Finite Group Databasebeta

← #25976540

Subgroups — #25976540

Order 11008.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148396C211yesmaximal, characteristic, complemented
2#19147342C214yesmaximal, complemented
3#19147309C212yesmaximal, complemented
4#19147298C212yesmaximal, complemented
5#19147251C214yesmaximal, complemented
6#19147240C212yesmaximal, complemented
7#19147226C212yesmaximal, complemented
8#19144949C212yesmaximal, complemented
9#19144917C211yesmaximal, characteristic, complemented
10#19144446C212yesmaximal, complemented
11#19144392C211yesmaximal, characteristic, complemented
12#19144094C212yesmaximal, complemented
13#19144055C211yesmaximal, characteristic, complemented
14#19143530C211yesmaximal, characteristic, complemented
15#19143423C212yesmaximal, complemented
16C2×C4×#10621882C211yesmaximal, characteristic, complemented
17C43×#3506C211yesmaximal, characteristic, complemented
18C2×#13063350C2212yes—
19C22×#10621882C2211yescharacteristic
20#14583610—21no—
21#14583609C2212yescomplemented
22#14583609C2214yescomplemented
23#14583605—22no—
24Q8×D172C2212yescomplemented
25#14583564—21no—
26#14583527C2212yes—
27#14583524—22no—
28#14583456C2211yescharacteristic
29C22⋊Q8×D43—22no—
30#14583373C2212yes—
31C2×C4×D172C2211yescharacteristic
32#14583263C2214yescomplemented
33#14583258C2214yescomplemented
34#14583253C2212yescomplemented
35#14583253C2212yescomplemented
36#14583253C2214yescomplemented
37#14583249C2211yescharacteristic, complemented
38#14583249C2211yescharacteristic, complemented
39#14583245C2211yescharacteristic, complemented
40#14583245C2211yescharacteristic, complemented
41#14583245C2214yescomplemented
42#14583206C2214yescomplemented
43#14583199C2214yescomplemented
44#14583199C2214yescomplemented
45#14583194C2214yescomplemented
46#14583189C2212yescomplemented
47#14583179C2212yescomplemented
48#14583179C2214yescomplemented
49#14583111C2214yes—
50#14583111C2214yes—
51#14583111C2214yescomplemented
52#14583101C2212yescomplemented
53#14583091C2214yes—
54#14583091C2214yes—
55#14583091C2212yescomplemented
56#14583030C2212yescomplemented
57#14583030C2212yescomplemented
58Q8×C43⋊C8C2212yescomplemented
59Q8×C43⋊C8C2212yescomplemented
60#14583009C2214yescomplemented
61#14582997C2214yescomplemented
62C4×#10621884C2214yescomplemented
63C4×#10621882C2212yes—
64C4×#10621882C2212yes—
65C4×#10621882C2212yes—
66C4×#10621882C2212yes—
67C4×#10621882C2214yescomplemented
68#14582939C2212yes—
69C2×#13063258C2211yescharacteristic
70#14582926C2212yes—
71#14582923C2211yescharacteristic
72#14582904C2212yes—
73#14582900C2212yes—
74#14582895C2212yes—
75#14582895C2212yes—
76C2×#13063246C2211yescharacteristic
77C2×#13063245C2211yescharacteristic
78#14582855C2212yes—
79C2×C4×C43⋊C8C2211yescharacteristic
80C43×#559C2214yescomplemented
81C43×#556C2212yescomplemented
82C43×#555—21no—
83C43×#553—22no—
84C43×#550C2212yescomplemented
85C43×#547—21no—
86C43×#538—22no—
87C43×#535C2212yes—
88C43×#533C2211yescharacteristic
89C43×#532C2211yescharacteristic
90C43×#525—22no—
91C43×#520C2212yes—
92C2×C4×D4×C43C2211yescharacteristic
93C2×Q8×D43—22no—
94C22×D172C2311yescharacteristic
95C22×C4×D43—21no—
96#13063350—28no—
97C2×#10621884C2314yes—
98C2×#10621882—24no—
99C2×#10621882C2314yes—
100C2×#10621882C2312yes—
101C2×#10621882C2312yes—
102C2×#10621877C2312yes—
103C22×C43⋊C8C2311yescharacteristic
104C22×C43⋊C8C2311yescharacteristic
105#13063325C2311yescharacteristic
106#13063325C2314yes—
107#13063325C2311yescharacteristic
108#13063324—22no—
109#13063317C2312yes—
110#13063317C2314yes—
111#13063316—22no—
112#13063305—24no—
113#13063305—22no—
114#13063304—21no—
115#13063304—21no—
116#13063303—24no—
117#13063303—24no—
118#13063303—24no—
119#13063302—24no—
120#13063301—22no—
121#13063301—24no—
122C4×Dic86—21no—
123C4×Dic86—21no—
124C4×D172—21no—
125C4×D172—21no—
126C4×D172C2314yes—
127C4×D172C2312yes—
128C4×D172C2314yes—
129C4×D172C2312yes—
130#13063287—22no—
131#13063287—22no—
132#13063284C2312yes—
133C2×C4⋊Dic43C2311yescharacteristic
134C4⋊C4×D43—24no—
135C4⋊C4×D43—22no—
136C2×(C2×D43)⋊C4—21no—
137C22⋊C4×D43—24no—
138#13063258C2312yes—
139#13063258C2314yes—
140#13063258C2312yes—
141#13063256C2314yes—
142C4⋊(C43⋊C8)C2314yes—
143C4⋊(C43⋊C8)C2314yes—
144C4⋊(C43⋊C8)C2312yes—
145C4⋊(C43⋊C8)C2312yes—
146#13063249C2314yes—
147#13063249C2312yes—
148#13063249C2312yes—
149#13063249C2312yes—
150#13063249C2312yes—
151#13063246C2312yes—
152#13063246C2312yes—
153#13063246C2314yes—
154#13063246C2314yes—
155#13063246C2314yes—
156#13063246C2312yes—
157#13063246C2312yes—
158#13063246C2312yes—
159#13063246C2312yes—
160#13063245C2312yes—
161#13063245C2312yes—
162#13063236C2314yes—
163C4×C43⋊C8C2311yescharacteristic
164C4×C43⋊C8C2311yescharacteristic
165C4×C43⋊C8C2311yescharacteristic
166C4×C43⋊C8C2311yescharacteristic
167C4×C43⋊C8C2314yes—
168C2×#41×C43—22no—
169C2×#41×C43C2312yes—
170C22×D4×C43C2311yescharacteristic
171C23×C4×C43—21no—
172C4⋊Q8×C43D411yescharacteristic
173C4⋊Q8×C43D411yescharacteristic
174C4⋊Q8×C43C2311yescharacteristic
175#127×C43C2311yescharacteristic
176#127×C43C2314yes—
177#126×C43—24no—
178#125×C43D412yes—
179#124×C43—24no—
180#124×C43C2312yes—
181#124×C43C2314yes—
182#123×C43—24no—
183#123×C43—24no—
184C22⋊Q8×C43—22no—
185C22⋊Q8×C43D412yes—
186C22⋊Q8×C43D412yes—
187#121×C43—21no—
188#121×C43—21no—
189#121×C43—22no—
190#121×C43—22no—
191#121×C43—22no—
192#121×C43—24no—
193#120×C43—24no—
194C4×Q8×C43C2314yes—
195C4×Q8×C43C2312yes—
196C4×Q8×C43C2312yes—
197C4×D4×C43—24no—
198C4×D4×C43—24no—
199C4×D4×C43—21no—
200C4×D4×C43—21no—
201C4×D4×C43—21no—
202C4×D4×C43—21no—
203C4×D4×C43C2312yes—
204C4×D4×C43C2312yes—
205C4×D4×C43C2314yes—
206#117×C43—22no—
207#117×C43—22no—
208#117×C43C2312yes—
209C2×C4⋊C4×C43—22no—
210C2×C4⋊C4×C43C2311yescharacteristic
211C2×C22⋊C4×C43—21no—
212C2×C42×C43C2311yescharacteristic
213C24×C43—21no—
214C23×D43—21no—
215#41×C43—24no—
216#41×C43—24no—
217#41×C43—84no—
218C2×Q8×C43C2×D412yes—
219C2×Q8×C43C2×D412yes—
220C2×Q8×C43C2412yes—
221C2×D4×C43—21no—
222C2×D4×C43—21no—
223C2×D4×C43—24no—
224C2×D4×C43—21no—
225C2×D4×C43—24no—
226C2×D4×C43—22no—
227C2×D4×C43—22no—
228C2×D4×C43—22no—
229C2×D4×C43C2412yes—
230C2×D4×C43C2412yes—
231C22×C4×C43—22no—
232C22×C4×C43—22no—
233C22×C4×C43—24no—
234C22×C4×C43—22no—
235C22×C4×C43—21no—
236C22×C4×C43—82no—
237C22×C4×C43C2×D411yescharacteristic
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2411yescharacteristic
240C22×Dic43—21no—
241Q8×D43—84no—
242C2×D172—21no—
243C2×D172—22no—
244C2×D172#4114yescomplemented
245C2×D172C2412yes—
246C2×C4×D43—22no—
247C2×C4×D43—24no—
248C2×C4×D43—24no—
249C2×C4×D43—22no—
250C2×C4×D43—82no—
251C2×Dic86—21no—
252C2×Dic86—21no—
253C2×Dic86—24no—
254C4⋊C4×C43—21no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43C2×D412yes—
259C4⋊C4×C43C2×D412yes—
260C4⋊C4×C43C2×D412yes—
261C4⋊C4×C43C2×D414yes—
262C4⋊C4×C43C2×D414yes—
263C4⋊C4×C43C2×D412yes—
264C4⋊C4×C43C2412yes—
265C22⋊C4×C43—22no—
266C22⋊C4×C43—22no—
267C22⋊C4×C43—24no—
268C22⋊C4×C43—24no—
269C22⋊C4×C43—22no—
270C22⋊C4×C43—24no—
271C22⋊C4×C43—22no—
272C22⋊C4×C43C2×D414yes—
273C42×C43—24no—
274C42×C43C2×D411yescharacteristic
275C42×C43C2×D411yescharacteristic
276C42×C43C2411yescharacteristic
277C42×C43C2411yescharacteristic
278C42×C43C2414yes—
279C22⋊Dic43—22no—
280#10621884—28no—
281#10621882—24no—
282#10621882—24no—
283#10621882—28no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—22no—
287(C2×D43)⋊C4—22no—
288C4⋊Dic43—21no—
289C4⋊Dic43—24no—
290C4⋊Dic43—21no—
291C4⋊Dic43—21no—
292C4⋊Dic43C2412yes—
293C4⋊Dic43C2412yes—
294C4⋊Dic43C2412yes—
295Dic43⋊C4—22no—
296Dic43⋊C4—24no—
297Dic43⋊C4—24no—
298Dic43⋊C4—22no—
299C4×Dic43—22no—
300#10621877—24no—
301C2×C43⋊C8—22no—
302C2×C43⋊C8—22no—
303C2×C43⋊C8C2411yescharacteristic
304C2×C43⋊C8C2411yescharacteristic
305C2×C43⋊C8C2411yescharacteristic
306C2×C43⋊C8C2411yescharacteristic
307C2×C43⋊C8C2414yes—
308C23×C43—22no—
309C23×C43—22no—
310C23×C43—42no—
311C23×C43—81no—
312C23×C43—81no—
313C23×C43C22×D411yescharacteristic
314C22×D43—22no—
315C22×D43—24no—
316C22×D43—81no—
317C22×D43—81no—
318Q8×C43—24no—
319Q8×C43—22no—
320Q8×C43—22no—
321Q8×C43—42no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—22no—
325D4×C43—22no—
326D4×C43—44no—
327D4×C43—42no—
328D4×C43—42no—
329D4×C43—81no—
330D4×C43—84no—
331D4×C43—84no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—41no—
336C2×C4×C43—44no—
337C2×C4×C43—44no—
338C2×C4×C43—82no—
339C2×C4×C43—84no—
340C2×C4×C43—81no—
341C2×C4×C43C22×D411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D414yes—
344C2×C4×C43C22×D414yes—
345C2×C4×C43C22×D411yescharacteristic
346C2×C4×C43C22×D411yescharacteristic
347C2×C4×C43C22×D411yescharacteristic
348C2×C4×C43C2×#4112yes—
349C2×C4×C432−1+412yes—
350C2×C4×C43C2511yescharacteristic
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—81no—
355D172—24no—
356D172—22no—
357D172C2×#4114yes—
358C4×D43—44no—
359C4×D43—84no—
360C4×D43—82no—
361C4×D43—84no—
362Dic86—42no—
363Dic86—81no—
364Dic86—84no—
365C43⋊C8—21no—
366C43⋊C8—21no—
367C43⋊C8—24no—
368C43⋊C8—21no—
369C43⋊C8—21no—
370#61325—431nomaximal, Sylow
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—84no—
380C22×C43#54812yes—
381C22×C43C23×D411yescharacteristic
382C2×D43—24no—
383C2×D43—42no—
384C2×D43—42no—
385C2×D43—84no—
386C4×C43—21no—
387C4×C43—24no—
388C4×C43—21no—
389C4×C43—24no—
390C4×C43—21no—
391C4×C43—42no—
392C4×C43—42no—
393C4×C43#54812yes—
394C4×C43#57612yes—
395C4×C43C22×#4111yescharacteristic
396C4×C43C2×2−1+411yescharacteristic
397Dic43—42no—
398Dic43—42no—
399Dic43—42no—
400#3506D4311yescharacteristic, complemented
401#3501—431no—
402#3370—434no—
403#3367—432no—
404#3366—432no—
405#3361—434no—
406#3360—432no—
407#3358—432no—
408#3136—432no—
409#3131—431no—
410#3083—432no—
411#3077—431no—
412#3041—432no—
413#3036—431no—
414#2960—431no—
415#2946—432no—
416C2×C4×D8—431no—
417C2×C43—22no—
418C2×C43—82no—
419C2×C43—82no—
420C2×C43C2×#54811yescharacteristic
421C2×C43C2×#57611yescharacteristic
422C2×C43#358411yescharacteristic
423D43—44no—
424C2×AGL(1,ℤ/8)—432no—
425C22×D8—431no—
426#559C2×D4314yescomplemented
427#556C2×D4312yescomplemented
428#555—21no—
429#554—432no—
430#554—434no—
431#554—861no—
432#554—862no—
433#553—22no—
434#550C2×D4312yescomplemented
435D4×Q8—432no—
436D4×Q8—861no—
437#547—21no—
438#544—432no—
439#543—862no—
440#538—22no—
441#535C2×D4312yes—
442#533—431no—
443#533C2×D4311yescharacteristic
444#532C2×D4311yescharacteristic
445#525—22no—
446C2×C22⋊Q8—862no—
447#520C2×D4312yes—
448#518—432no—
449C2×C4×D4—431no—
450C2×C4×D4C2×D4311yescharacteristic
451#490—434no—
452#489—434no—
453#488—434no—
454#488—432no—
455#488—432no—
456#487—431no—
457#487—431no—
458#486—431no—
459#486—434no—
460#486—431no—
461#479—434no—
462#478—434no—
463#478—434no—
464#477—434no—
465#476—432no—
466#474—432no—
467#474—434no—
468#463—434no—
469#463—434no—
470#463—434no—
471#461—432no—
472#459—432no—
473#459—434no—
474#459—434no—
475#446—432no—
476#446—432no—
477C8×Q8—432no—
478C8×Q8—432no—
479#442—434no—
480#440—434no—
481C4×SD16—434no—
482C4×D8—432no—
483C4×D8—434no—
484C4×D8—432no—
485C4×D8—432no—
486C4×D8—432no—
487#428—432no—
488C2×#107—431no—
489#424—432no—
490#423—431no—
491#418—432no—
492#417—432no—
493#416—432no—
494#416—432no—
495C2×#102—431no—
496C2×#102—431no—
497#405—432no—
498C2×C4×C8—431no—
499C43#6132511yescharacteristic, complemented, Sylow
500C2×#41—22no—
501C2×#41C22×D4312yes—
502C22×Q8—862no—
503C22×D4—431no—
504C22×D4C22×D4311yescharacteristic
505C23×C4—21no—
506C23×C4—861no—
507AGL(1,ℤ/8)—868no—
508C2×SD16—434no—
509C2×D8—432no—
510C2×D8—432no—
511C2×D8—434no—
512C2×D8—864no—
513C2×M16—432no—
514C22×C8—431no—
515C22×C8—431no—
516C4⋊Q8—431no—
517C4⋊Q8—431no—
518C4⋊Q8—434no—
519C4⋊Q8—862no—
520C4⋊Q8C22⋊D4311yescharacteristic
521C4⋊Q8C22⋊D4311yescharacteristic
522C4⋊Q8C22×D4311yescharacteristic
523#127C22×D4311yescharacteristic
524#127C22×D4314yes—
525#126—24no—
526#125—432no—
527#125—434no—
528#125—862no—
529#125C22⋊D4312yes—
530#124—24no—
531#124C22×D4312yes—
532#124C22×D4314yes—
533#123—24no—
534#123—24no—
535C22⋊Q8—22no—
536C22⋊Q8—862no—
537C22⋊Q8—864no—
538C22⋊Q8—861no—
539C22⋊Q8—861no—
540C22⋊Q8—862no—
541C22⋊Q8—864no—
542C22⋊Q8—864no—
543C22⋊Q8—864no—
544C22⋊Q8—864no—
545C22⋊Q8—864no—
546C22⋊Q8C22⋊D4312yes—
547C22⋊Q8C22⋊D4312yes—
548#121—21no—
549#121—21no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—24no—
554#120—24no—
555C4×Q8—861no—
556C4×Q8—861no—
557C4×Q8C22×D4314yes—
558C4×Q8C22×D4312yes—
559C4×Q8C22×D4312yes—
560C4×D4—24no—
561C4×D4—24no—
562C4×D4—21no—
563C4×D4—21no—
564C4×D4—21no—
565C4×D4—21no—
566C4×D4—432no—
567C4×D4—432no—
568C4×D4—434no—
569C4×D4—434no—
570C4×D4—862no—
571C4×D4—862no—
572C4×D4—861no—
573C4×D4—861no—
574C4×D4C22×D4312yes—
575C4×D4C22×D4312yes—
576C4×D4C22×D4314yes—
577#117—22no—
578#117—22no—
579#117—432no—
580#117C22×D4312yes—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—431no—
583C2×C4⋊C4—864no—
584C2×C4⋊C4—862no—
585C2×C4⋊C4C22×D4311yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—861no—
588C2×C22⋊C4—864no—
589C2×C42C22×D4311yescharacteristic
590#107—432no—
591#107—432no—
592#107—434no—
593#106—434no—
594C4⋊C8—432no—
595C4⋊C8—432no—
596C4⋊C8—434no—
597C4⋊C8—434no—
598#103—432no—
599#103—432no—
600#103—432no—
601#103—432no—
602#103—434no—
603#102—432no—
604#102—432no—
605#102—432no—
606#102—432no—
607#102—432no—
608#102—432no—
609#102—434no—
610#102—434no—
611#102—434no—
612#102—432no—
613#102—432no—
614#97—434no—
615C4×C8—431no—
616C4×C8—431no—
617C4×C8—431no—
618C4×C8—431no—
619C4×C8—434no—
620C24—21no—
621C24—861no—
622#41—24no—
623#41—24no—
624#41—84no—
625C2×Q8—861no—
626C2×Q8—864no—
627C2×Q8—861no—
628C2×Q8—3444no—
629C2×Q8C2×C22⋊D4312yes—
630C2×Q8C2×C22⋊D4312yes—
631C2×Q8C23×D4312yes—
632C2×D4—22no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—24no—
636C2×D4—21no—
637C2×D4—24no—
638C2×D4—22no—
639C2×D4—22no—
640C2×D4—434no—
641C2×D4—432no—
642C2×D4—861no—
643C2×D4—862no—
644C2×D4C23×D4312yes—
645C2×D4C23×D4312yes—
646C22×C4—21no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—24no—
650C22×C4—22no—
651C22×C4—82no—
652C22×C4—861no—
653C22×C4—864no—
654C22×C4—864no—
655C22×C4—862no—
656C22×C4—862no—
657C22×C4—3442no—
658C22×C4C2×C22⋊D4311yescharacteristic
659C22×C4C2×C22⋊D4311yescharacteristic
660C22×C4C23×D4311yescharacteristic
661SD16—868no—
662D8—864no—
663D8—864no—
664D8—868no—
665M16—864no—
666C2×C8—431no—
667C2×C8—431no—
668C2×C8—431no—
669C2×C8—431no—
670C2×C8—434no—
671C2×C8—862no—
672C2×C8—862no—
673C4⋊C4—21no—
674C4⋊C4—24no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—432no—
678C4⋊C4—432no—
679C4⋊C4—432no—
680C4⋊C4—861no—
681C4⋊C4—862no—
682C4⋊C4—861no—
683C4⋊C4—864no—
684C4⋊C4—864no—
685C4⋊C4—864no—
686C4⋊C4—862no—
687C4⋊C4—861no—
688C4⋊C4C2×C22⋊D4312yes—
689C4⋊C4C2×C22⋊D4312yes—
690C4⋊C4C2×C22⋊D4314yes—
691C4⋊C4C2×C22⋊D4312yes—
692C4⋊C4C2×C22⋊D4314yes—
693C4⋊C4C2×C22⋊D4312yes—
694C4⋊C4C23×D4312yes—
695C22⋊C4—22no—
696C22⋊C4—22no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—22no—
700C22⋊C4—24no—
701C22⋊C4—22no—
702C22⋊C4—862no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—862no—
706C22⋊C4—862no—
707C22⋊C4C2×C22⋊D4314yes—
708C42—24no—
709C42—862no—
710C42C2×C22⋊D4311yescharacteristic
711C42C2×C22⋊D4311yescharacteristic
712C42C23×D4311yescharacteristic
713C42C23×D4311yescharacteristic
714C42C23×D4314yes—
715C23—22no—
716C23—22no—
717C23—42no—
718C23—81no—
719C23—81no—
720C23—864no—
721C23—862no—
722C23—3441no—
723C23—3441no—
724C23C22×C22⋊D4311yescharacteristic
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—42no—
729Q8—3444no—
730Q8—3441no—
731Q8—1722no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—42no—
738D4—42no—
739D4—84no—
740D4—81no—
741D4—84no—
742D4—434no—
743D4—864no—
744D4—862no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—41no—
749C2×C4—44no—
750C2×C4—44no—
751C2×C4—82no—
752C2×C4—84no—
753C2×C4—81no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—3442no—
758C2×C4—3444no—
759C2×C4—3444no—
760C2×C4—3441no—
761C2×C4—1724no—
762C2×C4C22×C22⋊D4314yes—
763C2×C4C22×C22⋊D4311yescharacteristic
764C2×C4C22×C22⋊D4311yescharacteristic
765C2×C4C22×C22⋊D4311yescharacteristic
766C2×C4C22×C22⋊D4314yes—
767C2×C4C22×C22⋊D4311yescharacteristic
768C2×C4C22×C22⋊D4311yescharacteristic
769C2×C4#41×D4312yes—
770C2×C4#1306337212yes—
771C2×C4C24×D4311yescharacteristic
772C8—861no—
773C8—861no—
774C8—864no—
775C8—861no—
776C8—861no—
777C22—21no—
778C22—21no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—864no—
787C22—3444no—
788C22—1722no—
789C22—1722no—
790C22#1458355612yes—
791C22C23×C22⋊D4311yescharacteristic
792C4—21no—
793C4—24no—
794C4—21no—
795C4—21no—
796C4—24no—
797C4—42no—
798C4—42no—
799C4—1722no—
800C4—1722no—
801C4—1722no—
802C4#1458355612yes—
803C4#1458370212yes—
804C4C2×#41×D4311yescharacteristic
805C4C2×#1306337211yescharacteristic
806C2—22no—
807C2—82no—
808C2—82no—
809C2—1724no—
810C2C2×#1458355611yescharacteristic
811C2C2×#1458370211yescharacteristic
812C2#1914936611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3506C2
socleC22×C43C23×D4
hypercenter#3506D43
hypocenterC43#61325
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #533 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #19148396C2semidirect
2. #19147342C2semidirect
3. #19147309C2semidirect
4. #19147298C2semidirect
5. #19147251C2semidirect
6. #19147240C2semidirect
7. #19147226C2semidirect
8. #19144949C2semidirect
9. #19144917C2semidirect
10. #19144446C2semidirect
11. #19144392C2semidirect
12. #19144094C2semidirect
13. #19144055C2semidirect
14. #19143530C2semidirect
15. #19143423C2semidirect
16. C2×C4×#10621882C2semidirect
17. C43×#3506C2semidirect
21. #14583609C22semidirect
22. #14583609C22semidirect
24. Q8×D172C22semidirect
32. #14583263C22semidirect
33. #14583258C22semidirect
34. #14583253C22semidirect
35. #14583253C22semidirect
36. #14583253C22semidirect
37. #14583249C22semidirect
38. #14583249C22semidirect
39. #14583245C22semidirect
40. #14583245C22semidirect
41. #14583245C22semidirect
42. #14583206C22semidirect
43. #14583199C22semidirect
44. #14583199C22semidirect
45. #14583194C22semidirect
46. #14583189C22semidirect
47. #14583179C22semidirect
48. #14583179C22semidirect
51. #14583111C22semidirect
52. #14583101C22semidirect
55. #14583091C22semidirect
56. #14583030C22semidirect
57. #14583030C22semidirect
58. Q8×C43⋊C8C22semidirect
59. Q8×C43⋊C8C22semidirect
60. #14583009C22semidirect
61. #14582997C22semidirect
62. C4×#10621884C22semidirect
67. C4×#10621882C22semidirect
80. C43×#559C22semidirect
81. C43×#556C22semidirect
84. C43×#550C22semidirect
244. C2×D172#41semidirect
400. #3506D43semidirect
426. #559C2×D43semidirect
427. #556C2×D43semidirect
434. #550C2×D43semidirect
499. C43#61325semidirect

Maximal subgroups

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

subgroupindex
#191483962
#191473422
#191473092
#191472982
#191472512
#191472402
#191472262
#191449492
#191449172
#191444462
#191443922
#191440942
#191440552
#191435302
#191434232
C2×C4×#106218822
C43×#35062
#6132543