Finite Group Databasebeta

← #25964411

Subgroups — #25964411

Order 11008.

2346 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#525×D43C211yesmaximal, characteristic
2C2×#117×D43C211yesmaximal, characteristic, complemented
3#19144542C214yesmaximal, complemented
4#19144534C214yesmaximal, complemented
5#19144528C211yesmaximal, characteristic, complemented
6#19144526C211yesmaximal, characteristic, complemented
7#19144524C211yesmaximal, characteristic, complemented
8#19144521C212yesmaximal, complemented
9#19144516C212yesmaximal, complemented
10#19144513C214yesmaximal, complemented
11#19144507C214yesmaximal, complemented
12#19143182C212yesmaximal, complemented
13#19143111C212yesmaximal, complemented
14#407×D43C211yesmaximal, characteristic, complemented
15C43×#3093C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C23×C4×D43C2211yescharacteristic
18C2×M16×D43C2212yes—
19#14583412C2212yes—
20#14583411C2211yescharacteristic
21#14583410C2211yescharacteristic
22#14583409C2212yes—
23#14583408—22no—
24#14583407—21no—
25#14583406C2211yescharacteristic
26#14583405—21no—
27#123×D43—21no—
28C22⋊Q8×D43C2212yes—
29#121×D43C2212yes—
30#120×D43—21no—
31C4×D4×D43—22no—
32C2×#13063284C2211yescharacteristic, complemented
33C2×#13063283C2212yes—
34C2×#13063282—21no—
35C2×#13063281—21no—
36#117×D43—22no—
37#117×D43—22no—
38#117×D43C2211yescharacteristic
39#117×D43C2214yes—
40#117×D43C2214yescomplemented
41C2×C4⋊C4×D43C2212yescomplemented
42C2×C22⋊C4×D43—21no—
43C2×C42×D43—21no—
44#14583241C2214yescomplemented
45#14583240C2214yescomplemented
46#14583237C2214yescomplemented
47#14583236C2214yescomplemented
48#14583233C2214yescomplemented
49#14583231C2214yescomplemented
50#14583228C2214yescomplemented
51#14583224C2214yescomplemented
52#14583223C2214yescomplemented
53#14583220C2214yescomplemented
54#14583219C2214yescomplemented
55#14583216C2214yescomplemented
56#14583214C2214yescomplemented
57#14583211C2214yescomplemented
58#14582942C2212yescomplemented
59#14582941C2212yescomplemented
60#14582940C2214yescomplemented
61#14582939C2212yescomplemented
62#14582938C2214yescomplemented
63#14582936C2214yescomplemented
64#14582934C2214yescomplemented
65#14582906C2214yescomplemented
66#14582902C2214yescomplemented
67#14582901C2212yescomplemented
68#14582900C2212yescomplemented
69#14582898C2212yescomplemented
70#14582894C2214yescomplemented
71#14582892C2214yescomplemented
72#14582863C2211yescharacteristic, complemented
73#14582862C2212yescomplemented
74#14582861C2214yes—
75C22⋊C8×D43C2214yescomplemented
76C43×#525C2211yescharacteristic
77C2×#117×C43C2211yescharacteristic, complemented
78C43×#485C2214yescomplemented
79C43×#482C2214yescomplemented
80C43×#428C2212yescomplemented
81C43×#417C2212yescomplemented
82C43×#407C2211yescharacteristic, complemented
83C24×D43D411yescharacteristic
84C2×#10621902C2311yescharacteristic
85C2×#10621898—21no—
86C2×#10621898C2311yescharacteristic
87C2×#10621900—21no—
88C2×#10621900C2311yescharacteristic
89#41×D43—28no—
90C2×Q8×D43C2311yescharacteristic
91C2×D4×D43—22no—
92C2×D4×D43—21no—
93C2×D4×D43C2311yescharacteristic
94C23×Dic43D411yescharacteristic
95C22×C4×D43—28no—
96C22×C4×D43—22no—
97C22×C4×D43—21no—
98C22×C4×D43D411yescharacteristic
99C22×C4×D43D412yes—
100C22×C4×D43D412yes—
101C22×C4×D43D411yescharacteristic
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2312yes—
104C22×C4×D43C2312yes—
105C22×C4×D43C2311yescharacteristic
106C2×#10621877C2312yes—
107C2×#10621872C2314yes—
108M16×D43—28no—
109C2×C8×D43C2314yes—
110#13063310—22no—
111#13063309—21no—
112#13063308—21no—
113#13063307—22no—
114#13063306—21no—
115#13063305C2312yes—
116#13063304C2312yes—
117#13063303—22no—
118#13063302—22no—
119#13063301C2312yes—
120#13063300C2312yes—
121#13063299C2312yes—
122#13063298—22no—
123#13063297—22no—
124#13063296C2312yes—
125#13063295—21no—
126#13063295—22no—
127#13063294—21no—
128#13063293—21no—
129#13063293—22no—
130C4×D172—22no—
131D4×Dic43—22no—
132#13063287—22no—
133C4×C22⋊D43—22no—
134C4×C22⋊D43—22no—
135(C22⋊D43)⋊C4—22no—
136(C22⋊D43)⋊C4—22no—
137#13063284—22no—
138#13063284C2314yes—
139#13063284C2311yescharacteristic
140#13063283—22no—
141#13063283—22no—
142#13063283C2314yes—
143#13063283C2312yes—
144#13063283C2314yes—
145#13063282—24no—
146#13063282—24no—
147#13063282—21no—
148#13063281—24no—
149#13063281—24no—
150#13063281—21no—
151C2×C4⋊Dic43C2312yes—
152C2×Dic43⋊C4—22no—
153C4⋊C4×D43—22no—
154C4⋊C4×D43—22no—
155C4⋊C4×D43—22no—
156C4⋊C4×D43C2314yes—
157C4⋊C4×D43C2314yes—
158C4⋊C4×D43C2312yes—
159C2×C22⋊Dic43—21no—
160C2×(C2×D43)⋊C4—22no—
161C22⋊C4×D43—24no—
162C22⋊C4×D43—24no—
163C22⋊C4×D43—21no—
164C22⋊C4×D43—22no—
165C22⋊C4×D43—22no—
166C2×C4×Dic43—21no—
167C2×C4×Dic43—22no—
168C42×D43—24no—
169C42×D43—24no—
170C42×D43—21no—
171#13063259C2314yescomplemented
172#13063258C2314yescomplemented
173#13063258C2314yescomplemented
174#13063257C2314yescomplemented
175#13063256C2314yescomplemented
176#13063256C2314yescomplemented
177#13063250C2314yescomplemented
178#13063249C2314yescomplemented
179#13063248C2314yescomplemented
180#13063247C2314yescomplemented
181#13063246C2314yescomplemented
182#13063245C2314yescomplemented
183C22⋊(C43⋊C8)C2314yes—
184(C2×D43)⋊C8C2314yes—
185(C2×D43)⋊C8C2314yes—
186C2×#41×C43C2311yescharacteristic
187C23×C4×C43C2311yescharacteristic
188C2×M16×C43C2312yes—
189#123×C43—21no—
190C22⋊Q8×C43C2312yes—
191#121×C43C2312yes—
192#120×C43—21no—
193C4×D4×C43—22no—
194#117×C43—22no—
195#117×C43C2314yes—
196#117×C43C2311yescharacteristic
197C2×C4⋊C4×C43C2312yes—
198C2×C22⋊C4×C43—21no—
199C2×C42×C43—21no—
200#107×C43C2314yescomplemented
201#106×C43C2314yescomplemented
202#103×C43C2314yescomplemented
203#102×C43C2314yescomplemented
204C22⋊C8×C43C2314yes—
205C24×C43C2×D411yescharacteristic
206C23×D43—24no—
207C23×D43—21no—
208C23×D43—44no—
209C23×D43C2×D411yescharacteristic
210C23×D43C2×D412yes—
211C23×D43C2×D412yes—
212C23×D43C2×D411yescharacteristic
213#41×C43—24no—
214C2×Q8×C43C2411yescharacteristic
215C2×D4×C43—22no—
216C2×D4×C43—21no—
217C2×D4×C43C2411yescharacteristic
218C22×C4×C43—24no—
219C22×C4×C43—21no—
220C22×C4×C43—22no—
221C22×C4×C43C2×D411yescharacteristic
222C22×C4×C43C2×D412yes—
223C22×C4×C43C2412yes—
224C22×C4×C43C2411yescharacteristic
225C2×C22⋊D43—21no—
226C2×C22⋊D43—22no—
227C2×C22⋊D43—21no—
228C2×C22⋊D43—22no—
229C2×C22⋊D43—21no—
230C22×Dic43—24no—
231C22×Dic43—21no—
232C22×Dic43—22no—
233C22×Dic43C2×D411yescharacteristic
234C22×Dic43C2×D412yes—
235C22×Dic43C2×D412yes—
236C22×Dic43C2×D411yescharacteristic
237#10621902—24no—
238Q8×D43—24no—
239#10621900—24no—
240#10621900—44no—
241D4×D43—24no—
242D4×D43—48no—
243D4×D43—44no—
244#10621898—24no—
245#10621898—44no—
246C2×D172—22no—
247C2×D172—21no—
248C2×D172C2411yescharacteristic
249C2×C4×D43—24no—
250C2×C4×D43—24no—
251C2×C4×D43—28no—
252C2×C4×D43—28no—
253C2×C4×D43—28no—
254C2×C4×D43—28no—
255C2×C4×D43—21no—
256C2×C4×D43—21no—
257C2×C4×D43—24no—
258C2×C4×D43—24no—
259C2×C4×D43—24no—
260C2×C4×D43—22no—
261C2×C4×D43—21no—
262C2×C4×D43—48no—
263C2×C4×D43—44no—
264C2×C4×D43C2×D412yes—
265C2×C4×D43C2×D412yes—
266C2×C4×D43C2×D412yes—
267C2×C4×D43C2×D412yes—
268C2×C4×D43C2×D412yes—
269C2×C4×D43C2×D411yescharacteristic
270C2×C4×D43C2×D411yescharacteristic
271C2×C4×D43#4118yes—
272C2×C4×D43C2412yes—
273C2×C4×D43C2411yescharacteristic
274C2×C4×D43C2411yescharacteristic
275C2×Dic86—21no—
276C2×Dic86C2411yescharacteristic
277M16×C43—24no—
278C2×C8×C43C2414yes—
279C4⋊C4×C43—22no—
280C4⋊C4×C43—22no—
281C4⋊C4×C43C2414yes—
282C4⋊C4×C43C2412yes—
283C22⋊C4×C43—22no—
284C22⋊C4×C43—24no—
285C22⋊C4×C43—21no—
286C22⋊C4×C43—22no—
287C42×C43—24no—
288C42×C43—21no—
289C22⋊Dic43—22no—
290C22⋊Dic43—24no—
291C22⋊Dic43—21no—
292C22⋊Dic43—22no—
293(C2×D43)⋊C4—22no—
294(C2×D43)⋊C4—22no—
295(C2×D43)⋊C4—24no—
296(C2×D43)⋊C4—24no—
297(C2×D43)⋊C4—22no—
298(C2×D43)⋊C4—22no—
299(C2×D43)⋊C4—22no—
300C4⋊Dic43—22no—
301C4⋊Dic43—22no—
302C4⋊Dic43C2414yes—
303C4⋊Dic43C2412yes—
304Dic43⋊C4—22no—
305Dic43⋊C4—24no—
306Dic43⋊C4—24no—
307Dic43⋊C4—22no—
308Dic43⋊C4—22no—
309C4×Dic43—24no—
310C4×Dic43—21no—
311C4×Dic43—24no—
312C4×Dic43—24no—
313C4×Dic43—22no—
314#10621877—24no—
315C2×C43⋊C8C2414yes—
316#10621872—28no—
317C8×D43—28no—
318C23×C43—22no—
319C23×C43—21no—
320C23×C43—42no—
321C23×C43C22×D412yes—
322C23×C43C22×D411yescharacteristic
323C22×D43—22no—
324C22×D43—24no—
325C22×D43—24no—
326C22×D43—24no—
327C22×D43—24no—
328C22×D43—24no—
329C22×D43—21no—
330C22×D43—42no—
331C22×D43—42no—
332C22×D43—42no—
333C22×D43—416no—
334C22×D43—44no—
335C22×D43—42no—
336C22×D43#12314yes—
337C22×D43C22×D411yescharacteristic
338C22×D43C22×D411yescharacteristic
339C22×D43C22×D412yes—
340Q8×C43—22no—
341D4×C43—22no—
342D4×C43—44no—
343D4×C43—42no—
344C2×C4×C43—22no—
345C2×C4×C43—24no—
346C2×C4×C43—24no—
347C2×C4×C43—24no—
348C2×C4×C43—22no—
349C2×C4×C43—21no—
350C2×C4×C43—44no—
351C2×C4×C43—42no—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D411yescharacteristic
354C2×C4×C43C2×#4114yes—
355C2×C4×C43C2511yescharacteristic
356C22⋊D43—44no—
357C22⋊D43—42no—
358C22⋊D43—42no—
359C22⋊D43—44no—
360C22⋊D43—42no—
361C2×Dic43—22no—
362C2×Dic43—24no—
363C2×Dic43—24no—
364C2×Dic43—24no—
365C2×Dic43—22no—
366C2×Dic43—21no—
367C2×Dic43—44no—
368C2×Dic43—42no—
369C2×Dic43#12314yes—
370C2×Dic43C22×D412yes—
371C2×Dic43C22×D411yescharacteristic
372C2×Dic43C22×D411yescharacteristic
373D172—22no—
374D172—42no—
375D172—44no—
376C4×D43—24no—
377C4×D43—24no—
378C4×D43—24no—
379C4×D43—24no—
380C4×D43—24no—
381C4×D43—24no—
382C4×D43—48no—
383C4×D43—44no—
384C4×D43—42no—
385C4×D43—48no—
386C4×D43—42no—
387C4×D43—42no—
388C4×D43#12314yes—
389C4×D43#12314yes—
390C4×D43C2×#4114yes—
391C4×D43C2×#4114yes—
392Dic86—22no—
393Dic86—42no—
394C8×C43—24no—
395C43⋊C8—24no—
396#60511—431nomaximal, Sylow
397C22×C43—22no—
398C22×C43—22no—
399C22×C43—22no—
400C22×C43—22no—
401C22×C43—44no—
402C22×C43—41no—
403C22×C43—42no—
404C22×C43C2×#12312yes—
405C22×C43C23×D411yescharacteristic
406C2×D43—28no—
407C2×D43—22no—
408C2×D43—22no—
409C2×D43—22no—
410C2×D43—22no—
411C2×D43—44no—
412C2×D43—48no—
413C2×D43—48no—
414C2×D43—41no—
415C2×D43—42no—
416C2×D43—84no—
417C2×D43C2×#12312yes—
418C2×D43C2×#12312yes—
419C2×D43#57514yes—
420C4×C43—22no—
421C4×C43—41no—
422C4×C43—44no—
423C4×C43—42no—
424C4×C43C2×#12312yes—
425C4×C43C22×#4112yes—
426Dic43—22no—
427Dic43—41no—
428Dic43—44no—
429Dic43—42no—
430Dic43C2×#12312yes—
431Dic43C2×#12312yes—
432C2×#525—431no—
433C22×#117—431no—
434#3095—434no—
435#3094—434no—
436#3093—431no—
437#3093—431no—
438#3093—431no—
439#3093D4311yescharacteristic, complemented
440#3092—432no—
441#3092—432no—
442#3091—434no—
443#3091—434no—
444#2911—432no—
445#2896—432no—
446C2×#407—431no—
447C2×C43—22no—
448C2×C43—42no—
449C2×C43—81no—
450C2×C43C22×#12311yescharacteristic
451C2×C43C2×#57512yes—
452D43—24no—
453D43—22no—
454D43—22no—
455D43—81no—
456C22×#41—431no—
457C24×C4—431no—
458C22×M16—432no—
459#525—431no—
460#525—431no—
461#525—432no—
462#525—432no—
463#525—431no—
464#525—862no—
465#525—861no—
466#525—861no—
467#525C2×D4311yescharacteristic
468C2×#123—861no—
469C2×C22⋊Q8—432no—
470C2×#121—432no—
471C2×#120—861no—
472C2×C4×D4—862no—
473C2×#117—431no—
474C2×#117—434no—
475C2×#117—434no—
476C2×#117—431no—
477C2×#117—432no—
478C2×#117—861no—
479C2×#117—861no—
480C2×#117—862no—
481C2×#117—862no—
482C2×#117C2×D4311yescharacteristic, complemented
483C22×C4⋊C4—432no—
484C22×C22⋊C4—861no—
485C22×C42—861no—
486#485—434no—
487#485—434no—
488#485—434no—
489#485C2×D4314yescomplemented
490#484—434no—
491#484—434no—
492#483—434no—
493#483—434no—
494#482—434no—
495#482—434no—
496#482—434no—
497#482C2×D4314yescomplemented
498#481—434no—
499#481—434no—
500#480—434no—
501#480—434no—
502#428—432no—
503#428—432no—
504#428—432no—
505#428—434no—
506#428—434no—
507#428C2×D4312yescomplemented
508#427—434no—
509#427—434no—
510#419—434no—
511#418—434no—
512#417—432no—
513#417—432no—
514#417—432no—
515#417C2×D4312yescomplemented
516#416—434no—
517#416—434no—
518#407—431no—
519#407—432no—
520#407—434no—
521#407C2×D4311yescharacteristic, complemented
522C2×C22⋊C8—434no—
523C43#6051111yescharacteristic, complemented, Sylow
524C25—431no—
525C2×#41—431no—
526C2×#41—431no—
527C2×#41—431no—
528C2×#41—861no—
529C2×#41—861no—
530C2×#41—868no—
531C2×#41C22×D4311yescharacteristic
532C22×Q8—431no—
533C22×D4—431no—
534C22×D4—862no—
535C22×D4—861no—
536C23×C4—431no—
537C23×C4—431no—
538C23×C4—432no—
539C23×C4—431no—
540C23×C4—432no—
541C23×C4—431no—
542C23×C4—431no—
543C23×C4—432no—
544C23×C4—432no—
545C23×C4—868no—
546C23×C4—861no—
547C23×C4—862no—
548C23×C4C22×D4311yescharacteristic
549C2×M16—432no—
550C2×M16—434no—
551C2×M16—868no—
552C2×M16C22×D4312yes—
553C22×C8—434no—
554#123—21no—
555#123—862no—
556#123—861no—
557#123—862no—
558#123—861no—
559#123—861no—
560C22⋊Q8—432no—
561C22⋊Q8—432no—
562C22⋊Q8—432no—
563C22⋊Q8—862no—
564C22⋊Q8—862no—
565C22⋊Q8C22×D4312yes—
566#121—432no—
567#121—432no—
568#121—432no—
569#121—862no—
570#121—862no—
571#121C22×D4312yes—
572#120—21no—
573#120—861no—
574#120—862no—
575#120—862no—
576#120—861no—
577#120—861no—
578C4×D4—22no—
579C4×D4—862no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—862no—
584C4×D4—862no—
585C4×D4—862no—
586#117—22no—
587#117—434no—
588#117—431no—
589#117—434no—
590#117—434no—
591#117—432no—
592#117—864no—
593#117—864no—
594#117—861no—
595#117—864no—
596#117—864no—
597#117—861no—
598#117—862no—
599#117—862no—
600#117—862no—
601#117C22×D4314yes—
602#117C22×D4311yescharacteristic
603C2×C4⋊C4—432no—
604C2×C4⋊C4—434no—
605C2×C4⋊C4—434no—
606C2×C4⋊C4—432no—
607C2×C4⋊C4—862no—
608C2×C4⋊C4—862no—
609C2×C4⋊C4—862no—
610C2×C4⋊C4—862no—
611C2×C4⋊C4C22×D4312yes—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—862no—
614C2×C22⋊C4—864no—
615C2×C22⋊C4—864no—
616C2×C22⋊C4—861no—
617C2×C22⋊C4—862no—
618C2×C22⋊C4—862no—
619C2×C22⋊C4—861no—
620C2×C42—21no—
621C2×C42—864no—
622C2×C42—864no—
623C2×C42—861no—
624C2×C42—862no—
625C2×C42—861no—
626#107—434no—
627#107—434no—
628#107—434no—
629#107C22×D4314yescomplemented
630#106—434no—
631#106—434no—
632#106—434no—
633#106C22×D4314yescomplemented
634#103—434no—
635#103—434no—
636#103—434no—
637#103C22×D4314yescomplemented
638#102—434no—
639#102—434no—
640#102—434no—
641#102C22×D4314yescomplemented
642C22⋊C8—434no—
643C22⋊C8—434no—
644C22⋊C8—434no—
645C22⋊C8C22×D4314yes—
646C24—431no—
647C24—431no—
648C24—432no—
649C24—432no—
650C24—864no—
651C24—861no—
652C24—1724no—
653C24D4×D4311yescharacteristic
654#41—24no—
655#41—864no—
656#41—864no—
657#41—864no—
658#41—1724no—
659#41—1724no—
660C2×Q8—431no—
661C2×Q8—861no—
662C2×Q8—864no—
663C2×Q8C23×D4311yescharacteristic
664C2×D4—22no—
665C2×D4—21no—
666C2×D4—431no—
667C2×D4—862no—
668C2×D4—861no—
669C2×D4—864no—
670C2×D4—861no—
671C2×D4—862no—
672C2×D4—861no—
673C2×D4—862no—
674C2×D4—861no—
675C2×D4—1724no—
676C2×D4—1728no—
677C2×D4C23×D4311yescharacteristic
678C22×C4—24no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—431no—
682C22×C4—431no—
683C22×C4—431no—
684C22×C4—438no—
685C22×C4—431no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—432no—
693C22×C4—432no—
694C22×C4—432no—
695C22×C4—432no—
696C22×C4—864no—
697C22×C4—868no—
698C22×C4—868no—
699C22×C4—868no—
700C22×C4—868no—
701C22×C4—861no—
702C22×C4—864no—
703C22×C4—864no—
704C22×C4—864no—
705C22×C4—862no—
706C22×C4—861no—
707C22×C4—864no—
708C22×C4—861no—
709C22×C4—864no—
710C22×C4—862no—
711C22×C4—861no—
712C22×C4—1724no—
713C22×C4—1728no—
714C22×C4D4×D4311yescharacteristic
715C22×C4D4×D4312yes—
716C22×C4C23×D4312yes—
717C22×C4C23×D4311yescharacteristic
718M16—24no—
719M16—868no—
720M16—864no—
721C2×C8—434no—
722C2×C8—868no—
723C2×C8C23×D4314yes—
724C4⋊C4—22no—
725C4⋊C4—22no—
726C4⋊C4—434no—
727C4⋊C4—432no—
728C4⋊C4—864no—
729C4⋊C4—864no—
730C4⋊C4—862no—
731C4⋊C4—862no—
732C4⋊C4—862no—
733C4⋊C4—862no—
734C4⋊C4—862no—
735C4⋊C4C23×D4314yes—
736C4⋊C4C23×D4312yes—
737C22⋊C4—24no—
738C22⋊C4—21no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—862no—
742C22⋊C4—864no—
743C22⋊C4—864no—
744C22⋊C4—862no—
745C22⋊C4—862no—
746C22⋊C4—862no—
747C22⋊C4—862no—
748C22⋊C4—864no—
749C22⋊C4—861no—
750C22⋊C4—862no—
751C22⋊C4—862no—
752C42—24no—
753C42—21no—
754C42—864no—
755C42—864no—
756C42—862no—
757C42—864no—
758C42—861no—
759C23—22no—
760C23—21no—
761C23—42no—
762C23—431no—
763C23—431no—
764C23—432no—
765C23—434no—
766C23—864no—
767C23—864no—
768C23—864no—
769C23—864no—
770C23—864no—
771C23—862no—
772C23—861no—
773C23—1722no—
774C23—1722no—
775C23—1722no—
776C23—1722no—
777C23—1724no—
778C23—17216no—
779C23C2×D4×D4312yes—
780C23C2×D4×D4311yescharacteristic
781Q8—22no—
782Q8—862no—
783Q8—1722no—
784D4—22no—
785D4—44no—
786D4—42no—
787D4—862no—
788D4—1722no—
789D4—1724no—
790D4—1722no—
791D4—1724no—
792D4—1722no—
793D4—1724no—
794D4—1722no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—44no—
802C2×C4—42no—
803C2×C4—434no—
804C2×C4—431no—
805C2×C4—431no—
806C2×C4—434no—
807C2×C4—434no—
808C2×C4—434no—
809C2×C4—434no—
810C2×C4—432no—
811C2×C4—864no—
812C2×C4—864no—
813C2×C4—864no—
814C2×C4—864no—
815C2×C4—864no—
816C2×C4—864no—
817C2×C4—862no—
818C2×C4—864no—
819C2×C4—864no—
820C2×C4—864no—
821C2×C4—862no—
822C2×C4—861no—
823C2×C4—1722no—
824C2×C4—1722no—
825C2×C4—1728no—
826C2×C4—1728no—
827C2×C4—1724no—
828C2×C4—1722no—
829C2×C4—1724no—
830C2×C4—1722no—
831C2×C4C2×D4×D4312yes—
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4#41×D4314yes—
834C2×C4C24×D4311yescharacteristic
835C8—24no—
836C8—864no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—22no—
841C22—44no—
842C22—42no—
843C22—41no—
844C22—434no—
845C22—432no—
846C22—432no—
847C22—868no—
848C22—862no—
849C22—862no—
850C22—862no—
851C22—862no—
852C22—3444no—
853C22—1724no—
854C22—1728no—
855C22—1728no—
856C22—1722no—
857C22—1721no—
858C22#123×D4312yes—
859C22C22×D4×D4311yescharacteristic
860C4—22no—
861C4—44no—
862C4—42no—
863C4—41no—
864C4—432no—
865C4—432no—
866C4—862no—
867C4—1724no—
868C4—1722no—
869C4—1721no—
870C4#123×D4312yes—
871C4C2×#41×D4312yes—
872C2—22no—
873C2—42no—
874C2—81no—
875C2—864no—
876C2—862no—
877C2—862no—
878C2—3441no—
879C2C2×#123×D4311yescharacteristic
880C2#575×D4312yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3093C2
socleC22×C43C23×D4
prime radical#525×D43C2
hypercenter#3093D43
hypocenterC43#60511
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3093

Complements

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

NH ≅ G/Ntype
2. C2×#117×D43C2semidirect
3. #19144542C2semidirect
4. #19144534C2semidirect
5. #19144528C2semidirect
6. #19144526C2semidirect
7. #19144524C2semidirect
8. #19144521C2semidirect
9. #19144516C2semidirect
10. #19144513C2semidirect
11. #19144507C2semidirect
12. #19143182C2semidirect
13. #19143111C2semidirect
14. #407×D43C2semidirect
15. C43×#3093C2semidirect
32. C2×#13063284C22semidirect
40. #117×D43C22semidirect
41. C2×C4⋊C4×D43C22semidirect
44. #14583241C22semidirect
45. #14583240C22semidirect
46. #14583237C22semidirect
47. #14583236C22semidirect
48. #14583233C22semidirect
49. #14583231C22semidirect
50. #14583228C22semidirect
51. #14583224C22semidirect
52. #14583223C22semidirect
53. #14583220C22semidirect
54. #14583219C22semidirect
55. #14583216C22semidirect
56. #14583214C22semidirect
57. #14583211C22semidirect
58. #14582942C22semidirect
59. #14582941C22semidirect
60. #14582940C22semidirect
61. #14582939C22semidirect
62. #14582938C22semidirect
63. #14582936C22semidirect
64. #14582934C22semidirect
65. #14582906C22semidirect
66. #14582902C22semidirect
67. #14582901C22semidirect
68. #14582900C22semidirect
69. #14582898C22semidirect
70. #14582894C22semidirect
71. #14582892C22semidirect
72. #14582863C22semidirect
73. #14582862C22semidirect
75. C22⋊C8×D43C22semidirect
77. C2×#117×C43C22semidirect
78. C43×#485C22semidirect
79. C43×#482C22semidirect
80. C43×#428C22semidirect
81. C43×#417C22semidirect
82. C43×#407C22semidirect
171. #13063259C23semidirect
172. #13063258C23semidirect
173. #13063258C23semidirect
174. #13063257C23semidirect
175. #13063256C23semidirect
176. #13063256C23semidirect
177. #13063250C23semidirect
178. #13063249C23semidirect
179. #13063248C23semidirect
180. #13063247C23semidirect
181. #13063246C23semidirect
182. #13063245C23semidirect
200. #107×C43C23semidirect
201. #106×C43C23semidirect
202. #103×C43C23semidirect
203. #102×C43C23semidirect
439. #3093D43semidirect
482. C2×#117C2×D43semidirect
489. #485C2×D43semidirect
497. #482C2×D43semidirect
507. #428C2×D43semidirect
515. #417C2×D43semidirect
521. #407C2×D43semidirect
523. C43#60511semidirect
629. #107C22×D43semidirect
633. #106C22×D43semidirect
637. #103C22×D43semidirect
641. #102C22×D43semidirect

Maximal subgroups

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

subgroupindex
#525×D432
C2×#117×D432
#191445422
#191445342
#191445282
#191445262
#191445242
#191445212
#191445162
#191445132
#191445072
#191431822
#191431112
#407×D432
C43×#30932
#6051143