Finite Group Databasebeta

← #25112381

Subgroups — #25112381

Order 11008.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063351C211yesmaximal, characteristic
2C2×#14582996C211yesmaximal, characteristic, complemented
3C2×#14582990C211yesmaximal, characteristic, complemented
4#19137432C211yesmaximal, characteristic, complemented
5D4×C22⋊Dic43C211yesmaximal, characteristic, complemented
6#19135468C211yesmaximal, characteristic, complemented
7#19135458C211yesmaximal, characteristic, complemented
8#19134947C211yesmaximal, characteristic, complemented
9#19134947C211yesmaximal, characteristic, complemented
10#19134941C211yesmaximal, characteristic, complemented
11#19134941C211yesmaximal, 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×#13063290C2211yescharacteristic, complemented
26C2×#13063290C2211yescharacteristic, complemented
27C2×D4×Dic43C2211yescharacteristic
28C2×D4×Dic43C2211yescharacteristic
29C22×C22⋊Dic43—21no—
30#14582996—24no—
31#14582990—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#14582802C2211yescharacteristic
41#14582802C2211yescharacteristic
42#14582800C2211yescharacteristic, complemented
43#14582800C2211yescharacteristic, complemented
44#14582799—21no—
45#14582799—21no—
46#14582779—21no—
47#14582779—21no—
48#14582759C2211yescharacteristic
49#14582758—21no—
50#14582755—21no—
51C4×C22⋊Dic43C2211yescharacteristic
52#14582746—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—
76#13063351—232no—
77C2×#10621883—22no—
78C2×#10621883—22no—
79C2×#10621883C2×C414yes—
80C2×#10621883C2×C414yescomplemented
81C2×#10621883D414yes—
82C2×#10621883D414yes—
83C2×#10621882—22no—
84C2×#10621882—22no—
85C2×#10621882—22no—
86C2×#10621882—22no—
87C2×#10621882C2×C414yes—
88C2×#10621882C2×C414yescomplemented
89C2×#10621877—22no—
90C2×#10621877—22no—
91C2×#10621877C2×C414yescomplemented
92C22×C43⋊C8C2311yescharacteristic
93C22×C43⋊C8C2311yescharacteristic
94#13063290—22no—
95#13063290—22no—
96#13063290—41no—
97#13063290—41no—
98D4×Dic43—22no—
99D4×Dic43—22no—
100D4×Dic43—41no—
101D4×Dic43—41no—
102C2×C4⋊Dic43C2311yescharacteristic
103C2×C4⋊Dic43C2311yescharacteristic
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4—21no—
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×(C2×D43)⋊C4—21no—
119C2×(C2×D43)⋊C4—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123C2×C4×Dic43C2311yescharacteristic
124#13063258—22no—
125#13063256—22no—
126#13063250—22no—
127#13063250—22no—
128#13063247—41no—
129#13063247—41no—
130#13063235—22no—
131C8×Dic43—22no—
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×C414yes—
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×D172—21no—
221C2×D172—21no—
222C2×D172C22×C412yes—
223C2×C4×D43—24no—
224C2×C4×D43—42no—
225C2×C4×D43—42no—
226C2×Dic86—21no—
227C2×Dic86—21no—
228C2×Dic86—21no—
229C2×Dic86C22×C412yes—
230C2×Dic86C2×D412yes—
231C2×Dic86C2×D412yes—
232C2×C8×C43—21no—
233C2×C8×C43—21no—
234C2×C8×C43—21no—
235C2×C8×C43—21no—
236C2×C8×C43—21no—
237C2×C8×C43—21no—
238C4⋊C4×C43—21no—
239C4⋊C4×C43—21no—
240C4⋊C4×C43—21no—
241C4⋊C4×C43—21no—
242C22⋊C4×C43—81no—
243C22⋊Dic43—22no—
244C22⋊Dic43—41no—
245C22⋊Dic43—42no—
246C22⋊Dic43—42no—
247C22⋊Dic43—42no—
248C22⋊Dic43—42no—
249C22⋊Dic43—42no—
250C22⋊Dic43—81no—
251C22⋊Dic43—81no—
252#10621883—28no—
253#10621883C22⋊C4116yescomplemented
254#10621882—28no—
255#10621882—28no—
256(C2×D43)⋊C4—42no—
257(C2×D43)⋊C4—42no—
258(C2×D43)⋊C4—81no—
259(C2×D43)⋊C4—81no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264Dic43⋊C4—42no—
265Dic43⋊C4—42no—
266C4×Dic43—21no—
267C4×Dic43—21no—
268C4×Dic43—21no—
269C4×Dic43—21no—
270C4×Dic43—42no—
271C4×Dic43—42no—
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—41no—
310C22×D43—41no—
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—22no—
345C2×Dic43—21no—
346C2×Dic43—22no—
347C2×Dic43—22no—
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—21no—
357C2×Dic43—21no—
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—41no—
370D172—41no—
371C4×D43—48no—
372Dic86—22no—
373Dic86—22no—
374Dic86—22no—
375Dic86C2×C22⋊C414yescomplemented
376C8×C43—41no—
377C8×C43—41no—
378C43⋊C8—22no—
379C43⋊C8C2×C22⋊C414yescomplemented
380#22443—431nomaximal, Sylow
381C22×C43—24no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—22no—
385C22×C43—42no—
386C22×C43—42no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—41no—
390C22×C43—42no—
391C22×C43—41no—
392C22×C43—42no—
393C22×C43—41no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—816no—
399C22×C43—81no—
400C22×C43—81no—
401C22×C43—81no—
402C22×C43—81no—
403C22×C43C2×C4×D411yescharacteristic
404C22×C43D4211yescharacteristic
405C22×C43D4211yescharacteristic
406C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
407C22×C43#57511yescharacteristic
408C22×C43#57611yescharacteristic
409C22×C43#57711yescharacteristic
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—81no—
414C2×D43—81no—
415C2×D43—81no—
416C2×D43—81no—
417C4×C43—22no—
418C4×C43—81no—
419C4×C43—81no—
420C4×C43C22×C22⋊C411yescharacteristic
421C4×C43#51811yescharacteristic
422C4×C43#54611yescharacteristic
423C4×C43#54611yescharacteristic
424Dic43—24no—
425Dic43—22no—
426Dic43—41no—
427Dic43—41no—
428Dic43—41no—
429Dic43—81no—
430Dic43—81no—
431C22×AGL(1,ℤ/8)—431no—
432C2×#440—431no—
433C2×C4×SD16—431no—
434#2341—431no—
435D4×C22⋊C4—431no—
436#1972—431no—
437#1970—431no—
438#1880—431no—
439#1880—431no—
440#1879—431no—
441#1879—431no—
442#1809—431no—
443#1788—431no—
444#1786D4311yescharacteristic, complemented
445#1753—431no—
446C2×C43—42no—
447C2×C43—44no—
448C2×C43—82no—
449C2×C43D4×C22⋊C411yescharacteristic
450C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
451C2×C43#294611yescharacteristic
452C2×C43#326511yescharacteristic
453C2×C43#326811yescharacteristic
454C2×C43#327411yescharacteristic
455C2×C43#327511yescharacteristic
456D43—82no—
457C22×#41—431no—
458C23×D4C2×D4311yescharacteristic
459C2×AGL(1,ℤ/8)—438no—
460C2×AGL(1,ℤ/8)—864no—
461C2×AGL(1,ℤ/8)—864no—
462C22×SD16—431no—
463C22×SD16—431no—
464C22×D8—431no—
465C22×D8—431no—
466C22×M16—431no—
467C2×C4×Q8—431no—
468C2×C4×Q8—431no—
469C2×C4×D4—431no—
470C2×C4×D4—431no—
471C22×C22⋊C4—861no—
472#440—864no—
473C4×SD16—864no—
474C2×#107—431no—
475C2×#106—431no—
476C2×#103—431no—
477C2×#103—431no—
478C2×#102—431no—
479C2×#102—431no—
480C2×#102C2×D4311yescharacteristic
481C2×#102C2×D4311yescharacteristic
482C2×#102C2×D4311yescharacteristic
483C2×#102C2×D4311yescharacteristic
484C2×C22⋊C8C2×D4311yescharacteristic
485C2×#97—431no—
486C2×C4×C8—431no—
487#390—431no—
488#390—431no—
489#390—431no—
490#390—431no—
491#390—861no—
492#390—861no—
493#386—861no—
494#386—861no—
495#380—431no—
496#380—861no—
497#380C2×D4311yescharacteristic
498#379—861no—
499C4×C22⋊C4—431no—
500C4×C22⋊C4—861no—
501#340—431no—
502#340—431no—
503#336—431no—
504#336—431no—
505C43#2244311yescharacteristic, complemented, Sylow
506C25—21no—
507C2×#41—434no—
508C2×#41—862no—
509C2×#41—862no—
510C2×#41—862no—
511C2×#41—1721no—
512C2×#41—1721no—
513C22×Q8—431no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—22no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—431no—
521C22×D4—861no—
522C22×D4C4×D4314yes—
523C22×D4C22×D4311yescharacteristic
524C22×D4C22×D4311yescharacteristic
525C23×C4—861no—
526C23×C4—861no—
527C23×C4—861no—
528C23×C4C22×D4311yescharacteristic
529AGL(1,ℤ/8)—8632no—
530C2×SD16—434no—
531C2×SD16—434no—
532C2×SD16—434no—
533C2×SD16—434no—
534C2×SD16—862no—
535C2×SD16—862no—
536C2×D8—434no—
537C2×D8—434no—
538C2×D8—862no—
539C2×D8—862no—
540C2×D8—862no—
541C2×D8—862no—
542C2×M16—434no—
543C2×M16—862no—
544C2×M16—862no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8C22×D4311yescharacteristic
548C22×C8C22×D4311yescharacteristic
549C4×Q8—862no—
550C4×Q8—862no—
551C4×Q8—1721no—
552C4×Q8—1721no—
553C4×D4—862no—
554C4×D4—862no—
555C4×D4—1721no—
556C4×D4—1721no—
557C2×C4⋊C4—431no—
558C2×C4⋊C4—431no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C4⋊C4C22×D4311yescharacteristic
562C2×C4⋊C4C22×D4311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—431no—
565C2×C22⋊C4—431no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
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—
580C2×C42—861no—
581C2×C42—861no—
582#107—862no—
583#106—862no—
584#103—862no—
585#103—862no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590#102—1721no—
591#102—1721no—
592C22⋊C8—22no—
593#97—862no—
594C4×C8—862no—
595#95—21no—
596#95—431no—
597#95—431no—
598#95—861no—
599C24—21no—
600C24—21no—
601C24—24no—
602C24—42no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—81no—
607C24—81no—
608C24—861no—
609C24D4×D4311yescharacteristic
610#41—868no—
611#41—1724no—
612#41—1724no—
613#41—1724no—
614C2×Q8—432no—
615C2×Q8—432no—
616C2×Q8—432no—
617C2×Q8—861no—
618C2×Q8—861no—
619C2×Q8—861no—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—44no—
631C2×D4—44no—
632C2×D4—44no—
633C2×D4—42no—
634C2×D4—42no—
635C2×D4—432no—
636C2×D4—864no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—1722no—
643C2×D4—1722no—
644C2×D4C2×C4×D4312yes—
645C2×D4C2×C4×D4312yes—
646C2×D4D4×D4312yes—
647C2×D4D4×D4312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—431no—
658C22×C4—861no—
659C22×C4—864no—
660C22×C4—861no—
661C22×C4—861no—
662C22×C4—3441no—
663C22×C4—3441no—
664C22×C4—1722no—
665C22×C4—1722no—
666C22×C4—1722no—
667C22×C4—1722no—
668C22×C4—1722no—
669C22×C4—1722no—
670C22×C4C2×C4×D4312yes—
671C22×C4D4×D4311yescharacteristic
672C22×C4#1062190012yes—
673C22×C4C23×D4311yescharacteristic
674SD16—4316no—
675SD16—868no—
676D8—868no—
677D8—868no—
678M16—868no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—432no—
686C2×C8—432no—
687C2×C8—432no—
688C2×C8—432no—
689C2×C8—861no—
690C2×C8—861no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4—861no—
699C4⋊C4—1722no—
700C4⋊C4—1722no—
701C22⋊C4—81no—
702C22⋊C4—862no—
703C22⋊C4—3441no—
704C22⋊C4—3441no—
705C22⋊C4—3441no—
706C22⋊C4—3441no—
707C22⋊C4—1722no—
708C22⋊C4—1722no—
709C22⋊C4—1722no—
710C22⋊C4—1721no—
711C22⋊C4—1722no—
712C22⋊C4—1722no—
713C22⋊C4—1722no—
714C22⋊C4—1722no—
715C42—861no—
716C42—861no—
717C42—861no—
718C42—861no—
719C42—1722no—
720C42—1722no—
721C23—22no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—22no—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—48no—
732C23—48no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—84no—
744C23—84no—
745C23—84no—
746C23—84no—
747C23—84no—
748C23—862no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23(C22⋊D43)⋊C412yes—
756C23C2×D4×D4311yescharacteristic
757Q8—434no—
758Q8—862no—
759Q8—862no—
760Q8—862no—
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—48no—
767D4—41no—
768D4—41no—
769D4—862no—
770D4—862no—
771D4—1728no—
772D4—1721no—
773D4—1721no—
774D4C22⋊C4×D4314yes—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—432no—
788C2×C4—862no—
789C2×C4—861no—
790C2×C4—861no—
791C2×C4—862no—
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—1728no—
805C2×C4—1721no—
806C2×C4—1721no—
807C2×C4—1721no—
808C2×C4—1721no—
809C2×C4—1721no—
810C2×C4—1721no—
811C2×C4(C22⋊D43)⋊C412yes—
812C2×C4C22×C4×D4311yescharacteristic
813C2×C4C2×D4×D4311yescharacteristic
814C2×C4C2×D4×D4311yescharacteristic
815C2×C4C2×#1062190011yescharacteristic
816C2×C4#1306337011yescharacteristic
817C2×C4#1306337011yescharacteristic
818C8—41no—
819C8—41no—
820C8—434no—
821C8—862no—
822C22—22no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—42no—
833C22—41no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—816no—
840C22—81no—
841C22—81no—
842C22—81no—
843C22—81no—
844C22—3441no—
845C22—3441no—
846C22—3441no—
847C22—3441no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22C2×(C22⋊D43)⋊C411yescharacteristic
852C22#1458353111yescharacteristic
853C22#1458353111yescharacteristic
854C22AGL(1,ℤ/8)×D4311yescharacteristic
855C22#1458369511yescharacteristic
856C22#1458370011yescharacteristic
857C22#1458370511yescharacteristic
858C4—22no—
859C4—81no—
860C4—81no—
861C4—862no—
862C4—864no—
863C4—3441no—
864C4—3441no—
865C4—1721no—
866C4—1721no—
867C4—1721no—
868C4C2×C22⋊C4×D4311yescharacteristic
869C4#1458337211yescharacteristic
870C4#1458353611yescharacteristic
871C4#1458353611yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—3442no—
876C2#1913741111yescharacteristic
877C2#1914339911yescharacteristic
878C2#1914342111yescharacteristic
879C2#1914608811yescharacteristic
880C2#1914613311yescharacteristic
881C2#1914621311yescharacteristic
882C2#1914623011yescharacteristic
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#22443
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×#14582996C2semidirect
3. C2×#14582990C2semidirect
4. #19137432C2semidirect
5. D4×C22⋊Dic43C2semidirect
6. #19135468C2semidirect
7. #19135458C2semidirect
8. #19134947C2semidirect
9. #19134947C2semidirect
10. #19134941C2semidirect
11. #19134941C2semidirect
12. #19134626C2semidirect
13. #19134536C2semidirect
14. #19134381C2semidirect
15. C43×#1786C2semidirect
19. C2×#13063351C4semidirect
25. C2×#13063290C22semidirect
26. C2×#13063290C22semidirect
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
42. #14582800C22semidirect
43. #14582800C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
69. C2×#10621898C2×C4semidirect
80. C2×#10621883C2×C4semidirect
88. C2×#10621882C2×C4semidirect
91. C2×#10621877C2×C4semidirect
253. #10621883C22⋊C4semidirect
366. C2×Dic43AGL(1,ℤ/8)semidirect
375. Dic86C2×C22⋊C4semidirect
379. C43⋊C8C2×C22⋊C4semidirect
444. #1786D43semidirect
505. C43#22443semidirect

Maximal subgroups

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

subgroupindex
C22×#130633512
C2×#145829962
C2×#145829902
#191374322
D4×C22⋊Dic432
#191354682
#191354582
#191349472
#191349412
#191346262
#191345362
#191343812
C43×#17862
#2244343