C2×C4—1722no—
769C2×C4C2×D4×D4311yescharacteristic
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4C2×D4×D4311yescharacteristic
772C2×C4C2×D4×D4311yescharacteristic
773C2×C4C2×D4×D4311yescharacteristic
774C2×C4C2×#1062190212yes—
775C2×C4#1306337312yes—
776C2×C4C24×D4311yescharacteristic
777C8—22no—
778C8—862no—
779C8—862no—
780C8C2×#1062190214yes—
781C22—21no—
782C22—21no—
783C22—864no—
784C22—864no—
785C22—864no—
786C22—3444no—
787C22—1721no—
788C22—1722no—
789C22—1722no—
790C22—1721no—
791C22—1721no—
792C22—1722no—
793C22#1458355212yes—
794C22C22×D4×D4311yescharacteristic
795C4—21no—
796C4—21no—
797C4—21no—
798C4—42no—
799C4—44no—
800C4—42no—
801C4—864no—
802C4—1721no—
803C4—1722no—
804C4—1721no—
805C4—1721no—
806C4#1458355212yes—
807C4#1458370812yes—
808C4C22×#1062190211yescharacteristic
809C4C2×#1306337311yescharacteristic
810C2—22no—
811C2—3442no—
812C2—3441no—
813C2—1724no—
814C2C2×#1458355211yescharacteristic
815C2C2×#1458370811yescharacteristic
816C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3165C2
socleC22×C43C23×D4
hypercenter#3165D43
hypocenterC43#61279
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3165

Complements

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

NH ≅ G/Ntype
1. #19148508C2semidirect
2. #19148449C2semidirect
3. #19147220C2semidirect
4. #19147189C2semidirect
5. #19147139C2semidirect
6. #19147064C2semidirect
7. #19147017C2semidirect
8. #19146951C2semidirect
9. #19144588C2semidirect
10. #19144555C2semidirect
11. #19144377C2semidirect
12. C2×#14583186C2semidirect
13. #19144276C2semidirect
14. C4×#13063353C2semidirect
15. #19143341C2semidirect
16. #19143189C2semidirect
17. C43×#3165C2semidirect
21. #14583623C22semidirect
24. #14583615C22semidirect
25. #14583610C22semidirect
31. #14583552C22semidirect
44. #14583242C22semidirect
45. #14583231C22semidirect
47. #14583226C22semidirect
50. #14583219C22semidirect
52. #14583203C22semidirect
53. #14583196C22semidirect
54. #14583191C22semidirect
58. #14583186C22semidirect
59. #14583181C22semidirect
60. #14583176C22semidirect
69. #14582978C22semidirect
70. #14582972C22semidirect
71. C8×D172C22semidirect
73. #14582940C22semidirect
74. #14582938C22semidirect
75. #14582936C22semidirect
78. #106×D43C22semidirect
87. C43×#501C22semidirect
88. C43×#500C22semidirect
89. C43×#498C22semidirect
257. M16×C43#41semidirect
410. #3165D43semidirect
454. #501C2×D43semidirect
455. #500C2×D43semidirect
456. #498C2×D43semidirect
501. C43#61279semidirect
669. M16#10621902semidirect

Maximal subgroups

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

subgroupindex
#191485082
#191484492
#191472202
#191471892
#191471392
#191470642
#191470172
#191469512
#191445882
#191445552
#191443772
C2×#145831862
#191442762
C4×#130633532
#191433412
#191431892
C43×#31652
#6127943