Finite Group Databasebeta

← #25964216

Subgroups — #25964216

Order 11008.

1962 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147998C211yesmaximal, characteristic
2C2×#14583375C211yesmaximal, characteristic
3#19144436C214yesmaximal, complemented
4#19144434C214yesmaximal, complemented
5#19144432C214yesmaximal, complemented
6#19144430C214yesmaximal, complemented
7#19144402C211yesmaximal, characteristic, complemented
8#19144400C211yesmaximal, characteristic, complemented
9#19144399C212yesmaximal, complemented
10#19144397C212yesmaximal, complemented
11#19144396C211yesmaximal, characteristic, complemented
12#19143182C212yesmaximal
13#19143157C211yesmaximal, characteristic
14#419×D43C212yesmaximal
15C43×#3078C211yesmaximal, characteristic, complemented
16C22×Q8×D43C2211yescharacteristic
17C2×M16×D43C2212yes—
18#14583529C2212yes—
19#14583529C2212yes—
20#14583528—21no—
21#14583528—21no—
22#14583526C2212yes—
23#14583526C2212yes—
24#14583524—21no—
25#14583524—21no—
26#14583456C2211yescharacteristic
27#14583453—22no—
28#14583453—22no—
29#14583452C2212yes—
30#14583375—22no—
31#14583375—22no—
32#14583375C2214yes—
33#14583375C2214yes—
34C2×Q8×Dic43C2211yescharacteristic
35C2×C4×Dic86—21no—
36C2×C4×Dic86C2211yescharacteristic
37C2×#13063290—21no—
38C2×#13063290C2211yescharacteristic
39C2×#13063283—21no—
40C2×#13063283C2211yescharacteristic
41C2×#13063282—21no—
42C2×#13063282C2211yescharacteristic
43#117×D43C2212yes—
44#14583209C2214yescomplemented
45#14583208C2214yescomplemented
46#14583207C2214yescomplemented
47#14583206C2214yescomplemented
48#14583205C2214yescomplemented
49#14583204C2214yescomplemented
50#14583203C2214yescomplemented
51#14583195C2212yescomplemented
52#14583194C2212yescomplemented
53#14583193C2214yescomplemented
54#14583192C2214yescomplemented
55#14583191C2212yescomplemented
56#14583185C2212yescomplemented
57#14583184C2212yescomplemented
58#14583183C2214yescomplemented
59#14583182C2214yescomplemented
60#14583181C2212yescomplemented
61#14582942C2212yes—
62#14582941C2212yes—
63#14582940C2214yes—
64#14582939C2212yes—
65#14582938C2214yes—
66#14582936C2214yes—
67#14582934C2214yes—
68#14582924C2214yes—
69#14582924C2214yes—
70#14582923C2211yescharacteristic
71#14582922C2212yes—
72#14582909C2212yes—
73#14582908C2212yes—
74#14582907C2212yes—
75#14582906C2214yes—
76#14582906C2214yes—
77#103×D43C2214yes—
78#103×D43C2214yes—
79C43×#533C2211yescharacteristic
80C2×C4×Q8×C43C2211yescharacteristic
81C43×#479C2214yescomplemented
82C43×#477C2212yescomplemented
83C43×#475C2212yescomplemented
84C43×#428C2212yes—
85C43×#423C2211yescharacteristic
86C43×#419C2212yes—
87C22×Dic86—21no—
88C22×Dic86C2311yescharacteristic
89C2×Q8×D43—22no—
90C2×Q8×D43—24no—
91C2×Q8×D43Q818yescomplemented
92C2×Q8×D43C2314yes—
93C22×C4×D43—21no—
94C22×C4×D43C2311yescharacteristic
95C2×#10621877C2312yes—
96C2×#10621872C2314yes—
97M16×D43—28no—
98C2×C8×D43C2314yes—
99#13063325C2311yescharacteristic
100#13063325C2311yescharacteristic
101#13063324—22no—
102#13063324—22no—
103#13063324C2312yes—
104#13063324C2312yes—
105#13063323—22no—
106#13063323—22no—
107#13063317C2312yes—
108#13063316C2312yes—
109#13063316C2312yes—
110#13063315—22no—
111#13063315—22no—
112#13063315—22no—
113#13063315—22no—
114#13063305—22no—
115#13063305—22no—
116#13063304—21no—
117#13063304—21no—
118#13063303—22no—
119#13063303—22no—
120#13063303—22no—
121#13063303—22no—
122#13063302—22no—
123#13063302—22no—
124#13063301—22no—
125#13063301—22no—
126Q8×Dic43—22no—
127Q8×Dic43C2314yes—
128C4×Dic86—21no—
129C4×Dic86—21no—
130C4×Dic86—21no—
131C4×Dic86—21no—
132C4×Dic86—24no—
133C4×Dic86—24no—
134C4×Dic86—22no—
135C4×Dic86—22no—
136C4×Dic86C2312yes—
137C4×Dic86C2312yes—
138#13063290—24no—
139#13063290—24no—
140#13063290—22no—
141#13063290C2314yes—
142#13063284C2312yes—
143#13063283—22no—
144#13063283—24no—
145#13063283—24no—
146#13063283C2312yes—
147#13063283C2312yes—
148#13063283C2314yes—
149#13063282—22no—
150#13063282—24no—
151#13063282—24no—
152#13063282D412yes—
153#13063282D412yes—
154#13063282C2312yes—
155#13063282C2312yes—
156#13063281—22no—
157C2×C4⋊Dic43—21no—
158C2×C4⋊Dic43C2311yescharacteristic
159C2×Dic43⋊C4—21no—
160C2×Dic43⋊C4—21no—
161C2×Dic43⋊C4D411yescharacteristic
162C2×Dic43⋊C4D411yescharacteristic
163C4⋊C4×D43C2312yes—
164C4⋊C4×D43C2312yes—
165C2×(C2×D43)⋊C4—21no—
166C2×(C2×D43)⋊C4D411yescharacteristic
167C2×(C2×D43)⋊C4D411yescharacteristic
168C22⋊C4×D43—22no—
169C2×C4×Dic43—21no—
170C2×C4×Dic43—21no—
171C2×C4×Dic43—21no—
172C2×C4×Dic43—21no—
173C2×C4×Dic43C2311yescharacteristic
174C42×D43—22no—
175#13063259C2314yes—
176#13063258C2314yes—
177#13063258C2314yes—
178#13063257C2314yes—
179#13063256C2314yes—
180#13063256C2314yes—
181C4⋊(C43⋊C8)C2312yes—
182C4⋊(C43⋊C8)C2312yes—
183Dic43⋊C8C2314yes—
184Dic43⋊C8C2314yes—
185#13063250C2314yes—
186#13063250C2314yes—
187#13063249C2314yes—
188#13063249C2314yes—
189#13063248C2314yes—
190#13063248C2314yes—
191C22×Q8×C43C2311yescharacteristic
192C2×M16×C43C2312yes—
193C4⋊Q8×C43C2311yescharacteristic
194C4⋊Q8×C43C2311yescharacteristic
195#125×C43C2312yes—
196C22⋊Q8×C43—21no—
197C22⋊Q8×C43—21no—
198C4×Q8×C43—21no—
199C4×Q8×C43—21no—
200C4×Q8×C43—21no—
201C4×Q8×C43—21no—
202C4×Q8×C43C2312yes—
203C4×Q8×C43C2312yes—
204#117×C43C2312yes—
205C2×C4⋊C4×C43—21no—
206C2×C4⋊C4×C43C2311yescharacteristic
207C2×C42×C43—21no—
208C2×C42×C43C2311yescharacteristic
209#107×C43C2314yes—
210#106×C43C2314yes—
211C4⋊C8×C43C2312yes—
212C4⋊C8×C43C2312yes—
213#103×C43C2314yes—
214#103×C43C2314yes—
215C23×D43C2×D411yescharacteristic
216C2×Q8×C43—21no—
217C2×Q8×C43—21no—
218C2×Q8×C43—21no—
219C2×Q8×C43—22no—
220C2×Q8×C43C2×Q814yes—
221C2×Q8×C43C2412yes—
222C22×C4×C43—21no—
223C22×C4×C43—21no—
224C22×C4×C43C2×D411yescharacteristic
225C22×C4×C43C2×D411yescharacteristic
226C22×C4×C43C2411yescharacteristic
227C22×Dic43—21no—
228C22×Dic43—21no—
229C22×Dic43C2×D411yescharacteristic
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232Q8×D43—216no—
233Q8×D43—28no—
234Q8×D43C2×Q8116yes—
235C2×C4×D43—28no—
236C2×C4×D43—24no—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43C2×D412yes—
240C2×C4×D43C2×Q814yes—
241C2×C4×D43#4114yes—
242C2×C4×D43C2412yes—
243C2×Dic86—21no—
244C2×Dic86—22no—
245C2×Dic86—28no—
246C2×Dic86—24no—
247C2×Dic86—21no—
248C2×Dic86—21no—
249C2×Dic86—22no—
250C2×Dic86—22no—
251C2×Dic86C2×Q814yes—
252C2×Dic86C2412yes—
253M16×C43—24no—
254C2×C8×C43C2414yes—
255C4⋊C4×C43—22no—
256C4⋊C4×C43—22no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—22no—
259C4⋊C4×C43—22no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43C2412yes—
263C4⋊C4×C43C2412yes—
264C4⋊C4×C43C2412yes—
265C22⋊C4×C43—22no—
266C42×C43—22no—
267C42×C43—22no—
268C42×C43—22no—
269C42×C43C2×D411yescharacteristic
270C42×C43C2×D411yescharacteristic
271C42×C43C2411yescharacteristic
272C42×C43C2411yescharacteristic
273C22⋊Dic43—22no—
274(C2×D43)⋊C4—22no—
275(C2×D43)⋊C4—22no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4C2×D412yes—
278(C2×D43)⋊C4C2×D412yes—
279(C2×D43)⋊C4C2×D412yes—
280(C2×D43)⋊C4C2×D412yes—
281C4⋊Dic43—21no—
282C4⋊Dic43—21no—
283C4⋊Dic43—21no—
284C4⋊Dic43—24no—
285C4⋊Dic43—22no—
286C4⋊Dic43—22no—
287C4⋊Dic43C2412yes—
288C4⋊Dic43C2412yes—
289C4⋊Dic43C2412yes—
290Dic43⋊C4—22no—
291Dic43⋊C4—22no—
292Dic43⋊C4—22no—
293Dic43⋊C4—22no—
294Dic43⋊C4—22no—
295Dic43⋊C4—22no—
296Dic43⋊C4—24no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299Dic43⋊C4—22no—
300Dic43⋊C4—22no—
301Dic43⋊C4C2×D412yes—
302Dic43⋊C4C2×D412yes—
303Dic43⋊C4C2×D412yes—
304Dic43⋊C4C2×D412yes—
305C4×Dic43—22no—
306C4×Dic43—22no—
307C4×Dic43—22no—
308C4×Dic43—22no—
309C4×Dic43—22no—
310C4×Dic43—24no—
311C4×Dic43—24no—
312C4×Dic43—24no—
313C4×Dic43C2×D412yes—
314C4×Dic43C2412yes—
315#10621877—24no—
316C2×C43⋊C8C2414yes—
317#10621872—28no—
318C8×D43—28no—
319C23×C43C22×D411yescharacteristic
320C22×D43—41no—
321C22×D43—41no—
322C22×D43C22⋊Q814yes—
323C22×D43C22×D412yes—
324Q8×C43—24no—
325Q8×C43—22no—
326Q8×C43—81no—
327Q8×C43—81no—
328Q8×C43C22×Q814yes—
329C2×C4×C43—24no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—42no—
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×Q812yes—
343C2×C4×C43C2×#4112yes—
344C2×C4×C43C2511yescharacteristic
345C2×Dic43—24no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—41no—
351C2×Dic43—41no—
352C2×Dic43—42no—
353C2×Dic43C22⋊Q814yes—
354C2×Dic43C22×D412yes—
355C2×Dic43C22×D412yes—
356C2×Dic43C22×D412yes—
357C4×D43—216no—
358C4×D43—82no—
359C4×D43—82no—
360C4×D43C22⋊Q818yes—
361C4×D43C22×Q814yes—
362C4×D43C2×#4114yes—
363Dic86—24no—
364Dic86—22no—
365Dic86—216no—
366Dic86—82no—
367Dic86—82no—
368Dic86—81no—
369Dic86—81no—
370Dic86C22×Q814yes—
371C8×C43—24no—
372C43⋊C8—24no—
373#60491—431nomaximal, Sylow
374C22×C43—21no—
375C22×C43—21no—
376C22×C43C2×C22⋊Q812yes—
377C22×C43C23×D411yescharacteristic
378C2×D43—22no—
379C2×D43—22no—
380C2×D43—44no—
381C2×D43C2×C22⋊Q814yes—
382C4×C43—21no—
383C4×C43—21no—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—24no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43C2×C22⋊Q812yes—
391C4×C43C23×Q811yescharacteristic
392C4×C43C22×#4111yescharacteristic
393Dic43—22no—
394Dic43—22no—
395Dic43—24no—
396Dic43—42no—
397Dic43—42no—
398Dic43—42no—
399Dic43C2×C22⋊Q814yes—
400#3458—431no—
401C2×#519—431no—
402#3082—434no—
403#3082—434no—
404#3082—434no—
405#3082—434no—
406#3078—432no—
407#3078—431no—
408#3078—432no—
409#3078—431no—
410#3078—431no—
411#3078D4311yescharacteristic, complemented
412#2911—432no—
413#2905—431no—
414C2×#419—432no—
415C2×C43—22no—
416C2×C43C22×C22⋊Q811yescharacteristic
417C2×C43#358611yescharacteristic
418C2×C43#358611yescharacteristic
419D43—24no—
420C23×Q8—431no—
421C22×M16—432no—
422#544—432no—
423#544—432no—
424#544—432no—
425#544—432no—
426#544—861no—
427#544—861no—
428#543—861no—
429#543—861no—
430#533—432no—
431#533—431no—
432#533—862no—
433#533—862no—
434#533C2×D4311yescharacteristic
435#519—434no—
436#519—434no—
437#519—862no—
438#519—862no—
439C2×C4×Q8—431no—
440C2×C4×Q8—431no—
441C2×C4×Q8—431no—
442C2×C4×Q8—861no—
443C2×C4×Q8—861no—
444C2×C4×Q8C2×D4311yescharacteristic
445C2×#117—431no—
446C2×#117—432no—
447C2×#117—431no—
448C2×#117—861no—
449C2×#117—861no—
450#479—434no—
451#479—434no—
452#479—434no—
453#479—434no—
454#479—434no—
455#479—434no—
456#479—434no—
457#479C2×D4314yescomplemented
458#477—432no—
459#477—432no—
460#477—434no—
461#477—432no—
462#477—434no—
463#477C2×D4312yescomplemented
464#475—432no—
465#475—432no—
466#475—434no—
467#475—432no—
468#475—434no—
469#475C2×D4312yescomplemented
470#428—432no—
471#428—432no—
472#428—432no—
473#428—434no—
474#428—434no—
475#428C2×D4312yes—
476#427—434no—
477#427—434no—
478#424—434no—
479#424—434no—
480#423—432no—
481#423—431no—
482#423C2×D4311yescharacteristic
483#419—432no—
484#419—432no—
485#419—432no—
486#419—434no—
487#419—434no—
488#419C2×D4312yes—
489C2×#103—434no—
490C2×#103—434no—
491C43#6049111yescharacteristic, complemented, Sylow
492C22×Q8—438no—
493C22×Q8—434no—
494C22×Q8—431no—
495C22×Q8—861no—
496C22×Q8—862no—
497C22×Q8—864no—
498C22×Q8C22×D4311yescharacteristic
499C23×C4—431no—
500C23×C4—861no—
501C2×M16—432no—
502C2×M16—434no—
503C2×M16—868no—
504C2×M16C22×D4312yes—
505C22×C8—434no—
506C4⋊Q8—432no—
507C4⋊Q8—432no—
508C4⋊Q8—431no—
509C4⋊Q8—431no—
510C4⋊Q8—862no—
511C4⋊Q8—862no—
512C4⋊Q8—862no—
513C4⋊Q8—862no—
514C4⋊Q8C22×D4311yescharacteristic
515C4⋊Q8C22×D4311yescharacteristic
516#125—432no—
517#125—432no—
518#125—432no—
519#125—862no—
520#125—862no—
521#125—862no—
522#125—862no—
523#125C22×D4312yes—
524C22⋊Q8—21no—
525C22⋊Q8—21no—
526C22⋊Q8—862no—
527C22⋊Q8—862no—
528C22⋊Q8—862no—
529C22⋊Q8—862no—
530C22⋊Q8—862no—
531C22⋊Q8—862no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536C22⋊Q8—861no—
537C22⋊Q8—861no—
538C4×Q8—21no—
539C4×Q8—21no—
540C4×Q8—21no—
541C4×Q8—21no—
542C4×Q8—434no—
543C4×Q8—434no—
544C4×Q8—432no—
545C4×Q8—432no—
546C4×Q8—862no—
547C4×Q8—862no—
548C4×Q8—864no—
549C4×Q8—864no—
550C4×Q8—862no—
551C4×Q8—862no—
552C4×Q8—864no—
553C4×Q8—864no—
554C4×Q8—861no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×Q8—861no—
558C4×Q8C22×D4312yes—
559C4×Q8C22×D4312yes—
560#117—432no—
561#117—432no—
562#117—432no—
563#117—432no—
564#117—432no—
565#117—434no—
566#117—432no—
567#117—432no—
568#117—864no—
569#117—864no—
570#117—862no—
571#117—862no—
572#117—864no—
573#117—864no—
574#117—862no—
575#117C22×D4312yes—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—431no—
578C2×C4⋊C4—431no—
579C2×C4⋊C4—431no—
580C2×C4⋊C4—432no—
581C2×C4⋊C4—432no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4—861no—
584C2×C4⋊C4—861no—
585C2×C4⋊C4C22×D4311yescharacteristic
586C2×C22⋊C4—431no—
587C2×C22⋊C4—431no—
588C2×C22⋊C4—862no—
589C2×C22⋊C4—861no—
590C2×C42—21no—
591C2×C42—431no—
592C2×C42—862no—
593C2×C42—861no—
594C2×C42—861no—
595C2×C42—861no—
596C2×C42—861no—
597C2×C42C22×D4311yescharacteristic
598#107—434no—
599#107—434no—
600#107—434no—
601#107C22×D4314yes—
602#106—434no—
603#106—434no—
604#106—434no—
605#106C22×D4314yes—
606C4⋊C8—434no—
607C4⋊C8—434no—
608C4⋊C8—432no—
609C4⋊C8—432no—
610C4⋊C8C22×D4312yes—
611C4⋊C8C22×D4312yes—
612#103—434no—
613#103—434no—
614#103—434no—
615#103—434no—
616#103—434no—
617#103—434no—
618#103C22×D4314yes—
619#103C22×D4314yes—
620C24—431no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—22no—
625C2×Q8—4316no—
626C2×Q8—434no—
627C2×Q8—432no—
628C2×Q8—864no—
629C2×Q8—868no—
630C2×Q8—862no—
631C2×Q8—862no—
632C2×Q8—8616no—
633C2×Q8—868no—
634C2×Q8—861no—
635C2×Q8—861no—
636C2×Q8—861no—
637C2×Q8—862no—
638C2×Q8Q8×D4314yes—
639C2×Q8C23×D4312yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—431no—
643C22×C4—432no—
644C22×C4—434no—
645C22×C4—434no—
646C22×C4—432no—
647C22×C4—431no—
648C22×C4—431no—
649C22×C4—864no—
650C22×C4—868no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—861no—
654C22×C4—861no—
655C22×C4D4×D4311yescharacteristic
656C22×C4D4×D4311yescharacteristic
657C22×C4C23×D4311yescharacteristic
658M16—24no—
659M16—868no—
660M16—864no—
661C2×C8—434no—
662C2×C8—868no—
663C2×C8C23×D4314yes—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—22no—
671C4⋊C4—432no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—432no—
675C4⋊C4—432no—
676C4⋊C4—432no—
677C4⋊C4—432no—
678C4⋊C4—862no—
679C4⋊C4—862no—
680C4⋊C4—864no—
681C4⋊C4—864no—
682C4⋊C4—862no—
683C4⋊C4—862no—
684C4⋊C4—862no—
685C4⋊C4—862no—
686C4⋊C4—862no—
687C4⋊C4—862no—
688C4⋊C4—861no—
689C4⋊C4—862no—
690C4⋊C4—862no—
691C4⋊C4—862no—
692C4⋊C4—862no—
693C4⋊C4—861no—
694C4⋊C4—861no—
695C4⋊C4C23×D4312yes—
696C4⋊C4C23×D4312yes—
697C4⋊C4C23×D4312yes—
698C22⋊C4—22no—
699C22⋊C4—432no—
700C22⋊C4—432no—
701C22⋊C4—432no—
702C22⋊C4—432no—
703C22⋊C4—864no—
704C22⋊C4—862no—
705C22⋊C4—862no—
706C22⋊C4—862no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—432no—
711C42—432no—
712C42—864no—
713C42—862no—
714C42—862no—
715C42—864no—
716C42—864no—
717C42—862no—
718C42—862no—
719C42—862no—
720C42D4×D4311yescharacteristic
721C42D4×D4311yescharacteristic
722C42C23×D4311yescharacteristic
723C42C23×D4311yescharacteristic
724C23—432no—
725C23—434no—
726C23—1721no—
727C23—1721no—
728C23C2×D4×D4311yescharacteristic
729Q8—24no—
730Q8—22no—
731Q8—81no—
732Q8—81no—
733Q8—434no—
734Q8—8616no—
735Q8—864no—
736Q8—862no—
737Q8—3441no—
738Q8—3441no—
739Q8—3442no—
740Q8—3442no—
741Q8C2×Q8×D4314yes—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—434no—
751C2×C4—432no—
752C2×C4—438no—
753C2×C4—434no—
754C2×C4—434no—
755C2×C4—432no—
756C2×C4—432no—
757C2×C4—8616no—
758C2×C4—864no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—3442no—
764C2×C4—3442no—
765C2×C4—1721no—
766C2×C4—1721no—
767C2×C4—1722no—
768C2×C4C2×D4×D4311yescharacteristic
769C2×C4C2×D4×D4311yescharacteristic
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4C2×D4×D4311yescharacteristic
772C2×C4C2×D4×D4311yescharacteristic
773C2×C4C2×Q8×D4312yes—
774C2×C4#41×D4312yes—
775C2×C4C24×D4311yescharacteristic
776C8—24no—
777C8—864no—
778C22—21no—
779C22—21no—
780C22—434no—
781C22—862no—
782C22—862no—
783C22—1724no—
784C22C22⋊Q8×D4312yes—
785C22C22×D4×D4311yescharacteristic
786C4—24no—
787C4—21no—
788C4—21no—
789C4—21no—
790C4—21no—
791C4—42no—
792C4—42no—
793C4—42no—
794C4—434no—
795C4—864no—
796C4—862no—
797C4—862no—
798C4—1722no—
799C4—1722no—
800C4—1722no—
801C4C22⋊Q8×D4312yes—
802C4C22×Q8×D4311yescharacteristic
803C4C2×#41×D4311yescharacteristic
804C2—22no—
805C2—864no—
806C2C2×C22⋊Q8×D4311yescharacteristic
807C2#1914937811yescharacteristic
808C2#1914937911yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3078C2
socleC22×C43C23×D4
prime radicalC23×D43C2×D4
hypercenter#3078D43
hypocenterC43#60491
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3078

Complements

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

NH ≅ G/Ntype
3. #19144436C2semidirect
4. #19144434C2semidirect
5. #19144432C2semidirect
6. #19144430C2semidirect
7. #19144402C2semidirect
8. #19144400C2semidirect
9. #19144399C2semidirect
10. #19144397C2semidirect
11. #19144396C2semidirect
15. C43×#3078C2semidirect
44. #14583209C22semidirect
45. #14583208C22semidirect
46. #14583207C22semidirect
47. #14583206C22semidirect
48. #14583205C22semidirect
49. #14583204C22semidirect
50. #14583203C22semidirect
51. #14583195C22semidirect
52. #14583194C22semidirect
53. #14583193C22semidirect
54. #14583192C22semidirect
55. #14583191C22semidirect
56. #14583185C22semidirect
57. #14583184C22semidirect
58. #14583183C22semidirect
59. #14583182C22semidirect
60. #14583181C22semidirect
81. C43×#479C22semidirect
82. C43×#477C22semidirect
83. C43×#475C22semidirect
91. C2×Q8×D43Q8semidirect
411. #3078D43semidirect
457. #479C2×D43semidirect
463. #477C2×D43semidirect
469. #475C2×D43semidirect
491. C43#60491semidirect

Maximal subgroups

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

subgroupindex
#191479982
C2×#145833752
#191444362
#191444342
#191444322
#191444302
#191444022
#191444002
#191443992
#191443972
#191443962
#191431822
#191431572
#419×D432
C43×#30782
#6049143