Finite Group Databasebeta

← #25968977

Subgroups — #25968977

Order 11008.

1690 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147998C211yesmaximal, characteristic, complemented
2C2×#14583521C211yesmaximal, characteristic
3#19145900C214yesmaximal, complemented
4#19145898C214yesmaximal, complemented
5#19145885C214yesmaximal, complemented
6#19145883C214yesmaximal, complemented
7#19145139C212yesmaximal, complemented
8#19144983C212yesmaximal, complemented
9#19144541C212yesmaximal, complemented
10#19144537C212yesmaximal
11#19144400C211yesmaximal, characteristic, complemented
12#19144394C211yesmaximal, characteristic, complemented
13#19144388C211yesmaximal, characteristic, complemented
14#19143232C211yesmaximal, characteristic, complemented
15C43×#3078C211yesmaximal, characteristic, complemented
16#14583529C2212yescomplemented
17#14583529C2212yescomplemented
18#14583528—21no—
19#14583528—21no—
20#14583526C2212yescomplemented
21#14583526C2212yescomplemented
22#14583524—21no—
23#14583524—21no—
24#14583521—22no—
25#14583521—22no—
26#14583521C2214yes—
27#14583521C2214yes—
28#14583456C2211yescharacteristic
29#14583453—22no—
30#14583453—22no—
31#14583452C2212yes—
32C2×#13063324C2211yescharacteristic
33C2×#13063319—21no—
34C2×#13063314C2211yescharacteristic
35C2×#13063313—21no—
36C2×#13063310—21no—
37C2×#13063303—21no—
38C2×#13063301C2211yescharacteristic
39C2×#13063300C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×#13063282C2211yescharacteristic
42#117×D43C2212yes—
43#14583307C2214yescomplemented
44#14583306C2214yescomplemented
45#14583303C2214yescomplemented
46#14583296C2214yescomplemented
47#14583260C2214yescomplemented
48#14583260C2214yescomplemented
49#14583255C2214yescomplemented
50#14583255C2214yescomplemented
51#14583239C2214yescomplemented
52#14583238C2214yescomplemented
53#14583233C2214yescomplemented
54#14583228C2214yescomplemented
55#14583226C2214yes—
56#14583225C2214yes—
57#14583219C2214yes—
58#14583214C2214yes—
59#14583206C2214yescomplemented
60#14583200C2214yescomplemented
61#14583196C2214yescomplemented
62#14583194C2212yescomplemented
63#14583190C2212yescomplemented
64#14583186C2212yescomplemented
65#14583184C2212yescomplemented
66#14583180C2212yescomplemented
67#14583176C2212yescomplemented
68#14582959C2214yescomplemented
69#14582959C2214yescomplemented
70#14582942C2212yes—
71#14582941C2212yes—
72#14582939C2212yes—
73#14582923C2211yescharacteristic
74#14582908C2212yes—
75#14582905C2212yes—
76#14582903C2212yes—
77#14582862C2212yes—
78M16×Dic43C2212yes—
79C43×#533C2211yescharacteristic
80C2×C4×Q8×C43C2211yescharacteristic
81C43×#479C2214yescomplemented
82C43×#477C2212yescomplemented
83C43×#475C2212yescomplemented
84C43×#428C2212yes—
85C43×#423C2211yescharacteristic
86C43×#419C2212yes—
87C22×Dic86—21no—
88C22×D172—21no—
89C22×D172C2311yescharacteristic
90C22×C4×D43—21no—
91C22×C4×D43C2311yescharacteristic
92C2×#10621877C2312yes—
93#13063325C2311yescharacteristic
94#13063325C2311yescharacteristic
95#13063324—22no—
96#13063324—22no—
97#13063324—22no—
98#13063324C2312yes—
99#13063324C2314yes—
100#13063324C2312yes—
101#13063323—22no—
102#13063323—22no—
103#13063319—24no—
104#13063319—24no—
105#13063317C2312yes—
106#13063316C2312yes—
107#13063316C2312yes—
108#13063315—22no—
109#13063315—22no—
110#13063315—22no—
111#13063315—22no—
112#13063314—22no—
113#13063314C2314yes—
114#13063313—24no—
115#13063313—24no—
116#13063310—24no—
117#13063310—24no—
118#13063305—22no—
119#13063305—22no—
120#13063304—21no—
121#13063304—21no—
122#13063303—22no—
123#13063303—22no—
124#13063303—22no—
125#13063303—22no—
126#13063303—24no—
127#13063303—24no—
128#13063302—22no—
129#13063302—22no—
130#13063301—22no—
131#13063301—22no—
132#13063301—22no—
133#13063301C2314yes—
134#13063300—22no—
135#13063300C2314yes—
136C4×Dic86—21no—
137C4×Dic86—21no—
138C4×Dic86—22no—
139C4×Dic86—22no—
140C4×D172—21no—
141C4×D172—21no—
142C4×D172C2312yes—
143C4×D172C2312yes—
144#13063284C2312yes—
145#13063283C2312yes—
146#13063283C2312yes—
147#13063282—22no—
148#13063282D412yes—
149#13063282D412yes—
150#13063282C2312yes—
151#13063282C2312yes—
152#13063281—22no—
153C2×C4⋊Dic43C2311yescharacteristic
154C2×Dic43⋊C4—21no—
155C2×Dic43⋊C4—21no—
156C2×Dic43⋊C4D411yescharacteristic
157C2×Dic43⋊C4D411yescharacteristic
158C4⋊C4×D43C2312yes—
159C4⋊C4×D43C2312yes—
160C2×(C2×D43)⋊C4—21no—
161C2×(C2×D43)⋊C4—21no—
162C2×(C2×D43)⋊C4—21no—
163C2×(C2×D43)⋊C4—21no—
164C2×(C2×D43)⋊C4—21no—
165C2×(C2×D43)⋊C4D411yescharacteristic
166C2×(C2×D43)⋊C4D411yescharacteristic
167C22⋊C4×D43—22no—
168C2×C4×Dic43C2311yescharacteristic
169C42×D43—22no—
170#13063259C2314yes—
171#13063258C2314yes—
172#13063258C2314yes—
173#13063257C2314yes—
174#13063256C2314yes—
175#13063256C2314yes—
176C4⋊(C43⋊C8)C2312yes—
177C4⋊(C43⋊C8)C2312yes—
178#13063249C2314yes—
179#13063249C2314yes—
180#13063247C2314yes—
181#13063247C2314yes—
182#13063245C2314yes—
183#13063245C2314yes—
184(C2×D43)⋊C8C2314yes—
185(C2×D43)⋊C8C2314yes—
186#13063235C2314yes—
187C8×Dic43C2314yes—
188C22×Q8×C43C2311yescharacteristic
189C2×M16×C43C2312yes—
190C4⋊Q8×C43C2311yescharacteristic
191C4⋊Q8×C43C2311yescharacteristic
192#125×C43C2312yes—
193C22⋊Q8×C43—21no—
194C22⋊Q8×C43—21no—
195C4×Q8×C43—21no—
196C4×Q8×C43—21no—
197C4×Q8×C43—21no—
198C4×Q8×C43—21no—
199C4×Q8×C43C2312yes—
200C4×Q8×C43C2312yes—
201#117×C43C2312yes—
202C2×C4⋊C4×C43—21no—
203C2×C4⋊C4×C43C2311yescharacteristic
204C2×C42×C43—21no—
205C2×C42×C43C2311yescharacteristic
206#107×C43C2314yes—
207#106×C43C2314yes—
208C4⋊C8×C43C2312yes—
209C4⋊C8×C43C2312yes—
210#103×C43C2314yes—
211#103×C43C2314yes—
212C23×D43—21no—
213C23×D43C2×D411yescharacteristic
214C2×Q8×C43—21no—
215C2×Q8×C43—21no—
216C2×Q8×C43—21no—
217C2×Q8×C43—22no—
218C2×Q8×C43—22no—
219C2×Q8×C43C2412yes—
220C22×C4×C43—21no—
221C22×C4×C43—21no—
222C22×C4×C43C2×D411yescharacteristic
223C22×C4×C43C2×D411yescharacteristic
224C22×C4×C43C2411yescharacteristic
225C22×Dic43—21no—
226C22×Dic43C2×D411yescharacteristic
227C22×Dic43C2×D411yescharacteristic
228C22×Dic43C2×D411yescharacteristic
229C2×D172—21no—
230C2×D172—24no—
231C2×D172—22no—
232C2×D172—22no—
233C2×D172—82no—
234C2×D172C2412yes—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43—22no—
241C2×C4×D43—82no—
242C2×C4×D43C2×D412yes—
243C2×C4×D43C2412yes—
244C2×Dic86—21no—
245C2×Dic86—21no—
246C2×Dic86—22no—
247C2×Dic86—22no—
248C2×Dic86—24no—
249C2×Dic86—82no—
250M16×C43—24no—
251C2×C8×C43C2414yes—
252C4⋊C4×C43—22no—
253C4⋊C4×C43—22no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—22no—
256C4⋊C4×C43—22no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43—21no—
259C4⋊C4×C43C2412yes—
260C4⋊C4×C43C2412yes—
261C4⋊C4×C43C2412yes—
262C22⋊C4×C43—22no—
263C42×C43—22no—
264C42×C43—22no—
265C42×C43—22no—
266C42×C43C2×D411yescharacteristic
267C42×C43C2×D411yescharacteristic
268C42×C43C2411yescharacteristic
269C42×C43C2411yescharacteristic
270C22⋊Dic43—22no—
271(C2×D43)⋊C4—22no—
272(C2×D43)⋊C4—22no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—22no—
277(C2×D43)⋊C4—22no—
278(C2×D43)⋊C4—24no—
279(C2×D43)⋊C4C2×D412yes—
280(C2×D43)⋊C4C2×D412yes—
281(C2×D43)⋊C4C2×D412yes—
282(C2×D43)⋊C4C2×D412yes—
283C4⋊Dic43—21no—
284C4⋊Dic43—21no—
285C4⋊Dic43—21no—
286C4⋊Dic43—22no—
287C4⋊Dic43—22no—
288C4⋊Dic43C2412yes—
289C4⋊Dic43C2412yes—
290C4⋊Dic43C2412yes—
291Dic43⋊C4—22no—
292Dic43⋊C4—22no—
293Dic43⋊C4—22no—
294Dic43⋊C4—22no—
295Dic43⋊C4—24no—
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×Dic43C2×D412yes—
309C4×Dic43C2412yes—
310#10621877—24no—
311C2×C43⋊C8C2414yes—
312C23×C43C22×D411yescharacteristic
313C22×D43—22no—
314C22×D43—22no—
315C22×D43—41no—
316C22×D43—41no—
317C22×D43—42no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43C22×D412yes—
321Q8×C43—22no—
322Q8×C43—22no—
323Q8×C43—42no—
324Q8×C43—81no—
325Q8×C43—81no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—42no—
333C2×C4×C43—42no—
334C2×C4×C43C22×D411yescharacteristic
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C22×D411yescharacteristic
337C2×C4×C43C22×D411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C432−1+412yes—
340C2×C4×C432−1+412yes—
341C2×C4×C43C2511yescharacteristic
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—41no—
347C2×Dic43—41no—
348C2×Dic43—42no—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351C2×Dic43C22×D412yes—
352D172—22no—
353D172—22no—
354D172—42no—
355D172—84no—
356C4×D43—24no—
357C4×D43—22no—
358C4×D43—22no—
359C4×D43—82no—
360C4×D43—82no—
361C4×D43—82no—
362C4×D43—82no—
363Dic86—82no—
364Dic86—82no—
365Dic86—84no—
366Dic86—81no—
367Dic86—81no—
368C8×C43—24no—
369C43⋊C8—24no—
370#60870—431nomaximal, Sylow
371C22×C43—21no—
372C22×C43—21no—
373C22×C43#53612yes—
374C22×C43C23×D411yescharacteristic
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—42no—
379C2×D43—42no—
380C2×D43—42no—
381C2×D43—82no—
382C2×D43—84no—
383C4×C43—21no—
384C4×C43—21no—
385C4×C43—21no—
386C4×C43—21no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43—42no—
391C4×C43#53612yes—
392C4×C43C2×2−1+411yescharacteristic
393C4×C43C2×2−1+411yescharacteristic
394Dic43—22no—
395Dic43—22no—
396Dic43—22no—
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400#3458—431no—
401C2×#542—431no—
402#3244—434no—
403#3244—434no—
404#3243—434no—
405#3243—434no—
406#3165—432no—
407#3140—432no—
408#3095—432no—
409#3094—432no—
410#3078—431no—
411#3078D4311yescharacteristic, complemented
412#3077—431no—
413#3077—431no—
414#2921—431no—
415C2×C43—22no—
416C2×C43C2×#53611yescharacteristic
417C2×C43#358511yescharacteristic
418C2×C43#358611yescharacteristic
419D43—42no—
420D43—82no—
421#544—432no—
422#544—432no—
423#544—432no—
424#544—432no—
425#544—861no—
426#544—861no—
427#543—861no—
428#543—861no—
429#542—434no—
430#542—434no—
431#542—862no—
432#542—862no—
433#533—432no—
434#533—431no—
435#533—862no—
436#533—862no—
437#533C2×D4311yescharacteristic
438C2×C4⋊Q8—431no—
439C2×#126—861no—
440C2×#124—431no—
441C2×#124—861no—
442C2×#123—861no—
443C2×C22⋊Q8—431no—
444C2×C22⋊Q8—861no—
445C2×#121—431no—
446C2×C4×Q8C2×D4311yescharacteristic
447C2×C4×D4—431no—
448C2×#117—431no—
449C2×#117—432no—
450#501—434no—
451#501—434no—
452#500—434no—
453#498—434no—
454#489—434no—
455#489—434no—
456#488—434no—
457#488—434no—
458#485—434no—
459#485—434no—
460#484—434no—
461#483—434no—
462#482—434no—
463#482—434no—
464#481—434no—
465#480—434no—
466#479—434no—
467#479C2×D4314yescomplemented
468#478—434no—
469#478—434no—
470#477—432no—
471#477C2×D4312yescomplemented
472#476—432no—
473#476—432no—
474#475—432no—
475#475C2×D4312yescomplemented
476#474—432no—
477#474—432no—
478#433—434no—
479#433—434no—
480#428—432no—
481#428—432no—
482#428—432no—
483#428C2×D4312yes—
484#423—431no—
485#423C2×D4311yescharacteristic
486#419—432no—
487#419C2×D4312yes—
488#418—432no—
489#418—432no—
490#407—432no—
491C4×M16—432no—
492C43#6087011yescharacteristic, complemented, Sylow
493C22×Q8—861no—
494C22×Q8C22×D4311yescharacteristic
495C22×D4—431no—
496C22×D4—861no—
497C23×C4—431no—
498C23×C4—861no—
499C2×M16—432no—
500C2×M16C22×D4312yes—
501C4⋊Q8—434no—
502C4⋊Q8—432no—
503C4⋊Q8—432no—
504C4⋊Q8—431no—
505C4⋊Q8—431no—
506C4⋊Q8—862no—
507C4⋊Q8—862no—
508C4⋊Q8—862no—
509C4⋊Q8—862no—
510C4⋊Q8—862no—
511C4⋊Q8C22×D4311yescharacteristic
512C4⋊Q8C22×D4311yescharacteristic
513#126—864no—
514#126—864no—
515#125—432no—
516#125—432no—
517#125—432no—
518#125—862no—
519#125—862no—
520#125—862no—
521#125—862no—
522#125C22×D4312yes—
523#124—434no—
524#124—864no—
525#124—864no—
526#124—862no—
527#123—864no—
528#123—864no—
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—434no—
532C22⋊Q8—862no—
533C22⋊Q8—862no—
534C22⋊Q8—862no—
535C22⋊Q8—862no—
536C22⋊Q8—862no—
537C22⋊Q8—862no—
538C22⋊Q8—862no—
539C22⋊Q8—862no—
540C22⋊Q8—862no—
541C22⋊Q8—862no—
542C22⋊Q8—864no—
543C22⋊Q8—864no—
544C22⋊Q8—862no—
545C22⋊Q8—861no—
546C22⋊Q8—861no—
547#121—434no—
548#121—862no—
549C4×Q8—21no—
550C4×Q8—21no—
551C4×Q8—21no—
552C4×Q8—21no—
553C4×Q8—862no—
554C4×Q8—862no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×Q8C22×D4312yes—
558C4×Q8C22×D4312yes—
559C4×D4—432no—
560C4×D4—432no—
561C4×D4—861no—
562C4×D4—861no—
563#117—432no—
564#117—432no—
565#117—432no—
566#117—432no—
567#117—432no—
568#117—432no—
569#117—432no—
570#117—862no—
571#117—862no—
572#117C22×D4312yes—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—431no—
577C2×C4⋊C4—432no—
578C2×C4⋊C4—432no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4C22×D4311yescharacteristic
582C2×C22⋊C4—431no—
583C2×C22⋊C4—431no—
584C2×C22⋊C4—862no—
585C2×C22⋊C4—861no—
586C2×C22⋊C4—861no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—861no—
589C2×C22⋊C4—861no—
590C2×C42—21no—
591C2×C42—431no—
592C2×C42—862no—
593C2×C42C22×D4311yescharacteristic
594#107—434no—
595#107—434no—
596#107—434no—
597#107C22×D4314yes—
598#106—434no—
599#106—434no—
600#106—434no—
601#106C22×D4314yes—
602C4⋊C8—432no—
603C4⋊C8—432no—
604C4⋊C8C22×D4312yes—
605C4⋊C8C22×D4312yes—
606#103—434no—
607#103—434no—
608#103C22×D4314yes—
609#103C22×D4314yes—
610#102—434no—
611#102—434no—
612#102—434no—
613#102—434no—
614C22⋊C8—434no—
615C22⋊C8—434no—
616#97—434no—
617C4×C8—434no—
618C24—431no—
619C24—861no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—22no—
624C2×Q8—22no—
625C2×Q8—862no—
626C2×Q8—862no—
627C2×Q8—864no—
628C2×Q8—861no—
629C2×Q8—861no—
630C2×Q8—3442no—
631C2×Q8C23×D4312yes—
632C2×D4—432no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—862no—
636C2×D4—862no—
637C2×D4—3442no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—431no—
641C22×C4—431no—
642C22×C4—431no—
643C22×C4—432no—
644C22×C4—432no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—861no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—3442no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656M16—24no—
657M16—864no—
658C2×C8—434no—
659C2×C8C23×D4314yes—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—22no—
667C4⋊C4—432no—
668C4⋊C4—432no—
669C4⋊C4—432no—
670C4⋊C4—432no—
671C4⋊C4—432no—
672C4⋊C4—432no—
673C4⋊C4—432no—
674C4⋊C4—862no—
675C4⋊C4—862no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—862no—
679C4⋊C4—862no—
680C4⋊C4—862no—
681C4⋊C4—862no—
682C4⋊C4—862no—
683C4⋊C4—862no—
684C4⋊C4—861no—
685C4⋊C4—862no—
686C4⋊C4—862no—
687C4⋊C4—861no—
688C4⋊C4—861no—
689C4⋊C4C23×D4312yes—
690C4⋊C4C23×D4312yes—
691C4⋊C4C23×D4312yes—
692C22⋊C4—22no—
693C22⋊C4—432no—
694C22⋊C4—432no—
695C22⋊C4—432no—
696C22⋊C4—432no—
697C22⋊C4—864no—
698C22⋊C4—864no—
699C22⋊C4—864no—
700C22⋊C4—862no—
701C22⋊C4—862no—
702C22⋊C4—864no—
703C22⋊C4—862no—
704C22⋊C4—862no—
705C22⋊C4—862no—
706C42—22no—
707C42—22no—
708C42—22no—
709C42—432no—
710C42—432no—
711C42—862no—
712C42—862no—
713C42—862no—
714C42D4×D4311yescharacteristic
715C42D4×D4311yescharacteristic
716C42C23×D4311yescharacteristic
717C42C23×D4311yescharacteristic
718C23—432no—
719C23—862no—
720C23—862no—
721C23—1721no—
722C23—1721no—
723C23—1722no—
724C23—1722no—
725C23—1722no—
726C23C2×D4×D4311yescharacteristic
727Q8—22no—
728Q8—22no—
729Q8—42no—
730Q8—81no—
731Q8—81no—
732Q8—3441no—
733Q8—3441no—
734Q8—3444no—
735Q8—3442no—
736Q8—3442no—
737D4—862no—
738D4—862no—
739D4—3444no—
740D4—1722no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—432no—
750C2×C4—432no—
751C2×C4—432no—
752C2×C4—862no—
753C2×C4—864no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—3442no—
760C2×C4—3442no—
761C2×C4—3442no—
762C2×C4—3442no—
763C2×C4—1721no—
764C2×C4—1721no—
765C2×C4—1722no—
766C2×C4C2×D4×D4311yescharacteristic
767C2×C4C2×D4×D4311yescharacteristic
768C2×C4C2×D4×D4311yescharacteristic
769C2×C4C2×D4×D4311yescharacteristic
770C2×C4C2×D4×D4311yescharacteristic
771C2×C4#1306337212yes—
772C2×C4#1306337312yes—
773C2×C4C24×D4311yescharacteristic
774C8—24no—
775C8—864no—
776C22—21no—
777C22—21no—
778C22—862no—
779C22—862no—
780C22—862no—
781C22—3444no—
782C22—3442no—
783C22—1722no—
784C22—1722no—
785C22—1722no—
786C22#1458347212yes—
787C22C22×D4×D4311yescharacteristic
788C4—21no—
789C4—21no—
790C4—21no—
791C4—21no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—862no—
797C4—862no—
798C4—862no—
799C4—1722no—
800C4—1722no—
801C4—1722no—
802C4#1458347212yes—
803C4C2×#1306337211yescharacteristic
804C4C2×#1306337311yescharacteristic
805C2—22no—
806C2—3442no—
807C2—1722no—
808C2C2×#1458347211yescharacteristic
809C2#1914937211yescharacteristic
810C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3078C2
socleC22×C43C23×D4
prime radicalC2×#13063300C22
hypercenter#3078D43
hypocenterC43#60870
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
1. #19147998C2semidirect
3. #19145900C2semidirect
4. #19145898C2semidirect
5. #19145885C2semidirect
6. #19145883C2semidirect
7. #19145139C2semidirect
8. #19144983C2semidirect
9. #19144541C2semidirect
11. #19144400C2semidirect
12. #19144394C2semidirect
13. #19144388C2semidirect
14. #19143232C2semidirect
15. C43×#3078C2semidirect
16. #14583529C22semidirect
17. #14583529C22semidirect
20. #14583526C22semidirect
21. #14583526C22semidirect
43. #14583307C22semidirect
44. #14583306C22semidirect
45. #14583303C22semidirect
46. #14583296C22semidirect
47. #14583260C22semidirect
48. #14583260C22semidirect
49. #14583255C22semidirect
50. #14583255C22semidirect
51. #14583239C22semidirect
52. #14583238C22semidirect
53. #14583233C22semidirect
54. #14583228C22semidirect
59. #14583206C22semidirect
60. #14583200C22semidirect
61. #14583196C22semidirect
62. #14583194C22semidirect
63. #14583190C22semidirect
64. #14583186C22semidirect
65. #14583184C22semidirect
66. #14583180C22semidirect
67. #14583176C22semidirect
68. #14582959C22semidirect
69. #14582959C22semidirect
81. C43×#479C22semidirect
82. C43×#477C22semidirect
83. C43×#475C22semidirect
411. #3078D43semidirect
467. #479C2×D43semidirect
471. #477C2×D43semidirect
475. #475C2×D43semidirect
492. C43#60870semidirect

Maximal subgroups

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

subgroupindex
#191479982
C2×#145835212
#191459002
#191458982
#191458852
#191458832
#191451392
#191449832
#191445412
#191445372
#191444002
#191443942
#191443882
#191432322
C43×#30782
#6087043