Finite Group Databasebeta

← #25964497

Subgroups — #25964497

Order 11008.

2106 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583472C211yesmaximal, characteristic
2#19147796C211yesmaximal, characteristic
3#19144563C214yesmaximal, complemented
4#19144561C214yesmaximal, complemented
5#19144559C214yesmaximal, complemented
6#19144557C214yesmaximal, complemented
7#19144545C212yesmaximal, complemented
8#19144544C211yesmaximal, characteristic, complemented
9#19144543C211yesmaximal, characteristic, complemented
10#19144541C212yesmaximal, complemented
11#19144539C211yesmaximal, characteristic, complemented
12#19143182C212yesmaximal, complemented
13#419×D43C212yesmaximal, complemented
14#19143038C211yesmaximal, characteristic
15C43×#3095C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×Q8×D43C2211yescharacteristic
18C2×M16×D43C2212yes—
19#14583472—22no—
20#14583472—22no—
21#14583472C2214yes—
22#14583472C2214yes—
23C2×#13063324—21no—
24C2×#13063311—21no—
25C2×#13063310—21no—
26C2×#13063307—21no—
27C2×#13063305C2211yescharacteristic
28C2×#13063304C2211yescharacteristic
29C2×#13063301C2211yescharacteristic
30#14583380C2212yes—
31#14583380C2212yes—
32#14583379C2212yes—
33#14583379C2212yes—
34#14583376—21no—
35#14583373—21no—
36#14583372—21no—
37#14583372—21no—
38C4×#10621898—22no—
39#14583367—22no—
40C2×#13063284C2211yescharacteristic
41C2×#13063283C2211yescharacteristic
42#117×D43C2212yes—
43#117×D43C2212yes—
44#14583243C2214yescomplemented
45#14583242C2214yescomplemented
46#14583241C2214yescomplemented
47#14583240C2214yescomplemented
48#14583239C2214yescomplemented
49#14583238C2214yescomplemented
50#14583237C2214yescomplemented
51#14583236C2214yescomplemented
52#14583235C2212yescomplemented
53#14583234C2212yescomplemented
54#14583233C2214yescomplemented
55#14583232C2212yescomplemented
56#14583231C2214yescomplemented
57#14583230C2212yescomplemented
58#14583229C2212yescomplemented
59#14583228C2214yescomplemented
60#14583227C2212yescomplemented
61#14582942C2212yes—
62#14582941C2212yes—
63#14582940C2214yescomplemented
64#14582939C2212yes—
65#14582938C2214yescomplemented
66#14582936C2214yescomplemented
67#14582934C2214yescomplemented
68#14582909C2212yes—
69#14582908C2212yes—
70#14582907C2212yes—
71#14582906C2214yescomplemented
72#14582906C2214yescomplemented
73#103×D43C2214yescomplemented
74#103×D43C2214yescomplemented
75#14582864C2214yes—
76#14582864C2214yes—
77#14582863C2211yescharacteristic
78#14582862C2212yes—
79C2×C22⋊Q8×C43C2211yescharacteristic
80C2×#117×C43C2211yescharacteristic
81C43×#485C2214yescomplemented
82C43×#484C2212yescomplemented
83C43×#483C2212yescomplemented
84C43×#428C2212yes—
85C43×#419C2212yes—
86C43×#407C2211yescharacteristic
87C2×#10621898—28no—
88C2×#10621898D412yes—
89C2×#10621898D412yes—
90C2×#10621898C2312yes—
91C2×#10621898C2312yes—
92C22×Dic86—21no—
93C22×Dic86D411yescharacteristic
94C22×Dic86C2311yescharacteristic
95C2×Q8×D43—22no—
96C2×Q8×D43—28no—
97C2×Q8×D43C2314yes—
98C22×D172D411yescharacteristic
99C22×C22⋊D43D411yescharacteristic
100C22×C22⋊D43D411yescharacteristic
101C22×C4×D43—21no—
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2311yescharacteristic
104C2×#10621877C2312yes—
105C2×#10621872C2314yes—
106M16×D43—28no—
107C2×C8×D43C2314yes—
108#13063324—24no—
109#13063324—24no—
110#13063311—24no—
111#13063311—24no—
112#13063310—24no—
113#13063310—24no—
114#13063307—24no—
115#13063307—24no—
116#13063305—22no—
117#13063305C2314yes—
118#13063304—21no—
119#13063304—21no—
120#13063304C2312yes—
121#13063304C2312yes—
122#13063301—22no—
123#13063301C2314yes—
124C4×Dic86—22no—
125C4×Dic86—22no—
126#13063290—22no—
127#13063290—22no—
128C4×D172—22no—
129C4×D172—22no—
130#13063287—22no—
131#13063287—22no—
132C4×C22⋊D43—22no—
133C4×C22⋊D43—22no—
134C4×C22⋊D43—22no—
135C4×C22⋊D43—22no—
136(C22⋊D43)⋊C4—22no—
137(C22⋊D43)⋊C4—22no—
138(C22⋊D43)⋊C4—22no—
139(C22⋊D43)⋊C4—22no—
140#13063284—21no—
141#13063284—21no—
142#13063284C2312yes—
143#13063284C2312yes—
144#13063283—22no—
145#13063283C2312yes—
146#13063283C2312yes—
147#13063283C2312yes—
148#13063283C2312yes—
149#13063283C2314yes—
150#13063282—22no—
151#13063282—22no—
152#13063281—22no—
153#13063281—22no—
154C2×C4⋊Dic43—21no—
155C2×C4⋊Dic43C2311yescharacteristic
156C2×C4⋊Dic43C2311yescharacteristic
157C2×C4⋊Dic43C2311yescharacteristic
158C2×Dic43⋊C4—21no—
159C2×Dic43⋊C4—21no—
160C4⋊C4×D43C2312yes—
161C4⋊C4×D43C2312yes—
162C4⋊C4×D43C2312yes—
163C4⋊C4×D43C2312yes—
164C2×C22⋊Dic43—21no—
165C2×C22⋊Dic43—21no—
166C2×(C2×D43)⋊C4—21no—
167C2×(C2×D43)⋊C4—21no—
168C2×(C2×D43)⋊C4—21no—
169C22⋊C4×D43—22no—
170C22⋊C4×D43—22no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C42×D43—22no—
174C42×D43—22no—
175#13063259C2314yes—
176#13063258C2314yes—
177#13063258C2314yes—
178#13063257C2314yes—
179#13063256C2314yes—
180#13063256C2314yes—
181#13063250C2314yes—
182#13063250C2314yes—
183#13063249C2314yes—
184#13063249C2314yes—
185#13063248C2314yes—
186#13063248C2314yes—
187C22⋊(C43⋊C8)C2312yes—
188C22⋊(C43⋊C8)C2312yes—
189(C2×D43)⋊C8C2314yes—
190(C2×D43)⋊C8C2314yes—
191C22×Q8×C43C2311yescharacteristic
192C23×C4×C43C2311yescharacteristic
193C2×M16×C43C2312yes—
194C22⋊Q8×C43—21no—
195C22⋊Q8×C43—21no—
196C22⋊Q8×C43C2312yes—
197C22⋊Q8×C43C2312yes—
198#117×C43—21no—
199#117×C43—21no—
200#117×C43C2312yes—
201#117×C43C2312yes—
202C2×C4⋊C4×C43—21no—
203C2×C4⋊C4×C43C2311yescharacteristic
204C2×C4⋊C4×C43C2311yescharacteristic
205C2×C4⋊C4×C43C2311yescharacteristic
206C2×C22⋊C4×C43—21no—
207C2×C22⋊C4×C43—21no—
208C2×C42×C43—21no—
209#107×C43C2314yes—
210#106×C43C2314yes—
211#103×C43C2314yes—
212#103×C43C2314yes—
213C22⋊C8×C43C2312yes—
214C22⋊C8×C43C2312yes—
215C24×C43C2×D411yescharacteristic
216C23×D43C2×D411yescharacteristic
217C23×D43C2×D411yescharacteristic
218C2×Q8×C43—21no—
219C2×Q8×C43—24no—
220C2×Q8×C43C2412yes—
221C22×C4×C43—24no—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43—21no—
225C22×C4×C43—21no—
226C22×C4×C43C2×D411yescharacteristic
227C22×C4×C43C2×D411yescharacteristic
228C22×C4×C43C2×D411yescharacteristic
229C22×C4×C43C2411yescharacteristic
230C22×C4×C43C2411yescharacteristic
231C22×C4×C43C2411yescharacteristic
232C2×C22⋊D43—24no—
233C2×C22⋊D43—24no—
234C2×C22⋊D43C2×D412yes—
235C2×C22⋊D43C2×D412yes—
236C2×C22⋊D43C2×D412yes—
237C2×C22⋊D43C2×D412yes—
238C22×Dic43—21no—
239C22×Dic43—21no—
240C22×Dic43—21no—
241C22×Dic43—21no—
242C22×Dic43C2×D411yescharacteristic
243C22×Dic43C2×D411yescharacteristic
244Q8×D43—28no—
245Q8×D43—28no—
246Q8×D43—48no—
247#10621898—28no—
248#10621898—28no—
249#10621898—24no—
250#10621898—24no—
251#10621898—24no—
252#10621898—24no—
253C2×D172—24no—
254C2×D172C2×D412yes—
255C2×D172C2×D412yes—
256C2×C4×D43—24no—
257C2×C4×D43—24no—
258C2×C4×D43—22no—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—22no—
262C2×C4×D43—44no—
263C2×C4×D43C2×D412yes—
264C2×C4×D43C2×D412yes—
265C2×C4×D43#4118yes—
266C2×C4×D43C2412yes—
267C2×C4×D43C2412yes—
268C2×Dic86—24no—
269C2×Dic86—24no—
270C2×Dic86—21no—
271C2×Dic86—24no—
272C2×Dic86—44no—
273C2×Dic86C2×D412yes—
274C2×Dic86C2×D412yes—
275C2×Dic86C2412yes—
276M16×C43—24no—
277C2×C8×C43C2414yes—
278C4⋊C4×C43—22no—
279C4⋊C4×C43—22no—
280C4⋊C4×C43—21no—
281C4⋊C4×C43—21no—
282C4⋊C4×C43—21no—
283C4⋊C4×C43C2412yes—
284C4⋊C4×C43C2412yes—
285C4⋊C4×C43C2412yes—
286C22⋊C4×C43—22no—
287C22⋊C4×C43—22no—
288C22⋊C4×C43—22no—
289C22⋊C4×C43—22no—
290C42×C43—22no—
291C42×C43—22no—
292C22⋊Dic43—22no—
293C22⋊Dic43—22no—
294C22⋊Dic43—22no—
295C22⋊Dic43—22no—
296(C2×D43)⋊C4—22no—
297(C2×D43)⋊C4—22no—
298(C2×D43)⋊C4—22no—
299(C2×D43)⋊C4—22no—
300(C2×D43)⋊C4—24no—
301(C2×D43)⋊C4—24no—
302(C2×D43)⋊C4—24no—
303C4⋊Dic43—21no—
304C4⋊Dic43—21no—
305C4⋊Dic43—21no—
306C4⋊Dic43—24no—
307C4⋊Dic43C2412yes—
308C4⋊Dic43C2412yes—
309C4⋊Dic43C2412yes—
310Dic43⋊C4—22no—
311Dic43⋊C4—22no—
312Dic43⋊C4—22no—
313Dic43⋊C4—22no—
314Dic43⋊C4—22no—
315Dic43⋊C4—22no—
316Dic43⋊C4—24no—
317C4×Dic43—22no—
318C4×Dic43—22no—
319C4×Dic43—22no—
320C4×Dic43—22no—
321C4×Dic43—22no—
322C4×Dic43—22no—
323C4×Dic43—24no—
324#10621877—24no—
325C2×C43⋊C8C2414yes—
326#10621872—28no—
327C8×D43—28no—
328C23×C43—22no—
329C23×C43—41no—
330C23×C43—41no—
331C23×C43C22×D411yescharacteristic
332C23×C43C22×D411yescharacteristic
333C23×C43C22×D411yescharacteristic
334C22×D43—22no—
335C22×D43—41no—
336C22×D43—41no—
337C22×D43—41no—
338C22×D43—41no—
339C22×D43#12314yes—
340C22×D43C22×D412yes—
341C22×D43C22×D412yes—
342Q8×C43—24no—
343Q8×C43—42no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—22no—
351C2×C4×C43—22no—
352C2×C4×C43—22no—
353C2×C4×C43—42no—
354C2×C4×C43—42no—
355C2×C4×C43—81no—
356C2×C4×C43—81no—
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C2×#4114yes—
361C2×C4×C43C2511yescharacteristic
362C22⋊D43—24no—
363C22⋊D43—24no—
364C22⋊D43—24no—
365C22⋊D43—24no—
366C2×Dic43—22no—
367C2×Dic43—22no—
368C2×Dic43—22no—
369C2×Dic43—22no—
370C2×Dic43—22no—
371C2×Dic43—42no—
372C2×Dic43—42no—
373C2×Dic43—81no—
374C2×Dic43—81no—
375C2×Dic43#12314yes—
376C2×Dic43C22×D412yes—
377C2×Dic43C22×D412yes—
378D172—24no—
379D172—24no—
380C4×D43—24no—
381C4×D43—22no—
382C4×D43—22no—
383C4×D43—48no—
384C4×D43—82no—
385C4×D43—82no—
386C4×D43—82no—
387C4×D43—82no—
388C4×D43#12318yes—
389C4×D43C2×#4114yes—
390C4×D43C2×#4114yes—
391Dic86—24no—
392Dic86—24no—
393Dic86—24no—
394Dic86—42no—
395Dic86—48no—
396C8×C43—24no—
397C43⋊C8—24no—
398#60519—431nomaximal, Sylow
399C22×C43—21no—
400C22×C43—21no—
401C22×C43—21no—
402C22×C43—21no—
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—21no—
406C22×C43—21no—
407C22×C43—82no—
408C22×C43C2×#12312yes—
409C22×C43C23×D411yescharacteristic
410C2×D43—22no—
411C2×D43—22no—
412C2×D43—22no—
413C2×D43—22no—
414C2×D43—22no—
415C2×D43—44no—
416C2×D43—82no—
417C2×D43C2×#12314yes—
418C4×C43—21no—
419C4×C43—21no—
420C4×C43—42no—
421C4×C43—42no—
422C4×C43—42no—
423C4×C43—42no—
424C4×C43C2×#12312yes—
425C4×C43C22×#4112yes—
426Dic43—22no—
427Dic43—42no—
428Dic43—42no—
429Dic43—42no—
430Dic43—42no—
431Dic43C2×#12314yes—
432C2×#536—431no—
433#3428—431no—
434#3097—434no—
435#3097—434no—
436#3097—434no—
437#3097—434no—
438#3095—432no—
439#3095—432no—
440#3095—431no—
441#3095—431no—
442#3095—431no—
443#3095D4311yescharacteristic, complemented
444#2911—432no—
445C2×#419—432no—
446#2879—431no—
447C2×C43—22no—
448C2×C43—41no—
449C2×C43—41no—
450C2×C43C22×#12311yescharacteristic
451C2×C43#358611yescharacteristic
452C2×C43#358611yescharacteristic
453D43—24no—
454D43—42no—
455C22×#41—431no—
456C23×Q8—431no—
457C22×M16—432no—
458#536—434no—
459#536—434no—
460#536—862no—
461#536—862no—
462C2×C4⋊Q8—861no—
463C2×#124—861no—
464C2×#123—861no—
465C2×#123—861no—
466C2×C22⋊Q8—431no—
467C2×C22⋊Q8—431no—
468C2×C22⋊Q8—431no—
469C2×C22⋊Q8C2×D4311yescharacteristic
470#520—432no—
471#520—432no—
472#520—432no—
473#520—432no—
474#519—861no—
475#518—861no—
476#518—861no—
477#518—861no—
478C4×#41—862no—
479C4×#41—862no—
480C2×#117—431no—
481C2×#117—432no—
482C2×#117—432no—
483C2×#117—431no—
484C2×#117C2×D4311yescharacteristic
485#485—434no—
486#485—434no—
487#485—434no—
488#485—434no—
489#485—434no—
490#485—434no—
491#485—434no—
492#485C2×D4314yescomplemented
493#484—432no—
494#484—432no—
495#484—434no—
496#484—434no—
497#484—432no—
498#484C2×D4312yescomplemented
499#483—432no—
500#483—432no—
501#483—434no—
502#483—434no—
503#483—432no—
504#483C2×D4312yescomplemented
505#428—432no—
506#428—432no—
507#428—432no—
508#428—434no—
509#428—434no—
510#428C2×D4312yes—
511#427—434no—
512#427—434no—
513#419—432no—
514#419—432no—
515#419—432no—
516#419—434no—
517#419—434no—
518#419C2×D4312yes—
519C2×#103—434no—
520C2×#103—434no—
521#408—434no—
522#408—434no—
523#407—431no—
524#407—432no—
525#407C2×D4311yescharacteristic
526C43#6051911yescharacteristic, complemented, Sylow
527C2×#41—432no—
528C2×#41—432no—
529C2×#41—432no—
530C2×#41—432no—
531C2×#41—868no—
532C22×Q8—431no—
533C22×Q8—434no—
534C22×Q8—431no—
535C22×Q8—861no—
536C22×Q8—862no—
537C22×Q8—868no—
538C22×Q8C22×D4311yescharacteristic
539C22×D4—431no—
540C22×D4—431no—
541C22×D4—431no—
542C23×C4—431no—
543C23×C4—431no—
544C23×C4—861no—
545C23×C4C22×D4311yescharacteristic
546C2×M16—432no—
547C2×M16—434no—
548C2×M16—868no—
549C2×M16C22×D4312yes—
550C22×C8—434no—
551C4⋊Q8—864no—
552C4⋊Q8—864no—
553#124—864no—
554#124—864no—
555#123—864no—
556#123—864no—
557#123—864no—
558#123—864no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—434no—
562C22⋊Q8—432no—
563C22⋊Q8—432no—
564C22⋊Q8—434no—
565C22⋊Q8—862no—
566C22⋊Q8—862no—
567C22⋊Q8—861no—
568C22⋊Q8—861no—
569C22⋊Q8C22×D4312yes—
570C22⋊Q8C22×D4312yes—
571C4×Q8—862no—
572C4×Q8—862no—
573C4×Q8—862no—
574C4×Q8—862no—
575C4×D4—862no—
576C4×D4—862no—
577C4×D4—862no—
578C4×D4—862no—
579C4×D4—862no—
580C4×D4—862no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—862no—
584C4×D4—862no—
585C4×D4—862no—
586C4×D4—862no—
587#117—21no—
588#117—21no—
589#117—432no—
590#117—432no—
591#117—432no—
592#117—432no—
593#117—432no—
594#117—432no—
595#117—434no—
596#117—862no—
597#117—862no—
598#117—862no—
599#117—862no—
600#117—862no—
601#117—861no—
602#117—861no—
603#117C22×D4312yes—
604#117C22×D4312yes—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—431no—
607C2×C4⋊C4—431no—
608C2×C4⋊C4—431no—
609C2×C4⋊C4—432no—
610C2×C4⋊C4—432no—
611C2×C4⋊C4—432no—
612C2×C4⋊C4—432no—
613C2×C4⋊C4—861no—
614C2×C4⋊C4—861no—
615C2×C4⋊C4—861no—
616C2×C4⋊C4C22×D4311yescharacteristic
617C2×C4⋊C4C22×D4311yescharacteristic
618C2×C4⋊C4C22×D4311yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—862no—
622C2×C22⋊C4—862no—
623C2×C22⋊C4—861no—
624C2×C22⋊C4—861no—
625C2×C22⋊C4—861no—
626C2×C22⋊C4—861no—
627C2×C22⋊C4—861no—
628C2×C42—21no—
629C2×C42—862no—
630C2×C42—862no—
631C2×C42—861no—
632C2×C42—861no—
633#107—434no—
634#107—434no—
635#107—434no—
636#107C22×D4314yes—
637#106—434no—
638#106—434no—
639#106—434no—
640#106C22×D4314yes—
641#103—434no—
642#103—434no—
643#103—434no—
644#103—434no—
645#103—434no—
646#103—434no—
647#103C22×D4314yes—
648#103C22×D4314yes—
649C22⋊C8—432no—
650C22⋊C8—432no—
651C22⋊C8—434no—
652C22⋊C8—434no—
653C22⋊C8C22×D4312yes—
654C22⋊C8C22×D4312yes—
655C24—431no—
656C24—431no—
657C24D4×D4311yescharacteristic
658#41—868no—
659#41—868no—
660#41—864no—
661#41—864no—
662#41—864no—
663#41—864no—
664C2×Q8—21no—
665C2×Q8—24no—
666C2×Q8—432no—
667C2×Q8—432no—
668C2×Q8—432no—
669C2×Q8—864no—
670C2×Q8—864no—
671C2×Q8—868no—
672C2×Q8—868no—
673C2×Q8—861no—
674C2×Q8—864no—
675C2×Q8—1724no—
676C2×Q8—1728no—
677C2×Q8C23×D4312yes—
678C2×D4—432no—
679C2×D4—432no—
680C2×D4—432no—
681C2×D4—432no—
682C2×D4—432no—
683C2×D4—432no—
684C2×D4—864no—
685C2×D4—864no—
686C2×D4—864no—
687C22×C4—24no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—431no—
693C22×C4—432no—
694C22×C4—438no—
695C22×C4—432no—
696C22×C4—431no—
697C22×C4—432no—
698C22×C4—432no—
699C22×C4—862no—
700C22×C4—862no—
701C22×C4—862no—
702C22×C4—862no—
703C22×C4—864no—
704C22×C4—864no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—1724no—
710C22×C4D4×D4311yescharacteristic
711C22×C4D4×D4311yescharacteristic
712C22×C4D4×D4311yescharacteristic
713C22×C4C23×D4311yescharacteristic
714C22×C4C23×D4311yescharacteristic
715C22×C4C23×D4311yescharacteristic
716M16—24no—
717M16—868no—
718M16—864no—
719C2×C8—434no—
720C2×C8—868no—
721C2×C8C23×D4314yes—
722C4⋊C4—22no—
723C4⋊C4—22no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—432no—
728C4⋊C4—432no—
729C4⋊C4—432no—
730C4⋊C4—862no—
731C4⋊C4—862no—
732C4⋊C4—862no—
733C4⋊C4—862no—
734C4⋊C4—864no—
735C4⋊C4—864no—
736C4⋊C4—861no—
737C4⋊C4—861no—
738C4⋊C4—861no—
739C4⋊C4—862no—
740C4⋊C4—862no—
741C4⋊C4C23×D4312yes—
742C4⋊C4C23×D4312yes—
743C4⋊C4C23×D4312yes—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—22no—
748C22⋊C4—862no—
749C22⋊C4—862no—
750C22⋊C4—862no—
751C22⋊C4—862no—
752C22⋊C4—864no—
753C22⋊C4—864no—
754C22⋊C4—864no—
755C22⋊C4—862no—
756C22⋊C4—862no—
757C22⋊C4—862no—
758C22⋊C4—862no—
759C42—22no—
760C42—22no—
761C42—862no—
762C42—862no—
763C42—862no—
764C42—862no—
765C42—864no—
766C42—862no—
767C42—862no—
768C23—22no—
769C23—41no—
770C23—41no—
771C23—432no—
772C23—434no—
773C23—432no—
774C23—862no—
775C23—1721no—
776C23—1721no—
777C23—1721no—
778C23—1721no—
779C23C2×D4×D4311yescharacteristic
780C23C2×D4×D4311yescharacteristic
781C23C2×D4×D4311yescharacteristic
782Q8—24no—
783Q8—42no—
784Q8—864no—
785Q8—864no—
786Q8—864no—
787Q8—1728no—
788Q8—1722no—
789D4—864no—
790D4—864no—
791D4—864no—
792D4—864no—
793D4—864no—
794D4—864no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—81no—
807C2×C4—81no—
808C2×C4—434no—
809C2×C4—432no—
810C2×C4—438no—
811C2×C4—434no—
812C2×C4—434no—
813C2×C4—432no—
814C2×C4—862no—
815C2×C4—864no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—862no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—3442no—
823C2×C4—3442no—
824C2×C4—3442no—
825C2×C4—3442no—
826C2×C4—3441no—
827C2×C4—3441no—
828C2×C4—1728no—
829C2×C4—1722no—
830C2×C4—1722no—
831C2×C4C2×D4×D4311yescharacteristic
832C2×C4C2×D4×D4311yescharacteristic
833C2×C4C2×D4×D4311yescharacteristic
834C2×C4#41×D4314yes—
835C2×C4C24×D4311yescharacteristic
836C8—24no—
837C8—864no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—82no—
847C22—434no—
848C22—862no—
849C22—862no—
850C22—862no—
851C22—862no—
852C22—862no—
853C22—3442no—
854C22—1724no—
855C22#123×D4312yes—
856C22C22×D4×D4311yescharacteristic
857C4—21no—
858C4—21no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—434no—
864C4—862no—
865C4—1722no—
866C4—1722no—
867C4—1722no—
868C4—1722no—
869C4#123×D4312yes—
870C4C2×#41×D4312yes—
871C2—22no—
872C2—41no—
873C2—41no—
874C2—864no—
875C2—1722no—
876C2C2×#123×D4311yescharacteristic
877C2#1914937811yescharacteristic
878C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3095C2
socleC22×C43C23×D4
prime radicalC22×#10621898C22
hypercenter#3095D43
hypocenterC43#60519
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3095

Complements

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

NH ≅ G/Ntype
3. #19144563C2semidirect
4. #19144561C2semidirect
5. #19144559C2semidirect
6. #19144557C2semidirect
7. #19144545C2semidirect
8. #19144544C2semidirect
9. #19144543C2semidirect
10. #19144541C2semidirect
11. #19144539C2semidirect
12. #19143182C2semidirect
13. #419×D43C2semidirect
15. C43×#3095C2semidirect
44. #14583243C22semidirect
45. #14583242C22semidirect
46. #14583241C22semidirect
47. #14583240C22semidirect
48. #14583239C22semidirect
49. #14583238C22semidirect
50. #14583237C22semidirect
51. #14583236C22semidirect
52. #14583235C22semidirect
53. #14583234C22semidirect
54. #14583233C22semidirect
55. #14583232C22semidirect
56. #14583231C22semidirect
57. #14583230C22semidirect
58. #14583229C22semidirect
59. #14583228C22semidirect
60. #14583227C22semidirect
63. #14582940C22semidirect
65. #14582938C22semidirect
66. #14582936C22semidirect
67. #14582934C22semidirect
71. #14582906C22semidirect
72. #14582906C22semidirect
73. #103×D43C22semidirect
74. #103×D43C22semidirect
81. C43×#485C22semidirect
82. C43×#484C22semidirect
83. C43×#483C22semidirect
443. #3095D43semidirect
492. #485C2×D43semidirect
498. #484C2×D43semidirect
504. #483C2×D43semidirect
526. C43#60519semidirect

Maximal subgroups

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

subgroupindex
C2×#145834722
#191477962
#191445632
#191445612
#191445592
#191445572
#191445452
#191445442
#191445432
#191445412
#191445392
#191431822
#419×D432
#191430382
C43×#30952
#6051943