Finite Group Databasebeta

← #25965134

Subgroups — #25965134

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583510C211yesmaximal, characteristic, complemented
2#19147794C211yesmaximal, characteristic
3#19144893C214yesmaximal, complemented
4#19144845C214yesmaximal, complemented
5#19144808C214yesmaximal, complemented
6#19144806C214yesmaximal, complemented
7#19144541C212yesmaximal, complemented
8#19144418C211yesmaximal, characteristic, complemented
9#19144417C211yesmaximal, characteristic, complemented
10#19144078C211yesmaximal, characteristic, complemented
11#19143851C212yesmaximal
12#137×Dic43C212yesmaximal, complemented
13#19143410C212yesmaximal, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3039C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×#13063356C2212yes—
18#14583510—21no—
19#14583510—21no—
20#14583510—21no—
21#14583510—21no—
22#14583510C2214yes—
23#14583510C2214yescomplemented
24C2×#13063320—22no—
25C2×#13063317C2211yescharacteristic, complemented
26C2×#13063315—22no—
27C2×#13063301C2212yes—
28#14583381C2212yes—
29#14583378—22no—
30#14583378C2212yes—
31#14583375C2212yes—
32#14583371—22no—
33#14583371C2212yes—
34#41×Dic43C2211yescharacteristic
35C4×#10621898—21no—
36C4×#10621898C2211yescharacteristic
37#14583367—21no—
38#14583367C2211yescharacteristic
39C2×Q8×Dic43C2212yescomplemented
40C2×#13063282—21no—
41C2×#13063282C2211yescharacteristic
42#117×D43—21no—
43#117×D43C2211yescharacteristic
44#14583239C2214yes—
45#14583238C2214yes—
46#14583233C2214yescomplemented
47#14583228C2214yescomplemented
48#14583207C2214yescomplemented
49#14583206C2214yescomplemented
50#14583200C2214yescomplemented
51#14583199C2214yescomplemented
52#14583106C2214yescomplemented
53#14583101C2214yescomplemented
54#14583060C2214yes—
55#14583058C2214yes—
56#14583053C2214yes—
57#14583048C2214yes—
58#14583006C2214yescomplemented
59#14583003C2214yescomplemented
60#14583002C2214yescomplemented
61#14583000C2214yescomplemented
62Q16×Dic43C2214yescomplemented
63#14582991C2214yescomplemented
64SD16×Dic43C2214yescomplemented
65#14582984C2214yescomplemented
66#14582959C2214yes—
67#14582959C2214yescomplemented
68#14582942C2212yescomplemented
69#14582941C2212yescomplemented
70#14582923C2211yescharacteristic, complemented
71#14582908C2212yescomplemented
72#14582901C2212yes—
73#14582900C2212yes—
74#14582862C2212yes—
75M16×Dic43C2212yescomplemented
76C2×#137×C43C2212yes—
77C2×C4⋊Q8×C43C2211yescharacteristic, complemented
78C4×#41×C43C2211yescharacteristic
79C43×#462C2214yescomplemented
80C43×#461C2214yescomplemented
81C43×#423C2211yescharacteristic, complemented
82C43×#419C2212yescomplemented
83C2×#10621902C2311yescharacteristic
84C2×#10621898—21no—
85C2×#10621898C2311yescharacteristic
86C2×#10621900—21no—
87C2×#10621900C2311yescharacteristic
88#41×D43—24no—
89#41×D43—24no—
90C2×Q8×D43C2311yescharacteristic
91C2×D4×D43—21no—
92C2×D4×D43C2311yescharacteristic
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95#13063356—28no—
96C2×#10621885C2314yes—
97C2×#10621884C2314yes—
98C2×#10621877C2312yes—
99#13063320—24no—
100#13063320—24no—
101#13063320—24no—
102#13063320—24no—
103#13063317—21no—
104#13063317—21no—
105#13063317C2314yes—
106#13063315—24no—
107#13063315—24no—
108#13063315—24no—
109#13063315—24no—
110#13063301—22no—
111#13063301—22no—
112#13063301C2314yes—
113#13063301C2314yes—
114Q8×Dic43—22no—
115Q8×Dic43—22no—
116Q8×Dic43C2314yes—
117Q8×Dic43C2314yes—
118Q8×Dic43C2312yes—
119C4×Dic86—22no—
120C4×Dic86C2312yes—
121#13063290—22no—
122#13063290C2312yes—
123C4×D172—22no—
124C4×D172C2312yes—
125D4×Dic43—22no—
126D4×Dic43C2312yes—
127#13063287—22no—
128#13063287C2312yes—
129C4×C22⋊D43—22no—
130C4×C22⋊D43—22no—
131C4×C22⋊D43—22no—
132(C22⋊D43)⋊C4—22no—
133(C22⋊D43)⋊C4—22no—
134(C22⋊D43)⋊C4—22no—
135#13063284—21no—
136#13063284C2311yescharacteristic
137#13063283—22no—
138#13063283C2312yes—
139#13063282—21no—
140#13063282—21no—
141#13063282—22no—
142#13063282—22no—
143#13063282—21no—
144#13063282D411yescharacteristic
145#13063282D411yescharacteristic
146#13063282D411yescharacteristic
147#13063282D411yescharacteristic
148#13063282C2312yes—
149#13063282C2312yes—
150#13063281—21no—
151#13063281—22no—
152C2×C4⋊Dic43—22no—
153C2×C4⋊Dic43C2312yes—
154C2×Dic43⋊C4—22no—
155C2×Dic43⋊C4—22no—
156C2×Dic43⋊C4—22no—
157C2×Dic43⋊C4D412yes—
158C4⋊C4×D43—22no—
159C4⋊C4×D43C2312yes—
160C2×(C2×D43)⋊C4—22no—
161C2×(C2×D43)⋊C4—22no—
162C2×(C2×D43)⋊C4D412yes—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—22no—
165C2×C4×Dic43—22no—
166C2×C4×Dic43—21no—
167C2×C4×Dic43C2311yescharacteristic
168C42×D43—21no—
169C42×D43—21no—
170C42×D43—21no—
171#13063259C2314yes—
172#13063258C2314yes—
173#13063257C2314yes—
174#13063256C2314yes—
175C4⋊(C43⋊C8)C2314yes—
176#13063250C2314yes—
177#13063249C2314yes—
178#13063249C2314yes—
179#13063249C2314yes—
180#13063247C2314yes—
181#13063246C2314yes—
182(C2×D43)⋊C8C2314yes—
183(C2×D43)⋊C8C2314yes—
184#13063235C2314yes—
185C8×Dic43C2314yes—
186C2×#41×C43C2311yescharacteristic
187C22×Q8×C43C2312yes—
188#137×C43—28no—
189C2×Q16×C43C2314yes—
190C2×SD16×C43C2314yes—
191C2×M16×C43C2312yes—
192C4⋊Q8×C43—21no—
193C4⋊Q8×C43—21no—
194C4⋊Q8×C43C2314yes—
195C4×Q8×C43C2312yes—
196C4×D4×C43—22no—
197C4×D4×C43C2312yes—
198#117×C43—21no—
199#117×C43C2311yescharacteristic
200C2×C4⋊C4×C43—22no—
201C2×C42×C43—21no—
202C2×C42×C43C2311yescharacteristic
203C4⋊C8×C43C2314yes—
204#103×C43C2314yes—
205#103×C43C2314yes—
206C23×D43—21no—
207C23×D43C2×D411yescharacteristic
208#41×C43—22no—
209#41×C43#4114yes—
210C2×Q8×C43—22no—
211C2×Q8×C43—24no—
212C2×Q8×C43—24no—
213C2×Q8×C43C2414yes—
214C2×Q8×C43C2411yescharacteristic
215C2×D4×C43—21no—
216C2×D4×C43C2411yescharacteristic
217C22×C4×C43—21no—
218C22×C4×C43—22no—
219C22×C4×C43—22no—
220C22×C4×C43C2×D412yes—
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—21no—
223C2×C22⋊D43—21no—
224C2×C22⋊D43—21no—
225C22×Dic43—21no—
226C22×Dic43—22no—
227C22×Dic43—22no—
228C22×Dic43C2×D411yescharacteristic
229C22×Dic43C2×D412yes—
230#10621902—22no—
231#10621902—22no—
232Q8×D43—22no—
233Q8×D43—22no—
234#10621900—28no—
235#10621900—22no—
236#10621900—22no—
237D4×D43—28no—
238D4×D43—22no—
239D4×D43—22no—
240#10621898—28no—
241#10621898—22no—
242#10621898#4114yes—
243C2×D172—21no—
244C2×D172C2411yescharacteristic
245C2×C4×D43—28no—
246C2×C4×D43—21no—
247C2×C4×D43—22no—
248C2×C4×D43—22no—
249C2×C4×D43—21no—
250C2×C4×D43—22no—
251C2×C4×D43—22no—
252C2×C4×D43—21no—
253C2×C4×D43—22no—
254C2×C4×D43C2×D411yescharacteristic
255C2×C4×D43C2×D411yescharacteristic
256C2×C4×D43C2411yescharacteristic
257C2×C4×D43C2411yescharacteristic
258C2×Dic86—21no—
259C2×Dic86C2411yescharacteristic
260Q16×C43—28no—
261SD16×C43—28no—
262M16×C43—24no—
263C2×C8×C43C2414yes—
264C4⋊C4×C43—24no—
265C4⋊C4×C43—24no—
266C4⋊C4×C43—22no—
267C4⋊C4×C43C2412yes—
268C22⋊C4×C43—22no—
269C22⋊C4×C43—21no—
270C42×C43—21no—
271C42×C43—22no—
272C42×C43C2×D411yescharacteristic
273C42×C43C2×D411yescharacteristic
274C42×C43C2412yes—
275C22⋊Dic43—22no—
276C22⋊Dic43—21no—
277#10621885—28no—
278#10621884—28no—
279(C2×D43)⋊C4—22no—
280(C2×D43)⋊C4—22no—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4C2×D412yes—
285(C2×D43)⋊C4C2×D412yes—
286(C2×D43)⋊C4C2×D412yes—
287(C2×D43)⋊C4C2×D412yes—
288C4⋊Dic43—22no—
289C4⋊Dic43—22no—
290C4⋊Dic43—24no—
291C4⋊Dic43—24no—
292C4⋊Dic43C2414yes—
293C4⋊Dic43C2412yes—
294Dic43⋊C4—22no—
295Dic43⋊C4—24no—
296Dic43⋊C4—24no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299Dic43⋊C4—24no—
300Dic43⋊C4—24no—
301Dic43⋊C4C2×D412yes—
302Dic43⋊C4C2×D412yes—
303Dic43⋊C4C2×D412yes—
304Dic43⋊C4C2×D412yes—
305C4×Dic43—21no—
306C4×Dic43—22no—
307C4×Dic43—22no—
308C4×Dic43—22no—
309C4×Dic43—22no—
310C4×Dic43—24no—
311C4×Dic43—24no—
312C4×Dic43C2×D411yescharacteristic
313C4×Dic43C2×D411yescharacteristic
314C4×Dic43C2412yes—
315#10621877—24no—
316C2×C43⋊C8C2414yes—
317C23×C43—21no—
318C23×C43C22×D411yescharacteristic
319C22×D43—21no—
320C22×D43—24no—
321C22×D43—22no—
322C22×D43—42no—
323C22×D43—82no—
324C22×D43C22×D411yescharacteristic
325C22×D43C22×D411yescharacteristic
326Q8×C43—21no—
327Q8×C43—24no—
328Q8×C43—24no—
329Q8×C43—44no—
330Q8×C43C2×#4112yes—
331D4×C43—24no—
332D4×C43—21no—
333D4×C43C2×#4112yes—
334C2×C4×C43—21no—
335C2×C4×C43—24no—
336C2×C4×C43—24no—
337C2×C4×C43—22no—
338C2×C4×C43—42no—
339C2×C4×C43—44no—
340C2×C4×C43—82no—
341C2×C4×C43C22×D412yes—
342C2×C4×C43C22×D412yes—
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4112yes—
345C2×C4×C43C2×#4112yes—
346C2×C4×C43C2511yescharacteristic
347C22⋊D43—24no—
348C22⋊D43—24no—
349C22⋊D43—24no—
350C2×Dic43—24no—
351C2×Dic43—22no—
352C2×Dic43—21no—
353C2×Dic43—22no—
354C2×Dic43—24no—
355C2×Dic43—42no—
356C2×Dic43—44no—
357C2×Dic43—82no—
358C2×Dic43C22×D412yes—
359C2×Dic43C22×D412yes—
360C2×Dic43C22×D411yescharacteristic
361C2×Dic43C22×D411yescharacteristic
362D172—24no—
363D172—21no—
364D172C2×#4112yes—
365C4×D43—24no—
366C4×D43—24no—
367C4×D43—22no—
368C4×D43—24no—
369C4×D43—22no—
370C4×D43—21no—
371C4×D43—21no—
372C4×D43—21no—
373C4×D43—21no—
374C4×D43—82no—
375C4×D43—82no—
376C4×D43—82no—
377Dic86—24no—
378Dic86—21no—
379Dic86C2×#4112yes—
380C8×C43—24no—
381C43⋊C8—24no—
382#60569—431nomaximal, Sylow
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—42no—
386C22×C43#52512yes—
387C22×C43C23×D411yescharacteristic
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—21no—
391C2×D43—22no—
392C2×D43—21no—
393C2×D43—42no—
394C2×D43—82no—
395C2×D43—84no—
396C4×C43—22no—
397C4×C43—22no—
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—44no—
401C4×C43#52512yes—
402C4×C43C22×#4111yescharacteristic
403C4×C43C22×#4111yescharacteristic
404Dic43—22no—
405Dic43—22no—
406Dic43—21no—
407Dic43—22no—
408Dic43—21no—
409Dic43—42no—
410Dic43—44no—
411C2×#541—431no—
412#3428—431no—
413#3127—434no—
414#3123—434no—
415#3120—434no—
416#3120—434no—
417#3095—432no—
418#3080—431no—
419#3080—431no—
420#3039—431no—
421#3039D4311yescharacteristic, complemented
422#3007—432no—
423C4×#137—432no—
424C4×#137—432no—
425#2921—431no—
426C2×C43—22no—
427C2×C43—42no—
428C2×C43C2×#52511yescharacteristic
429C2×C43#358612yes—
430D43—41no—
431D43—41no—
432D43—42no—
433C22×#41—431no—
434C2×#137—432no—
435C2×#137C2×D4312yes—
436#541—434no—
437#541—434no—
438#541—861no—
439#541—861no—
440#541—861no—
441#541—861no—
442C2×C4⋊Q8C2×D4311yescharacteristic, complemented
443C2×#126—862no—
444C2×#125—431no—
445C2×#125—862no—
446C2×C22⋊Q8—432no—
447#520—432no—
448#520—432no—
449#520—862no—
450#519—432no—
451#518—432no—
452#518—862no—
453C4×#41—431no—
454C4×#41—431no—
455C4×#41—431no—
456C4×#41—861no—
457C4×#41—861no—
458C4×#41C2×D4311yescharacteristic
459C2×C4×Q8—432no—
460C2×#117—431no—
461C2×#117—431no—
462C2×#117—861no—
463C2×#117—861no—
464#485—434no—
465#485—434no—
466#484—434no—
467#483—434no—
468#479—434no—
469#479—434no—
470#478—434no—
471#478—434no—
472#462—434no—
473#462C2×D4314yescomplemented
474#461—434no—
475#461C2×D4314yescomplemented
476#452—434no—
477#452—434no—
478#451—434no—
479#450—434no—
480#441—434no—
481#441—434no—
482#440—434no—
483#440—434no—
484C4×Q16—434no—
485C4×Q16—434no—
486C4×SD16—434no—
487C4×SD16—434no—
488#433—434no—
489#433—434no—
490#428—432no—
491#428—432no—
492#423—431no—
493#423C2×D4311yescharacteristic, complemented
494#419—432no—
495#419C2×D4312yescomplemented
496#417—432no—
497#417—432no—
498#407—432no—
499C4×M16—432no—
500C43#6056911yescharacteristic, complemented, Sylow
501C2×#41—431no—
502C2×#41—431no—
503C2×#41—431no—
504C2×#41—861no—
505C2×#41—861no—
506C2×#41—864no—
507C2×#41—864no—
508C2×#41C22×D4311yescharacteristic
509C22×Q8—431no—
510C22×Q8C22×D4312yes—
511C22×D4—431no—
512C22×D4—861no—
513C23×C4—431no—
514C23×C4—861no—
515#137—28no—
516#137—868no—
517C2×Q16—434no—
518C2×Q16C22×D4314yes—
519C2×SD16—434no—
520C2×SD16C22×D4314yes—
521C2×M16—432no—
522C2×M16C22×D4312yes—
523C4⋊Q8—21no—
524C4⋊Q8—21no—
525C4⋊Q8C22×D4314yes—
526#126—864no—
527#126—864no—
528#126—864no—
529#126—864no—
530#125—434no—
531#125—864no—
532#125—864no—
533#125—864no—
534#125—864no—
535#125—861no—
536#125—861no—
537C22⋊Q8—434no—
538C22⋊Q8—434no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541C4×Q8—434no—
542C4×Q8—434no—
543C4×Q8—432no—
544C4×Q8—432no—
545C4×Q8—432no—
546C4×Q8—862no—
547C4×Q8—862no—
548C4×Q8—862no—
549C4×Q8—862no—
550C4×Q8C22×D4312yes—
551C4×D4—22no—
552C4×D4—432no—
553C4×D4—432no—
554C4×D4—432no—
555C4×D4—862no—
556C4×D4—862no—
557C4×D4—862no—
558C4×D4—862no—
559C4×D4—862no—
560C4×D4—862no—
561C4×D4—862no—
562C4×D4—862no—
563C4×D4—862no—
564C4×D4C22×D4312yes—
565#117—21no—
566#117—431no—
567#117—431no—
568#117—431no—
569#117—431no—
570#117—432no—
571#117—432no—
572#117—431no—
573#117—432no—
574#117—861no—
575#117—862no—
576#117—862no—
577#117—861no—
578#117—861no—
579#117—862no—
580#117—861no—
581#117—862no—
582#117—861no—
583#117C22×D4311yescharacteristic
584C2×C4⋊C4—22no—
585C2×C4⋊C4—432no—
586C2×C4⋊C4—432no—
587C2×C4⋊C4—432no—
588C2×C4⋊C4—862no—
589C2×C4⋊C4—862no—
590C2×C4⋊C4—862no—
591C2×C4⋊C4—862no—
592C2×C4⋊C4—862no—
593C2×C22⋊C4—432no—
594C2×C22⋊C4—862no—
595C2×C22⋊C4—861no—
596C2×C22⋊C4—862no—
597C2×C22⋊C4—862no—
598C2×C42—21no—
599C2×C42—431no—
600C2×C42—861no—
601C2×C42—861no—
602C2×C42—861no—
603C2×C42—862no—
604C2×C42—861no—
605C2×C42C22×D4311yescharacteristic
606#107—434no—
607#107—434no—
608#106—434no—
609#106—434no—
610C4⋊C8—434no—
611C4⋊C8C22×D4314yes—
612#103—434no—
613#103—434no—
614#103—434no—
615#103—434no—
616#103C22×D4314yes—
617#103C22×D4314yes—
618#102—434no—
619#102—434no—
620C22⋊C8—434no—
621C22⋊C8—434no—
622#97—434no—
623C4×C8—434no—
624C24—431no—
625C24—861no—
626#41—22no—
627#41—434no—
628#41—868no—
629#41—862no—
630#41—868no—
631#41—862no—
632#41—862no—
633#41—862no—
634#41—862no—
635#41#1062190014yes—
636C2×Q8—22no—
637C2×Q8—24no—
638C2×Q8—24no—
639C2×Q8—431no—
640C2×Q8—861no—
641C2×Q8—862no—
642C2×Q8—862no—
643C2×Q8C23×D4314yes—
644C2×Q8C23×D4311yescharacteristic
645C2×D4—21no—
646C2×D4—431no—
647C2×D4—861no—
648C2×D4—861no—
649C2×D4—862no—
650C2×D4—868no—
651C2×D4—861no—
652C2×D4—861no—
653C2×D4—862no—
654C2×D4C23×D4311yescharacteristic
655C22×C4—21no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—431no—
659C22×C4—432no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—431no—
663C22×C4—431no—
664C22×C4—861no—
665C22×C4—862no—
666C22×C4—861no—
667C22×C4—868no—
668C22×C4—862no—
669C22×C4—861no—
670C22×C4—862no—
671C22×C4—861no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—862no—
675C22×C4—862no—
676C22×C4D4×D4312yes—
677C22×C4C23×D4311yescharacteristic
678Q16—28no—
679Q16—868no—
680SD16—28no—
681SD16—868no—
682M16—24no—
683M16—864no—
684C2×C8—434no—
685C2×C8C23×D4314yes—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—22no—
689C4⋊C4—432no—
690C4⋊C4—432no—
691C4⋊C4—432no—
692C4⋊C4—432no—
693C4⋊C4—434no—
694C4⋊C4—432no—
695C4⋊C4—862no—
696C4⋊C4—862no—
697C4⋊C4—862no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C4⋊C4—864no—
701C4⋊C4—864no—
702C4⋊C4—862no—
703C4⋊C4—862no—
704C4⋊C4—864no—
705C4⋊C4—864no—
706C4⋊C4C23×D4312yes—
707C22⋊C4—21no—
708C22⋊C4—22no—
709C22⋊C4—432no—
710C22⋊C4—432no—
711C22⋊C4—432no—
712C22⋊C4—432no—
713C22⋊C4—862no—
714C22⋊C4—862no—
715C22⋊C4—864no—
716C22⋊C4—864no—
717C22⋊C4—862no—
718C22⋊C4—861no—
719C22⋊C4—862no—
720C42—21no—
721C42—22no—
722C42—431no—
723C42—431no—
724C42—432no—
725C42—862no—
726C42—862no—
727C42—862no—
728C42—864no—
729C42—864no—
730C42—861no—
731C42—862no—
732C42D4×D4311yescharacteristic
733C42D4×D4311yescharacteristic
734C42C23×D4312yes—
735C23—21no—
736C23—431no—
737C23—431no—
738C23—864no—
739C23—862no—
740C23—861no—
741C23—3442no—
742C23—1722no—
743C23C2×D4×D4311yescharacteristic
744Q8—21no—
745Q8—24no—
746Q8—24no—
747Q8—44no—
748Q8—432no—
749Q8—864no—
750Q8—861no—
751Q8C2×#1062190012yes—
752D4—24no—
753D4—21no—
754D4—432no—
755D4—864no—
756D4—864no—
757D4—864no—
758D4—864no—
759D4—861no—
760D4C2×#1062190012yes—
761C2×C4—21no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—42no—
766C2×C4—44no—
767C2×C4—82no—
768C2×C4—432no—
769C2×C4—432no—
770C2×C4—431no—
771C2×C4—431no—
772C2×C4—864no—
773C2×C4—864no—
774C2×C4—864no—
775C2×C4—862no—
776C2×C4—861no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—864no—
780C2×C4—861no—
781C2×C4—861no—
782C2×C4—861no—
783C2×C4—861no—
784C2×C4—862no—
785C2×C4—864no—
786C2×C4—3442no—
787C2×C4—3442no—
788C2×C4—3442no—
789C2×C4—3442no—
790C2×C4—1722no—
791C2×C4—1724no—
792C2×C4C2×D4×D4312yes—
793C2×C4C2×D4×D4312yes—
794C2×C4C2×D4×D4311yescharacteristic
795C2×C4#41×D4312yes—
796C2×C4C2×#1062190012yes—
797C2×C4C24×D4311yescharacteristic
798C8—24no—
799C8—864no—
800C22—22no—
801C22—22no—
802C22—42no—
803C22—861no—
804C22—862no—
805C22—861no—
806C22—862no—
807C22—862no—
808C22—3442no—
809C22—3444no—
810C22—1722no—
811C22#1458340912yes—
812C22C22×D4×D4311yescharacteristic
813C4—22no—
814C4—22no—
815C4—22no—
816C4—44no—
817C4—42no—
818C4—861no—
819C4—861no—
820C4—862no—
821C4—862no—
822C4—862no—
823C4—1722no—
824C4—1724no—
825C4#1458340912yes—
826C4C2×#41×D4311yescharacteristic
827C4C22×#1062190011yescharacteristic
828C2—22no—
829C2—42no—
830C2—1721no—
831C2—1721no—
832C2—1722no—
833C2C2×#1458340911yescharacteristic
834C2#1914937812yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3039C2
socleC22×C43C23×D4
prime radicalC2×#41×D43C22
hypercenter#3039D43
hypocenterC43#60569
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

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

NH ≅ G/Ntype
1. C2×#14583510C2semidirect
3. #19144893C2semidirect
4. #19144845C2semidirect
5. #19144808C2semidirect
6. #19144806C2semidirect
7. #19144541C2semidirect
8. #19144418C2semidirect
9. #19144417C2semidirect
10. #19144078C2semidirect
12. #137×Dic43C2semidirect
13. #19143410C2semidirect
14. #19143232C2semidirect
15. C43×#3039C2semidirect
23. #14583510C22semidirect
25. C2×#13063317C22semidirect
39. C2×Q8×Dic43C22semidirect
46. #14583233C22semidirect
47. #14583228C22semidirect
48. #14583207C22semidirect
49. #14583206C22semidirect
50. #14583200C22semidirect
51. #14583199C22semidirect
52. #14583106C22semidirect
53. #14583101C22semidirect
58. #14583006C22semidirect
59. #14583003C22semidirect
60. #14583002C22semidirect
61. #14583000C22semidirect
62. Q16×Dic43C22semidirect
63. #14582991C22semidirect
64. SD16×Dic43C22semidirect
65. #14582984C22semidirect
67. #14582959C22semidirect
68. #14582942C22semidirect
69. #14582941C22semidirect
70. #14582923C22semidirect
71. #14582908C22semidirect
75. M16×Dic43C22semidirect
77. C2×C4⋊Q8×C43C22semidirect
79. C43×#462C22semidirect
80. C43×#461C22semidirect
81. C43×#423C22semidirect
82. C43×#419C22semidirect
421. #3039D43semidirect
442. C2×C4⋊Q8C2×D43semidirect
473. #462C2×D43semidirect
475. #461C2×D43semidirect
493. #423C2×D43semidirect
495. #419C2×D43semidirect
500. C43#60569semidirect

Maximal subgroups

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

subgroupindex
C2×#145835102
#191477942
#191448932
#191448452
#191448082
#191448062
#191445412
#191444182
#191444172
#191440782
#191438512
#137×Dic432
#191434102
#191432322
C43×#30392
#6056943