Finite Group Databasebeta

← #25112366

Subgroups — #25112366

Order 11008.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063351C211yesmaximal, characteristic
2C2×#14583008C211yesmaximal, characteristic, complemented
3C2×#14582979C211yesmaximal, characteristic, complemented
4#19137423C211yesmaximal, characteristic, complemented
5D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
6#19135477C211yesmaximal, characteristic, complemented
7#19135450C211yesmaximal, characteristic, complemented
8#19134940C211yesmaximal, characteristic, complemented
9#19134940C211yesmaximal, characteristic, complemented
10#19134927C211yesmaximal, characteristic, complemented
11#19134927C211yesmaximal, characteristic, complemented
12#19134626C211yesmaximal, characteristic, complemented
13#19134536C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C43×#1786C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C2×#13063351—24no—
18C2×#13063351—24no—
19C2×#13063351C418yescomplemented
20C22×#10621883C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621877C2211yescharacteristic
25C2×D4×Dic43C2211yescharacteristic
26C2×D4×Dic43C2211yescharacteristic
27C2×#13063287C2211yescharacteristic, complemented
28C2×#13063287C2211yescharacteristic, complemented
29C22×C22⋊Dic43—21no—
30#14583008—24no—
31#14582979—24no—
32C2×#13063258C2211yescharacteristic, complemented
33C2×#13063256C2211yescharacteristic, complemented
34C2×#13063250C2211yescharacteristic, complemented
35C2×#13063250C2211yescharacteristic, complemented
36C2×#13063247C2211yescharacteristic, complemented
37C2×#13063247C2211yescharacteristic, complemented
38C2×#13063235C2211yescharacteristic, complemented
39C2×C8×Dic43C2211yescharacteristic, complemented
40#14582804C2211yescharacteristic, complemented
41#14582804C2211yescharacteristic, complemented
42#14582802C2211yescharacteristic
43#14582802C2211yescharacteristic
44#14582779—21no—
45#14582779—21no—
46#14582775—21no—
47#14582775—21no—
48#14582761—21no—
49#14582759C2211yescharacteristic
50#14582755—21no—
51C4×C22⋊Dic43C2211yescharacteristic
52#95×D43—21no—
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C23×D4×C43C2211yescharacteristic
58C2×#102×C43C2211yescharacteristic
59C2×#102×C43C2211yescharacteristic
60C2×#102×C43C2211yescharacteristic
61C2×#102×C43C2211yescharacteristic
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C2×#10621898—22no—
65C2×#10621898—22no—
66C2×#10621898—22no—
67C2×#10621898—41no—
68C2×#10621898—41no—
69C2×#10621898C2×C414yescomplemented
70C22×Dic86C2311yescharacteristic
71C22×D172C2311yescharacteristic
72C22×C22⋊D43—21no—
73C23×Dic43—21no—
74C23×Dic43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43—21no—
78#13063351—232no—
79C2×#10621883—22no—
80C2×#10621883—22no—
81C2×#10621883—22no—
82C2×#10621883—22no—
83C2×#10621883C2×C414yescomplemented
84C2×#10621883C2×C414yescomplemented
85C2×#10621882—22no—
86C2×#10621882—22no—
87C2×#10621882C2×C414yes—
88C2×#10621882C2×C414yescomplemented
89C2×#10621882D414yes—
90C2×#10621882D414yes—
91C2×#10621877—22no—
92C2×#10621877—22no—
93C2×#10621877C2×C414yescomplemented
94C22×C43⋊C8C2311yescharacteristic
95C22×C43⋊C8C2311yescharacteristic
96D4×Dic43—22no—
97D4×Dic43—22no—
98D4×Dic43—41no—
99D4×Dic43—41no—
100#13063287—22no—
101#13063287—22no—
102#13063287—41no—
103#13063287—41no—
104C2×C4⋊Dic43C2311yescharacteristic
105C2×C4⋊Dic43C2311yescharacteristic
106C2×C22⋊Dic43—21no—
107C2×C22⋊Dic43—21no—
108C2×C22⋊Dic43—21no—
109C2×C22⋊Dic43—21no—
110C2×C22⋊Dic43—21no—
111C2×C22⋊Dic43—21no—
112C2×C22⋊Dic43—21no—
113C2×C22⋊Dic43—44no—
114C2×C22⋊Dic43D411yescharacteristic
115C2×C22⋊Dic43D411yescharacteristic
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×C4×Dic43C2311yescharacteristic
119C2×C4×Dic43C2311yescharacteristic
120#13063258—22no—
121#13063256—22no—
122#13063250—41no—
123#13063250—41no—
124#13063247—22no—
125#13063247—22no—
126#13063235—22no—
127C8×Dic43—22no—
128C43⋊#95—21no—
129C43⋊#95—21no—
130C43⋊#95—21no—
131C43⋊#95—21no—
132C43⋊#95—21no—
133C43⋊#95D411yescharacteristic
134C43⋊#95D411yescharacteristic
135C25×C43—21no—
136C22×D4×C43—22no—
137C22×D4×C43—22no—
138C22×D4×C43—21no—
139C22×D4×C43—22no—
140C22×D4×C43—41no—
141C22×D4×C43—41no—
142C22×D4×C43C2×C414yescomplemented
143C22×D4×C43C2311yescharacteristic
144C22×D4×C43C2311yescharacteristic
145C23×C4×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—21no—
151#102×C43—22no—
152#102×C43—22no—
153#102×C43—41no—
154#102×C43—41no—
155C22⋊C8×C43—22no—
156#95×C43—21no—
157C24×C43—21no—
158C24×C43—21no—
159C24×C43—24no—
160C24×C43—42no—
161C24×C43—42no—
162C24×C43—42no—
163C24×C43—42no—
164C24×C43—81no—
165C24×C43—81no—
166C24×C43C2×D411yescharacteristic
167C23×D43—21no—
168C2×D4×C43—24no—
169C2×D4×C43—21no—
170C2×D4×C43—21no—
171C2×D4×C43—21no—
172C2×D4×C43—21no—
173C2×D4×C43—28no—
174C2×D4×C43—21no—
175C2×D4×C43—21no—
176C2×D4×C43—21no—
177C2×D4×C43—21no—
178C2×D4×C43—42no—
179C2×D4×C43—42no—
180C2×D4×C43—44no—
181C2×D4×C43—44no—
182C2×D4×C43—44no—
183C2×D4×C43C22×C412yes—
184C2×D4×C43C22×C412yes—
185C2×D4×C43C2×D412yes—
186C2×D4×C43C2×D412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43C22×C412yes—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43#4112yes—
196C22×C4×C43C2411yescharacteristic
197C2×C22⋊D43—24no—
198C2×C22⋊D43—42no—
199C2×C22⋊D43—42no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43—42no—
204C22×Dic43—42no—
205C22×Dic43—42no—
206C22×Dic43—42no—
207C22×Dic43—81no—
208C22×Dic43—81no—
209C22×Dic43C2×D411yescharacteristic
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213#10621898—28no—
214#10621898—44no—
215#10621898—44no—
216#10621898—44no—
217C2×D172—21no—
218C2×D172—21no—
219C2×D172—21no—
220C2×D172C22×C412yes—
221C2×D172C2×D412yes—
222C2×D172C2×D412yes—
223C2×C4×D43—24no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×C4×D43—42no—
227C2×C4×D43—42no—
228C2×C4×D43—42no—
229C2×C4×D43—42no—
230C2×C4×D43—81no—
231C2×C4×D43—81no—
232C2×Dic86—21no—
233C2×Dic86—21no—
234C2×Dic86—21no—
235C2×Dic86—21no—
236C2×Dic86—21no—
237C2×Dic86C22×C412yes—
238C2×C8×C43—21no—
239C2×C8×C43—21no—
240C2×C8×C43—21no—
241C2×C8×C43—21no—
242C2×C8×C43—21no—
243C2×C8×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43—21no—
246C4⋊C4×C43—21no—
247C4⋊C4×C43—21no—
248C22⋊C4×C43—81no—
249C22⋊Dic43—22no—
250C22⋊Dic43—41no—
251C22⋊Dic43—42no—
252C22⋊Dic43—42no—
253C22⋊Dic43—42no—
254C22⋊Dic43—42no—
255C22⋊Dic43—42no—
256C22⋊Dic43—81no—
257C22⋊Dic43—81no—
258#10621883—28no—
259#10621883—28no—
260#10621882—28no—
261#10621882C22⋊C4116yescomplemented
262(C2×D43)⋊C4—42no—
263(C2×D43)⋊C4—42no—
264C4⋊Dic43—21no—
265C4⋊Dic43—21no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4×Dic43—21no—
269C4×Dic43—21no—
270C4×Dic43—21no—
271C4×Dic43—21no—
272#10621877—28no—
273C2×C43⋊C8—21no—
274C2×C43⋊C8—21no—
275C2×C43⋊C8C22×C412yes—
276C2×C43⋊C8C22×C412yes—
277C2×C43⋊C8C2×D412yes—
278C2×C43⋊C8C2×D412yes—
279C23×C43—22no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—21no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—22no—
289C23×C43—48no—
290C23×C43—48no—
291C23×C43—41no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—41no—
295C23×C43—41no—
296C23×C43—41no—
297C23×C43—41no—
298C23×C43—41no—
299C23×C43—41no—
300C23×C43—41no—
301C23×C43—84no—
302C23×C43—84no—
303C23×C43—84no—
304C23×C43—84no—
305C23×C43—84no—
306C23×C43C4×D412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—41no—
312C22×D43—41no—
313C22×D43—41no—
314C22×D43—41no—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—48no—
321D4×C43—41no—
322D4×C43—41no—
323D4×C43C2×C22⋊C414yes—
324C2×C4×C43—21no—
325C2×C4×C43—21no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—41no—
331C2×C4×C43—41no—
332C2×C4×C43—41no—
333C2×C4×C43—41no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43C4×D412yes—
337C2×C4×C43C23×C411yescharacteristic
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×D411yescharacteristic
340C2×C4×C43C2×#4111yescharacteristic
341C2×C4×C43H(5,𝔽2)11yescharacteristic
342C2×C4×C43H(5,𝔽2)11yescharacteristic
343C22⋊D43—48no—
344C2×Dic43—21no—
345C2×Dic43—21no—
346C2×Dic43—22no—
347C2×Dic43—21no—
348C2×Dic43—21no—
349C2×Dic43—21no—
350C2×Dic43—21no—
351C2×Dic43—21no—
352C2×Dic43—21no—
353C2×Dic43—21no—
354C2×Dic43—21no—
355C2×Dic43—21no—
356C2×Dic43—41no—
357C2×Dic43—41no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43—84no—
365C2×Dic43—84no—
366C2×Dic43AGL(1,ℤ/8)12yescomplemented
367D172—22no—
368D172—22no—
369D172—22no—
370D172C2×C22⋊C414yescomplemented
371C4×D43—48no—
372C4×D43—84no—
373C4×D43—84no—
374Dic86—22no—
375Dic86—22no—
376Dic86—41no—
377Dic86—41no—
378C8×C43—41no—
379C8×C43—41no—
380C43⋊C8—22no—
381C43⋊C8C2×C22⋊C414yescomplemented
382#22442—431nomaximal, Sylow
383C22×C43—24no—
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—42no—
388C22×C43—42no—
389C22×C43—41no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—41no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—42no—
400C22×C43—816no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43—81no—
404C22×C43—81no—
405C22×C43C2×C4×D411yescharacteristic
406C22×C43D4211yescharacteristic
407C22×C43D4211yescharacteristic
408C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
409C22×C43#57511yescharacteristic
410C22×C43#57611yescharacteristic
411C22×C43#57711yescharacteristic
412C2×D43—24no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—42no—
419C4×C43—22no—
420C4×C43—81no—
421C4×C43—81no—
422C4×C43C22×C22⋊C411yescharacteristic
423C4×C43#51811yescharacteristic
424C4×C43#54611yescharacteristic
425C4×C43#54611yescharacteristic
426Dic43—22no—
427Dic43—42no—
428Dic43—41no—
429Dic43—41no—
430Dic43—41no—
431Dic43—81no—
432Dic43—81no—
433C22×AGL(1,ℤ/8)—431no—
434C2×#442—431no—
435C2×C4×D8—431no—
436#2339—431no—
437D4×C22⋊C4—431no—
438#1973—431no—
439#1968—431no—
440#1879—431no—
441#1879—431no—
442#1877—431no—
443#1877—431no—
444#1809—431no—
445#1788—431no—
446#1786D4311yescharacteristic, complemented
447#1753—431no—
448C2×C43—42no—
449C2×C43—44no—
450C2×C43—82no—
451C2×C43D4×C22⋊C411yescharacteristic
452C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
453C2×C43#294611yescharacteristic
454C2×C43#326411yescharacteristic
455C2×C43#326711yescharacteristic
456C2×C43#327211yescharacteristic
457C2×C43#327311yescharacteristic
458D43—44no—
459C22×#41—431no—
460C23×D4C2×D4311yescharacteristic
461C2×AGL(1,ℤ/8)—438no—
462C2×AGL(1,ℤ/8)—864no—
463C2×AGL(1,ℤ/8)—864no—
464C22×SD16—431no—
465C22×SD16—431no—
466C22×D8—431no—
467C22×D8—431no—
468C22×M16—431no—
469C2×C4×D4—431no—
470C2×C4×D4—431no—
471C2×C4×D4—431no—
472C2×C4×D4—431no—
473C22×C22⋊C4—861no—
474#442—864no—
475C4×D8—864no—
476C2×#107—431no—
477C2×#106—431no—
478C2×#103—431no—
479C2×#103—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102C2×D4311yescharacteristic
483C2×#102C2×D4311yescharacteristic
484C2×#102C2×D4311yescharacteristic
485C2×#102C2×D4311yescharacteristic
486C2×C22⋊C8C2×D4311yescharacteristic
487C2×#97—431no—
488C2×C4×C8—431no—
489#391—431no—
490#391—431no—
491#390—431no—
492#390—431no—
493#386—861no—
494#386—861no—
495#386—861no—
496#386—861no—
497#381—861no—
498#380—431no—
499#380C2×D4311yescharacteristic
500#379—861no—
501C4×C22⋊C4—431no—
502C2×#95—861no—
503#340—431no—
504#340—431no—
505#336—431no—
506#336—431no—
507C43#2244211yescharacteristic, complemented, Sylow
508C25—21no—
509C2×#41—434no—
510C2×#41—862no—
511C2×#41—862no—
512C2×#41—862no—
513C2×#41—1721no—
514C2×#41—1721no—
515C22×Q8—431no—
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—431no—
523C22×D4—861no—
524C22×D4C4×D4314yescomplemented
525C22×D4C22×D4311yescharacteristic
526C22×D4C22×D4311yescharacteristic
527C23×C4—861no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4—861no—
531C23×C4—861no—
532C23×C4C22×D4311yescharacteristic
533AGL(1,ℤ/8)—8632no—
534C2×SD16—434no—
535C2×SD16—434no—
536C2×SD16—862no—
537C2×SD16—862no—
538C2×SD16—862no—
539C2×SD16—862no—
540C2×D8—434no—
541C2×D8—434no—
542C2×D8—434no—
543C2×D8—434no—
544C2×D8—862no—
545C2×D8—862no—
546C2×M16—434no—
547C2×M16—862no—
548C2×M16—862no—
549C22×C8—431no—
550C22×C8—431no—
551C22×C8C22×D4311yescharacteristic
552C22×C8C22×D4311yescharacteristic
553C4×D4—862no—
554C4×D4—862no—
555C4×D4—862no—
556C4×D4—862no—
557C4×D4—1721no—
558C4×D4—1721no—
559C4×D4—1721no—
560C4×D4—1721no—
561C2×C4⋊C4—431no—
562C2×C4⋊C4—431no—
563C2×C4⋊C4C22×D4311yescharacteristic
564C2×C4⋊C4C22×D4311yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—431no—
567C2×C22⋊C4—431no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C22⋊C4—861no—
572C2×C22⋊C4—861no—
573C2×C22⋊C4—861no—
574C2×C22⋊C4—861no—
575C2×C22⋊C4—861no—
576C2×C22⋊C4—861no—
577C2×C22⋊C4—1724no—
578C2×C42—431no—
579C2×C42—431no—
580#107—862no—
581#106—862no—
582#103—1721no—
583#103—1721no—
584#102—22no—
585#102—22no—
586#102—41no—
587#102—41no—
588#102—862no—
589#102—862no—
590C22⋊C8—22no—
591#97—862no—
592C4×C8—862no—
593#95—21no—
594#95—431no—
595#95—431no—
596#95—861no—
597#95—861no—
598#95—861no—
599#95—861no—
600#95—861no—
601C24—21no—
602C24—21no—
603C24—24no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—81no—
609C24—81no—
610C24—861no—
611C24D4×D4311yescharacteristic
612#41—868no—
613#41—1724no—
614#41—1724no—
615#41—1724no—
616C2×Q8—432no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×Q8—861no—
621C2×Q8—861no—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—44no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—42no—
637C2×D4—432no—
638C2×D4—432no—
639C2×D4—432no—
640C2×D4—864no—
641C2×D4—861no—
642C2×D4—861no—
643C2×D4—861no—
644C2×D4—1722no—
645C2×D4—1722no—
646C2×D4C2×C4×D4312yes—
647C2×D4C2×C4×D4312yes—
648C2×D4D4×D4312yes—
649C2×D4D4×D4312yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—861no—
661C22×C4—864no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—3441no—
665C22×C4—3441no—
666C22×C4—3441no—
667C22×C4—3441no—
668C22×C4—1722no—
669C22×C4—1722no—
670C22×C4—1722no—
671C22×C4—1722no—
672C22×C4—1722no—
673C22×C4—1722no—
674C22×C4—1722no—
675C22×C4—1722no—
676C22×C4—1722no—
677C22×C4—1722no—
678C22×C4C2×C4×D4312yes—
679C22×C4D4×D4311yescharacteristic
680C22×C4#1062190012yes—
681C22×C4C23×D4311yescharacteristic
682SD16—868no—
683SD16—868no—
684D8—4316no—
685D8—868no—
686M16—868no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—432no—
694C2×C8—432no—
695C2×C8—432no—
696C2×C8—432no—
697C2×C8—861no—
698C2×C8—861no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—861no—
704C4⋊C4—861no—
705C4⋊C4—861no—
706C4⋊C4—861no—
707C22⋊C4—81no—
708C22⋊C4—862no—
709C22⋊C4—3441no—
710C22⋊C4—3441no—
711C22⋊C4—1722no—
712C22⋊C4—1722no—
713C22⋊C4—1722no—
714C22⋊C4—1721no—
715C22⋊C4—1722no—
716C22⋊C4—1722no—
717C22⋊C4—1722no—
718C22⋊C4—1722no—
719C42—861no—
720C42—861no—
721C42—861no—
722C42—861no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—22no—
729C23—22no—
730C23—21no—
731C23—21no—
732C23—22no—
733C23—48no—
734C23—48no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—84no—
749C23—84no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—1721no—
754C23—1721no—
755C23—1721no—
756C23—1721no—
757C23(C22⋊D43)⋊C412yes—
758C23C2×D4×D4311yescharacteristic
759Q8—862no—
760Q8—862no—
761Q8—1721no—
762Q8—1721no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—41no—
770D4—41no—
771D4—434no—
772D4—862no—
773D4—862no—
774D4—862no—
775D4—1728no—
776D4C22⋊C4×D4314yes—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—432no—
790C2×C4—861no—
791C2×C4—861no—
792C2×C4—862no—
793C2×C4—861no—
794C2×C4—861no—
795C2×C4—861no—
796C2×C4—861no—
797C2×C4—861no—
798C2×C4—861no—
799C2×C4—861no—
800C2×C4—861no—
801C2×C4—861no—
802C2×C4—3444no—
803C2×C4—3444no—
804C2×C4—3444no—
805C2×C4—3444no—
806C2×C4—1728no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4—1721no—
812C2×C4—1721no—
813C2×C4—1721no—
814C2×C4—1721no—
815C2×C4(C22⋊D43)⋊C412yes—
816C2×C4C22×C4×D4311yescharacteristic
817C2×C4C2×D4×D4311yescharacteristic
818C2×C4C2×D4×D4311yescharacteristic
819C2×C4C2×#1062190011yescharacteristic
820C2×C4#1306337011yescharacteristic
821C2×C4#1306337011yescharacteristic
822C8—41no—
823C8—41no—
824C8—434no—
825C8—862no—
826C22—22no—
827C22—24no—
828C22—22no—
829C22—22no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—41no—
836C22—41no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—816no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—864no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22C2×(C22⋊D43)⋊C411yescharacteristic
856C22#1458353111yescharacteristic
857C22#1458353111yescharacteristic
858C22AGL(1,ℤ/8)×D4311yescharacteristic
859C22#1458369511yescharacteristic
860C22#1458370011yescharacteristic
861C22#1458370511yescharacteristic
862C4—22no—
863C4—81no—
864C4—81no—
865C4—862no—
866C4—3441no—
867C4—3441no—
868C4—1722no—
869C4—1721no—
870C4—1721no—
871C4—1721no—
872C4C2×C22⋊C4×D4311yescharacteristic
873C4#1458337211yescharacteristic
874C4#1458353611yescharacteristic
875C4#1458353611yescharacteristic
876C2—42no—
877C2—44no—
878C2—82no—
879C2—1724no—
880C2#1913741111yescharacteristic
881C2#1914339911yescharacteristic
882C2#1914342111yescharacteristic
883C2#1914607311yescharacteristic
884C2#1914611811yescharacteristic
885C2#1914619311yescharacteristic
886C2#1914620611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1786C2
socleC23×C43C22×D4
prime radicalC22×#13063351C2
cosocleC22×C4×C43C24
hypercenter#1786D43
hypocenterC43#22442
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1786

Complements

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

NH ≅ G/Ntype
2. C2×#14583008C2semidirect
3. C2×#14582979C2semidirect
4. #19137423C2semidirect
5. D4×C22⋊Dic43C2semidirect
6. #19135477C2semidirect
7. #19135450C2semidirect
8. #19134940C2semidirect
9. #19134940C2semidirect
10. #19134927C2semidirect
11. #19134927C2semidirect
12. #19134626C2semidirect
13. #19134536C2semidirect
14. #19134381C2semidirect
15. C43×#1786C2semidirect
19. C2×#13063351C4semidirect
27. C2×#13063287C22semidirect
28. C2×#13063287C22semidirect
32. C2×#13063258C22semidirect
33. C2×#13063256C22semidirect
34. C2×#13063250C22semidirect
35. C2×#13063250C22semidirect
36. C2×#13063247C22semidirect
37. C2×#13063247C22semidirect
38. C2×#13063235C22semidirect
39. C2×C8×Dic43C22semidirect
40. #14582804C22semidirect
41. #14582804C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
69. C2×#10621898C2×C4semidirect
83. C2×#10621883C2×C4semidirect
84. C2×#10621883C2×C4semidirect
88. C2×#10621882C2×C4semidirect
93. C2×#10621877C2×C4semidirect
142. C22×D4×C43C2×C4semidirect
261. #10621882C22⋊C4semidirect
366. C2×Dic43AGL(1,ℤ/8)semidirect
370. D172C2×C22⋊C4semidirect
381. C43⋊C8C2×C22⋊C4semidirect
446. #1786D43semidirect
507. C43#22442semidirect
524. C22×D4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633512
C2×#145830082
C2×#145829792
#191374232
D4×C22⋊Dic432
#191354772
#191354502
#191349402
#191349272
#191346262
#191345362
#191343812
C43×#17862
#2244243