Finite Group Databasebeta

← #25117289

Subgroups — #25117289

Order 11008.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583044C211yesmaximal, characteristic
2C2×#14582984C211yesmaximal, characteristic, complemented
3#19137611C211yesmaximal, characteristic, complemented
4#19137436C211yesmaximal, characteristic, complemented
5#19135468C211yesmaximal, characteristic, complemented
6#19135275C211yesmaximal, characteristic, complemented
7#19135225C211yesmaximal, characteristic, complemented
8#19135033C211yesmaximal, characteristic, complemented
9#19134948C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134861C211yesmaximal, characteristic, complemented
12#19134788C211yesmaximal, characteristic, complemented
13#19134427C211yesmaximal, characteristic, complemented
14#19134376C211yesmaximal, characteristic, complemented
15C2×C43×#417C211yesmaximal, characteristic, complemented
16C22×#10621884C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C2×#13063299C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×#13063287C2211yescharacteristic
22C2×C4×C22⋊D43—21no—
23#14583044C418yescomplemented
24#14582984—24no—
25C2×#13063256C2211yescharacteristic
26C2×#13063256C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063247C2211yescharacteristic
29C2×#13063247C2211yescharacteristic
30C2×#13063246C2211yescharacteristic
31C2×C22⋊(C43⋊C8)C2211yescharacteristic
32C2×#13063235C2211yescharacteristic
33C2×C8×Dic43C2211yescharacteristic
34#14582802—21no—
35#14582802—21no—
36#14582802C2211yescharacteristic
37#14582802C2211yescharacteristic
38#14582800C2211yescharacteristic
39#14582795C2211yescharacteristic
40#14582789—21no—
41#14582778—21no—
42#14582770—21no—
43#14582759—21no—
44#14582759C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×C22⋊Dic43—21no—
47C4×C22⋊Dic43C2211yescharacteristic
48#14582662C2211yescharacteristic
49#14582662C2211yescharacteristic
50#14582661C2211yescharacteristic
51#14582661C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C22×#41×C43C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C22×C4⋊C4×C43C2211yescharacteristic
57C43×#417—24no—
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C22×D172C2311yescharacteristic
63C22×C22⋊D43—21no—
64C22×C4×D43—21no—
65C2×#10621884—22no—
66C2×#10621884—22no—
67C2×#10621884C2×C414yescomplemented
68C2×#10621882—41no—
69C2×#10621882—41no—
70C2×#10621882C2×C414yescomplemented
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73#13063299—22no—
74#13063299C2×C414yes—
75Q8×Dic43—22no—
76Q8×Dic43—22no—
77Q8×Dic43—41no—
78Q8×Dic43—41no—
79#13063287—22no—
80#13063287—41no—
81C4×C22⋊D43—44no—
82C2×C4⋊Dic43—21no—
83C2×C4⋊Dic43—21no—
84C2×C4⋊Dic43C2311yescharacteristic
85C2×C4⋊Dic43C2311yescharacteristic
86C2×C4⋊Dic43C2311yescharacteristic
87C2×Dic43⋊C4—21no—
88C2×C22⋊Dic43—21no—
89C2×C22⋊Dic43—21no—
90C2×C22⋊Dic43—21no—
91C2×C22⋊Dic43—21no—
92C2×C22⋊Dic43—21no—
93C2×C22⋊Dic43D411yescharacteristic
94C2×C22⋊Dic43D411yescharacteristic
95C2×(C2×D43)⋊C4—21no—
96C2×(C2×D43)⋊C4—21no—
97C2×(C2×D43)⋊C4—21no—
98C2×(C2×D43)⋊C4—21no—
99C2×C4×Dic43—21no—
100C2×C4×Dic43—21no—
101C2×C4×Dic43—21no—
102C2×C4×Dic43C2311yescharacteristic
103C2×C4×Dic43C2311yescharacteristic
104#13063256—22no—
105#13063256—41no—
106#13063249C2×C414yescomplemented
107#13063247—22no—
108#13063247—41no—
109#13063246C2×C414yescomplemented
110C22⋊(C43⋊C8)C2×C414yescomplemented
111#13063235—41no—
112C8×Dic43—22no—
113C43⋊#95—21no—
114C43⋊#95—21no—
115C43⋊#95—21no—
116C43⋊#95D411yescharacteristic
117C43⋊#95D411yescharacteristic
118C2×#41×C43—22no—
119C2×#41×C43—22no—
120C2×#41×C43—22no—
121C2×#41×C43—41no—
122C2×#41×C43—41no—
123C2×#41×C43C2×C414yescomplemented
124C22×Q8×C43C2311yescharacteristic
125C22×D4×C43—21no—
126C22×D4×C43C2311yescharacteristic
127C23×C4×C43—21no—
128C23×C4×C43—21no—
129C23×C4×C43C2311yescharacteristic
130C2×M16×C43—22no—
131C2×M16×C43—22no—
132C2×M16×C43—41no—
133C22×C8×C43C2311yescharacteristic
134C22×C8×C43C2311yescharacteristic
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43—21no—
137C2×C4⋊C4×C43—41no—
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140#103×C43—22no—
141#103×C43D414yescomplemented
142#102×C43—22no—
143#102×C43—22no—
144C24×C43—21no—
145C24×C43C2×D411yescharacteristic
146C23×D43—21no—
147#41×C43—28no—
148#41×C43—44no—
149#41×C43—44no—
150#41×C43—44no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43C22×C412yes—
155C2×Q8×C43C2×D412yes—
156C2×Q8×C43#4112yes—
157C2×D4×C43—21no—
158C2×D4×C43—24no—
159C2×D4×C43—21no—
160C2×D4×C43—21no—
161C2×D4×C43—21no—
162C2×D4×C43—21no—
163C2×D4×C43—42no—
164C2×D4×C43—42no—
165C2×D4×C43C22×C412yes—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—24no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—42no—
175C22×C4×C43—42no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43—81no—
179C22×C4×C43C22×C412yes—
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43#4112yes—
182C22×C4×C43C2411yescharacteristic
183C2×C22⋊D43—24no—
184C2×C22⋊D43—42no—
185C2×C22⋊D43—42no—
186C22×Dic43—21no—
187C22×Dic43—21no—
188C22×Dic43—21no—
189C22×Dic43C2×D411yescharacteristic
190C22×Dic43C2×D411yescharacteristic
191C22×Dic43C2×D411yescharacteristic
192C22×Dic43C2×D411yescharacteristic
193C2×D172—21no—
194C2×D172—21no—
195C2×D172—21no—
196C2×D172—21no—
197C2×D172—21no—
198C2×D172C22×C412yes—
199C2×C4×D43—42no—
200C2×C4×D43—42no—
201C2×C4×D43—81no—
202M16×C43—44no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C2×D412yes—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—42no—
213C4⋊C4×C43C2×D412yes—
214C22⋊Dic43—22no—
215C22⋊Dic43—41no—
216C22⋊Dic43—42no—
217C22⋊Dic43—42no—
218C22⋊Dic43—81no—
219C22⋊Dic43—81no—
220C22⋊Dic43—81no—
221#10621884—28no—
222#10621882—44no—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—81no—
227C4⋊Dic43—21no—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—42no—
233C4⋊Dic43—42no—
234C4⋊Dic43C22×C412yes—
235Dic43⋊C4—42no—
236C4×Dic43—21no—
237C4×Dic43—21no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—42no—
241C4×Dic43—42no—
242C4×Dic43—42no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8C22×C412yes—
248C2×C43⋊C8C22×C412yes—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—22no—
256C23×C43—41no—
257C23×C43—41no—
258C23×C43—41no—
259C23×C43—41no—
260C23×C43—41no—
261C23×C43—41no—
262C23×C43C4×D412yes—
263C23×C43C22×D411yescharacteristic
264C22×D43—22no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43—41no—
271Q8×C43—22no—
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43C4×D414yescomplemented
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—48no—
278D4×C43—41no—
279D4×C43—41no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—22no—
284C2×C4×C43—21no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—48no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43—41no—
296C2×C4×C43—84no—
297C2×C4×C43C4×D412yes—
298C2×C4×C43C23×C411yescharacteristic
299C2×C4×C43C22×D411yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43C2×#4111yescharacteristic
302C2×C4×C43H(5,𝔽2)11yescharacteristic
303C2×C4×C43H(5,𝔽2)11yescharacteristic
304C22⋊D43—48no—
305C2×Dic43—21no—
306C2×Dic43—21no—
307C2×Dic43—22no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—41no—
318C2×Dic43—41no—
319C2×Dic43—41no—
320C2×Dic43—41no—
321C2×Dic43—41no—
322C2×Dic43—41no—
323C2×Dic43—41no—
324C2×Dic43—41no—
325C2×Dic43AGL(1,ℤ/8)12yes—
326D172—22no—
327D172—22no—
328D172—41no—
329D172—41no—
330C4×D43—84no—
331C8×C43—22no—
332C8×C43—41no—
333C43⋊C8—22no—
334C43⋊C8—22no—
335#22883—431nomaximal, Sylow
336C22×C43—22no—
337C22×C43—22no—
338C22×C43—22no—
339C22×C43—41no—
340C22×C43—41no—
341C22×C43—41no—
342C22×C43—41no—
343C22×C43—42no—
344C22×C43—42no—
345C22×C43—42no—
346C22×C43—81no—
347C22×C43—81no—
348C22×C43—81no—
349C22×C43—81no—
350C22×C43C2×C4×D411yescharacteristic
351C22×C43D4211yescharacteristic
352C22×C43#54611yescharacteristic
353C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C43#57511yescharacteristic
355C22×C43#57711yescharacteristic
356C22×C43#57711yescharacteristic
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C2×D43—81no—
364C4×C43—22no—
365C4×C43—24no—
366C4×C43—42no—
367C4×C43—81no—
368C4×C43C2×C4×D411yescharacteristic
369C4×C43#51811yescharacteristic
370C4×C43#54611yescharacteristic
371C4×C43#55111yescharacteristic
372Dic43—22no—
373Dic43—41no—
374Dic43—42no—
375Dic43—41no—
376Dic43—41no—
377Dic43—81no—
378Dic43—81no—
379C2×#449—431no—
380C2×C4×SD16—431no—
381C2×#417D4311yescharacteristic, complemented
382#2361—431no—
383#2341—431no—
384#1972—431no—
385#1934—431no—
386#1926—431no—
387#1895—431no—
388#1880—431no—
389#1879—431no—
390#1865—431no—
391#1853—431no—
392#1763—431no—
393#1753—431no—
394C2×C43—42no—
395C2×C43—82no—
396C2×C43#235811yescharacteristic
397C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
398C2×C43#295211yescharacteristic
399C2×C43#326511yescharacteristic
400C2×C43#327111yescharacteristic
401C2×C43#332611yescharacteristic
402C2×C43#333211yescharacteristic
403D43—82no—
404C22×#41C2×D4311yescharacteristic
405C22×SD16—431no—
406C22×D8—431no—
407C22×M16C2×D4311yescharacteristic
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8—431no—
411C2×C4×D4—431no—
412C2×C4×D4—861no—
413C22×C4⋊C4C2×D4311yescharacteristic
414#449—438no—
415C4×SD16—864no—
416C2×#106—431no—
417C2×#106—431no—
418#417—24no—
419C2×#103—431no—
420C2×#103C2×D4311yescharacteristic
421C2×#103C2×D4311yescharacteristic
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102C2×D4311yescharacteristic
426C2×#102C2×D4311yescharacteristic
427C2×C22⋊C8—431no—
428C2×#97—431no—
429C2×C4×C8—431no—
430#390—431no—
431#390—431no—
432#390—431no—
433#390—861no—
434#390—861no—
435#389—431no—
436#388—861no—
437#386—861no—
438#385—861no—
439#380—431no—
440#380—861no—
441C4×C4⋊C4—431no—
442C4×C22⋊C4—431no—
443C4×C22⋊C4—861no—
444#340—431no—
445#340—431no—
446#340—431no—
447#340—431no—
448#336—431no—
449#336—431no—
450C43#2288311yescharacteristic, complemented, Sylow
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41C4×D4314yescomplemented
457C22×Q8C22×D4311yescharacteristic
458C22×D4—21no—
459C22×D4—431no—
460C22×D4—861no—
461C22×D4C22×D4311yescharacteristic
462C23×C4—21no—
463C23×C4—21no—
464C23×C4—861no—
465C23×C4C22×D4311yescharacteristic
466C2×SD16—434no—
467C2×SD16—862no—
468C2×SD16—862no—
469C2×D8—434no—
470C2×D8—1721no—
471C2×D8—1721no—
472C2×M16—22no—
473C2×M16—22no—
474C2×M16—41no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479#121—434no—
480#121—862no—
481C4×Q8—862no—
482C4×Q8—862no—
483C4×Q8—1721no—
484C4×Q8—1721no—
485C4×D4—862no—
486C4×D4—1721no—
487C4×D4—1724no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—41no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—431no—
493C2×C4⋊C4—431no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—431no—
500C2×C22⋊C4—431no—
501C2×C22⋊C4—861no—
502C2×C22⋊C4—861no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C22⋊C4—861no—
507C2×C22⋊C4—861no—
508C2×C22⋊C4—861no—
509C2×C22⋊C4—861no—
510C2×C42—431no—
511C2×C42—431no—
512C2×C42—861no—
513C2×C42—861no—
514C2×C42—861no—
515#106—862no—
516#106—1721no—
517#103—22no—
518#103—434no—
519#103C22⋊D4314yescomplemented
520#102—22no—
521#102—22no—
522#102—434no—
523#102—862no—
524#102—1721no—
525C22⋊C8—434no—
526#97—1721no—
527C4×C8—862no—
528#95—431no—
529#95—431no—
530#95—861no—
531#95—861no—
532#95—861no—
533C24—21no—
534C24—861no—
535C24D4×D4311yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C4×D4312yes—
544C2×Q8#1062189812yes—
545C2×Q8C2×C22⋊D4312yes—
546C2×D4—24no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—432no—
555C2×D4—864no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—861no—
560C2×D4—861no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4C2×C4×D4312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—21no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—81no—
577C22×C4—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—3441no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4C2×C4×D4312yes—
588C22×C4D4×D4311yescharacteristic
589C22×C4#1062190012yes—
590C22×C4C23×D4311yescharacteristic
591SD16—868no—
592D8—1724no—
593M16—44no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—432no—
600C2×C8—432no—
601C2×C8—861no—
602C2×C8—861no—
603C2×C8—861no—
604C2×C8—861no—
605C2×C8C2×C22⋊D4312yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—42no—
610C4⋊C4—432no—
611C4⋊C4—861no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—1722no—
617C4⋊C4—1722no—
618C4⋊C4—1722no—
619C4⋊C4C2×C22⋊D4312yes—
620C22⋊C4—862no—
621C22⋊C4—864no—
622C22⋊C4—3441no—
623C22⋊C4—3441no—
624C22⋊C4—3441no—
625C22⋊C4—3441no—
626C22⋊C4—1722no—
627C22⋊C4—1722no—
628C22⋊C4—1722no—
629C22⋊C4—1721no—
630C22⋊C4—1722no—
631C42—861no—
632C42—861no—
633C42—861no—
634C42—861no—
635C42—1722no—
636C42—1722no—
637C42—1722no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—862no—
652C23—1721no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23(C22⋊D43)⋊C412yes—
659C23C2×D4×D4311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8C4×C22⋊D4314yescomplemented
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4—862no—
670D4—862no—
671D4—1728no—
672D4—1721no—
673D4—1721no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—84no—
691C2×C4—432no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—862no—
695C2×C4—861no—
696C2×C4—861no—
697C2×C4—861no—
698C2×C4—861no—
699C2×C4—861no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—861no—
704C2×C4—3444no—
705C2×C4—1721no—
706C2×C4—1721no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4(C22⋊D43)⋊C412yes—
714C2×C4C22×C4×D4311yescharacteristic
715C2×C4C22×C22⋊D4311yescharacteristic
716C2×C4C2×#1062190011yescharacteristic
717C2×C4C2×#1062189811yescharacteristic
718C2×C4#1306337011yescharacteristic
719C2×C4#1306337011yescharacteristic
720C8—22no—
721C8—41no—
722C8—862no—
723C8—862no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—81no—
738C22—3441no—
739C22—3441no—
740C22—3441no—
741C22—3441no—
742C22—1722no—
743C22—1722no—
744C22—1722no—
745C22C2×(C22⋊D43)⋊C411yescharacteristic
746C22D4×C22⋊D4311yescharacteristic
747C22#1458353911yescharacteristic
748C22AGL(1,ℤ/8)×D4311yescharacteristic
749C22#1458369811yescharacteristic
750C22#1458370811yescharacteristic
751C22#1458370911yescharacteristic
752C4—22no—
753C4—24no—
754C4—42no—
755C4—81no—
756C4—862no—
757C4—3441no—
758C4—3441no—
759C4—1721no—
760C4—1721no—
761C4—1721no—
762C4—1722no—
763C4C2×C4×C22⋊D4311yescharacteristic
764C4#1458337211yescharacteristic
765C4#1458354311yescharacteristic
766C4#1458357511yescharacteristic
767C2—42no—
768C2—82no—
769C2—3442no—
770C2#1913757411yescharacteristic
771C2#1914340811yescharacteristic
772C2#1914347411yescharacteristic
773C2#1914608411yescharacteristic
774C2#1914617411yescharacteristic
775C2#1914684911yescharacteristic
776C2#1914691811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
prime radicalC2×#14583044C2
cosocleC22×C4×C43C24
hypercenterC2×#417D43
hypocenterC43#22883
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#14582984C2semidirect
3. #19137611C2semidirect
4. #19137436C2semidirect
5. #19135468C2semidirect
6. #19135275C2semidirect
7. #19135225C2semidirect
8. #19135033C2semidirect
9. #19134948C2semidirect
10. #19134940C2semidirect
11. #19134861C2semidirect
12. #19134788C2semidirect
13. #19134427C2semidirect
14. #19134376C2semidirect
15. C2×C43×#417C2semidirect
23. #14583044C4semidirect
67. C2×#10621884C2×C4semidirect
70. C2×#10621882C2×C4semidirect
106. #13063249C2×C4semidirect
109. #13063246C2×C4semidirect
110. C22⋊(C43⋊C8)C2×C4semidirect
123. C2×#41×C43C2×C4semidirect
141. #103×C43D4semidirect
274. Q8×C43C4×D4semidirect
381. C2×#417D43semidirect
450. C43#22883semidirect
456. C2×#41C4×D43semidirect
519. #103C22⋊D43semidirect
663. Q8C4×C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145830442
C2×#145829842
#191376112
#191374362
#191354682
#191352752
#191352252
#191350332
#191349482
#191349402
#191348612
#191347882
#191344272
#191343762
C2×C43×#4172
#2288343