Finite Group Databasebeta

← #25117295

Subgroups — #25117295

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×#14583043C211yesmaximal, characteristic
2C2×SD16×Dic43C211yesmaximal, characteristic, complemented
3C2×#14582899C211yesmaximal, characteristic, complemented
4#19137616C211yesmaximal, characteristic, complemented
5#19137433C211yesmaximal, characteristic, complemented
6#19135470C211yesmaximal, characteristic, complemented
7#19135276C211yesmaximal, characteristic, complemented
8#19135223C211yesmaximal, characteristic, complemented
9#19135030C211yesmaximal, characteristic, complemented
10#19134941C211yesmaximal, characteristic, complemented
11#19134861C211yesmaximal, characteristic, complemented
12#19134789C211yesmaximal, characteristic, complemented
13#19134425C211yesmaximal, characteristic, complemented
14#19134377C211yesmaximal, characteristic, complemented
15C43×#1880C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621882C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C2×#13063296C2211yescharacteristic
20C2×Q8×Dic43C2211yescharacteristic
21C2×D4×Dic43C2211yescharacteristic
22C2×(C22⋊D43)⋊C4—21no—
23C2×C4⋊C4×D43C2211yescharacteristic
24#14583043C418yescomplemented
25SD16×Dic43—24no—
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2211yescharacteristic
28#14582899—24no—
29C2×#13063249C2211yescharacteristic
30C2×#13063249C2211yescharacteristic
31C2×#13063247C2211yescharacteristic
32C2×#13063247C2211yescharacteristic
33C2×#13063246C2211yescharacteristic
34C2×#13063245C2211yescharacteristic
35C2×(C2×D43)⋊C8C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37C2×C8×Dic43C2211yescharacteristic
38#14582801—21no—
39#14582801C2211yescharacteristic
40#14582800—21no—
41#14582800C2211yescharacteristic
42#14582795C2211yescharacteristic
43#14582787—21no—
44#14582775—21no—
45#14582771—21no—
46#14582756—21no—
47#14582756C2211yescharacteristic
48C4×C4⋊Dic43C2211yescharacteristic
49C4×(C2×D43)⋊C4—21no—
50C4×(C2×D43)⋊C4C2211yescharacteristic
51#14582662C2211yescharacteristic
52#14582661C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×SD16×C43C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×#103×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C43×#390C2211yescharacteristic
60C43×#340C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C2×#10621902—22no—
63C2×#10621902—22no—
64C2×#10621902—22no—
65C2×#10621902—41no—
66C2×#10621902—41no—
67C2×#10621902C2×C414yescomplemented
68C22×D172—21no—
69C22×D172C2311yescharacteristic
70C22×C22⋊D43—21no—
71C23×Dic43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43C2311yescharacteristic
75C2×#10621882—41no—
76C2×#10621882—41no—
77C2×#10621882C2×C414yescomplemented
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872—41no—
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83#13063296—22no—
84#13063296C2×C414yes—
85Q8×Dic43—22no—
86Q8×Dic43—41no—
87D4×Dic43—22no—
88D4×Dic43—41no—
89(C22⋊D43)⋊C4—44no—
90C2×C4⋊Dic43—21no—
91C2×C4⋊Dic43C2311yescharacteristic
92C2×C4⋊Dic43C2311yescharacteristic
93C2×C4⋊Dic43C2311yescharacteristic
94C2×Dic43⋊C4—21no—
95C2×Dic43⋊C4—21no—
96C4⋊C4×D43—22no—
97C4⋊C4×D43—41no—
98C2×C22⋊Dic43—21no—
99C2×C22⋊Dic43—21no—
100C2×(C2×D43)⋊C4—21no—
101C2×(C2×D43)⋊C4—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×(C2×D43)⋊C4D411yescharacteristic
106C2×(C2×D43)⋊C4D411yescharacteristic
107C2×C4×Dic43—21no—
108C2×C4×Dic43—21no—
109C2×C4×Dic43C2311yescharacteristic
110#13063257—22no—
111#13063256—41no—
112#13063249C2×C414yescomplemented
113#13063249D414yescomplemented
114#13063247—22no—
115#13063247C2×C414yescomplemented
116#13063246—22no—
117#13063245—22no—
118(C2×D43)⋊C8C2×C414yescomplemented
119#13063236—41no—
120C8×Dic43—22no—
121C43⋊#95—21no—
122C43⋊#95—21no—
123C43⋊#95—21no—
124C43⋊#95D411yescharacteristic
125C43⋊#95D411yescharacteristic
126C22×Q8×C43C2311yescharacteristic
127C22×D4×C43C2311yescharacteristic
128C2×SD16×C43—22no—
129C2×SD16×C43—22no—
130C2×SD16×C43C2×C414yescomplemented
131C22×C8×C43C2311yescharacteristic
132C22×C8×C43C2311yescharacteristic
133C4×Q8×C43—22no—
134C4×Q8×C43—41no—
135C2×C4⋊C4×C43—21no—
136C2×C4⋊C4×C43C2311yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C22⋊C4×C43—21no—
139C2×C22⋊C4×C43—21no—
140C2×C42×C43—21no—
141C2×C42×C43C2311yescharacteristic
142#103×C43—22no—
143#102×C43—41no—
144C24×C43—21no—
145C23×D43—21no—
146C23×D43C2×D411yescharacteristic
147C2×Q8×C43—21no—
148C2×Q8×C43—21no—
149C2×Q8×C43—21no—
150C2×Q8×C43C22×C412yes—
151C2×Q8×C43C2×D412yes—
152C2×Q8×C43#4112yes—
153C2×D4×C43—21no—
154C2×D4×C43—21no—
155C2×D4×C43—21no—
156C2×D4×C43—21no—
157C2×D4×C43—21no—
158C2×D4×C43C22×C412yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43C2×D411yescharacteristic
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C2×C22⋊D43—24no—
166C2×C22⋊D43—42no—
167C2×C22⋊D43—42no—
168C22×Dic43—21no—
169C22×Dic43—21no—
170C22×Dic43—21no—
171C22×Dic43—42no—
172C22×Dic43—42no—
173C22×Dic43—81no—
174C22×Dic43C2×D411yescharacteristic
175C22×Dic43C2×D411yescharacteristic
176C22×Dic43C2×D411yescharacteristic
177#10621902—28no—
178#10621902—44no—
179#10621902—44no—
180#10621902—44no—
181C2×D172—21no—
182C2×D172—24no—
183C2×D172—21no—
184C2×D172—21no—
185C2×D172—21no—
186C2×D172—21no—
187C2×D172—42no—
188C2×D172—42no—
189C2×D172C22×C412yes—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—24no—
195C2×C4×D43—42no—
196C2×C4×D43—42no—
197C2×C4×D43—42no—
198C2×C4×D43—42no—
199C2×C4×D43—81no—
200C2×C4×D43C22×C412yes—
201C2×C4×D43#4112yes—
202SD16×C43—28no—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43C22×C412yes—
209C4⋊C4×C43—21no—
210C4⋊C4×C43—21no—
211C4⋊C4×C43—21no—
212C4⋊C4×C43—21no—
213C4⋊C4×C43—42no—
214C22⋊C4×C43—42no—
215C22⋊C4×C43—81no—
216C42×C43—21no—
217C42×C43—21no—
218C42×C43—42no—
219C22⋊Dic43—24no—
220C22⋊Dic43—42no—
221#10621882—44no—
222(C2×D43)⋊C4—22no—
223(C2×D43)⋊C4—41no—
224(C2×D43)⋊C4—42no—
225(C2×D43)⋊C4—42no—
226(C2×D43)⋊C4—81no—
227(C2×D43)⋊C4—81no—
228(C2×D43)⋊C4—81no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—21no—
232C4⋊Dic43—21no—
233C4⋊Dic43—42no—
234C4⋊Dic43C22×C412yes—
235C4⋊Dic43C2×D412yes—
236Dic43⋊C4—42no—
237Dic43⋊C4—42no—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—42no—
241C4×Dic43—42no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8—21no—
244C2×C43⋊C8—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8C22×C412yes—
247C2×C43⋊C8C2×D412yes—
248#10621872—44no—
249C23×C43—22no—
250C23×C43—41no—
251C23×C43—41no—
252C23×C43—41no—
253C23×C43—41no—
254C23×C43—41no—
255C23×C43—41no—
256C23×C43C22×D411yescharacteristic
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43—21no—
262C22×D43—21no—
263C22×D43—22no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43—41no—
267C22×D43—41no—
268C22×D43—41no—
269C22×D43—41no—
270C22×D43C4×D412yes—
271Q8×C43—22no—
272Q8×C43—22no—
273Q8×C43—22no—
274Q8×C43C4×D414yescomplemented
275D4×C43—22no—
276D4×C43—22no—
277D4×C43—41no—
278D4×C43—41no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—21no—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—41no—
289C2×C4×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43C23×C411yescharacteristic
295C2×C4×C43C22×D411yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×C4×C43C2×#4111yescharacteristic
298C2×C4×C43H(5,𝔽2)11yescharacteristic
299C2×C4×C43H(5,𝔽2)11yescharacteristic
300C22⋊D43—48no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—21no—
305C2×Dic43—22no—
306C2×Dic43—21no—
307C2×Dic43—22no—
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315C2×Dic43—41no—
316C2×Dic43—41no—
317C2×Dic43—84no—
318C2×Dic43C4×D412yes—
319C2×Dic43AGL(1,ℤ/8)12yes—
320D172—22no—
321D172—22no—
322D172—48no—
323D172—41no—
324D172—41no—
325C4×D43—22no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—48no—
330C4×D43—84no—
331C8×C43—22no—
332C8×C43—41no—
333C43⋊C8—22no—
334C43⋊C8—22no—
335#22883—431nomaximal, Sylow
336C22×C43—42no—
337C22×C43—42no—
338C22×C43—42no—
339C22×C43—81no—
340C22×C43—81no—
341C22×C43—81no—
342C22×C43—81no—
343C22×C43C2×C4×D411yescharacteristic
344C22×C43D4211yescharacteristic
345C22×C43#54611yescharacteristic
346C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C43#57511yescharacteristic
348C22×C43#57711yescharacteristic
349C22×C43#57711yescharacteristic
350C2×D43—22no—
351C2×D43—22no—
352C2×D43—22no—
353C2×D43—41no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—81no—
361C2×D43—81no—
362C2×D43—81no—
363C2×D43—81no—
364C4×C43—24no—
365C4×C43—41no—
366C4×C43—41no—
367C4×C43—81no—
368C4×C43—81no—
369C4×C43C2×C4×D411yescharacteristic
370C4×C43#51811yescharacteristic
371C4×C43#54611yescharacteristic
372C4×C43#55111yescharacteristic
373Dic43—22no—
374Dic43—22no—
375Dic43—42no—
376Dic43—42no—
377Dic43—41no—
378Dic43—81no—
379C2×#449—431no—
380C2×C4×SD16—431no—
381C2×#417—431no—
382#2361—431no—
383#2341—431no—
384#1972—431no—
385#1934—431no—
386#1926—431no—
387#1895—431no—
388#1880D4311yescharacteristic, complemented
389#1879—431no—
390#1865—431no—
391#1853—431no—
392#1763—431no—
393#1753—431no—
394C2×C43—82no—
395C2×C43#235811yescharacteristic
396C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
397C2×C43#295211yescharacteristic
398C2×C43#326511yescharacteristic
399C2×C43#327111yescharacteristic
400C2×C43#332611yescharacteristic
401C2×C43#333211yescharacteristic
402D43—42no—
403D43—82no—
404C22×#41—431no—
405C22×SD16C2×D4311yescharacteristic
406C22×D8—431no—
407C22×M16—431no—
408C2×#121—431no—
409C2×C4×Q8—431no—
410C2×C4×Q8C2×D4311yescharacteristic
411C2×C4×D4—431no—
412C2×C4×D4—861no—
413C22×C4⋊C4—431no—
414#449—438no—
415C4×SD16—864no—
416C2×#106—431no—
417C2×#106—431no—
418#417—864no—
419C2×#103—431no—
420C2×#103—431no—
421C2×#103C2×D4311yescharacteristic
422C2×#102—431no—
423C2×#102—431no—
424C2×#102—431no—
425C2×#102—431no—
426C2×#102C2×D4311yescharacteristic
427C2×C22⋊C8—431no—
428C2×#97—431no—
429C2×C4×C8—431no—
430#390—431no—
431#390—431no—
432#390—861no—
433#390—861no—
434#390C2×D4311yescharacteristic
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#340C2×D4311yescharacteristic
448#336—431no—
449#336C2×D4311yescharacteristic
450C43#2288311yescharacteristic, complemented, Sylow
451C2×#41—434no—
452C2×#41—862no—
453C2×#41—862no—
454C2×#41—862no—
455C2×#41—1721no—
456C2×#41—1721no—
457C22×Q8C22×D4311yescharacteristic
458C22×D4—431no—
459C22×D4—861no—
460C22×D4—861no—
461C22×D4C22×D4311yescharacteristic
462C23×C4—431no—
463C23×C4—861no—
464C23×C4—861no—
465C23×C4—861no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16C4×D4314yescomplemented
469C2×D8—434no—
470C2×D8—1721no—
471C2×D8—1721no—
472C2×M16—862no—
473C2×M16—862no—
474C2×M16—1721no—
475C22×C8—431no—
476C22×C8—431no—
477C22×C8C22×D4311yescharacteristic
478C22×C8C22×D4311yescharacteristic
479#121—434no—
480#121—862no—
481C4×Q8—22no—
482C4×Q8—41no—
483C4×Q8—862no—
484C4×Q8—1721no—
485C4×D4—862no—
486C4×D4—1721no—
487C4×D4—1724no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—431no—
491C2×C4⋊C4—431no—
492C2×C4⋊C4—862no—
493C2×C4⋊C4—861no—
494C2×C4⋊C4—861no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—1721no—
497C2×C4⋊C4C22×D4311yescharacteristic
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—431no—
502C2×C22⋊C4—431no—
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—21no—
511C2×C42—431no—
512C2×C42—861no—
513C2×C42—861no—
514C2×C42C22×D4311yescharacteristic
515#106—862no—
516#106—1721no—
517#103—22no—
518#103—434no—
519#103—434no—
520#102—41no—
521#102—434no—
522#102—862no—
523#102—862no—
524#102—862no—
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—431no—
535C24—861no—
536#41—868no—
537#41—1724no—
538#41—1724no—
539#41—1724no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×C4×D4312yes—
544C2×Q8D4×D4312yes—
545C2×Q8#1062190012yes—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—432no—
552C2×D4—864no—
553C2×D4—864no—
554C2×D4—861no—
555C2×D4—861no—
556C2×D4—861no—
557C2×D4—861no—
558C2×D4—861no—
559C2×D4—1722no—
560C2×D4—1722no—
561C2×D4—1722no—
562C2×D4—1722no—
563C2×D4C2×C4×D4312yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—431no—
568C22×C4—431no—
569C22×C4—432no—
570C22×C4—432no—
571C22×C4—431no—
572C22×C4—864no—
573C22×C4—861no—
574C22×C4—861no—
575C22×C4—861no—
576C22×C4—861no—
577C22×C4—861no—
578C22×C4—861no—
579C22×C4—861no—
580C22×C4—3441no—
581C22×C4—3441no—
582C22×C4—1722no—
583C22×C4—1722no—
584C22×C4—1722no—
585C22×C4—1722no—
586C22×C4—1722no—
587C22×C4—1722no—
588C22×C4D4×D4311yescharacteristic
589C22×C4D4×D4311yescharacteristic
590C22×C4C23×D4311yescharacteristic
591SD16—28no—
592D8—1724no—
593M16—1724no—
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×C4×D4312yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—42no—
611C4⋊C4—432no—
612C4⋊C4—432no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4—861no—
616C4⋊C4—861no—
617C4⋊C4—1722no—
618C4⋊C4—1722no—
619C4⋊C4—1722no—
620C22⋊C4—42no—
621C22⋊C4—81no—
622C22⋊C4—862no—
623C22⋊C4—864no—
624C22⋊C4—3441no—
625C22⋊C4—3441no—
626C22⋊C4—3441no—
627C22⋊C4—1721no—
628C22⋊C4—1722no—
629C22⋊C4—1722no—
630C22⋊C4—1722no—
631C42—21no—
632C42—21no—
633C42—42no—
634C42—861no—
635C42—861no—
636C42—1722no—
637C42—1722no—
638C23—22no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—432no—
646C23—861no—
647C23—861no—
648C23—861no—
649C23—861no—
650C23—861no—
651C23—861no—
652C23—862no—
653C23—1721no—
654C23—1721no—
655C23—1721no—
656C23—1721no—
657C23—1721no—
658C23—1721no—
659C23C2×D4×D4311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8(C22⋊D43)⋊C414yescomplemented
664D4—22no—
665D4—22no—
666D4—41no—
667D4—41no—
668D4—862no—
669D4—862no—
670D4—1728no—
671D4—1728no—
672D4—1721no—
673D4—1721no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—432no—
690C2×C4—432no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—861no—
695C2×C4—862no—
696C2×C4—862no—
697C2×C4—862no—
698C2×C4—862no—
699C2×C4—862no—
700C2×C4—861no—
701C2×C4—861no—
702C2×C4—861no—
703C2×C4—862no—
704C2×C4—3444no—
705C2×C4—3444no—
706C2×C4—1728no—
707C2×C4—1721no—
708C2×C4—1721no—
709C2×C4—1721no—
710C2×C4—1721no—
711C2×C4—1721no—
712C2×C4—1721no—
713C2×C4—1721no—
714C2×C4C22×C4×D4311yescharacteristic
715C2×C4C2×D4×D4311yescharacteristic
716C2×C4#41×D4311yescharacteristic
717C2×C4C2×#1062190011yescharacteristic
718C2×C4#1306337011yescharacteristic
719C2×C4#1306337111yescharacteristic
720C8—22no—
721C8—41no—
722C8—862no—
723C8—862no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22—862no—
732C22—862no—
733C22—862no—
734C22—3441no—
735C22—3441no—
736C22—3441no—
737C22—3441no—
738C22—1722no—
739C22—1722no—
740C22—1722no—
741C22—1721no—
742C22—1721no—
743C22—1721no—
744C22—1721no—
745C22C4×D4×D4311yescharacteristic
746C22#1458353311yescharacteristic
747C22#1458353611yescharacteristic
748C22AGL(1,ℤ/8)×D4311yescharacteristic
749C22#1458369811yescharacteristic
750C22#1458370511yescharacteristic
751C22#1458370611yescharacteristic
752C4—24no—
753C4—41no—
754C4—41no—
755C4—81no—
756C4—81no—
757C4—862no—
758C4—862no—
759C4—3441no—
760C4—1722no—
761C4—1721no—
762C4—1722no—
763C4C2×(C22⋊D43)⋊C411yescharacteristic
764C4#1458337111yescharacteristic
765C4#1458353811yescharacteristic
766C4#1458357211yescharacteristic
767C2—82no—
768C2—3442no—
769C2—1722no—
770C2#1913757511yescharacteristic
771C2#1914340011yescharacteristic
772C2#1914347311yescharacteristic
773C2#1914608511yescharacteristic
774C2#1914618611yescharacteristic
775C2#1914685211yescharacteristic
776C2#1914691511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1880C2
socleC23×C43C22×D4
prime radicalC2×#14583043C2
cosocleC22×C4×C43C24
hypercenter#1880D43
hypocenterC43#22883
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×SD16×Dic43C2semidirect
3. C2×#14582899C2semidirect
4. #19137616C2semidirect
5. #19137433C2semidirect
6. #19135470C2semidirect
7. #19135276C2semidirect
8. #19135223C2semidirect
9. #19135030C2semidirect
10. #19134941C2semidirect
11. #19134861C2semidirect
12. #19134789C2semidirect
13. #19134425C2semidirect
14. #19134377C2semidirect
15. C43×#1880C2semidirect
24. #14583043C4semidirect
67. C2×#10621902C2×C4semidirect
77. C2×#10621882C2×C4semidirect
112. #13063249C2×C4semidirect
113. #13063249D4semidirect
115. #13063247C2×C4semidirect
118. (C2×D43)⋊C8C2×C4semidirect
130. C2×SD16×C43C2×C4semidirect
274. Q8×C43C4×D4semidirect
388. #1880D43semidirect
450. C43#22883semidirect
468. C2×SD16C4×D43semidirect
663. Q8(C22⋊D43)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#145830432
C2×SD16×Dic432
C2×#145828992
#191376162
#191374332
#191354702
#191352762
#191352232
#191350302
#191349412
#191348612
#191347892
#191344252
#191343772
C43×#18802
#2288343