Finite Group Databasebeta

← C2×#19144114 #25963500

Subgroups — C2×#19144114 #25963500

Order 11008.

2858 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063357C211yesmaximal, characteristic, complemented
2C22×SD16×D43C211yesmaximal, characteristic, complemented
3C2×#14583467C211yesmaximal, characteristic
4C2×#14583375C211yesmaximal, characteristic, complemented
5#19144114C2116yesmaximal, direct product factor
6C2×#14583124C211yesmaximal, characteristic, complemented
7C2×#14583123C211yesmaximal, characteristic, complemented
8C2×#14583118C211yesmaximal, characteristic, complemented
9C2×#14583100C211yesmaximal, characteristic, complemented
10C2×#14583099C211yesmaximal, characteristic, complemented
11C2×#14583098C211yesmaximal, characteristic, complemented
12C2×#14583097C211yesmaximal, characteristic, complemented
13C2×#14582924C211yesmaximal, characteristic, complemented
14C2×#14582902C211yesmaximal, characteristic, complemented
15C2×#14582894C211yesmaximal, characteristic, complemented
16C2×C43×#464C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20C2×#13063357—28no—
21C2×#13063357C2218yescomplemented
22C22×#10621885C2211yescharacteristic, complemented
23C22×#10621873C2211yescharacteristic
24C22×#10621873C2211yescharacteristic, complemented
25C22×#10621883C2211yescharacteristic
26C22×#10621884C2211yescharacteristic
27C22×#10621884C2211yescharacteristic, complemented
28C2×SD16×D43—28no—
29C2×SD16×D43C2218yescomplemented
30C22×#10621872C2211yescharacteristic
31C22×C8×D43C2211yescharacteristic
32#14583467—24no—
33#14583467C2218yes—
34C2×#13063322C2211yescharacteristic
35C2×#13063321C2211yescharacteristic
36C2×#13063314C2211yescharacteristic
37C2×#13063298—21no—
38C2×#13063298—21no—
39C2×#13063295—21no—
40C2×#13063295—21no—
41#14583375—24no—
42#14583375C2218yescomplemented
43C2×Q8×Dic43C2211yescharacteristic, complemented
44C2×C4×Dic86—21no—
45C2×C4×Dic86C2211yescharacteristic, complemented
46C2×#13063290—21no—
47C2×#13063290C2211yescharacteristic, complemented
48C2×#13063283—21no—
49C2×#13063283C2211yescharacteristic
50C2×#13063282—21no—
51C2×#13063282C2211yescharacteristic
52#14583124C2218yescomplemented
53#14583123C2218yescomplemented
54#14583118C2218yescomplemented
55#14583100C2218yescomplemented
56#14583099C2218yescomplemented
57#14583098C2218yescomplemented
58#14583097C2218yescomplemented
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
61C2×Dic43⋊C8C2211yescharacteristic, complemented
62C2×Dic43⋊C8C2211yescharacteristic, complemented
63#14582902C2218yescomplemented
64#14582894C2218yescomplemented
65C2×#13063249C2211yescharacteristic, complemented
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic, complemented
68C2×#13063246C2211yescharacteristic
69C2×#13063245C2211yescharacteristic
70C2×#13063245C2211yescharacteristic, complemented
71C22×Q16×C43C2211yescharacteristic, complemented
72C22×SD16×C43C2211yescharacteristic
73C2×#124×C43C2211yescharacteristic
74C2×C4×Q8×C43C2211yescharacteristic, complemented
75C43×#464C2218yescomplemented
76C2×C4⋊C8×C43C2211yescharacteristic, complemented
77C2×#103×C43C2211yescharacteristic, complemented
78C2×#102×C43C2211yescharacteristic
79C24×D43—21no—
80C2×#10621902—22no—
81C2×#10621902—24no—
82C2×#10621902—24no—
83C2×#10621902C2314yes—
84C22×Dic86—21no—
85C22×Dic86C2311yescharacteristic
86C2×Q8×D43—22no—
87C2×Q8×D43—24no—
88C2×Q8×D43D418yescomplemented
89C2×Q8×D43C2314yes—
90C22×D172—21no—
91C22×D172—21no—
92C22×D172—21no—
93C22×D172C2311yescharacteristic
94C22×D172C2311yescharacteristic
95C22×C22⋊D43—21no—
96C22×C22⋊D43—21no—
97C22×C22⋊D43—21no—
98C2×D4×D43—24no—
99C2×D4×D43—22no—
100C2×D4×D43—24no—
101C2×D4×D43C2314yes—
102C22×C4×D43—21no—
103C22×C4×D43—21no—
104C22×C4×D43C2311yescharacteristic
105#13063357—232no—
106C2×#10621885—24no—
107C2×#10621885C2314yescomplemented
108C2×#10621873—24no—
109C2×#10621873—24no—
110C2×#10621873C2314yes—
111C2×#10621873C2314yescomplemented
112C2×#10621883—24no—
113C2×#10621883C2314yes—
114C2×#10621884—24no—
115C2×#10621884—24no—
116C2×#10621884C2314yes—
117C2×#10621884C2314yescomplemented
118SD16×D43—232no—
119C2×#10621872—24no—
120C2×#10621872C2314yes—
121C22×C43⋊C8C2311yescharacteristic
122C22×C43⋊C8C2311yescharacteristic
123C2×C8×D43—24no—
124C2×C8×D43C2314yes—
125#13063322—22no—
126#13063322C2314yes—
127#13063321—22no—
128#13063321C2314yes—
129#13063314—22no—
130#13063314C2314yes—
131#13063298—28no—
132#13063298—28no—
133#13063295—28no—
134#13063295—28no—
135Q8×Dic43—22no—
136Q8×Dic43C2314yescomplemented
137C4×Dic86—22no—
138C4×Dic86—28no—
139C4×Dic86C2314yescomplemented
140#13063290—28no—
141#13063290—22no—
142#13063290C2314yescomplemented
143#13063283—22no—
144#13063283—28no—
145#13063283C2314yes—
146#13063282—28no—
147#13063282D414yes—
148#13063282C2314yes—
149C2×C4⋊Dic43—21no—
150C2×C4⋊Dic43C2311yescharacteristic
151C2×Dic43⋊C4—21no—
152C2×Dic43⋊C4—21no—
153C2×Dic43⋊C4D411yescharacteristic
154C2×Dic43⋊C4D411yescharacteristic
155C2×(C2×D43)⋊C4—21no—
156C2×(C2×D43)⋊C4—21no—
157C2×(C2×D43)⋊C4—21no—
158C2×(C2×D43)⋊C4D411yescharacteristic
159C2×(C2×D43)⋊C4D411yescharacteristic
160C2×C4×Dic43—21no—
161C2×C4×Dic43—21no—
162C2×C4×Dic43—21no—
163C2×C4×Dic43—21no—
164C2×C4×Dic43C2311yescharacteristic
165C4⋊(C43⋊C8)C2314yescomplemented
166Dic43⋊C8C2314yescomplemented
167Dic43⋊C8C2314yescomplemented
168#13063249C2314yescomplemented
169#13063247C2314yes—
170#13063247C2314yescomplemented
171#13063246C2314yes—
172#13063245C2314yes—
173#13063245C2314yescomplemented
174C22×Q8×C43C2311yescharacteristic
175C22×Q8×C43C2311yescharacteristic
176C22×D4×C43C2311yescharacteristic
177C2×Q16×C43—24no—
178C2×Q16×C43C2314yescomplemented
179C2×SD16×C43—24no—
180C2×SD16×C43C2314yes—
181C22×C8×C43C2311yescharacteristic
182C22×C8×C43C2311yescharacteristic
183#124×C43—22no—
184#124×C43C2314yes—
185C4×Q8×C43—22no—
186C4×Q8×C43C2314yescomplemented
187C2×C4⋊C4×C43—21no—
188C2×C4⋊C4×C43C2311yescharacteristic
189C2×C22⋊C4×C43—21no—
190C2×C22⋊C4×C43—21no—
191C2×C42×C43—21no—
192C2×C42×C43C2311yescharacteristic
193C4⋊C8×C43C2314yescomplemented
194#103×C43C2314yescomplemented
195#102×C43C2314yes—
196C24×C43—21no—
197C23×D43—21no—
198C23×D43—21no—
199C23×D43—24no—
200C23×D43—44no—
201C23×D43—82no—
202C23×D43—82no—
203C23×D43C2×D411yescharacteristic
204C2×Q8×C43—21no—
205C2×Q8×C43—21no—
206C2×Q8×C43—22no—
207C2×Q8×C43—22no—
208C2×Q8×C43—22no—
209C2×Q8×C43C2×D414yes—
210C2×Q8×C43C2412yes—
211C2×Q8×C43C2412yes—
212C2×D4×C43—21no—
213C2×D4×C43—22no—
214C2×D4×C43—22no—
215C2×D4×C43C2412yes—
216C22×C4×C43—21no—
217C22×C4×C43—21no—
218C22×C4×C43—21no—
219C22×C4×C43C2×D411yescharacteristic
220C22×C4×C43C2×D411yescharacteristic
221C22×C4×C43C2411yescharacteristic
222C2×C22⋊D43—24no—
223C2×C22⋊D43—24no—
224C2×C22⋊D43—24no—
225C2×C22⋊D43—44no—
226C2×C22⋊D43—82no—
227C2×C22⋊D43—82no—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233#10621902—28no—
234#10621902—28no—
235#10621902—48no—
236Q8×D43—216no—
237Q8×D43—28no—
238Q8×D43C2×D4116yescomplemented
239D4×D43—28no—
240D4×D43—28no—
241D4×D43—48no—
242C2×D172—21no—
243C2×D172—21no—
244C2×D172—24no—
245C2×D172—24no—
246C2×D172—24no—
247C2×D172—22no—
248C2×D172—22no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172—44no—
252C2×D172—82no—
253C2×D172—82no—
254C2×D172C2412yes—
255C2×D172C2412yes—
256C2×C4×D43—24no—
257C2×C4×D43—28no—
258C2×C4×D43—24no—
259C2×C4×D43—44no—
260C2×C4×D43C2×D414yes—
261C2×C4×D43C2×D412yes—
262C2×C4×D43#4114yes—
263C2×C4×D43C2412yes—
264C2×Dic86—21no—
265C2×Dic86—22no—
266C2×Dic86—28no—
267C2×Dic86—24no—
268C2×Dic86C2×D414yes—
269C2×Dic86C2412yes—
270Q16×C43—28no—
271SD16×C43—28no—
272C2×C8×C43—22no—
273C2×C8×C43—22no—
274C2×C8×C43C2412yes—
275C2×C8×C43C2412yes—
276C4⋊C4×C43—24no—
277C4⋊C4×C43—21no—
278C4⋊C4×C43C2412yes—
279C22⋊C4×C43—24no—
280C22⋊C4×C43—24no—
281C42×C43—24no—
282C42×C43C2×D412yes—
283C42×C43C2412yes—
284#10621885—28no—
285#10621884—28no—
286#10621884—28no—
287#10621883—28no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4—24no—
290(C2×D43)⋊C4—24no—
291(C2×D43)⋊C4C2×D414yes—
292(C2×D43)⋊C4C2×D414yes—
293C4⋊Dic43—21no—
294C4⋊Dic43—24no—
295C4⋊Dic43C2412yes—
296Dic43⋊C4—24no—
297Dic43⋊C4—24no—
298Dic43⋊C4C2×D414yes—
299Dic43⋊C4C2×D414yes—
300C4×Dic43—24no—
301C4×Dic43—24no—
302C4×Dic43—24no—
303C4×Dic43—24no—
304C4×Dic43C2×D412yes—
305C4×Dic43C2412yes—
306C2×C43⋊C8—22no—
307C2×C43⋊C8—22no—
308C2×C43⋊C8C2412yes—
309C2×C43⋊C8C2412yes—
310#10621873—28no—
311#10621873—28no—
312#10621872—28no—
313C8×D43—28no—
314C23×C43—22no—
315C23×C43—42no—
316C23×C43—42no—
317C23×C43—42no—
318C23×C43C22×D411yescharacteristic
319C22×D43—22no—
320C22×D43—22no—
321C22×D43—22no—
322C22×D43—22no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—48no—
330C22×D43—84no—
331C22×D43—84no—
332C22×D43—816no—
333C22×D43#12114yes—
334C22×D43C22×D412yes—
335Q8×C43—24no—
336Q8×C43—22no—
337Q8×C43—22no—
338Q8×C43—22no—
339Q8×C43—42no—
340Q8×C43C22×D414yes—
341D4×C43—22no—
342D4×C43—22no—
343D4×C43—42no—
344C2×C4×C43—24no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—22no—
348C2×C4×C43—22no—
349C2×C4×C43—22no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43C22×D412yes—
353C2×C4×C43C22×D412yes—
354C2×C4×C43C22×D411yescharacteristic
355C2×C4×C43C22×D412yes—
356C2×C4×C43C2×#4112yes—
357C2×C4×C43C2511yescharacteristic
358C22⋊D43—48no—
359C22⋊D43—84no—
360C22⋊D43—84no—
361C2×Dic43—24no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—42no—
367C2×Dic43#12114yes—
368C2×Dic43C22×D412yes—
369C2×Dic43C22×D412yes—
370C2×Dic43C22×D412yes—
371D172—22no—
372D172—22no—
373D172—22no—
374D172—22no—
375D172—48no—
376D172—42no—
377D172—42no—
378D172—84no—
379D172—84no—
380C4×D43—216no—
381C4×D43—48no—
382C4×D43#12118yes—
383C4×D43C22×D414yes—
384C4×D43C2×#4114yes—
385Dic86—24no—
386Dic86—22no—
387Dic86—216no—
388Dic86C22×D414yes—
389C8×C43—22no—
390C8×C43—22no—
391C43⋊C8—22no—
392C43⋊C8—22no—
393C2×#3043—431nomaximal, Sylow
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—84no—
398C22×C43C2×#12112yes—
399C22×C43#57712yes—
400C22×C43#57712yes—
401C22×C43C23×D411yescharacteristic
402C2×D43—28no—
403C2×D43—22no—
404C2×D43—22no—
405C2×D43—42no—
406C2×D43—42no—
407C2×D43—42no—
408C2×D43—42no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—816no—
412C2×D43—84no—
413C2×D43—84no—
414C2×D43C2×#12114yes—
415C4×C43—24no—
416C4×C43—22no—
417C4×C43—22no—
418C4×C43—42no—
419C4×C43—42no—
420C4×C43C2×#12112yes—
421C4×C43C23×D411yescharacteristic
422C4×C43C22×#4111yescharacteristic
423Dic43—24no—
424Dic43—22no—
425Dic43—22no—
426Dic43—42no—
427Dic43C2×#12114yes—
428C22×#137—431no—
429C23×SD16—431no—
430C2×#535—431no—
431C2×#519—431no—
432#3043—4316no—
433C2×#464—431no—
434C2×#464—431no—
435C2×#464—431no—
436C2×#464D4311yescharacteristic, complemented
437C2×#460—431no—
438C2×#460—431no—
439C2×#460—431no—
440C2×#460—431no—
441C2×#424—431no—
442C2×#418—431no—
443C2×#416—431no—
444C2×C43—82no—
445C2×C43#304314yescomplemented
446C2×C43C22×#12111yescharacteristic
447C2×C43C2×#57711yescharacteristic
448C2×C43C2×#57711yescharacteristic
449D43—24no—
450D43—82no—
451D43—82no—
452C22×#41—431no—
453C23×Q8—431no—
454C23×D4—431no—
455C2×#137—438no—
456C2×#137—868no—
457C22×Q16—431no—
458C22×Q16C2×D4311yescharacteristic, complemented
459C22×SD16—431no—
460C22×SD16—431no—
461C22×SD16—431no—
462C22×SD16—438no—
463C22×SD16—431no—
464C22×SD16—431no—
465C22×SD16—868no—
466C22×SD16C2×D4311yescharacteristic
467C22×M16—431no—
468C23×C8—431no—
469#535—438no—
470#535—864no—
471C2×#127—431no—
472C2×#127—431no—
473C2×#124—431no—
474C2×#124C2×D4311yescharacteristic
475C2×#121—861no—
476C2×#121—861no—
477C2×#120—861no—
478C2×#120—861no—
479#519—438no—
480#519—864no—
481C2×C4×Q8—431no—
482C2×C4×Q8—431no—
483C2×C4×Q8—431no—
484C2×C4×Q8—861no—
485C2×C4×Q8—861no—
486C2×C4×Q8C2×D4311yescharacteristic, complemented
487C2×#117—431no—
488C2×#117—431no—
489C2×#117—861no—
490C2×#117—861no—
491#464—438no—
492#464—438no—
493#464—438no—
494#464C2×D4318yescomplemented
495#460—438no—
496#460—438no—
497#460—438no—
498#460—438no—
499#424—438no—
500C2×C4⋊C8—431no—
501C2×C4⋊C8—431no—
502C2×C4⋊C8—431no—
503C2×C4⋊C8C2×D4311yescharacteristic, complemented
504#418—438no—
505#416—438no—
506C2×#103—431no—
507C2×#103C2×D4311yescharacteristic, complemented
508C2×#102—431no—
509C2×#102—431no—
510C2×#102—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102C2×D4311yescharacteristic
514C43C2×#304311yescharacteristic, complemented, Sylow
515C25—861no—
516C2×#41—434no—
517C2×#41—862no—
518C2×#41—864no—
519C2×#41—864no—
520C22×Q8—438no—
521C22×Q8—434no—
522C22×Q8—431no—
523C22×Q8—861no—
524C22×Q8—862no—
525C22×Q8—864no—
526C22×Q8C22×D4311yescharacteristic
527C22×Q8C22×D4311yescharacteristic
528C22×D4—434no—
529C22×D4—431no—
530C22×D4—431no—
531C22×D4—861no—
532C22×D4—864no—
533C22×D4—864no—
534C22×D4—862no—
535C22×D4—861no—
536C22×D4—861no—
537C22×D4—861no—
538C22×D4—861no—
539C22×D4—861no—
540C22×D4C22×D4311yescharacteristic
541C23×C4—431no—
542C23×C4—861no—
543C23×C4—861no—
544#137—8632no—
545C2×Q16—24no—
546C2×Q16—434no—
547C2×Q16—864no—
548C2×Q16C22×D4314yescomplemented
549C2×SD16—24no—
550C2×SD16—434no—
551C2×SD16—434no—
552C2×SD16—434no—
553C2×SD16—434no—
554C2×SD16—434no—
555C2×SD16—864no—
556C2×SD16—864no—
557C2×SD16—8632no—
558C2×SD16—864no—
559C2×SD16—864no—
560C2×SD16—864no—
561C2×SD16C22×D4314yes—
562C2×M16—434no—
563C2×M16—864no—
564C22×C8—431no—
565C22×C8—431no—
566C22×C8—434no—
567C22×C8—864no—
568C22×C8C22×D4311yescharacteristic
569C22×C8C22×D4311yescharacteristic
570#127—434no—
571#127—434no—
572#127—862no—
573#127—862no—
574#124—22no—
575#124—434no—
576#124—862no—
577#124C22×D4314yes—
578#121—868no—
579#121—868no—
580#120—868no—
581#120—868no—
582C4×Q8—22no—
583C4×Q8—434no—
584C4×Q8—434no—
585C4×Q8—434no—
586C4×Q8—868no—
587C4×Q8—862no—
588C4×Q8—862no—
589C4×Q8—868no—
590C4×Q8—862no—
591C4×Q8C22×D4314yescomplemented
592#117—434no—
593#117—434no—
594#117—434no—
595#117—868no—
596#117—868no—
597#117—862no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4—861no—
605C2×C4⋊C4C22×D4311yescharacteristic
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—431no—
609C2×C22⋊C4—431no—
610C2×C22⋊C4—861no—
611C2×C22⋊C4—861no—
612C2×C22⋊C4—861no—
613C2×C42—21no—
614C2×C42—431no—
615C2×C42—861no—
616C2×C42—861no—
617C2×C42—861no—
618C2×C42—861no—
619C2×C42C22×D4311yescharacteristic
620C4⋊C8—434no—
621C4⋊C8—434no—
622C4⋊C8—434no—
623C4⋊C8C22×D4314yescomplemented
624#103—434no—
625#103C22×D4314yescomplemented
626#102—434no—
627#102—434no—
628#102—434no—
629#102—434no—
630#102—434no—
631#102C22×D4314yes—
632C24—21no—
633C24—431no—
634C24—864no—
635C24—861no—
636C24—861no—
637C24—3442no—
638C24—3442no—
639C24—1724no—
640#41—868no—
641#41—868no—
642#41—1728no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—22no—
648C2×Q8—4316no—
649C2×Q8—434no—
650C2×Q8—432no—
651C2×Q8—864no—
652C2×Q8—868no—
653C2×Q8—8616no—
654C2×Q8—868no—
655C2×Q8—861no—
656C2×Q8—862no—
657C2×Q8D4×D4314yes—
658C2×Q8C23×D4312yes—
659C2×Q8C23×D4312yes—
660C2×D4—22no—
661C2×D4—21no—
662C2×D4—22no—
663C2×D4—432no—
664C2×D4—432no—
665C2×D4—864no—
666C2×D4—868no—
667C2×D4—868no—
668C2×D4—864no—
669C2×D4—864no—
670C2×D4—864no—
671C2×D4—862no—
672C2×D4—862no—
673C2×D4—864no—
674C2×D4—864no—
675C2×D4—861no—
676C2×D4—861no—
677C2×D4—862no—
678C2×D4—862no—
679C2×D4—3442no—
680C2×D4—3442no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—1724no—
684C2×D4—1728no—
685C2×D4—1724no—
686C2×D4C23×D4312yes—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—431no—
691C22×C4—432no—
692C22×C4—434no—
693C22×C4—434no—
694C22×C4—432no—
695C22×C4—431no—
696C22×C4—431no—
697C22×C4—864no—
698C22×C4—864no—
699C22×C4—868no—
700C22×C4—861no—
701C22×C4—861no—
702C22×C4—1724no—
703C22×C4D4×D4311yescharacteristic
704C22×C4D4×D4311yescharacteristic
705C22×C4C23×D4311yescharacteristic
706Q16—28no—
707Q16—868no—
708SD16—28no—
709SD16—868no—
710SD16—868no—
711SD16—868no—
712SD16—868no—
713SD16—868no—
714M16—868no—
715C2×C8—22no—
716C2×C8—22no—
717C2×C8—432no—
718C2×C8—432no—
719C2×C8—868no—
720C2×C8—862no—
721C2×C8—862no—
722C2×C8C23×D4312yes—
723C2×C8C23×D4312yes—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—434no—
727C4⋊C4—434no—
728C4⋊C4—432no—
729C4⋊C4—864no—
730C4⋊C4—864no—
731C4⋊C4—861no—
732C4⋊C4—864no—
733C4⋊C4C23×D4312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—434no—
737C22⋊C4—434no—
738C22⋊C4—864no—
739C22⋊C4—864no—
740C22⋊C4—864no—
741C42—24no—
742C42—432no—
743C42—432no—
744C42—864no—
745C42—864no—
746C42—864no—
747C42—864no—
748C42D4×D4312yes—
749C42C23×D4312yes—
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—434no—
755C23—432no—
756C23—862no—
757C23—862no—
758C23—862no—
759C23—862no—
760C23—3444no—
761C23—3444no—
762C23—34416no—
763C23—1728no—
764C23—1722no—
765C23—1722no—
766C23—1722no—
767C23—1722no—
768C23—1722no—
769C23—1722no—
770C23C2×D4×D4311yescharacteristic
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—42no—
776Q8—434no—
777Q8—8616no—
778Q8—864no—
779Q8—862no—
780Q8C2×D4×D4314yes—
781D4—22no—
782D4—22no—
783D4—42no—
784D4—862no—
785D4—862no—
786D4—862no—
787D4—862no—
788D4—3444no—
789D4—3444no—
790D4—3444no—
791D4—3444no—
792D4—1728no—
793D4—1728no—
794D4—1722no—
795D4—1722no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—434no—
805C2×C4—432no—
806C2×C4—438no—
807C2×C4—434no—
808C2×C4—434no—
809C2×C4—432no—
810C2×C4—432no—
811C2×C4—8616no—
812C2×C4—864no—
813C2×C4—862no—
814C2×C4—862no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—1728no—
818C2×C4—1722no—
819C2×C4C2×D4×D4312yes—
820C2×C4C2×D4×D4312yes—
821C2×C4C2×D4×D4311yescharacteristic
822C2×C4C2×D4×D4312yes—
823C2×C4#41×D4312yes—
824C2×C4C24×D4311yescharacteristic
825C8—22no—
826C8—22no—
827C8—862no—
828C8—862no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—84no—
833C22—434no—
834C22—862no—
835C22—862no—
836C22—868no—
837C22—34416no—
838C22—3444no—
839C22—3444no—
840C22—1722no—
841C22—1722no—
842C22—1722no—
843C22—1722no—
844C22—1722no—
845C22—1722no—
846C22#121×D4312yes—
847C22#1458370612yes—
848C22#1458370812yes—
849C22C22×D4×D4311yescharacteristic
850C4—24no—
851C4—22no—
852C4—22no—
853C4—42no—
854C4—42no—
855C4—434no—
856C4—864no—
857C4—862no—
858C4—862no—
859C4—1722no—
860C4#121×D4312yes—
861C4C22×D4×D4311yescharacteristic
862C4C2×#41×D4311yescharacteristic
863C2—82no—
864C2—864no—
865C2—3442no—
866C2—3442no—
867C2#1914411414yesdirect product factor
868C2C2×#121×D4311yescharacteristic
869C2C2×#1458370611yescharacteristic
870C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#464C2
socleC23×C43C22×D4
prime radicalC2×#14583467C2
hypercenterC2×#464D43
hypocenterC43C2×#3043
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#13063357C2semidirect
2. C22×SD16×D43C2semidirect
4. C2×#14583375C2semidirect
5. #19144114C2direct (N × H)
6. C2×#14583124C2semidirect
7. C2×#14583123C2semidirect
8. C2×#14583118C2semidirect
9. C2×#14583100C2semidirect
10. C2×#14583099C2semidirect
11. C2×#14583098C2semidirect
12. C2×#14583097C2semidirect
13. C2×#14582924C2semidirect
14. C2×#14582902C2semidirect
15. C2×#14582894C2semidirect
16. C2×C43×#464C2semidirect
21. C2×#13063357C22semidirect
22. C22×#10621885C22semidirect
24. C22×#10621873C22semidirect
27. C22×#10621884C22semidirect
29. C2×SD16×D43C22semidirect
42. #14583375C22semidirect
43. C2×Q8×Dic43C22semidirect
45. C2×C4×Dic86C22semidirect
47. C2×#13063290C22semidirect
52. #14583124C22semidirect
53. #14583123C22semidirect
54. #14583118C22semidirect
55. #14583100C22semidirect
56. #14583099C22semidirect
57. #14583098C22semidirect
58. #14583097C22semidirect
59. #14582924C22semidirect
60. C2×C4⋊(C43⋊C8)C22semidirect
61. C2×Dic43⋊C8C22semidirect
62. C2×Dic43⋊C8C22semidirect
63. #14582902C22semidirect
64. #14582894C22semidirect
65. C2×#13063249C22semidirect
67. C2×#13063247C22semidirect
70. C2×#13063245C22semidirect
71. C22×Q16×C43C22semidirect
74. C2×C4×Q8×C43C22semidirect
75. C43×#464C22semidirect
76. C2×C4⋊C8×C43C22semidirect
77. C2×#103×C43C22semidirect
88. C2×Q8×D43D4semidirect
107. C2×#10621885C23semidirect
111. C2×#10621873C23semidirect
117. C2×#10621884C23semidirect
136. Q8×Dic43C23semidirect
139. C4×Dic86C23semidirect
142. #13063290C23semidirect
165. C4⋊(C43⋊C8)C23semidirect
166. Dic43⋊C8C23semidirect
167. Dic43⋊C8C23semidirect
168. #13063249C23semidirect
170. #13063247C23semidirect
173. #13063245C23semidirect
178. C2×Q16×C43C23semidirect
186. C4×Q8×C43C23semidirect
193. C4⋊C8×C43C23semidirect
194. #103×C43C23semidirect
238. Q8×D43C2×D4semidirect
436. C2×#464D43semidirect
445. C2×C43#3043semidirect
458. C22×Q16C2×D43semidirect
486. C2×C4×Q8C2×D43semidirect
494. #464C2×D43semidirect
503. C2×C4⋊C8C2×D43semidirect
507. C2×#103C2×D43semidirect
514. C43C2×#3043semidirect
548. C2×Q16C22×D43semidirect
591. C4×Q8C22×D43semidirect
623. C4⋊C8C22×D43semidirect
625. #103C22×D43semidirect
867. C2#19144114direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633572
C22×SD16×D432
C2×#145834672
C2×#145833752
#191441142
C2×#145831242
C2×#145831232
C2×#145831182
C2×#145831002
C2×#145830992
C2×#145830982
C2×#145830972
C2×#145829242
C2×#145829022
C2×#145828942
C2×C43×#4642
C2×#304343