Finite Group Databasebeta

← #25964996

Subgroups — #25964996

Order 11008.

2170 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147890C211yesmaximal, characteristic, complemented
2C2×C4×#10621900C211yesmaximal, characteristic, complemented
3#19144754C212yesmaximal, complemented
4#19144743C212yesmaximal, complemented
5#19144701C214yesmaximal, complemented
6#19144663C212yesmaximal, complemented
7#19144652C212yesmaximal, complemented
8#19144610C214yesmaximal, complemented
9#19144525C212yesmaximal, complemented
10#19144402C211yesmaximal, characteristic, complemented
11#19144392C211yesmaximal, characteristic, complemented
12#19144063C211yesmaximal, characteristic, complemented
13#19143834C212yesmaximal, complemented
14#19143419C212yesmaximal, complemented
15AGL(1,ℤ/8)×Dic43C212yesmaximal, complemented
16#19143227C211yesmaximal, characteristic, complemented
17C43×#3036C211yesmaximal, characteristic, complemented
18C22×#10621900C2211yescharacteristic
19C2×#13063355C2212yes—
20#14583456C2211yescharacteristic
21#14583454C2211yescharacteristic, complemented
22#14583454C2211yescharacteristic, complemented
23#14583447C2211yescharacteristic, complemented
24#14583447C2211yescharacteristic, complemented
25#14583431—21no—
26#14583431—21no—
27#14583430—21no—
28#14583430—21no—
29#14583428C2212yescomplemented
30#14583428C2212yescomplemented
31#14583409—21no—
32#14583409—21no—
33#14583406C2212yes—
34#41×Dic43C2212yes—
35C4×#10621900—21no—
36C4×#10621900—21no—
37C4×#10621900—21no—
38C4×#10621900—21no—
39C4×#10621900—21no—
40C4×#10621900—21no—
41C4×#10621900C2212yes—
42C4×#10621900C2212yes—
43C4×#10621900C2212yes—
44C4×#10621900C2212yes—
45C2×C4×Dic86C2211yescharacteristic
46C2×#13063290C2211yescharacteristic
47C2×D4×Dic43C2211yescharacteristic
48C2×C4×C22⋊D43—21no—
49C2×(C22⋊D43)⋊C4—21no—
50C2×#13063283C2211yescharacteristic
51C2×#13063281—21no—
52C22×C4×Dic43—21no—
53C2×C42×D43C2211yescharacteristic
54#14583239C2214yescomplemented
55#14583238C2214yescomplemented
56#14583222C2214yescomplemented
57#14583221C2214yescomplemented
58#14583207C2214yescomplemented
59#14583199C2214yescomplemented
60#14583195C2212yescomplemented
61#14583189C2212yescomplemented
62#14583185C2212yescomplemented
63#14583179C2212yescomplemented
64#14583118C2214yescomplemented
65#14583106C2212yescomplemented
66#14583096C2212yescomplemented
67#14583058C2214yes—
68#14583058C2214yes—
69#14583041C2214yes—
70#14583041C2214yes—
71#14583011C2214yescomplemented
72#14583003C2214yescomplemented
73#14583000C2214yescomplemented
74#14582996C2214yescomplemented
75#14582991C2214yescomplemented
76#14582990C2214yescomplemented
77SD16×Dic43C2214yescomplemented
78D8×Dic43C2214yescomplemented
79#14582955C2212yescomplemented
80#14582955C2212yescomplemented
81#14582951C2212yescomplemented
82#14582951C2212yescomplemented
83#14582941C2212yes—
84#14582939C2212yes—
85#14582923C2211yescharacteristic
86#14582909C2212yes—
87#14582904C2212yes—
88#14582900C2212yes—
89#14582862C2212yes—
90M16×Dic43C2212yes—
91C2×AGL(1,ℤ/8)×C43C2212yes—
92C43×#532C2211yescharacteristic
93C2×C4×D4×C43C2211yescharacteristic
94C43×#463C2214yescomplemented
95C43×#461C2212yescomplemented
96C43×#459C2212yescomplemented
97C43×#423C2211yescharacteristic
98C43×#417C2212yes—
99C2×#10621900—24no—
100C2×#10621900—21no—
101C2×#10621900—21no—
102C2×#10621900—21no—
103C2×#10621900—21no—
104C2×#10621900—24no—
105C2×#10621900C2312yes—
106C2×#10621900C2312yes—
107C22×Dic86C2311yescharacteristic
108C22×C22⋊D43—21no—
109C23×Dic43—21no—
110C23×Dic43—21no—
111C22×C4×D43D411yescharacteristic
112C22×C4×D43D411yescharacteristic
113C22×C4×D43C2311yescharacteristic
114#13063355—28no—
115C2×#10621885C2314yes—
116C2×#10621883C2314yes—
117C2×#10621877C2312yes—
118#13063325C2311yescharacteristic
119#13063325C2311yescharacteristic
120#13063318—22no—
121#13063318—22no—
122#13063317C2312yes—
123#13063316—21no—
124#13063316—21no—
125#13063312—21no—
126#13063312—21no—
127#13063307—22no—
128#13063307—22no—
129#13063306—22no—
130#13063305—21no—
131#13063305—21no—
132#13063304—21no—
133#13063304—21no—
134#13063301C2312yes—
135#13063301C2312yes—
136#13063296—21no—
137#13063296—21no—
138#13063296C2312yes—
139#13063296C2312yes—
140#13063293—22no—
141Q8×Dic43C2312yes—
142Q8×Dic43C2312yes—
143C4×Dic86—21no—
144C4×Dic86—21no—
145C4×Dic86—21no—
146C4×Dic86—21no—
147C4×Dic86C2312yes—
148C4×Dic86C2312yes—
149#13063290—21no—
150#13063290—21no—
151#13063290—21no—
152#13063290—21no—
153#13063290C2312yes—
154#13063290C2312yes—
155D4×Dic43—22no—
156D4×Dic43—22no—
157D4×Dic43—21no—
158D4×Dic43—21no—
159D4×Dic43—21no—
160D4×Dic43—21no—
161D4×Dic43C2312yes—
162D4×Dic43C2312yes—
163D4×Dic43C2312yes—
164D4×Dic43C2312yes—
165C4×C22⋊D43—22no—
166C4×C22⋊D43—22no—
167C4×C22⋊D43—22no—
168C4×C22⋊D43—22no—
169C4×C22⋊D43—22no—
170C4×C22⋊D43—22no—
171(C22⋊D43)⋊C4—22no—
172(C22⋊D43)⋊C4—22no—
173(C22⋊D43)⋊C4—22no—
174(C22⋊D43)⋊C4—22no—
175(C22⋊D43)⋊C4—22no—
176(C22⋊D43)⋊C4—22no—
177#13063284—22no—
178#13063284C2312yes—
179#13063283—21no—
180#13063283—21no—
181#13063283—21no—
182#13063283—21no—
183#13063283C2312yes—
184#13063283C2312yes—
185#13063281—22no—
186#13063281—22no—
187#13063281—22no—
188#13063281—22no—
189#13063281—22no—
190#13063281—22no—
191C2×C4⋊Dic43C2311yescharacteristic
192C2×Dic43⋊C4—21no—
193C2×Dic43⋊C4—21no—
194C2×C22⋊Dic43—21no—
195C2×(C2×D43)⋊C4—21no—
196C2×C4×Dic43—21no—
197C2×C4×Dic43—21no—
198C2×C4×Dic43—21no—
199C2×C4×Dic43—22no—
200C2×C4×Dic43—22no—
201C2×C4×Dic43—22no—
202C2×C4×Dic43—22no—
203C2×C4×Dic43—22no—
204C2×C4×Dic43D411yescharacteristic
205C2×C4×Dic43D411yescharacteristic
206C2×C4×Dic43C2311yescharacteristic
207C42×D43D411yescharacteristic
208C42×D43D411yescharacteristic
209C42×D43D411yescharacteristic
210C42×D43D411yescharacteristic
211C42×D43C2311yescharacteristic
212C42×D43C2311yescharacteristic
213C42×D43C2311yescharacteristic
214C42×D43C2311yescharacteristic
215#13063259C2314yes—
216#13063258C2314yes—
217#13063257C2314yes—
218#13063256C2314yes—
219C4⋊(C43⋊C8)C2312yes—
220C4⋊(C43⋊C8)C2312yes—
221#13063250C2314yes—
222#13063250C2314yes—
223#13063249C2314yes—
224#13063246C2314yes—
225#13063246C2314yes—
226#13063246C2314yes—
227(C2×D43)⋊C8C2314yes—
228(C2×D43)⋊C8C2314yes—
229#13063235C2314yes—
230C8×Dic43C2314yes—
231C2×#41×C43C2312yes—
232C22×D4×C43C2311yescharacteristic
233C23×C4×C43—21no—
234AGL(1,ℤ/8)×C43—28no—
235C2×SD16×C43C2314yes—
236C2×D8×C43C2314yes—
237C2×M16×C43C2312yes—
238C4⋊Q8×C43C2311yescharacteristic
239#127×C43C2311yescharacteristic
240#124×C43C2312yes—
241#121×C43—21no—
242#121×C43—21no—
243C4×D4×C43—21no—
244C4×D4×C43—21no—
245C4×D4×C43—21no—
246C4×D4×C43—21no—
247C4×D4×C43C2312yes—
248C4×D4×C43C2312yes—
249C2×C4⋊C4×C43C2311yescharacteristic
250C2×C22⋊C4×C43—21no—
251C2×C42×C43C2311yescharacteristic
252C4⋊C8×C43C2312yes—
253C4⋊C8×C43C2312yes—
254#103×C43C2314yes—
255#102×C43C2314yes—
256C24×C43—21no—
257C23×D43C2×D411yescharacteristic
258#41×C43—24no—
259#41×C43—24no—
260C2×Q8×C43C2412yes—
261C2×D4×C43—21no—
262C2×D4×C43—21no—
263C2×D4×C43—21no—
264C2×D4×C43—22no—
265C2×D4×C43—22no—
266C2×D4×C43#4114yescomplemented
267C2×D4×C43C2412yes—
268C2×D4×C43C2412yes—
269C22×C4×C43—22no—
270C22×C4×C43—22no—
271C22×C4×C43—22no—
272C22×C4×C43—21no—
273C22×C4×C43—44no—
274C22×C4×C43C2×D411yescharacteristic
275C22×C4×C43C2×D411yescharacteristic
276C22×C4×C43C2411yescharacteristic
277C2×C22⋊D43—28no—
278C2×C22⋊D43—22no—
279C2×C22⋊D43—22no—
280C2×C22⋊D43—22no—
281C2×C22⋊D43—22no—
282C22×Dic43—28no—
283C22×Dic43—22no—
284C22×Dic43—22no—
285C22×Dic43—22no—
286C22×Dic43—22no—
287C22×Dic43—22no—
288C22×Dic43—22no—
289C22×Dic43—21no—
290C22×Dic43—21no—
291C22×Dic43—44no—
292C22×Dic43C2×D411yescharacteristic
293C22×Dic43C2×D411yescharacteristic
294C22×Dic43C2×D411yescharacteristic
295#10621900—28no—
296#10621900—28no—
297#10621900—24no—
298#10621900—24no—
299#10621900—24no—
300#10621900—24no—
301#10621900—44no—
302#10621900—44no—
303C2×C4×D43—22no—
304C2×C4×D43—22no—
305C2×C4×D43—42no—
306C2×C4×D43—42no—
307C2×C4×D43C2×D411yescharacteristic
308C2×C4×D43C2×D411yescharacteristic
309C2×C4×D43C2×D411yescharacteristic
310C2×C4×D43C2×D411yescharacteristic
311C2×C4×D43C2×D411yescharacteristic
312C2×C4×D43C2×D411yescharacteristic
313C2×C4×D43C2×D411yescharacteristic
314C2×C4×D43C2×D411yescharacteristic
315C2×C4×D43C2×D411yescharacteristic
316C2×C4×D43C2×D411yescharacteristic
317C2×C4×D43C2411yescharacteristic
318C2×C4×D43C2411yescharacteristic
319C2×Dic86—21no—
320C2×Dic86—22no—
321C2×Dic86—21no—
322C2×Dic86—21no—
323C2×Dic86#4114yescomplemented
324C2×Dic86C2412yes—
325SD16×C43—28no—
326D8×C43—28no—
327M16×C43—24no—
328C2×C8×C43C2414yes—
329C4⋊C4×C43—21no—
330C4⋊C4×C43—21no—
331C4⋊C4×C43—21no—
332C4⋊C4×C43C2412yes—
333C22⋊C4×C43—22no—
334C22⋊C4×C43—22no—
335C22⋊C4×C43—22no—
336C22⋊C4×C43—22no—
337C42×C43C2×D411yescharacteristic
338C42×C43C2×D411yescharacteristic
339C42×C43C2411yescharacteristic
340C42×C43C2411yescharacteristic
341C22⋊Dic43—22no—
342C22⋊Dic43—22no—
343C22⋊Dic43—22no—
344C22⋊Dic43—22no—
345C22⋊Dic43—22no—
346C22⋊Dic43—22no—
347C22⋊Dic43—22no—
348#10621885—28no—
349#10621883—28no—
350(C2×D43)⋊C4—22no—
351(C2×D43)⋊C4—22no—
352(C2×D43)⋊C4—22no—
353(C2×D43)⋊C4—22no—
354C4⋊Dic43—21no—
355C4⋊Dic43—21no—
356C4⋊Dic43—21no—
357C4⋊Dic43—22no—
358C4⋊Dic43—22no—
359C4⋊Dic43C2412yes—
360C4⋊Dic43C2412yes—
361C4⋊Dic43C2412yes—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364Dic43⋊C4—22no—
365Dic43⋊C4—22no—
366Dic43⋊C4—22no—
367Dic43⋊C4—22no—
368Dic43⋊C4—22no—
369Dic43⋊C4—22no—
370C4×Dic43—22no—
371C4×Dic43—22no—
372C4×Dic43—22no—
373C4×Dic43—22no—
374C4×Dic43—22no—
375C4×Dic43—22no—
376C4×Dic43—22no—
377C4×Dic43—22no—
378C4×Dic43—22no—
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2×D411yescharacteristic
381C4×Dic43C2×D411yescharacteristic
382C4×Dic43C2×D411yescharacteristic
383C4×Dic43C2×D411yescharacteristic
384C4×Dic43C2×D411yescharacteristic
385C4×Dic43C2×D411yescharacteristic
386C4×Dic43C2×D411yescharacteristic
387C4×Dic43C2×D411yescharacteristic
388C4×Dic43C2×D411yescharacteristic
389C4×Dic43C2411yescharacteristic
390C4×Dic43C2411yescharacteristic
391#10621877—24no—
392C2×C43⋊C8C2414yes—
393C23×C43—24no—
394C23×C43—22no—
395C23×C43—22no—
396C23×C43—42no—
397C23×C43—42no—
398C23×C43C22×D411yescharacteristic
399C22×D43—22no—
400C22×D43—41no—
401C22×D43—41no—
402C22×D43C22×D411yescharacteristic
403C22×D43C22×D411yescharacteristic
404Q8×C43—22no—
405Q8×C43—22no—
406D4×C43—24no—
407D4×C43—22no—
408D4×C43—22no—
409D4×C43—22no—
410D4×C43—42no—
411D4×C43—44no—
412D4×C43—42no—
413D4×C43C2×#4114yes—
414C2×C4×C43—22no—
415C2×C4×C43—22no—
416C2×C4×C43—22no—
417C2×C4×C43—41no—
418C2×C4×C43—44no—
419C2×C4×C43—42no—
420C2×C4×C43—44no—
421C2×C4×C43—44no—
422C2×C4×C43C22×D411yescharacteristic
423C2×C4×C43C22×D411yescharacteristic
424C2×C4×C43C22×D411yescharacteristic
425C2×C4×C43C22×D411yescharacteristic
426C2×C4×C43C22×D411yescharacteristic
427C2×C4×C43C2×#4112yes—
428C2×C4×C43C2×#4112yes—
429C2×C4×C43C2511yescharacteristic
430C22⋊D43—28no—
431C22⋊D43—28no—
432C22⋊D43—44no—
433C22⋊D43—44no—
434C2×Dic43—28no—
435C2×Dic43—28no—
436C2×Dic43—24no—
437C2×Dic43—22no—
438C2×Dic43—22no—
439C2×Dic43—22no—
440C2×Dic43—22no—
441C2×Dic43—22no—
442C2×Dic43—22no—
443C2×Dic43—41no—
444C2×Dic43—44no—
445C2×Dic43—44no—
446C2×Dic43—42no—
447C2×Dic43—44no—
448C2×Dic43—44no—
449C2×Dic43C22×D411yescharacteristic
450C2×Dic43C22×D411yescharacteristic
451C2×Dic43C22×D411yescharacteristic
452C2×Dic43C22×D411yescharacteristic
453C2×Dic43C22×D411yescharacteristic
454C2×Dic43C22×D411yescharacteristic
455C4×D43—22no—
456C4×D43—22no—
457C4×D43—22no—
458C4×D43—22no—
459C4×D43—21no—
460C4×D43—21no—
461C4×D43—21no—
462C4×D43—21no—
463C4×D43—22no—
464C4×D43—22no—
465C4×D43—41no—
466C4×D43—41no—
467C4×D43—41no—
468C4×D43—41no—
469Dic86—24no—
470Dic86—22no—
471Dic86—42no—
472Dic86—42no—
473Dic86C2×#4114yes—
474C8×C43—24no—
475C43⋊C8—24no—
476#60559—431nomaximal, Sylow
477C22×C43—21no—
478C22×C43—21no—
479C22×C43—24no—
480C22×C43—48no—
481C22×C43—42no—
482C22×C43—42no—
483C22×C43—42no—
484C22×C43—42no—
485C22×C43—42no—
486C22×C43#52512yes—
487C22×C43C23×D411yescharacteristic
488C2×D43—21no—
489C2×D43—21no—
490C2×D43—21no—
491C2×D43—21no—
492C2×D43—21no—
493C2×D43—21no—
494C2×D43—44no—
495C4×C43—21no—
496C4×C43—21no—
497C4×C43—21no—
498C4×C43—42no—
499C4×C43—42no—
500C4×C43#52512yes—
501C4×C43#57512yes—
502C4×C43C22×#4111yescharacteristic
503C4×C43C22×#4111yescharacteristic
504Dic43—24no—
505Dic43—21no—
506Dic43—21no—
507Dic43—21no—
508Dic43—21no—
509Dic43—21no—
510Dic43—42no—
511Dic43—42no—
512Dic43—42no—
513Dic43#57512yes—
514#3444—431no—
515C2×C4×#41—431no—
516#3116—432no—
517#3115—432no—
518#3111—434no—
519#3107—432no—
520#3106—432no—
521#3102—434no—
522#3093—432no—
523#3078—431no—
524#3077—431no—
525#3037—431no—
526#3036D4311yescharacteristic, complemented
527#3005—432no—
528C4×#137—432no—
529C4×AGL(1,ℤ/8)—432no—
530#2920—431no—
531C2×C43—22no—
532C2×C43—44no—
533C2×C43—82no—
534C2×C43C2×#52511yescharacteristic
535C2×C43C2×#57511yescharacteristic
536C2×C43C2×#57511yescharacteristic
537D43—41no—
538D43—41no—
539C22×#41—431no—
540C2×#137—432no—
541C2×AGL(1,ℤ/8)C2×D4312yes—
542#533—431no—
543#533—431no—
544#533—431no—
545#532—431no—
546#532—431no—
547#532C2×D4311yescharacteristic
548#529—432no—
549#529—432no—
550#529—861no—
551#529—861no—
552#529—861no—
553#529—861no—
554#525—432no—
555#525—861no—
556#525—861no—
557C4×#41—432no—
558C4×#41—432no—
559C4×#41—432no—
560C4×#41—432no—
561C4×#41—432no—
562C4×#41—861no—
563C4×#41—861no—
564C4×#41—861no—
565C4×#41—861no—
566C4×#41—861no—
567C4×#41—861no—
568C2×C4×Q8—431no—
569C2×C4×Q8—431no—
570C2×C4×D4—431no—
571C2×C4×D4—861no—
572C2×C4×D4—861no—
573C2×C4×D4C2×D4311yescharacteristic
574C2×#117—431no—
575C2×#117—861no—
576C22×C42—431no—
577C22×C42—861no—
578#485—434no—
579#485—434no—
580#482—434no—
581#482—434no—
582#479—434no—
583#478—434no—
584#477—432no—
585#476—432no—
586#475—432no—
587#474—432no—
588#464—434no—
589#463C2×D4314yescomplemented
590#462—432no—
591#461C2×D4312yescomplemented
592#460—432no—
593#459C2×D4312yescomplemented
594#452—434no—
595#452—434no—
596#449—434no—
597#449—434no—
598#442—434no—
599#441—434no—
600#440—434no—
601#440—434no—
602C4×Q16—434no—
603C4×SD16—434no—
604C4×SD16—434no—
605C4×D8—434no—
606#432—432no—
607#432—432no—
608#431—432no—
609#431—432no—
610#428—432no—
611#428—432no—
612#423—431no—
613#423C2×D4311yescharacteristic
614#419—432no—
615#418—432no—
616#417—432no—
617#417C2×D4312yes—
618#407—432no—
619C4×M16—432no—
620C43#6055911yescharacteristic, complemented, Sylow
621C2×#41—432no—
622C2×#41—432no—
623C2×#41—861no—
624C2×#41—861no—
625C2×#41—861no—
626C2×#41—861no—
627C2×#41—864no—
628C2×#41—864no—
629C2×#41C22×D4312yes—
630C22×Q8—431no—
631C22×D4—861no—
632C22×D4C22×D4311yescharacteristic
633C23×C4—21no—
634C23×C4—431no—
635C23×C4—431no—
636C23×C4—431no—
637C23×C4—861no—
638C23×C4—861no—
639#137—868no—
640AGL(1,ℤ/8)—28no—
641C2×Q16—434no—
642C2×SD16—434no—
643C2×SD16C22×D4314yes—
644C2×D8C22×D4314yes—
645C2×M16—432no—
646C2×M16C22×D4312yes—
647C4⋊Q8—431no—
648C4⋊Q8—431no—
649C4⋊Q8C22×D4311yescharacteristic
650#127C22×D4311yescharacteristic
651#126—862no—
652#126—862no—
653#125—432no—
654#125—861no—
655#125—861no—
656#124—861no—
657#124—861no—
658#124C22×D4312yes—
659#123—862no—
660#123—862no—
661#123—862no—
662C22⋊Q8—432no—
663C22⋊Q8—432no—
664C22⋊Q8—861no—
665C22⋊Q8—861no—
666C22⋊Q8—861no—
667C22⋊Q8—861no—
668#121—21no—
669#121—21no—
670#121—432no—
671#121—432no—
672#121—861no—
673#121—861no—
674#120—862no—
675C4×Q8—432no—
676C4×Q8—432no—
677C4×Q8—432no—
678C4×Q8—432no—
679C4×Q8—432no—
680C4×Q8—432no—
681C4×Q8—861no—
682C4×Q8—861no—
683C4×Q8—861no—
684C4×Q8—861no—
685C4×Q8—861no—
686C4×Q8—861no—
687C4×Q8—861no—
688C4×Q8—861no—
689C4×D4—21no—
690C4×D4—21no—
691C4×D4—21no—
692C4×D4—21no—
693C4×D4—432no—
694C4×D4—432no—
695C4×D4—432no—
696C4×D4—432no—
697C4×D4—861no—
698C4×D4—861no—
699C4×D4—861no—
700C4×D4—861no—
701C4×D4—862no—
702C4×D4—862no—
703C4×D4—862no—
704C4×D4—862no—
705C4×D4—862no—
706C4×D4—862no—
707C4×D4—862no—
708C4×D4—862no—
709C4×D4—862no—
710C4×D4—862no—
711C4×D4—862no—
712C4×D4—862no—
713C4×D4—862no—
714C4×D4—862no—
715C4×D4C22×D4312yes—
716C4×D4C22×D4312yes—
717#117—432no—
718#117—432no—
719#117—432no—
720#117—862no—
721#117—862no—
722#117—862no—
723#117—862no—
724#117—862no—
725#117—862no—
726#117—862no—
727#117—861no—
728#117—861no—
729#117—861no—
730#117—861no—
731C2×C4⋊C4—431no—
732C2×C4⋊C4—861no—
733C2×C4⋊C4—861no—
734C2×C4⋊C4C22×D4311yescharacteristic
735C2×C22⋊C4—21no—
736C2×C22⋊C4—861no—
737C2×C22⋊C4—861no—
738C2×C42—431no—
739C2×C42—431no—
740C2×C42—431no—
741C2×C42—431no—
742C2×C42—431no—
743C2×C42—431no—
744C2×C42—431no—
745C2×C42—431no—
746C2×C42—431no—
747C2×C42—431no—
748C2×C42—431no—
749C2×C42—862no—
750C2×C42—862no—
751C2×C42—862no—
752C2×C42—862no—
753C2×C42—862no—
754C2×C42—861no—
755C2×C42—861no—
756C2×C42—861no—
757C2×C42C22×D4311yescharacteristic
758#107—434no—
759#107—434no—
760#106—434no—
761#106—434no—
762C4⋊C8—432no—
763C4⋊C8—432no—
764C4⋊C8C22×D4312yes—
765C4⋊C8C22×D4312yes—
766#103—434no—
767#103—434no—
768#103—434no—
769#103C22×D4314yes—
770#102—434no—
771#102—434no—
772#102—434no—
773#102C22×D4314yes—
774C22⋊C8—434no—
775C22⋊C8—434no—
776#97—434no—
777C4×C8—434no—
778C24—21no—
779C24—431no—
780#41—24no—
781#41—24no—
782#41—864no—
783#41—864no—
784#41—868no—
785#41—868no—
786#41—864no—
787#41—864no—
788#41—1724no—
789#41—1724no—
790C2×Q8—434no—
791C2×Q8—432no—
792C2×Q8—861no—
793C2×Q8—861no—
794C2×Q8—861no—
795C2×Q8—862no—
796C2×Q8C23×D4312yes—
797C2×D4—22no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—22no—
802C2×D4—862no—
803C2×D4—862no—
804C2×D4—868no—
805C2×D4—862no—
806C2×D4—862no—
807C2×D4#1062190014yescomplemented
808C2×D4C23×D4312yes—
809C2×D4C23×D4312yes—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—22no—
814C22×C4—44no—
815C22×C4—431no—
816C22×C4—431no—
817C22×C4—431no—
818C22×C4—431no—
819C22×C4—431no—
820C22×C4—431no—
821C22×C4—431no—
822C22×C4—431no—
823C22×C4—431no—
824C22×C4—431no—
825C22×C4—431no—
826C22×C4—431no—
827C22×C4—431no—
828C22×C4—431no—
829C22×C4—431no—
830C22×C4—862no—
831C22×C4—862no—
832C22×C4—862no—
833C22×C4—862no—
834C22×C4—862no—
835C22×C4—862no—
836C22×C4—868no—
837C22×C4—861no—
838C22×C4—862no—
839C22×C4—862no—
840C22×C4—861no—
841C22×C4—1722no—
842C22×C4—1722no—
843C22×C4—1724no—
844C22×C4D4×D4311yescharacteristic
845C22×C4D4×D4311yescharacteristic
846C22×C4C23×D4311yescharacteristic
847Q16—868no—
848SD16—28no—
849SD16—868no—
850D8—28no—
851M16—24no—
852M16—864no—
853C2×C8—434no—
854C2×C8C23×D4314yes—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—432no—
859C4⋊C4—432no—
860C4⋊C4—432no—
861C4⋊C4—862no—
862C4⋊C4—862no—
863C4⋊C4—862no—
864C4⋊C4—862no—
865C4⋊C4—862no—
866C4⋊C4—862no—
867C4⋊C4—861no—
868C4⋊C4—862no—
869C4⋊C4—862no—
870C4⋊C4—861no—
871C4⋊C4—861no—
872C4⋊C4—862no—
873C4⋊C4—862no—
874C4⋊C4C23×D4312yes—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—862no—
880C22⋊C4—862no—
881C22⋊C4—862no—
882C22⋊C4—862no—
883C22⋊C4—862no—
884C22⋊C4—862no—
885C22⋊C4—862no—
886C22⋊C4—862no—
887C22⋊C4—862no—
888C22⋊C4—862no—
889C22⋊C4—862no—
890C42—431no—
891C42—431no—
892C42—431no—
893C42—431no—
894C42—431no—
895C42—431no—
896C42—431no—
897C42—431no—
898C42—431no—
899C42—431no—
900C42—431no—
901C42—431no—
902C42—862no—
903C42—862no—
904C42—862no—
905C42—862no—
906C42—862no—
907C42—862no—
908C42—862no—
909C42—862no—
910C42—862no—
911C42D4×D4311yescharacteristic
912C42D4×D4311yescharacteristic
913C42C23×D4311yescharacteristic
914C42C23×D4311yescharacteristic
915C23—24no—
916C23—22no—
917C23—22no—
918C23—42no—
919C23—42no—
920C23—431no—
921C23—431no—
922C23—862no—
923C23—1721no—
924C23—1721no—
925C23C2×D4×D4311yescharacteristic
926Q8—22no—
927Q8—22no—
928Q8—434no—
929Q8—864no—
930Q8—862no—
931Q8—1722no—
932Q8—1722no—
933D4—24no—
934D4—22no—
935D4—22no—
936D4—22no—
937D4—42no—
938D4—44no—
939D4—42no—
940D4—868no—
941D4—868no—
942D4—1724no—
943D4—1724no—
944D4C2×#1062190014yes—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—41no—
949C2×C4—44no—
950C2×C4—42no—
951C2×C4—44no—
952C2×C4—44no—
953C2×C4—431no—
954C2×C4—431no—
955C2×C4—431no—
956C2×C4—431no—
957C2×C4—431no—
958C2×C4—431no—
959C2×C4—862no—
960C2×C4—862no—
961C2×C4—862no—
962C2×C4—868no—
963C2×C4—868no—
964C2×C4—862no—
965C2×C4—864no—
966C2×C4—862no—
967C2×C4—862no—
968C2×C4—862no—
969C2×C4—862no—
970C2×C4—862no—
971C2×C4—861no—
972C2×C4—861no—
973C2×C4—861no—
974C2×C4—861no—
975C2×C4—862no—
976C2×C4—862no—
977C2×C4—862no—
978C2×C4—1721no—
979C2×C4—1721no—
980C2×C4—1721no—
981C2×C4—1721no—
982C2×C4—1724no—
983C2×C4—1724no—
984C2×C4—1721no—
985C2×C4—1724no—
986C2×C4—1724no—
987C2×C4—1722no—
988C2×C4C2×D4×D4311yescharacteristic
989C2×C4C2×D4×D4311yescharacteristic
990C2×C4C2×D4×D4311yescharacteristic
991C2×C4C2×D4×D4311yescharacteristic
992C2×C4C2×D4×D4311yescharacteristic
993C2×C4#41×D4312yes—
994C2×C4C2×#1062190012yes—
995C2×C4C24×D4311yescharacteristic
996C8—24no—
997C8—864no—
998C22—21no—
999C22—21no—
1000C22—24no—
1001C22—48no—
1002C22—42no—
1003C22—42no—
1004C22—42no—
1005C22—42no—
1006C22—42no—
1007C22—861no—
1008C22—861no—
1009C22—861no—
1010C22—861no—
1011C22—861no—
1012C22—861no—
1013C22—1724no—
1014C22#1458340912yes—
1015C22C22×D4×D4311yescharacteristic
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—42no—
1020C4—42no—
1021C4—432no—
1022C4—861no—
1023C4—861no—
1024C4—861no—
1025C4—861no—
1026C4—861no—
1027C4—864no—
1028C4—1722no—
1029C4—1722no—
1030C4—1722no—
1031C4#1458340912yes—
1032C4#1458369512yes—
1033C4C2×#41×D4311yescharacteristic
1034C4C22×#1062190011yescharacteristic
1035C2—22no—
1036C2—44no—
1037C2—82no—
1038C2—1721no—
1039C2—1721no—
1040C2C2×#1458340911yescharacteristic
1041C2#575×D4311yescharacteristic
1042C2C2×#1458369511yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3036C2
socleC22×C43C23×D4
hypercenter#3036D43
hypocenterC43#60559
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3036

Complements

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

NH ≅ G/Ntype
1. #19147890C2semidirect
2. C2×C4×#10621900C2semidirect
3. #19144754C2semidirect
4. #19144743C2semidirect
5. #19144701C2semidirect
6. #19144663C2semidirect
7. #19144652C2semidirect
8. #19144610C2semidirect
9. #19144525C2semidirect
10. #19144402C2semidirect
11. #19144392C2semidirect
12. #19144063C2semidirect
13. #19143834C2semidirect
14. #19143419C2semidirect
15. AGL(1,ℤ/8)×Dic43C2semidirect
16. #19143227C2semidirect
17. C43×#3036C2semidirect
21. #14583454C22semidirect
22. #14583454C22semidirect
23. #14583447C22semidirect
24. #14583447C22semidirect
29. #14583428C22semidirect
30. #14583428C22semidirect
54. #14583239C22semidirect
55. #14583238C22semidirect
56. #14583222C22semidirect
57. #14583221C22semidirect
58. #14583207C22semidirect
59. #14583199C22semidirect
60. #14583195C22semidirect
61. #14583189C22semidirect
62. #14583185C22semidirect
63. #14583179C22semidirect
64. #14583118C22semidirect
65. #14583106C22semidirect
66. #14583096C22semidirect
71. #14583011C22semidirect
72. #14583003C22semidirect
73. #14583000C22semidirect
74. #14582996C22semidirect
75. #14582991C22semidirect
76. #14582990C22semidirect
77. SD16×Dic43C22semidirect
78. D8×Dic43C22semidirect
79. #14582955C22semidirect
80. #14582955C22semidirect
81. #14582951C22semidirect
82. #14582951C22semidirect
94. C43×#463C22semidirect
95. C43×#461C22semidirect
96. C43×#459C22semidirect
266. C2×D4×C43#41semidirect
323. C2×Dic86#41semidirect
526. #3036D43semidirect
589. #463C2×D43semidirect
591. #461C2×D43semidirect
593. #459C2×D43semidirect
620. C43#60559semidirect
807. C2×D4#10621900semidirect

Maximal subgroups

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

subgroupindex
#191478902
C2×C4×#106219002
#191447542
#191447432
#191447012
#191446632
#191446522
#191446102
#191445252
#191444022
#191443922
#191440632
#191438342
#191434192
AGL(1,ℤ/8)×Dic432
#191432272
C43×#30362
#6055943