Finite Group Databasebeta

← #25976519

Subgroups — #25976519

Order 11008.

1814 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148173C211yesmaximal, characteristic, complemented
2C2×#14583623C211yesmaximal, characteristic, complemented
3#19147432C214yesmaximal, complemented
4#19147417C214yesmaximal, complemented
5#19147340C212yesmaximal, complemented
6#19147318C212yesmaximal, complemented
7#19147285C212yesmaximal, complemented
8#19147249C212yesmaximal, complemented
9#19144983C212yesmaximal, complemented
10#19144397C212yesmaximal, complemented
11#19144388C211yesmaximal, characteristic, complemented
12#19144092C212yesmaximal
13#19144078C211yesmaximal, characteristic, complemented
14M16×Dic86C211yesmaximal, characteristic, complemented
15#19143410C212yesmaximal, complemented
16C4×#13063353C211yesmaximal, characteristic
17C43×#3139C211yesmaximal, characteristic, complemented
18C2×#13063356C2212yes—
19C2×#13063353C2211yescharacteristic
20#14583629C2211yescharacteristic, complemented
21#14583626C2212yescomplemented
22#14583624C2211yescharacteristic, complemented
23#14583623—21no—
24#14583623—21no—
25#14583623—22no—
26#14583623C2212yes—
27#14583623C2212yes—
28#14583623C2214yes—
29#14583610C2211yescharacteristic, complemented
30#14583607—21no—
31#14583605C2212yescomplemented
32#14583603—22no—
33#14583564C2211yescharacteristic, complemented
34#14583562—21no—
35#14583453—21no—
36#14583453—22no—
37#14583452C2212yes—
38C2×#13063320—22no—
39C2×#13063314C2212yes—
40C2×#13063305—21no—
41C4×#10621898C2211yescharacteristic
42#14583367C2212yes—
43C2×Q8×Dic43C2212yes—
44C2×C4×Dic86C2211yescharacteristic
45C4×Q8×D43—21no—
46C2×C4×D172C2211yescharacteristic
47C2×#13063283—21no—
48#14583260C2214yes—
49#14583260C2214yes—
50#14583255C2214yes—
51#14583255C2214yes—
52#14583208C2214yescomplemented
53#14583204C2214yescomplemented
54#14583196C2214yes—
55#14583192C2214yescomplemented
56#14583186C2212yes—
57#14583182C2214yescomplemented
58#14583176C2212yes—
59#14583124C2214yes—
60#14583124C2214yes—
61#14583117C2214yes—
62#14583117C2214yes—
63#14583106C2212yescomplemented
64#14583106C2212yescomplemented
65#14583101C2212yescomplemented
66#14583101C2212yescomplemented
67#14583029C2212yescomplemented
68#14583027C2214yescomplemented
69C8×Dic86C2212yescomplemented
70#14583012C2212yes—
71#14583003C2214yescomplemented
72#14583002C2214yescomplemented
73#14583001C2212yes—
74#14582991C2214yescomplemented
75C4×#10621873C2212yes—
76#14582984C2214yescomplemented
77C4×D344C2212yes—
78#14582942C2212yes—
79#14582941C2211yescharacteristic
80#14582923C2211yescharacteristic
81#14582922C2212yes—
82#14582908C2212yes—
83#14582905C2211yescharacteristic
84#14582903C2212yes—
85#14582901C2211yescharacteristic
86M16×Dic43C2212yes—
87C43×#533C2211yescharacteristic
88C2×C4⋊Q8×C43C2211yescharacteristic
89C43×#491C2214yescomplemented
90C43×#487C2212yescomplemented
91C43×#487C2212yescomplemented
92C43×#419C2212yes—
93C43×#419C2212yes—
94C4×M16×C43C2211yescharacteristic
95C2×#10621898C2311yescharacteristic
96C22×Dic86D411yescharacteristic
97C2×Q8×D43—21no—
98C22×D172C2311yescharacteristic
99C22×C4×D43—21no—
100#13063356—28no—
101#13063353—24no—
102C2×#10621885C2314yes—
103C2×#10621873C2312yes—
104C2×#10621884C2314yes—
105C2×D344C2312yes—
106C2×#10621877C2312yes—
107#13063324—22no—
108#13063324—21no—
109#13063324C2312yes—
110#13063324C2312yes—
111#13063323—21no—
112#13063323—22no—
113#13063320—24no—
114#13063320—24no—
115#13063320—24no—
116#13063320—24no—
117#13063316C2312yes—
118#13063316C2312yes—
119#13063315—22no—
120#13063315—22no—
121#13063315—22no—
122#13063314—22no—
123#13063314—22no—
124#13063314C2314yes—
125#13063314C2314yes—
126#13063305—21no—
127#13063305—22no—
128#13063305—22no—
129#13063305—24no—
130#13063305—22no—
131#13063303—22no—
132#13063303—22no—
133#13063303—22no—
134#13063302—22no—
135#13063302—22no—
136#13063301—21no—
137#13063301—22no—
138Q8×Dic43—21no—
139Q8×Dic43—22no—
140Q8×Dic43—22no—
141Q8×Dic43C2314yes—
142Q8×Dic43C2314yes—
143C4×Dic86—22no—
144C4×Dic86—22no—
145C4×Dic86D411yescharacteristic
146C4×Dic86D412yes—
147C4×Dic86D411yescharacteristic
148C4×Dic86C2311yescharacteristic
149C4×Dic86C2311yescharacteristic
150C4×Dic86C2311yescharacteristic
151C4×Dic86C2312yes—
152C4×Dic86C2311yescharacteristic
153#13063290—21no—
154#13063290—22no—
155#13063290C2312yes—
156#13063290C2312yes—
157C4×D172—21no—
158C4×D172—21no—
159C4×D172C2311yescharacteristic
160C4×D172C2311yescharacteristic
161C4×D172C2312yes—
162C4×D172C2312yes—
163#13063287C2312yes—
164#13063287C2312yes—
165C4×C22⋊D43—21no—
166C4×C22⋊D43—21no—
167(C22⋊D43)⋊C4—22no—
168(C22⋊D43)⋊C4—22no—
169#13063284C2311yescharacteristic
170#13063283—22no—
171#13063283—22no—
172#13063283—24no—
173#13063282—21no—
174#13063282—22no—
175C2×C4⋊Dic43—22no—
176C2×C4⋊Dic43D411yescharacteristic
177C2×C4⋊Dic43C2311yescharacteristic
178C2×Dic43⋊C4D412yes—
179C4⋊C4×D43—21no—
180C4⋊C4×D43—22no—
181C2×(C2×D43)⋊C4—21no—
182C2×(C2×D43)⋊C4—22no—
183C2×(C2×D43)⋊C4—22no—
184C2×C4×Dic43—22no—
185C2×C4×Dic43C2312yes—
186C42×D43—21no—
187C42×D43—22no—
188#13063259C2312yes—
189#13063258C2314yes—
190#13063257C2312yes—
191#13063256C2314yes—
192C4⋊(C43⋊C8)C2312yes—
193C4⋊(C43⋊C8)C2312yes—
194Dic43⋊C8C2314yes—
195Dic43⋊C8C2314yes—
196#13063250C2312yes—
197#13063249C2314yes—
198#13063249C2314yes—
199#13063247C2312yes—
200#13063247C2312yes—
201#13063247C2312yes—
202#13063245C2314yes—
203#13063245C2314yes—
204#13063235C2314yes—
205C8×Dic43C2314yes—
206C22×Q8×C43C2312yes—
207C2×M16×C43C2311yescharacteristic
208C2×M16×C43C2311yescharacteristic
209C4⋊Q8×C43—21no—
210C4⋊Q8×C43—21no—
211C4⋊Q8×C43C2312yes—
212C4⋊Q8×C43C2312yes—
213C4⋊Q8×C43C2311yescharacteristic
214C4⋊Q8×C43C2311yescharacteristic
215#125×C43C2312yes—
216C22⋊Q8×C43—21no—
217C22⋊Q8×C43—21no—
218C4×Q8×C43—21no—
219C4×Q8×C43—21no—
220#117×C43C2312yes—
221C2×C4⋊C4×C43—21no—
222C2×C4⋊C4×C43—21no—
223C2×C42×C43C2311yescharacteristic
224#103×C43C2314yes—
225#103×C43C2314yes—
226#103×C43C2314yes—
227#103×C43C2314yes—
228#97×C43C2312yes—
229C4×C8×C43C2312yes—
230C23×D43—21no—
231C2×Q8×C43—21no—
232C2×Q8×C43—22no—
233C2×Q8×C43—21no—
234C2×Q8×C43—24no—
235C2×Q8×C43—24no—
236C2×Q8×C43C2414yes—
237C22×C4×C43—22no—
238C22×C4×C43C2×D411yescharacteristic
239C22×C4×C43C2×D411yescharacteristic
240C22×C4×C43C2411yescharacteristic
241C2×C22⋊D43—21no—
242C22×Dic43—21no—
243C22×Dic43C2×D412yes—
244C22×Dic43C2×D412yes—
245Q8×D43—44no—
246#10621898—22no—
247#10621898#4114yes—
248C2×D172—21no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172C2412yes—
252C2×D172C2411yescharacteristic
253C2×C4×D43—21no—
254C2×C4×D43—21no—
255C2×C4×D43—22no—
256C2×C4×D43—22no—
257C2×C4×D43—22no—
258C2×C4×D43—21no—
259C2×C4×D43—22no—
260C2×C4×D43—44no—
261C2×Dic86—22no—
262C2×Dic86—22no—
263C2×Dic86—42no—
264C2×Dic86C2×D411yescharacteristic
265C2×Dic86C2×D411yescharacteristic
266C2×Dic86C2×D412yes—
267C2×Dic86C2411yescharacteristic
268M16×C43—22no—
269M16×C43—22no—
270C2×C8×C43C2412yes—
271C2×C8×C43C2412yes—
272C4⋊C4×C43—22no—
273C4⋊C4×C43—22no—
274C4⋊C4×C43—22no—
275C4⋊C4×C43—22no—
276C4⋊C4×C43—22no—
277C4⋊C4×C43—22no—
278C4⋊C4×C43—21no—
279C4⋊C4×C43—21no—
280C4⋊C4×C43C2412yes—
281C4⋊C4×C43C2412yes—
282C22⋊C4×C43—22no—
283C42×C43—22no—
284C42×C43C2×D411yescharacteristic
285C42×C43C2×D411yescharacteristic
286C42×C43C2411yescharacteristic
287C42×C43C2411yescharacteristic
288C22⋊Dic43—21no—
289#10621885—28no—
290#10621884—28no—
291(C2×D43)⋊C4—22no—
292(C2×D43)⋊C4—22no—
293(C2×D43)⋊C4—21no—
294(C2×D43)⋊C4—21no—
295(C2×D43)⋊C4—24no—
296(C2×D43)⋊C4—24no—
297(C2×D43)⋊C4—24no—
298(C2×D43)⋊C4—24no—
299(C2×D43)⋊C4—22no—
300(C2×D43)⋊C4—22no—
301C4⋊Dic43—21no—
302C4⋊Dic43—22no—
303C4⋊Dic43—24no—
304C4⋊Dic43—24no—
305C4⋊Dic43—22no—
306C4⋊Dic43C2×D411yescharacteristic
307C4⋊Dic43C2×D411yescharacteristic
308C4⋊Dic43C2×D412yes—
309C4⋊Dic43C2411yescharacteristic
310C4⋊Dic43C2411yescharacteristic
311C4⋊Dic43C2412yes—
312Dic43⋊C4—21no—
313Dic43⋊C4—21no—
314Dic43⋊C4—22no—
315Dic43⋊C4—22no—
316Dic43⋊C4—22no—
317Dic43⋊C4—22no—
318Dic43⋊C4—22no—
319Dic43⋊C4—22no—
320Dic43⋊C4C2×D412yes—
321Dic43⋊C4C2×D412yes—
322Dic43⋊C4C2×D412yes—
323Dic43⋊C4C2×D412yes—
324C4×Dic43—21no—
325C4×Dic43—21no—
326C4×Dic43—21no—
327C4×Dic43—22no—
328C4×Dic43—22no—
329C4×Dic43—24no—
330C4×Dic43—24no—
331C4×Dic43C2×D412yes—
332C4×Dic43C2×D412yes—
333C4×Dic43C2412yes—
334C4×Dic43C2412yes—
335#10621877—24no—
336C2×C43⋊C8C2414yes—
337D344—24no—
338#10621873—24no—
339C23×C43C22×D411yescharacteristic
340C22×D43—21no—
341C22×D43—22no—
342C22×D43—42no—
343C22×D43—42no—
344C22×D43—42no—
345Q8×C43—24no—
346Q8×C43—24no—
347Q8×C43—44no—
348Q8×C43—42no—
349Q8×C43—81no—
350C2×C4×C43—22no—
351C2×C4×C43—24no—
352C2×C4×C43—22no—
353C2×C4×C43—22no—
354C2×C4×C43—41no—
355C2×C4×C43—44no—
356C2×C4×C43C22×D411yescharacteristic
357C2×C4×C43C22×D411yescharacteristic
358C2×C4×C43C22×D411yescharacteristic
359C2×C4×C43C22×D411yescharacteristic
360C2×C4×C43C22×D411yescharacteristic
361C2×C4×C43C2×#4112yes—
362C2×C4×C432−1+412yes—
363C2×C4×C43C2511yescharacteristic
364C22⋊D43—24no—
365C2×Dic43—21no—
366C2×Dic43—22no—
367C2×Dic43—21no—
368C2×Dic43—21no—
369C2×Dic43—42no—
370C2×Dic43—42no—
371C2×Dic43—42no—
372C2×Dic43C22×D412yes—
373C2×Dic43C22×D412yes—
374C2×Dic43C22×D412yes—
375C2×Dic43C22×D412yes—
376D172—22no—
377D172—21no—
378D172—22no—
379D172—42no—
380D172C2×#4112yes—
381C4×D43—24no—
382C4×D43—44no—
383C4×D43—44no—
384C4×D43—44no—
385C4×D43—42no—
386C4×D43—82no—
387C4×D43—81no—
388Dic86—22no—
389Dic86—22no—
390Dic86—21no—
391Dic86—42no—
392Dic86—44no—
393Dic86—82no—
394Dic86C2×#4112yes—
395C8×C43—22no—
396C8×C43—22no—
397C43⋊C8—24no—
398#61323—431nomaximal, Sylow
399C22×C43—21no—
400C22×C43—21no—
401C22×C43#54812yes—
402C22×C43C23×D411yescharacteristic
403C2×D43—22no—
404C2×D43—41no—
405C2×D43—41no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—84no—
410C4×C43—21no—
411C4×C43—21no—
412C4×C43—21no—
413C4×C43—42no—
414C4×C43—44no—
415C4×C43—42no—
416C4×C43#54812yes—
417C4×C43#57512yes—
418C4×C43C22×#4111yescharacteristic
419C4×C43C2×2−1+411yescharacteristic
420Dic43—22no—
421Dic43—22no—
422Dic43—22no—
423Dic43—22no—
424Dic43—22no—
425Dic43—41no—
426Dic43—41no—
427Dic43—42no—
428Q8×#41—431no—
429C2×#556—431no—
430#3377—434no—
431#3376—434no—
432#3369—432no—
433#3367—432no—
434#3364—432no—
435#3360—432no—
436#3140—432no—
437#3139D4311yescharacteristic, complemented
438#3078—432no—
439#3077—431no—
440#3040—432no—
441#3039—431no—
442Q8×M16—431no—
443C4×#137—432no—
444C4×AGL(1,ℤ/8)—431no—
445C2×C43—22no—
446C2×C43C2×#54811yescharacteristic
447C2×C43C2×#57511yescharacteristic
448C2×C43#358611yescharacteristic
449D43—42no—
450D43—82no—
451C2×#137—432no—
452C2×AGL(1,ℤ/8)—431no—
453Q82—431no—
454#557—431no—
455#557—432no—
456#556—432no—
457#556—432no—
458#556—434no—
459#556—861no—
460#556—862no—
461#556—861no—
462#554—431no—
463#554—432no—
464#554—862no—
465#554—861no—
466D4×Q8—431no—
467D4×Q8—861no—
468#533—432no—
469#533—862no—
470#533—861no—
471#533C2×D4311yescharacteristic
472C2×C4⋊Q8C2×D4311yescharacteristic
473C2×#126—862no—
474C2×#124—432no—
475C2×C22⋊Q8—861no—
476C4×#41—432no—
477C4×#41—431no—
478C2×C4×Q8—431no—
479C2×C4×Q8—432no—
480C2×C4×Q8—861no—
481C2×C4×D4—431no—
482C2×#117—861no—
483#491C2×D4314yescomplemented
484#489—434no—
485#489—434no—
486#488—434no—
487#488—434no—
488#487C2×D4312yescomplemented
489#487C2×D4312yescomplemented
490#479—434no—
491#479—434no—
492#478—434no—
493#477—434no—
494#476—432no—
495#475—434no—
496#474—432no—
497#464—434no—
498#464—434no—
499#463—434no—
500#463—434no—
501#462—432no—
502#462—432no—
503#461—432no—
504#461—432no—
505#446—434no—
506#446—432no—
507C8×Q8—432no—
508#442—432no—
509#441—434no—
510#440—434no—
511#440—432no—
512C4×Q16—434no—
513C4×SD16—434no—
514C4×SD16—432no—
515C4×D8—432no—
516#428—431no—
517#428—432no—
518#423—432no—
519#423—431no—
520#419—432no—
521#419C2×D4312yes—
522#419C2×D4312yes—
523#418—431no—
524#418—432no—
525#417—431no—
526C4×M16—432no—
527C4×M16C2×D4311yescharacteristic
528C43#6132311yescharacteristic, complemented, Sylow
529C2×#41—431no—
530C22×Q8—431no—
531C22×Q8—861no—
532C22×Q8C22×D4312yes—
533C22×D4—431no—
534C23×C4—861no—
535#137—868no—
536AGL(1,ℤ/8)—864no—
537C2×Q16—434no—
538C2×SD16—434no—
539C2×SD16—432no—
540C2×D8—432no—
541C2×M16—432no—
542C2×M16C22×D4311yescharacteristic
543C2×M16C22×D4311yescharacteristic
544C4⋊Q8—21no—
545C4⋊Q8—21no—
546C4⋊Q8—432no—
547C4⋊Q8—432no—
548C4⋊Q8—861no—
549C4⋊Q8—862no—
550C4⋊Q8—862no—
551C4⋊Q8—861no—
552C4⋊Q8C22×D4312yes—
553C4⋊Q8C22×D4312yes—
554C4⋊Q8C22×D4311yescharacteristic
555C4⋊Q8C22×D4311yescharacteristic
556#126—864no—
557#126—864no—
558#126—864no—
559#126—864no—
560#125—432no—
561#125—432no—
562#125—862no—
563#125—862no—
564#125—862no—
565#125C22×D4312yes—
566#124—434no—
567#124—434no—
568#124—862no—
569#124—862no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—862no—
573C22⋊Q8—862no—
574C22⋊Q8—862no—
575C22⋊Q8—862no—
576C22⋊Q8—862no—
577C22⋊Q8—862no—
578C22⋊Q8—862no—
579C22⋊Q8—864no—
580C22⋊Q8—862no—
581C22⋊Q8—861no—
582C22⋊Q8—861no—
583C22⋊Q8—862no—
584C4×Q8—21no—
585C4×Q8—21no—
586C4×Q8—431no—
587C4×Q8—432no—
588C4×Q8—431no—
589C4×Q8—431no—
590C4×Q8—431no—
591C4×Q8—432no—
592C4×Q8—434no—
593C4×Q8—434no—
594C4×Q8—432no—
595C4×Q8—432no—
596C4×Q8—431no—
597C4×Q8—431no—
598C4×Q8—862no—
599C4×Q8—862no—
600C4×Q8—862no—
601C4×Q8—862no—
602C4×Q8—862no—
603C4×Q8—861no—
604C4×Q8—861no—
605C4×D4—432no—
606C4×D4—432no—
607C4×D4—432no—
608C4×D4—432no—
609C4×D4—431no—
610C4×D4—431no—
611C4×D4—862no—
612C4×D4—862no—
613C4×D4—861no—
614C4×D4—861no—
615C4×D4—861no—
616C4×D4—861no—
617#117—431no—
618#117—862no—
619#117—862no—
620#117—864no—
621#117—862no—
622#117—861no—
623#117C22×D4312yes—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—431no—
627C2×C4⋊C4—432no—
628C2×C4⋊C4—431no—
629C2×C4⋊C4—862no—
630C2×C4⋊C4—861no—
631C2×C4⋊C4—862no—
632C2×C22⋊C4—862no—
633C2×C22⋊C4—862no—
634C2×C22⋊C4—861no—
635C2×C42—432no—
636C2×C42—862no—
637C2×C42—862no—
638C2×C42—861no—
639C2×C42C22×D4311yescharacteristic
640#107—432no—
641#107—434no—
642#106—432no—
643#106—434no—
644C4⋊C8—434no—
645C4⋊C8—434no—
646C4⋊C8—432no—
647C4⋊C8—432no—
648#103—434no—
649#103—434no—
650#103—432no—
651#103C22×D4314yes—
652#103C22×D4314yes—
653#103C22×D4314yes—
654#103C22×D4314yes—
655#102—432no—
656#102—432no—
657#102—432no—
658#102—434no—
659#102—434no—
660#97—434no—
661#97C22×D4312yes—
662C4×C8—434no—
663C4×C8C22×D4312yes—
664C24—861no—
665#41—434no—
666#41—862no—
667C2×Q8—21no—
668C2×Q8—22no—
669C2×Q8—21no—
670C2×Q8—24no—
671C2×Q8—24no—
672C2×Q8—431no—
673C2×Q8—431no—
674C2×Q8—432no—
675C2×Q8—431no—
676C2×Q8—862no—
677C2×Q8—862no—
678C2×Q8—1722no—
679C2×Q8—1724no—
680C2×Q8C23×D4314yes—
681C2×D4—431no—
682C2×D4—432no—
683C2×D4—861no—
684C2×D4—861no—
685C2×D4—862no—
686C2×D4—862no—
687C22×C4—22no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—862no—
691C22×C4—862no—
692C22×C4—861no—
693C22×C4—861no—
694C22×C4—861no—
695C22×C4—861no—
696C22×C4—862no—
697C22×C4—862no—
698C22×C4—1724no—
699C22×C4D4×D4311yescharacteristic
700C22×C4D4×D4311yescharacteristic
701C22×C4C23×D4311yescharacteristic
702Q16—868no—
703SD16—864no—
704SD16—868no—
705D8—864no—
706M16—22no—
707M16—22no—
708M16—864no—
709C2×C8—434no—
710C2×C8C23×D4312yes—
711C2×C8C23×D4312yes—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—22no—
715C4⋊C4—22no—
716C4⋊C4—22no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—22no—
720C4⋊C4—431no—
721C4⋊C4—432no—
722C4⋊C4—432no—
723C4⋊C4—431no—
724C4⋊C4—432no—
725C4⋊C4—432no—
726C4⋊C4—432no—
727C4⋊C4—431no—
728C4⋊C4—431no—
729C4⋊C4—432no—
730C4⋊C4—864no—
731C4⋊C4—864no—
732C4⋊C4—862no—
733C4⋊C4—862no—
734C4⋊C4—862no—
735C4⋊C4—862no—
736C4⋊C4—862no—
737C4⋊C4—862no—
738C4⋊C4—862no—
739C4⋊C4—862no—
740C4⋊C4—861no—
741C4⋊C4—861no—
742C4⋊C4—861no—
743C4⋊C4C23×D4312yes—
744C4⋊C4C23×D4312yes—
745C22⋊C4—22no—
746C22⋊C4—864no—
747C22⋊C4—864no—
748C22⋊C4—864no—
749C22⋊C4—864no—
750C22⋊C4—862no—
751C22⋊C4—862no—
752C22⋊C4—861no—
753C22⋊C4—862no—
754C22⋊C4—862no—
755C22⋊C4—861no—
756C22⋊C4—861no—
757C42—22no—
758C42—432no—
759C42—432no—
760C42—432no—
761C42—432no—
762C42—864no—
763C42—864no—
764C42—862no—
765C42—862no—
766C42—861no—
767C42—861no—
768C42—861no—
769C42D4×D4311yescharacteristic
770C42D4×D4311yescharacteristic
771C42C23×D4311yescharacteristic
772C42C23×D4311yescharacteristic
773C23—861no—
774C23—862no—
775C23—1722no—
776C23—1722no—
777C23—1722no—
778C23C2×D4×D4311yescharacteristic
779Q8—24no—
780Q8—24no—
781Q8—44no—
782Q8—42no—
783Q8—81no—
784Q8—432no—
785Q8—862no—
786Q8—862no—
787Q8—861no—
788Q8—3442no—
789Q8—1722no—
790Q8—1724no—
791D4—432no—
792D4—864no—
793D4—862no—
794D4—861no—
795D4—862no—
796D4—1722no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—24no—
801C2×C4—41no—
802C2×C4—44no—
803C2×C4—432no—
804C2×C4—432no—
805C2×C4—432no—
806C2×C4—432no—
807C2×C4—861no—
808C2×C4—864no—
809C2×C4—862no—
810C2×C4—861no—
811C2×C4—861no—
812C2×C4—3441no—
813C2×C4—3442no—
814C2×C4—1724no—
815C2×C4—1724no—
816C2×C4—1722no—
817C2×C4—1722no—
818C2×C4—1722no—
819C2×C4—1724no—
820C2×C4—1722no—
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4311yescharacteristic
823C2×C4C2×D4×D4311yescharacteristic
824C2×C4C2×D4×D4311yescharacteristic
825C2×C4C2×D4×D4311yescharacteristic
826C2×C4#41×D4312yes—
827C2×C4#1306337212yes—
828C2×C4C24×D4311yescharacteristic
829C8—22no—
830C8—22no—
831C8—864no—
832C22—21no—
833C22—21no—
834C22—862no—
835C22—3444no—
836C22—1722no—
837C22—1722no—
838C22—1722no—
839C22—1721no—
840C22—1721no—
841C22#1458355712yes—
842C22C22×D4×D4311yescharacteristic
843C4—21no—
844C4—21no—
845C4—21no—
846C4—44no—
847C4—42no—
848C4—42no—
849C4—862no—
850C4—862no—
851C4—862no—
852C4—862no—
853C4—862no—
854C4—1722no—
855C4—1721no—
856C4—1721no—
857C4#1458355712yes—
858C4#1458369812yes—
859C4C2×#41×D4311yescharacteristic
860C4C2×#1306337211yescharacteristic
861C2—22no—
862C2—3442no—
863C2—1722no—
864C2C2×#1458355711yescharacteristic
865C2C2×#1458369811yescharacteristic
866C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3139C2
socleC22×C43C23×D4
prime radicalC2×#13063353C22
hypercenter#3139D43
hypocenterC43#61323
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
1. #19148173C2semidirect
2. C2×#14583623C2semidirect
3. #19147432C2semidirect
4. #19147417C2semidirect
5. #19147340C2semidirect
6. #19147318C2semidirect
7. #19147285C2semidirect
8. #19147249C2semidirect
9. #19144983C2semidirect
10. #19144397C2semidirect
11. #19144388C2semidirect
13. #19144078C2semidirect
14. M16×Dic86C2semidirect
15. #19143410C2semidirect
17. C43×#3139C2semidirect
20. #14583629C22semidirect
21. #14583626C22semidirect
22. #14583624C22semidirect
29. #14583610C22semidirect
31. #14583605C22semidirect
33. #14583564C22semidirect
52. #14583208C22semidirect
53. #14583204C22semidirect
55. #14583192C22semidirect
57. #14583182C22semidirect
63. #14583106C22semidirect
64. #14583106C22semidirect
65. #14583101C22semidirect
66. #14583101C22semidirect
67. #14583029C22semidirect
68. #14583027C22semidirect
69. C8×Dic86C22semidirect
71. #14583003C22semidirect
72. #14583002C22semidirect
74. #14582991C22semidirect
76. #14582984C22semidirect
89. C43×#491C22semidirect
90. C43×#487C22semidirect
91. C43×#487C22semidirect
437. #3139D43semidirect
483. #491C2×D43semidirect
488. #487C2×D43semidirect
489. #487C2×D43semidirect
528. C43#61323semidirect

Maximal subgroups

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

subgroupindex
#191481732
C2×#145836232
#191474322
#191474172
#191473402
#191473182
#191472852
#191472492
#191449832
#191443972
#191443882
#191440922
#191440782
M16×Dic862
#191434102
C4×#130633532
C43×#31392
#6132343