Finite Group Databasebeta

← #25112370

Subgroups — #25112370

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×#13063350C211yesmaximal, characteristic
2C2×#14583002C211yesmaximal, characteristic, complemented
3C2×#14582984C211yesmaximal, characteristic, complemented
4#19137436C211yesmaximal, characteristic, complemented
5#19137415C211yesmaximal, characteristic, complemented
6#19135468C211yesmaximal, characteristic, complemented
7#19135458C211yesmaximal, characteristic, complemented
8#19134948C211yesmaximal, characteristic, complemented
9#19134948C211yesmaximal, characteristic, complemented
10#19134940C211yesmaximal, characteristic, complemented
11#19134940C211yesmaximal, characteristic, complemented
12#19134626C211yesmaximal, characteristic, complemented
13#19134527C211yesmaximal, characteristic, complemented
14#19134381C211yesmaximal, characteristic, complemented
15C43×#1788C211yesmaximal, characteristic, complemented
16C23×D172C2211yescharacteristic
17C2×#13063350—24no—
18C2×#13063350—24no—
19C2×#13063350C418yescomplemented
20C22×#10621884C2211yescharacteristic
21C22×#10621884C2211yescharacteristic
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621877C2211yescharacteristic
25C2×Q8×Dic43C2211yescharacteristic, complemented
26C2×Q8×Dic43C2211yescharacteristic, complemented
27C2×#13063287C2211yescharacteristic
28C2×#13063287C2211yescharacteristic
29C2×C22⋊C4×D43—21no—
30#14583002—24no—
31#14582984—24no—
32C2×#13063258C2211yescharacteristic, complemented
33C2×#13063256C2211yescharacteristic, complemented
34C2×#13063247C2211yescharacteristic
35C2×#13063247C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063235C2211yescharacteristic, complemented
39C2×C8×Dic43C2211yescharacteristic, complemented
40#14582802—21no—
41#14582802—21no—
42#14582802C2211yescharacteristic, complemented
43#14582802C2211yescharacteristic, complemented
44#14582800C2211yescharacteristic
45#14582800C2211yescharacteristic
46#14582777—21no—
47#14582777—21no—
48#14582759—21no—
49#14582759C2211yescharacteristic
50#14582754—21no—
51C4×C22⋊Dic43—21no—
52C4×C22⋊Dic43C2211yescharacteristic
53#14582661C2211yescharacteristic, complemented
54#14582661C2211yescharacteristic, complemented
55#14582653C2211yescharacteristic, complemented
56#14582653C2211yescharacteristic, complemented
57C22×#41×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic, complemented
59C2×#103×C43C2211yescharacteristic, complemented
60C2×#102×C43C2211yescharacteristic, complemented
61C2×#102×C43C2211yescharacteristic, complemented
62C2×C22⋊C8×C43C2211yescharacteristic
63C43×#380C2211yescharacteristic
64C24×D43—21no—
65C22×D172—22no—
66C22×D172—22no—
67C22×D172—21no—
68C22×D172—22no—
69C22×D172—41no—
70C22×D172—41no—
71C22×D172C2×C414yes—
72C22×D172C2311yescharacteristic
73C22×D172C2311yescharacteristic
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76#13063350—232no—
77C2×#10621884—22no—
78C2×#10621884—22no—
79C2×#10621884C2×C414yes—
80C2×#10621884C2×C414yescomplemented
81C2×#10621884D414yes—
82C2×#10621884D414yes—
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
94Q8×Dic43—22no—
95Q8×Dic43—22no—
96Q8×Dic43—41no—
97Q8×Dic43—41no—
98#13063287—22no—
99#13063287—22no—
100#13063287—41no—
101#13063287—41no—
102C2×C4⋊Dic43—21no—
103C2×C4⋊Dic43—21no—
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⋊Dic43D411yescharacteristic
112C2×C22⋊Dic43D411yescharacteristic
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4—21no—
116C2×(C2×D43)⋊C4—21no—
117C2×(C2×D43)⋊C4—21no—
118C2×(C2×D43)⋊C4—21no—
119C22⋊C4×D43—44no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123C2×C4×Dic43C2311yescharacteristic
124#13063258—22no—
125#13063256—22no—
126#13063247—22no—
127#13063247—22no—
128#13063247—41no—
129#13063247—41no—
130#13063235—22no—
131C8×Dic43—22no—
132C43⋊#95—21no—
133C43⋊#95D411yescharacteristic
134C43⋊#95D411yescharacteristic
135C2×#41×C43—22no—
136C2×#41×C43—22no—
137C2×#41×C43—22no—
138C2×#41×C43—41no—
139C2×#41×C43—41no—
140C2×#41×C43C2×C414yescomplemented
141C22×Q8×C43C2311yescharacteristic
142C22×D4×C43—21no—
143C22×D4×C43C2311yescharacteristic
144C23×C4×C43—21no—
145C23×C4×C43C2311yescharacteristic
146C22×C8×C43C2311yescharacteristic
147C22×C8×C43C2311yescharacteristic
148C2×C4⋊C4×C43C2311yescharacteristic
149C2×C4⋊C4×C43C2311yescharacteristic
150C2×C22⋊C4×C43—21no—
151#103×C43—22no—
152#103×C43—22no—
153#102×C43—41no—
154#102×C43—41no—
155C22⋊C8×C43—22no—
156#95×C43—21no—
157C24×C43—21no—
158C24×C43C2×D411yescharacteristic
159C23×D43—21no—
160C23×D43—21no—
161C23×D43—24no—
162C23×D43—42no—
163C23×D43—42no—
164C23×D43—42no—
165C23×D43—42no—
166C23×D43—81no—
167C23×D43—81no—
168#41×C43—28no—
169#41×C43—44no—
170#41×C43—44no—
171#41×C43—44no—
172C2×Q8×C43—21no—
173C2×Q8×C43—21no—
174C2×Q8×C43—21no—
175C2×Q8×C43C22×C412yes—
176C2×Q8×C43C2×D412yes—
177C2×Q8×C43C2×D412yes—
178C2×D4×C43—21no—
179C2×D4×C43—24no—
180C2×D4×C43—21no—
181C2×D4×C43—21no—
182C2×D4×C43—21no—
183C2×D4×C43—21no—
184C2×D4×C43—42no—
185C2×D4×C43—42no—
186C2×D4×C43C22×C412yes—
187C22×C4×C43—21no—
188C22×C4×C43—21no—
189C22×C4×C43—21no—
190C22×C4×C43—21no—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—42no—
196C22×C4×C43—42no—
197C22×C4×C43C22×C412yes—
198C22×C4×C43C2×D411yescharacteristic
199C22×C4×C43#4112yes—
200C22×C4×C43C2411yescharacteristic
201C22×Dic43—21no—
202C22×Dic43—21no—
203C22×Dic43C2×D411yescharacteristic
204C22×Dic43C2×D411yescharacteristic
205C22×Dic43C2×D411yescharacteristic
206C22×Dic43C2×D411yescharacteristic
207C2×D172—21no—
208C2×D172—21no—
209C2×D172—21no—
210C2×D172—24no—
211C2×D172—21no—
212C2×D172—21no—
213C2×D172—21no—
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—28no—
217C2×D172—42no—
218C2×D172—42no—
219C2×D172—44no—
220C2×D172—44no—
221C2×D172—44no—
222C2×D172C22×C412yes—
223C2×D172C22×C412yes—
224C2×D172C2×D412yes—
225C2×D172C2×D412yes—
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×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—42no—
243C22⋊Dic43—22no—
244C22⋊Dic43—41no—
245C22⋊Dic43—42no—
246C22⋊Dic43—42no—
247C22⋊Dic43—81no—
248C22⋊Dic43—81no—
249C22⋊Dic43—81no—
250#10621884—28no—
251#10621884C22⋊C4116yescomplemented
252#10621882—28no—
253#10621882—28no—
254(C2×D43)⋊C4—42no—
255(C2×D43)⋊C4—42no—
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—
264C4⋊Dic43—42no—
265C4⋊Dic43—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—21no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—21no—
283C23×C43—21no—
284C23×C43—21no—
285C23×C43—22no—
286C23×C43—41no—
287C23×C43—41no—
288C23×C43—41no—
289C23×C43—41no—
290C23×C43—41no—
291C23×C43—41no—
292C23×C43C4×D412yes—
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—48no—
299C22×D43—41no—
300C22×D43—41no—
301C22×D43—41no—
302C22×D43—41no—
303C22×D43—48no—
304C22×D43—41no—
305C22×D43—41no—
306C22×D43—41no—
307C22×D43—41no—
308C22×D43—41no—
309C22×D43—41no—
310C22×D43—84no—
311C22×D43—84no—
312C22×D43—84no—
313C22×D43—84no—
314C22×D43—84no—
315Q8×C43—22no—
316Q8×C43—22no—
317Q8×C43—22no—
318Q8×C43C2×C22⋊C414yescomplemented
319D4×C43—22no—
320D4×C43—22no—
321D4×C43—48no—
322D4×C43—41no—
323D4×C43—41no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—21no—
328C2×C4×C43—21no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—48no—
334C2×C4×C43—41no—
335C2×C4×C43—41no—
336C2×C4×C43—41no—
337C2×C4×C43—41no—
338C2×C4×C43—41no—
339C2×C4×C43—41no—
340C2×C4×C43C4×D412yes—
341C2×C4×C43C23×C411yescharacteristic
342C2×C4×C43C22×D411yescharacteristic
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43C2×#4111yescharacteristic
345C2×C4×C43H(5,𝔽2)11yescharacteristic
346C2×C4×C43H(5,𝔽2)11yescharacteristic
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—21no—
357C2×Dic43—21no—
358C2×Dic43—41no—
359C2×Dic43—41no—
360C2×Dic43—41no—
361C2×Dic43—41no—
362C2×Dic43—41no—
363C2×Dic43—41no—
364C2×Dic43AGL(1,ℤ/8)12yescomplemented
365D172—22no—
366D172—22no—
367D172—22no—
368D172—22no—
369D172—22no—
370D172—48no—
371D172—41no—
372D172—41no—
373D172C2×C22⋊C414yes—
374C4×D43—84no—
375C4×D43—84no—
376C8×C43—41no—
377C8×C43—41no—
378C43⋊C8—22no—
379C43⋊C8C2×C22⋊C414yescomplemented
380#22443—431nomaximal, Sylow
381C22×C43—22no—
382C22×C43—22no—
383C22×C43—22no—
384C22×C43—41no—
385C22×C43—41no—
386C22×C43—41no—
387C22×C43—41no—
388C22×C43—42no—
389C22×C43—42no—
390C22×C43—42no—
391C22×C43—81no—
392C22×C43—81no—
393C22×C43—81no—
394C22×C43—81no—
395C22×C43C2×C4×D411yescharacteristic
396C22×C43D4211yescharacteristic
397C22×C43D4211yescharacteristic
398C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C43#57511yescharacteristic
400C22×C43#57611yescharacteristic
401C22×C43#57711yescharacteristic
402C2×D43—24no—
403C2×D43—42no—
404C2×D43—42no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—816no—
413C2×D43—81no—
414C2×D43—81no—
415C2×D43—81no—
416C2×D43—81no—
417C4×C43—22no—
418C4×C43—24no—
419C4×C43—81no—
420C4×C43—81no—
421C4×C43C22×C22⋊C411yescharacteristic
422C4×C43#51811yescharacteristic
423C4×C43#54611yescharacteristic
424C4×C43#54611yescharacteristic
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#1788D4311yescharacteristic, complemented
444#1786—431no—
445#1753—431no—
446C2×C43—42no—
447C2×C43—82no—
448C2×C43D4×C22⋊C411yescharacteristic
449C2×C43C4×AGL(1,ℤ/8)11yescharacteristic
450C2×C43#294611yescharacteristic
451C2×C43#326511yescharacteristic
452C2×C43#326811yescharacteristic
453C2×C43#327411yescharacteristic
454C2×C43#327511yescharacteristic
455D43—44no—
456D43—82no—
457C22×#41C2×D4311yescharacteristic
458C23×D4—431no—
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×#103C2×D4311yescharacteristic, complemented
477C2×#103C2×D4311yescharacteristic, complemented
478C2×#102—431no—
479C2×#102—431no—
480C2×#102—431no—
481C2×#102—431no—
482C2×#102C2×D4311yescharacteristic, complemented
483C2×#102C2×D4311yescharacteristic, complemented
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—861no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41C4×D4314yescomplemented
513C22×Q8C22×D4311yescharacteristic
514C22×D4—21no—
515C22×D4—434no—
516C22×D4—431no—
517C22×D4—431no—
518C22×D4—862no—
519C22×D4—862no—
520C22×D4—861no—
521C22×D4—862no—
522C22×D4—1721no—
523C22×D4—1721no—
524C22×D4C22×D4311yescharacteristic
525C23×C4—21no—
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—22no—
585#103—22no—
586#102—41no—
587#102—41no—
588#102—862no—
589#102—862no—
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—861no—
601C24—864no—
602C24—861no—
603C24—3441no—
604C24—3441no—
605C24—1722no—
606C24—1722no—
607C24—1722no—
608C24—1722no—
609C24D4×D4311yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8C2×C4×D4312yes—
618C2×Q8D4×D4312yes—
619C2×Q8D4×D4312yes—
620C2×D4—24no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—42no—
628C2×D4—432no—
629C2×D4—432no—
630C2×D4—432no—
631C2×D4—432no—
632C2×D4—868no—
633C2×D4—864no—
634C2×D4—861no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—861no—
638C2×D4—861no—
639C2×D4—861no—
640C2×D4—861no—
641C2×D4—861no—
642C2×D4—1724no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1722no—
646C2×D4—1722no—
647C2×D4C2×C4×D4312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—431no—
662C22×C4—861no—
663C22×C4—861no—
664C22×C4—3441no—
665C22×C4—3441no—
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—42no—
702C22⋊C4—862no—
703C22⋊C4—3441no—
704C22⋊C4—3441no—
705C22⋊C4—3441no—
706C22⋊C4—3441no—
707C22⋊C4—3441no—
708C22⋊C4—1722no—
709C22⋊C4—1722no—
710C22⋊C4—1722no—
711C22⋊C4—1722no—
712C22⋊C4—1722no—
713C22⋊C4—1721no—
714C22⋊C4—1722no—
715C42—861no—
716C42—861no—
717C42—861no—
718C42—861no—
719C42—1722no—
720C42—1722no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—22no—
728C23—41no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—862no—
735C23—862no—
736C23—862no—
737C23—862no—
738C23—3444no—
739C23—3444no—
740C23—3444no—
741C23—3444no—
742C23—3444no—
743C23—1728no—
744C23—1728no—
745C23—1721no—
746C23—1721no—
747C23—1721no—
748C23—1721no—
749C23—1721no—
750C23—1721no—
751C23—1721no—
752C23—1721no—
753C23—1721no—
754C23—1721no—
755C23(C22⋊D43)⋊C412yes—
756C23C2×D4×D4311yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C22⋊C4×D4314yescomplemented
761D4—22no—
762D4—22no—
763D4—48no—
764D4—41no—
765D4—41no—
766D4—434no—
767D4—862no—
768D4—862no—
769D4—862no—
770D4—862no—
771D4—862no—
772D4—1728no—
773D4—1721no—
774D4—1721no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—432no—
792C2×C4—861no—
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—861no—
803C2×C4—3444no—
804C2×C4—3444no—
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—22no—
824C22—22no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—81no—
833C22—81no—
834C22—81no—
835C22—81no—
836C22—864no—
837C22—34416no—
838C22—3441no—
839C22—3441no—
840C22—3441no—
841C22—3441no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22C2×(C22⋊D43)⋊C411yescharacteristic
852C22#1458353111yescharacteristic
853C22#1458353111yescharacteristic
854C22AGL(1,ℤ/8)×D4311yescharacteristic
855C22#1458369811yescharacteristic
856C22#1458370111yescharacteristic
857C22#1458370611yescharacteristic
858C4—22no—
859C4—24no—
860C4—81no—
861C4—81no—
862C4—862no—
863C4—3441no—
864C4—3441no—
865C4—1721no—
866C4—1721no—
867C4—1721no—
868C4C2×C22⋊C4×D4311yescharacteristic
869C4#1458337211yescharacteristic
870C4#1458353611yescharacteristic
871C4#1458353611yescharacteristic
872C2—42no—
873C2—82no—
874C2—3442no—
875C2—1724no—
876C2#1913741111yescharacteristic
877C2#1914340811yescharacteristic
878C2#1914343011yescharacteristic
879C2#1914609311yescharacteristic
880C2#1914613811yescharacteristic
881C2#1914620811yescharacteristic
882C2#1914621911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1788C2
socleC23×C43C22×D4
prime radicalC22×#13063350C2
cosocleC22×C4×C43C24
hypercenter#1788D43
hypocenterC43#22443
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
2. C2×#14583002C2semidirect
3. C2×#14582984C2semidirect
4. #19137436C2semidirect
5. #19137415C2semidirect
6. #19135468C2semidirect
7. #19135458C2semidirect
8. #19134948C2semidirect
9. #19134948C2semidirect
10. #19134940C2semidirect
11. #19134940C2semidirect
12. #19134626C2semidirect
13. #19134527C2semidirect
14. #19134381C2semidirect
15. C43×#1788C2semidirect
19. C2×#13063350C4semidirect
25. C2×Q8×Dic43C22semidirect
26. C2×Q8×Dic43C22semidirect
32. C2×#13063258C22semidirect
33. C2×#13063256C22semidirect
38. C2×#13063235C22semidirect
39. C2×C8×Dic43C22semidirect
42. #14582802C22semidirect
43. #14582802C22semidirect
53. #14582661C22semidirect
54. #14582661C22semidirect
55. #14582653C22semidirect
56. #14582653C22semidirect
58. C2×#103×C43C22semidirect
59. C2×#103×C43C22semidirect
60. C2×#102×C43C22semidirect
61. C2×#102×C43C22semidirect
80. C2×#10621884C2×C4semidirect
88. C2×#10621882C2×C4semidirect
91. C2×#10621877C2×C4semidirect
140. C2×#41×C43C2×C4semidirect
251. #10621884C22⋊C4semidirect
318. Q8×C43C2×C22⋊C4semidirect
364. C2×Dic43AGL(1,ℤ/8)semidirect
379. C43⋊C8C2×C22⋊C4semidirect
443. #1788D43semidirect
476. C2×#103C2×D43semidirect
477. C2×#103C2×D43semidirect
482. C2×#102C2×D43semidirect
483. C2×#102C2×D43semidirect
505. C43#22443semidirect
512. C2×#41C4×D43semidirect
760. Q8C22⋊C4×D43semidirect

Maximal subgroups

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

subgroupindex
C22×#130633502
C2×#145830022
C2×#145829842
#191374362
#191374152
#191354682
#191354582
#191349482
#191349402
#191346262
#191345272
#191343812
C43×#17882
#2244343