Finite Group Databasebeta

← #25975456

Subgroups — #25975456

Order 11008.

1892 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148162C211yesmaximal, characteristic, complemented
2C2×#14583615C211yesmaximal, characteristic, complemented
3#19147220C212yesmaximal, complemented
4#19147189C212yesmaximal, complemented
5#19147109C214yesmaximal, complemented
6#19147094C214yesmaximal, complemented
7#19147017C212yesmaximal, complemented
8#19147007C212yesmaximal, complemented
9#19144537C212yesmaximal, complemented
10#19144529C212yesmaximal, complemented
11#19144404C211yesmaximal, characteristic, complemented
12#19144388C211yesmaximal, characteristic, complemented
13#19144215C212yesmaximal, complemented
14C4×#13063353C211yesmaximal, characteristic, complemented
15M16×D172C211yesmaximal, characteristic, complemented
16#19143182C212yesmaximal, complemented
17C43×#3165C211yesmaximal, characteristic, complemented
18C2×#13063353C2211yescharacteristic
19C2×M16×D43C2212yes—
20#14583623C2211yescharacteristic, complemented
21#14583615—21no—
22#14583615—21no—
23#14583615—22no—
24#14583615C2212yes—
25#14583615C2214yes—
26#14583615C2212yes—
27#14583615C2211yescharacteristic, complemented
28#14583610C2211yescharacteristic, complemented
29#14583602C2212yescomplemented
30#14583591—21no—
31#14583587C2212yescomplemented
32#14583576—22no—
33#14583552C2211yescharacteristic, complemented
34#14583540—21no—
35#14583436—21no—
36#14583436—22no—
37C2×#13063314—22no—
38#14583411C2212yes—
39C2×#13063300—21no—
40C2×#13063300C2212yes—
41C4×#10621902—21no—
42C4×#10621898C2211yescharacteristic
43C2×C4×D172C2211yescharacteristic
44C2×C4×D172C2211yescharacteristic
45C2×#13063283—21no—
46C2×#13063283C2212yes—
47#117×D43C2212yes—
48#14583243C2214yescomplemented
49#14583242C2214yescomplemented
50#14583226C2214yescomplemented
51#14583226C2214yescomplemented
52#14583225C2214yescomplemented
53#14583225C2214yescomplemented
54#14583219C2214yescomplemented
55#14583214C2214yescomplemented
56#14583196C2214yescomplemented
57#14583191C2212yescomplemented
58#14583186C2212yescomplemented
59#14583186C2212yescomplemented
60#14583181C2212yescomplemented
61#14583176C2212yescomplemented
62#14583176C2212yescomplemented
63#14583153C2214yescomplemented
64#14583146C2214yescomplemented
65#14583136C2214yescomplemented
66#14583129C2214yescomplemented
67#14583012C2212yescomplemented
68#14583001C2212yescomplemented
69C4×#10621873C2212yescomplemented
70C4×D344C2212yescomplemented
71#14582978C2212yescomplemented
72#14582972C2214yescomplemented
73C8×D172C2212yescomplemented
74#14582942C2212yes—
75#14582941C2211yescharacteristic
76#14582940C2214yescomplemented
77#14582939C2212yes—
78#14582938C2214yescomplemented
79#14582936C2214yescomplemented
80#14582934C2214yescomplemented
81#14582923C2211yescharacteristic
82#14582905C2211yescharacteristic
83#14582903C2212yes—
84#14582901C2211yescharacteristic
85#14582898C2212yes—
86#14582862C2212yes—
87C43×#533C2211yescharacteristic
88C2×C4⋊Q8×C43C2211yescharacteristic
89C43×#501C2214yescomplemented
90C43×#500C2212yescomplemented
91C43×#498C2212yescomplemented
92C43×#428C2212yes—
93C43×#428C2212yes—
94C4×M16×C43C2211yescharacteristic
95C2×#10621902—21no—
96C2×#10621898C2311yescharacteristic
97C22×D172—22no—
98C22×D172D411yescharacteristic
99C22×D172C2311yescharacteristic
100C22×C4×D43—21no—
101C22×C4×D43C2312yes—
102#13063353—24no—
103C2×#10621873C2312yes—
104C2×D344C2312yes—
105C2×#10621877C2312yes—
106C2×#10621872C2314yes—
107M16×D43—28no—
108C2×C8×D43C2314yes—
109#13063320—22no—
110#13063320—22no—
111#13063320—22no—
112#13063316—22no—
113#13063316—21no—
114#13063314—21no—
115#13063314—22no—
116#13063314—24no—
117#13063314—24no—
118#13063314—24no—
119#13063314—24no—
120#13063310—22no—
121#13063310—22no—
122#13063310—22no—
123#13063309—22no—
124#13063305C2312yes—
125#13063305C2312yes—
126#13063301—22no—
127#13063301—21no—
128#13063300—22no—
129#13063300—22no—
130#13063300—22no—
131#13063300—24no—
132#13063300—21no—
133#13063300—22no—
134#13063300—22no—
135#13063300C2312yes—
136#13063300C2312yes—
137#13063300C2314yes—
138#13063300C2314yes—
139#13063295—22no—
140Q8×Dic43—21no—
141C4×Dic86C2311yescharacteristic
142C4×Dic86C2311yescharacteristic
143C4×D172—22no—
144C4×D172—22no—
145C4×D172—21no—
146C4×D172—21no—
147C4×D172D411yescharacteristic
148C4×D172D411yescharacteristic
149C4×D172D412yes—
150C4×D172C2311yescharacteristic
151C4×D172C2312yes—
152C4×D172C2311yescharacteristic
153C4×D172C2311yescharacteristic
154C4×D172C2311yescharacteristic
155C4×D172C2312yes—
156C4×D172C2312yes—
157#13063287—21no—
158#13063287—22no—
159C4×C22⋊D43—21no—
160C4×C22⋊D43—21no—
161#13063284C2311yescharacteristic
162#13063283—22no—
163#13063283—22no—
164#13063283—22no—
165#13063283—21no—
166#13063283—22no—
167#13063283—22no—
168#13063283—24no—
169#13063283C2312yes—
170#13063283C2312yes—
171#13063283C2314yes—
172#13063283C2314yes—
173#13063282—22no—
174#13063282—21no—
175#13063281—22no—
176C2×C4⋊Dic43D411yescharacteristic
177C2×C4⋊Dic43C2311yescharacteristic
178C4⋊C4×D43C2312yes—
179C4⋊C4×D43C2312yes—
180C2×(C2×D43)⋊C4—22no—
181C2×(C2×D43)⋊C4—21no—
182C2×(C2×D43)⋊C4—22no—
183C2×(C2×D43)⋊C4D412yes—
184C22⋊C4×D43—22no—
185C2×C4×Dic43—22no—
186C42×D43—22no—
187C42×D43—21no—
188#13063259C2312yes—
189#13063258C2314yes—
190#13063258C2314yes—
191#13063257C2312yes—
192#13063256C2314yes—
193#13063256C2314yes—
194C4⋊(C43⋊C8)C2312yes—
195C4⋊(C43⋊C8)C2312yes—
196#13063250C2312yes—
197#13063248C2314yes—
198#13063247C2312yes—
199#13063247C2312yes—
200#13063247C2312yes—
201#13063245C2314yes—
202#13063245C2314yes—
203#13063245C2314yes—
204(C2×D43)⋊C8C2314yes—
205(C2×D43)⋊C8C2314yes—
206C22×Q8×C43—21no—
207C2×M16×C43C2311yescharacteristic
208C2×M16×C43C2311yescharacteristic
209C4⋊Q8×C43—21no—
210C4⋊Q8×C43—21no—
211C4⋊Q8×C43C2311yescharacteristic
212C4⋊Q8×C43C2312yes—
213C4⋊Q8×C43C2311yescharacteristic
214C4⋊Q8×C43C2312yes—
215#125×C43C2312yes—
216C22⋊Q8×C43—21no—
217C22⋊Q8×C43—21no—
218C4×Q8×C43—21no—
219C4×Q8×C43—21no—
220#117×C43C2312yes—
221C2×C4⋊C4×C43—21no—
222C2×C4⋊C4×C43C2312yes—
223C2×C42×C43C2311yescharacteristic
224#107×C43C2314yes—
225#107×C43C2314yes—
226#106×C43C2314yes—
227#106×C43C2314yes—
228#97×C43C2312yes—
229C4×C8×C43C2312yes—
230C23×D43—21no—
231C23×D43C2×D412yes—
232C2×Q8×C43—21no—
233C2×Q8×C43—21no—
234C2×Q8×C43—22no—
235C2×Q8×C43—22no—
236C2×Q8×C43—82no—
237C22×C4×C43—22no—
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2411yescharacteristic
241C2×C22⋊D43—21no—
242C22×Dic43—21no—
243C22×Dic43C2×D412yes—
244#10621902—44no—
245#10621898—22no—
246#10621898—22no—
247C2×D172—21no—
248C2×D172—22no—
249C2×D172—22no—
250C2×D172—24no—
251C2×D172—24no—
252C2×D172—22no—
253C2×D172—22no—
254C2×D172—42no—
255C2×D172—84no—
256C2×D172C2×D411yescharacteristic
257C2×D172C2×D411yescharacteristic
258C2×D172C2×D412yes—
259C2×D172C2411yescharacteristic
260C2×D172C2412yes—
261C2×C4×D43—24no—
262C2×C4×D43—24no—
263C2×C4×D43—21no—
264C2×C4×D43—21no—
265C2×C4×D43—22no—
266C2×C4×D43—22no—
267C2×C4×D43—21no—
268C2×C4×D43—22no—
269C2×C4×D43—22no—
270C2×C4×D43—44no—
271C2×C4×D43C2×D412yes—
272C2×C4×D43C2×D412yes—
273C2×C4×D43C2412yes—
274C2×C4×D43C2412yes—
275C2×Dic86C2411yescharacteristic
276M16×C43—22no—
277M16×C43#4114yescomplemented
278C2×C8×C43C2412yes—
279C2×C8×C43C2412yes—
280C4⋊C4×C43—22no—
281C4⋊C4×C43—22no—
282C4⋊C4×C43—22no—
283C4⋊C4×C43—22no—
284C4⋊C4×C43—22no—
285C4⋊C4×C43—21no—
286C4⋊C4×C43—21no—
287C4⋊C4×C43C2412yes—
288C4⋊C4×C43C2414yes—
289C4⋊C4×C43C2412yes—
290C22⋊C4×C43—22no—
291C42×C43—22no—
292C42×C43C2×D411yescharacteristic
293C42×C43C2×D411yescharacteristic
294C42×C43C2411yescharacteristic
295C42×C43C2411yescharacteristic
296C22⋊Dic43—21no—
297(C2×D43)⋊C4—22no—
298(C2×D43)⋊C4—22no—
299(C2×D43)⋊C4—21no—
300(C2×D43)⋊C4—21no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4—24no—
303(C2×D43)⋊C4—22no—
304(C2×D43)⋊C4—22no—
305(C2×D43)⋊C4—22no—
306(C2×D43)⋊C4—22no—
307(C2×D43)⋊C4—24no—
308(C2×D43)⋊C4—24no—
309(C2×D43)⋊C4—22no—
310(C2×D43)⋊C4—22no—
311(C2×D43)⋊C4C2×D412yes—
312(C2×D43)⋊C4C2×D412yes—
313(C2×D43)⋊C4C2×D412yes—
314(C2×D43)⋊C4C2×D412yes—
315C4⋊Dic43—21no—
316C4⋊Dic43—22no—
317C4⋊Dic43—22no—
318C4⋊Dic43C2×D411yescharacteristic
319C4⋊Dic43C2×D411yescharacteristic
320C4⋊Dic43C2×D412yes—
321C4⋊Dic43C2411yescharacteristic
322C4⋊Dic43C2411yescharacteristic
323C4⋊Dic43C2412yes—
324Dic43⋊C4—21no—
325Dic43⋊C4—21no—
326Dic43⋊C4—22no—
327Dic43⋊C4—22no—
328C4×Dic43—21no—
329C4×Dic43—21no—
330C4×Dic43—21no—
331C4×Dic43—22no—
332C4×Dic43—22no—
333C4×Dic43—24no—
334C4×Dic43—24no—
335#10621877—24no—
336C2×C43⋊C8C2414yes—
337D344—24no—
338#10621873—24no—
339#10621872—28no—
340C8×D43—28no—
341C23×C43C22×D411yescharacteristic
342C22×D43—24no—
343C22×D43—21no—
344C22×D43—22no—
345C22×D43—42no—
346C22×D43—42no—
347C22×D43—42no—
348C22×D43—42no—
349C22×D43—42no—
350C22×D43C22×D412yes—
351C22×D43C22×D412yes—
352Q8×C43—42no—
353Q8×C43—81no—
354Q8×C43—82no—
355Q8×C43—82no—
356C2×C4×C43—22no—
357C2×C4×C43—24no—
358C2×C4×C43—22no—
359C2×C4×C43—22no—
360C2×C4×C43—41no—
361C2×C4×C43—44no—
362C2×C4×C43C22×D411yescharacteristic
363C2×C4×C43C22×D411yescharacteristic
364C2×C4×C43C22×D411yescharacteristic
365C2×C4×C43C22×D411yescharacteristic
366C2×C4×C43C22×D411yescharacteristic
367C2×C4×C43C2×#4112yes—
368C2×C4×C432−1+412yes—
369C2×C4×C43C2511yescharacteristic
370C22⋊D43—42no—
371C2×Dic43—24no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—22no—
375C2×Dic43—21no—
376C2×Dic43—42no—
377C2×Dic43C22×D412yes—
378C2×Dic43C22×D412yes—
379D172—22no—
380D172—22no—
381D172—22no—
382D172—21no—
383D172—22no—
384D172—21no—
385D172—42no—
386D172—44no—
387D172—42no—
388D172—82no—
389D172—84no—
390D172—84no—
391C4×D43—24no—
392C4×D43—24no—
393C4×D43—22no—
394C4×D43—22no—
395C4×D43—22no—
396C4×D43—22no—
397C4×D43—44no—
398C4×D43—44no—
399C4×D43—42no—
400C4×D43—44no—
401C4×D43—42no—
402C4×D43—81no—
403C4×D43—82no—
404Dic86—21no—
405Dic86—21no—
406C8×C43—22no—
407C8×C43C2×#4114yes—
408C43⋊C8—24no—
409#61256—431nomaximal, Sylow
410C22×C43—21no—
411C22×C43—21no—
412C22×C43#54712yes—
413C22×C43C23×D411yescharacteristic
414C2×D43—22no—
415C2×D43—22no—
416C2×D43—22no—
417C2×D43—22no—
418C2×D43—22no—
419C2×D43—22no—
420C2×D43—42no—
421C2×D43—41no—
422C2×D43—42no—
423C2×D43—41no—
424C2×D43—42no—
425C2×D43—41no—
426C2×D43—84no—
427C2×D43—84no—
428C4×C43—21no—
429C4×C43—21no—
430C4×C43—21no—
431C4×C43—42no—
432C4×C43—44no—
433C4×C43—42no—
434C4×C43#54712yes—
435C4×C43#57512yes—
436C4×C43C22×#4111yescharacteristic
437C4×C43C2×2−1+411yescharacteristic
438Dic43—22no—
439Dic43—22no—
440Dic43—41no—
441Dic43—41no—
442Dic43—41no—
443Dic43—42no—
444#3475—431no—
445C2×#555—431no—
446#3357—432no—
447#3354—432no—
448#3348—434no—
449#3347—434no—
450#3341—432no—
451#3340—432no—
452#3165D4311yescharacteristic, complemented
453#3094—432no—
454#3093—432no—
455#3079—431no—
456#3077—431no—
457#3055—432no—
458C4×AGL(1,ℤ/8)—431no—
459D4×M16—431no—
460#2911—432no—
461C2×C43—22no—
462C2×C43C2×#54711yescharacteristic
463C2×C43C2×#57511yescharacteristic
464C2×C43#358511yescharacteristic
465D43—42no—
466D43—42no—
467D43—81no—
468D43—82no—
469C2×AGL(1,ℤ/8)—431no—
470C22×M16—432no—
471#556—431no—
472#555—432no—
473#555—431no—
474#555—434no—
475#555—432no—
476#555—861no—
477#555—861no—
478#555—862no—
479#554—431no—
480#553—432no—
481#552—432no—
482#552—861no—
483#551—862no—
484#547—431no—
485#546—861no—
486#533C2×D4311yescharacteristic
487C2×C4⋊Q8C2×D4311yescharacteristic
488#529—862no—
489#529—861no—
490C2×#124—862no—
491#525—432no—
492C2×#121—432no—
493C2×#121—861no—
494C4×#41—431no—
495C4×#41—861no—
496C2×C4×D4—431no—
497C2×C4×D4—431no—
498C2×#117—432no—
499C2×#117—432no—
500C2×#117—861no—
501#501C2×D4314yescomplemented
502#500C2×D4312yescomplemented
503#498C2×D4312yescomplemented
504#485—434no—
505#485—434no—
506#482—434no—
507#482—434no—
508#482—434no—
509#482—434no—
510#481—434no—
511#480—434no—
512#478—434no—
513#477—432no—
514#476—432no—
515#476—432no—
516#475—432no—
517#474—432no—
518#474—432no—
519#469—434no—
520#468—434no—
521#466—434no—
522#465—434no—
523#442—432no—
524#440—432no—
525C4×SD16—432no—
526C4×D8—432no—
527#436—432no—
528#435—434no—
529C8×D4—432no—
530#428—431no—
531#428—432no—
532#428—432no—
533#428—434no—
534#428—434no—
535#428C2×D4312yes—
536#428C2×D4312yes—
537#427—434no—
538#427—434no—
539#423—431no—
540#418—431no—
541#418—432no—
542#417—431no—
543#417—432no—
544#407—432no—
545C4×M16C2×D4311yescharacteristic
546C43#6125611yescharacteristic, complemented, Sylow
547C2×#41—431no—
548C2×#41—861no—
549C22×Q8—21no—
550C22×D4—431no—
551C22×D4—431no—
552C22×D4—862no—
553C23×C4—432no—
554C23×C4—861no—
555AGL(1,ℤ/8)—864no—
556C2×SD16—432no—
557C2×D8—432no—
558C2×M16—432no—
559C2×M16—434no—
560C2×M16—868no—
561C2×M16C22×D4311yescharacteristic
562C2×M16C22×D4311yescharacteristic
563C22×C8—434no—
564C4⋊Q8—21no—
565C4⋊Q8—21no—
566C4⋊Q8C22×D4312yes—
567C4⋊Q8C22×D4312yes—
568C4⋊Q8C22×D4311yescharacteristic
569C4⋊Q8C22×D4311yescharacteristic
570#126—862no—
571#126—862no—
572#126—862no—
573#125—862no—
574#125—861no—
575#125C22×D4312yes—
576#124—864no—
577#124—864no—
578#124—864no—
579#124—864no—
580#124—862no—
581#124—861no—
582#123—862no—
583#123—862no—
584#123—862no—
585#123—862no—
586C22⋊Q8—21no—
587C22⋊Q8—21no—
588C22⋊Q8—432no—
589C22⋊Q8—432no—
590C22⋊Q8—862no—
591C22⋊Q8—861no—
592#121—434no—
593#121—434no—
594#121—432no—
595#121—432no—
596#121—862no—
597#121—862no—
598#121—862no—
599#121—862no—
600#121—864no—
601#121—862no—
602#121—861no—
603#120—862no—
604C4×Q8—21no—
605C4×Q8—21no—
606C4×Q8—431no—
607C4×Q8—431no—
608C4×Q8—861no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—432no—
612C4×D4—431no—
613C4×D4—432no—
614C4×D4—431no—
615C4×D4—432no—
616C4×D4—432no—
617C4×D4—431no—
618C4×D4—431no—
619C4×D4—862no—
620C4×D4—862no—
621C4×D4—862no—
622C4×D4—861no—
623C4×D4—861no—
624C4×D4—861no—
625C4×D4—861no—
626C4×D4—861no—
627#117—431no—
628#117—432no—
629#117—432no—
630#117—434no—
631#117—434no—
632#117—862no—
633#117—862no—
634#117—862no—
635#117—862no—
636#117—862no—
637#117—864no—
638#117—861no—
639#117—862no—
640#117—862no—
641#117—861no—
642#117C22×D4312yes—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—431no—
645C2×C4⋊C4—431no—
646C2×C4⋊C4—432no—
647C2×C4⋊C4—432no—
648C2×C4⋊C4C22×D4312yes—
649C2×C22⋊C4—432no—
650C2×C22⋊C4—862no—
651C2×C22⋊C4—862no—
652C2×C22⋊C4—862no—
653C2×C22⋊C4—861no—
654C2×C42—862no—
655C2×C42—862no—
656C2×C42—861no—
657C2×C42C22×D4311yescharacteristic
658#107—432no—
659#107—434no—
660#107—434no—
661#107C22×D4314yes—
662#107C22×D4314yes—
663#106—432no—
664#106—434no—
665#106—434no—
666#106C22×D4314yes—
667#106C22×D4314yes—
668C4⋊C8—432no—
669C4⋊C8—432no—
670#103—432no—
671#103—434no—
672#102—432no—
673#102—432no—
674#102—432no—
675#102—434no—
676#102—434no—
677#102—434no—
678C22⋊C8—434no—
679C22⋊C8—434no—
680#97C22×D4312yes—
681C4×C8C22×D4312yes—
682C24—432no—
683C24—861no—
684#41—862no—
685#41—862no—
686#41—1724no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—22no—
690C2×Q8—22no—
691C2×Q8—82no—
692C2×Q8—431no—
693C2×D4—431no—
694C2×D4—431no—
695C2×D4—432no—
696C2×D4—431no—
697C2×D4—432no—
698C2×D4—862no—
699C2×D4—864no—
700C2×D4—864no—
701C2×D4—862no—
702C2×D4—861no—
703C2×D4—861no—
704C2×D4—862no—
705C2×D4—862no—
706C2×D4—3444no—
707C2×D4—1722no—
708C22×C4—22no—
709C22×C4—432no—
710C22×C4—432no—
711C22×C4—432no—
712C22×C4—432no—
713C22×C4—432no—
714C22×C4—862no—
715C22×C4—862no—
716C22×C4—864no—
717C22×C4—864no—
718C22×C4—861no—
719C22×C4—861no—
720C22×C4—861no—
721C22×C4—861no—
722C22×C4—862no—
723C22×C4—862no—
724C22×C4—1724no—
725C22×C4D4×D4311yescharacteristic
726C22×C4D4×D4311yescharacteristic
727C22×C4C23×D4311yescharacteristic
728SD16—864no—
729D8—864no—
730M16—22no—
731M16—864no—
732M16—868no—
733M16#1062190214yescomplemented
734C2×C8—434no—
735C2×C8—868no—
736C2×C8C23×D4312yes—
737C2×C8C23×D4312yes—
738C4⋊C4—22no—
739C4⋊C4—22no—
740C4⋊C4—22no—
741C4⋊C4—21no—
742C4⋊C4—22no—
743C4⋊C4—22no—
744C4⋊C4—21no—
745C4⋊C4—431no—
746C4⋊C4—431no—
747C4⋊C4—432no—
748C4⋊C4—431no—
749C4⋊C4—431no—
750C4⋊C4—432no—
751C4⋊C4—862no—
752C4⋊C4—862no—
753C4⋊C4—862no—
754C4⋊C4—862no—
755C4⋊C4—861no—
756C4⋊C4—861no—
757C4⋊C4—861no—
758C4⋊C4C23×D4312yes—
759C4⋊C4C23×D4312yes—
760C4⋊C4C23×D4314yes—
761C22⋊C4—22no—
762C22⋊C4—432no—
763C22⋊C4—432no—
764C22⋊C4—432no—
765C22⋊C4—432no—
766C22⋊C4—864no—
767C22⋊C4—864no—
768C22⋊C4—862no—
769C22⋊C4—862no—
770C22⋊C4—864no—
771C22⋊C4—864no—
772C22⋊C4—862no—
773C22⋊C4—862no—
774C22⋊C4—862no—
775C22⋊C4—862no—
776C22⋊C4—861no—
777C22⋊C4—862no—
778C22⋊C4—862no—
779C22⋊C4—861no—
780C22⋊C4—861no—
781C42—22no—
782C42—864no—
783C42—864no—
784C42—862no—
785C42—862no—
786C42—861no—
787C42—861no—
788C42—861no—
789C42D4×D4311yescharacteristic
790C42D4×D4311yescharacteristic
791C42C23×D4311yescharacteristic
792C42C23×D4311yescharacteristic
793C23—432no—
794C23—432no—
795C23—864no—
796C23—861no—
797C23—862no—
798C23—1722no—
799C23—1722no—
800C23—1722no—
801C23—1722no—
802C23—1722no—
803C23C2×D4×D4311yescharacteristic
804Q8—42no—
805Q8—82no—
806Q8—82no—
807Q8—81no—
808Q8—861no—
809Q8—861no—
810D4—862no—
811D4—862no—
812D4—861no—
813D4—862no—
814D4—862no—
815D4—861no—
816D4—3444no—
817D4—3444no—
818D4—3442no—
819D4—1722no—
820D4—1724no—
821D4—1722no—
822D4—1722no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—24no—
827C2×C4—41no—
828C2×C4—44no—
829C2×C4—432no—
830C2×C4—432no—
831C2×C4—864no—
832C2×C4—864no—
833C2×C4—864no—
834C2×C4—862no—
835C2×C4—862no—
836C2×C4—862no—
837C2×C4—862no—
838C2×C4—862no—
839C2×C4—861no—
840C2×C4—861no—
841C2×C4—861no—
842C2×C4—3441no—
843C2×C4—3442no—
844C2×C4—1724no—
845C2×C4—1724no—
846C2×C4—1722no—
847C2×C4—1722no—
848C2×C4—1724no—
849C2×C4—1722no—
850C2×C4C2×D4×D4311yescharacteristic
851C2×C4C2×D4×D4311yescharacteristic
852C2×C4C2×D4×D4311yescharacteristic
853C2×C4C2×D4×D4311yescharacteristic
854C2×C4C2×D4×D4311yescharacteristic
855C2×C4C2×#1062190212yes—
856C2×C4#1306337312yes—
857C2×C4C24×D4311yescharacteristic
858C8—22no—
859C8—864no—
860C8C2×#1062190214yes—
861C22—21no—
862C22—21no—
863C22—862no—
864C22—862no—
865C22—862no—
866C22—862no—
867C22—862no—
868C22—862no—
869C22—3444no—
870C22—3444no—
871C22—1721no—
872C22—1722no—
873C22—1722no—
874C22—1721no—
875C22—1721no—
876C22—1722no—
877C22#1458355212yes—
878C22C22×D4×D4311yescharacteristic
879C4—21no—
880C4—21no—
881C4—21no—
882C4—42no—
883C4—44no—
884C4—42no—
885C4—862no—
886C4—862no—
887C4—1721no—
888C4—1722no—
889C4—1721no—
890C4—1721no—
891C4#1458355212yes—
892C4#1458369812yes—
893C4C22×#1062190211yescharacteristic
894C4C2×#1306337311yescharacteristic
895C2—22no—
896C2—3442no—
897C2—3441no—
898C2—1722no—
899C2—1722no—
900C2C2×#1458355211yescharacteristic
901C2C2×#1458369811yescharacteristic
902C2#1914937111yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3165C2
socleC22×C43C23×D4
hypercenter#3165D43
hypocenterC43#61256
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. #19148162C2semidirect
2. C2×#14583615C2semidirect
3. #19147220C2semidirect
4. #19147189C2semidirect
5. #19147109C2semidirect
6. #19147094C2semidirect
7. #19147017C2semidirect
8. #19147007C2semidirect
9. #19144537C2semidirect
10. #19144529C2semidirect
11. #19144404C2semidirect
12. #19144388C2semidirect
13. #19144215C2semidirect
14. C4×#13063353C2semidirect
15. M16×D172C2semidirect
16. #19143182C2semidirect
17. C43×#3165C2semidirect
20. #14583623C22semidirect
27. #14583615C22semidirect
28. #14583610C22semidirect
29. #14583602C22semidirect
31. #14583587C22semidirect
33. #14583552C22semidirect
48. #14583243C22semidirect
49. #14583242C22semidirect
50. #14583226C22semidirect
51. #14583226C22semidirect
52. #14583225C22semidirect
53. #14583225C22semidirect
54. #14583219C22semidirect
55. #14583214C22semidirect
56. #14583196C22semidirect
57. #14583191C22semidirect
58. #14583186C22semidirect
59. #14583186C22semidirect
60. #14583181C22semidirect
61. #14583176C22semidirect
62. #14583176C22semidirect
63. #14583153C22semidirect
64. #14583146C22semidirect
65. #14583136C22semidirect
66. #14583129C22semidirect
67. #14583012C22semidirect
68. #14583001C22semidirect
69. C4×#10621873C22semidirect
70. C4×D344C22semidirect
71. #14582978C22semidirect
72. #14582972C22semidirect
73. C8×D172C22semidirect
76. #14582940C22semidirect
78. #14582938C22semidirect
79. #14582936C22semidirect
80. #14582934C22semidirect
89. C43×#501C22semidirect
90. C43×#500C22semidirect
91. C43×#498C22semidirect
277. M16×C43#41semidirect
452. #3165D43semidirect
501. #501C2×D43semidirect
502. #500C2×D43semidirect
503. #498C2×D43semidirect
546. C43#61256semidirect
733. M16#10621902semidirect

Maximal subgroups

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

subgroupindex
#191481622
C2×#145836152
#191472202
#191471892
#191471092
#191470942
#191470172
#191470072
#191445372
#191445292
#191444042
#191443882
#191442152
C4×#130633532
M16×D1722
#191431822
C43×#31652
#6125643