Finite Group Databasebeta

← C2×#19145642 #25967925

Subgroups — C2×#19145642 #25967925

Order 11008.

2342 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583500C211yesmaximal, characteristic, complemented
2C2×#14583467C211yesmaximal, characteristic, complemented
3#19145642C2116yesmaximal, direct product factor
4C2×#14583285C211yesmaximal, characteristic, complemented
5C2×#14583274C211yesmaximal, characteristic, complemented
6C2×#14583262C211yesmaximal, characteristic, complemented
7C2×#14583255C211yesmaximal, characteristic, complemented
8C2×#14583111C211yesmaximal, characteristic, complemented
9C2×#14583095C211yesmaximal, characteristic, complemented
10C2×#14583094C211yesmaximal, characteristic, complemented
11C2×#14583047C211yesmaximal, characteristic, complemented
12C2×#14583043C211yesmaximal, characteristic, complemented
13C2×#14583034C211yesmaximal, characteristic, complemented
14C2×#14583031C211yesmaximal, characteristic, complemented
15C2×#14582959C211yesmaximal, characteristic, complemented
16C2×C43×#463C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621884C2211yescharacteristic, complemented
20C22×D344C2211yescharacteristic
21C22×D344C2211yescharacteristic, complemented
22C22×#10621882C2211yescharacteristic
23C22×#10621882C2211yescharacteristic
24C22×#10621882C2211yescharacteristic, complemented
25#14583500—24no—
26#14583500C2218yescomplemented
27#14583467—24no—
28#14583467C2218yescomplemented
29C2×#13063322C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31C2×#13063321C2211yescharacteristic, complemented
32C2×#13063316C2211yescharacteristic, complemented
33C2×#13063314C2211yescharacteristic
34C2×#13063308—21no—
35C2×#13063307—21no—
36C2×#13063300C2211yescharacteristic
37C2×#13063299—21no—
38C2×#13063298—21no—
39C2×#13063298—21no—
40C2×#13063298—21no—
41C2×#13063296C2211yescharacteristic
42C2×#13063295—21no—
43C2×#13063295—21no—
44C2×C4×D172C2211yescharacteristic, complemented
45C2×#13063282C2211yescharacteristic
46#14583285C2218yescomplemented
47#14583274C2218yescomplemented
48#14583262C2218yescomplemented
49#14583255C2218yescomplemented
50#14583111C2218yescomplemented
51#14583095C2218yescomplemented
52#14583094C2218yescomplemented
53#14583047C2218yescomplemented
54#14583043C2218yescomplemented
55#14583034C2218yescomplemented
56#14583031C2218yescomplemented
57#14582959C2218yescomplemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063247C2211yescharacteristic
61C2×#13063247C2211yescharacteristic, complemented
62C2×#13063246C2211yescharacteristic
63C2×#13063245C2211yescharacteristic
64C2×#13063245C2211yescharacteristic, complemented
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×#13063235C2211yescharacteristic, complemented
68C2×C8×Dic43C2211yescharacteristic, complemented
69C22×SD16×C43C2211yescharacteristic, complemented
70C22×D8×C43C2211yescharacteristic
71C2×#124×C43C2211yescharacteristic
72C2×C4×D4×C43C2211yescharacteristic, complemented
73C43×#463C2218yescomplemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—42no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×D172—21no—
83C22×D172—21no—
84C22×D172—21no—
85C22×D172—21no—
86C22×D172C2311yescharacteristic
87C22×D172C2311yescharacteristic
88C22×D172C2311yescharacteristic
89C22×C22⋊D43—21no—
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C22×C22⋊D43—21no—
95C2×D4×D43—22no—
96C2×D4×D43—42no—
97C2×D4×D43—42no—
98C2×D4×D43C2314yes—
99C22×C4×D43—21no—
100C22×C4×D43—21no—
101C22×C4×D43C2311yescharacteristic
102C2×#10621884—42no—
103C2×#10621884C2314yescomplemented
104C2×D344—42no—
105C2×D344—42no—
106C2×D344C2314yes—
107C2×D344C2314yescomplemented
108C2×#10621882—42no—
109C2×#10621882—42no—
110C2×#10621882—42no—
111C2×#10621882C2314yes—
112C2×#10621882C2314yes—
113C2×#10621882C2314yescomplemented
114C22×C43⋊C8C2311yescharacteristic
115C22×C43⋊C8C2311yescharacteristic
116#13063322—22no—
117#13063322C2314yes—
118#13063321—22no—
119#13063321—22no—
120#13063321C2314yes—
121#13063321C2314yescomplemented
122#13063316—22no—
123#13063316C2314yescomplemented
124#13063314—22no—
125#13063314C2314yes—
126#13063308—28no—
127#13063307—28no—
128#13063300—22no—
129#13063300C2314yes—
130#13063299—28no—
131#13063298—28no—
132#13063298—28no—
133#13063298—28no—
134#13063296—22no—
135#13063296C2314yes—
136#13063295—28no—
137#13063295—28no—
138C4×D172—22no—
139C4×D172C2314yescomplemented
140#13063282D414yes—
141#13063282C2314yes—
142C2×C4⋊Dic43—21no—
143C2×C4⋊Dic43C2311yescharacteristic
144C2×Dic43⋊C4—21no—
145C2×Dic43⋊C4D411yescharacteristic
146C2×Dic43⋊C4D411yescharacteristic
147C2×C22⋊Dic43—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4D411yescharacteristic
153C2×(C2×D43)⋊C4D411yescharacteristic
154C2×C4×Dic43C2311yescharacteristic
155C4⋊(C43⋊C8)C2314yescomplemented
156#13063249C2314yescomplemented
157#13063247C2314yes—
158#13063247C2314yescomplemented
159#13063246C2314yes—
160#13063245C2314yes—
161#13063245C2314yescomplemented
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164#13063235C2314yescomplemented
165C8×Dic43C2314yescomplemented
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C2×SD16×C43—42no—
171C2×SD16×C43C2314yescomplemented
172C2×D8×C43—42no—
173C2×D8×C43C2314yes—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176#124×C43—22no—
177#124×C43C2314yes—
178C4×D4×C43—22no—
179C4×D4×C43C2314yescomplemented
180C2×C4⋊C4×C43C2311yescharacteristic
181C2×C22⋊C4×C43—21no—
182C2×C22⋊C4×C43—21no—
183C2×C22⋊C4×C43—21no—
184C2×C42×C43C2311yescharacteristic
185C4⋊C8×C43C2314yescomplemented
186#103×C43C2314yescomplemented
187#102×C43C2314yes—
188C24×C43—21no—
189C24×C43—21no—
190C23×D43—21no—
191C23×D43—21no—
192C23×D43—21no—
193C23×D43—24no—
194C23×D43—44no—
195C23×D43—82no—
196C23×D43—82no—
197C23×D43C2×D411yescharacteristic
198C2×Q8×C43—21no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43C2412yes—
202C2×D4×C43—21no—
203C2×D4×C43—21no—
204C2×D4×C43—22no—
205C2×D4×C43—22no—
206C2×D4×C43—22no—
207C2×D4×C43—22no—
208C2×D4×C43C2412yes—
209C2×D4×C43C2412yes—
210C22×C4×C43—24no—
211C22×C4×C43—21no—
212C22×C4×C43—21no—
213C22×C4×C43—82no—
214C22×C4×C43C2×D411yescharacteristic
215C22×C4×C43C2×D411yescharacteristic
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—24no—
222C2×C22⋊D43—24no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—82no—
225C2×C22⋊D43—82no—
226C2×C22⋊D43—82no—
227C2×C22⋊D43—82no—
228C2×C22⋊D43—82no—
229C22×Dic43—21no—
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233#10621902—44no—
234#10621902—44no—
235#10621902—48no—
236D4×D43—44no—
237D4×D43—44no—
238D4×D43—48no—
239C2×D172—21no—
240C2×D172—21no—
241C2×D172—21no—
242C2×D172—24no—
243C2×D172—24no—
244C2×D172—24no—
245C2×D172—24no—
246C2×D172—22no—
247C2×D172—22no—
248C2×D172—22no—
249C2×D172—22no—
250C2×D172—22no—
251C2×D172—22no—
252C2×D172—44no—
253C2×D172—82no—
254C2×D172—82no—
255C2×D172—82no—
256C2×D172C2412yes—
257C2×D172C2412yes—
258C2×D172C2412yes—
259C2×C4×D43—22no—
260C2×C4×D43—22no—
261C2×C4×D43—24no—
262C2×C4×D43—24no—
263C2×C4×D43—44no—
264C2×C4×D43—82no—
265C2×C4×D43C2×D412yes—
266C2×C4×D43C2412yes—
267SD16×C43—44no—
268D8×C43—44no—
269C2×C8×C43—22no—
270C2×C8×C43—22no—
271C2×C8×C43C2412yes—
272C2×C8×C43C2412yes—
273C4⋊C4×C43—21no—
274C4⋊C4×C43C2412yes—
275C22⋊C4×C43—24no—
276C22⋊C4×C43—24no—
277C22⋊C4×C43—24no—
278C42×C43C2×D412yes—
279C42×C43C2412yes—
280C22⋊Dic43—24no—
281#10621884—44no—
282#10621882—44no—
283#10621882—44no—
284#10621882—44no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287(C2×D43)⋊C4—24no—
288(C2×D43)⋊C4—24no—
289(C2×D43)⋊C4C2×D414yes—
290(C2×D43)⋊C4C2×D414yes—
291C4⋊Dic43—21no—
292C4⋊Dic43—24no—
293C4⋊Dic43C2412yes—
294Dic43⋊C4—24no—
295Dic43⋊C4C2×D414yes—
296Dic43⋊C4C2×D414yes—
297C4×Dic43C2×D412yes—
298C4×Dic43C2412yes—
299C2×C43⋊C8—22no—
300C2×C43⋊C8—22no—
301C2×C43⋊C8C2412yes—
302C2×C43⋊C8C2412yes—
303D344—44no—
304D344—44no—
305C23×C43—22no—
306C23×C43—22no—
307C23×C43—42no—
308C23×C43—42no—
309C23×C43—42no—
310C23×C43—42no—
311C23×C43—42no—
312C23×C43—42no—
313C23×C43C22×D411yescharacteristic
314C22×D43—22no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—22no—
318C22×D43—22no—
319C22×D43—22no—
320C22×D43—48no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—42no—
327C22×D43—42no—
328C22×D43—42no—
329C22×D43—42no—
330C22×D43—84no—
331C22×D43—84no—
332C22×D43—816no—
333C22×D43C22×D412yes—
334Q8×C43—22no—
335Q8×C43—22no—
336Q8×C43—42no—
337D4×C43—22no—
338D4×C43—22no—
339D4×C43—22no—
340D4×C43—22no—
341D4×C43—42no—
342D4×C43—42no—
343C2×C4×C43—22no—
344C2×C4×C43—22no—
345C2×C4×C43—22no—
346C2×C4×C43—22no—
347C2×C4×C43—42no—
348C2×C4×C43—42no—
349C2×C4×C43—84no—
350C2×C4×C43C22×D412yes—
351C2×C4×C43C22×D412yes—
352C2×C4×C43C22×D411yescharacteristic
353C2×C4×C43H(5,𝔽2)12yes—
354C2×C4×C43H(5,𝔽2)12yes—
355C2×C4×C43C2511yescharacteristic
356C22⋊D43—48no—
357C22⋊D43—84no—
358C22⋊D43—84no—
359C22⋊D43—84no—
360C22⋊D43—84no—
361C22⋊D43—84no—
362C2×Dic43—22no—
363C2×Dic43—22no—
364C2×Dic43—22no—
365C2×Dic43—22no—
366C2×Dic43—42no—
367C2×Dic43C22×D412yes—
368C2×Dic43C22×D412yes—
369C2×Dic43C22×D412yes—
370D172—22no—
371D172—22no—
372D172—22no—
373D172—22no—
374D172—22no—
375D172—22no—
376D172—48no—
377D172—42no—
378D172—42no—
379D172—42no—
380D172—84no—
381D172—84no—
382D172—84no—
383C4×D43—24no—
384C4×D43—22no—
385C4×D43—22no—
386C4×D43—48no—
387C4×D43—84no—
388C8×C43—22no—
389C8×C43—22no—
390C43⋊C8—22no—
391C43⋊C8—22no—
392C2×#3220—431nomaximal, Sylow
393C22×C43—42no—
394C22×C43—42no—
395C22×C43—42no—
396C22×C43—42no—
397C22×C43—42no—
398C22×C43—42no—
399C22×C43—84no—
400C22×C43—84no—
401C22×C43#53512yes—
402C22×C43#57612yes—
403C22×C43#57612yes—
404C22×C43C23×D411yescharacteristic
405C2×D43—22no—
406C2×D43—22no—
407C2×D43—22no—
408C2×D43—44no—
409C2×D43—42no—
410C2×D43—42no—
411C2×D43—42no—
412C2×D43—42no—
413C2×D43—42no—
414C2×D43—42no—
415C2×D43—42no—
416C2×D43—42no—
417C2×D43—42no—
418C2×D43—816no—
419C2×D43—84no—
420C2×D43—84no—
421C2×D43—84no—
422C4×C43—22no—
423C4×C43—22no—
424C4×C43—42no—
425C4×C43—42no—
426C4×C43#53512yes—
427C4×C43C2×H(5,𝔽2)11yescharacteristic
428C4×C43C2×H(5,𝔽2)11yescharacteristic
429Dic43—22no—
430Dic43—22no—
431Dic43—22no—
432Dic43—42no—
433C2×#540—431no—
434C2×#535—431no—
435#3220—4316no—
436C2×#496—431no—
437C2×#493—431no—
438C2×#490—431no—
439C2×#488—431no—
440C2×#463—431no—
441C2×#463D4311yescharacteristic, complemented
442C2×#459—431no—
443C2×#459—431no—
444C2×#449—431no—
445C2×#449—431no—
446C2×#447—431no—
447C2×#447—431no—
448C2×#433—431no—
449C2×C43—82no—
450C2×C43—82no—
451C2×C43#322014yescomplemented
452C2×C43C2×#53511yescharacteristic
453C2×C43C2×#57611yescharacteristic
454C2×C43C2×#57611yescharacteristic
455D43—42no—
456D43—82no—
457D43—82no—
458D43—82no—
459C22×#41—431no—
460C23×D4—431no—
461C22×SD16—431no—
462C22×SD16C2×D4311yescharacteristic, complemented
463C22×D8—431no—
464C22×D8—431no—
465C22×D8—431no—
466C22×D8—431no—
467C22×D8—431no—
468C22×D8C2×D4311yescharacteristic
469#540—438no—
470#540—864no—
471#535—438no—
472#535—864no—
473C2×#127—431no—
474C2×#127—431no—
475C2×#127—431no—
476C2×#125—431no—
477C2×#124—431no—
478C2×#124C2×D4311yescharacteristic
479C2×#123—861no—
480C2×#123—861no—
481C2×#121—431no—
482C2×#121—431no—
483C2×#121—861no—
484C2×#121—861no—
485C2×#121—861no—
486C2×#121—861no—
487C2×#120—861no—
488C2×#120—861no—
489C2×C4×D4—431no—
490C2×C4×D4C2×D4311yescharacteristic, complemented
491C2×#117—431no—
492#496—438no—
493#493—438no—
494#490—438no—
495#488—438no—
496#463—438no—
497#463C2×D4318yescomplemented
498#459—438no—
499#459—438no—
500#449—438no—
501#449—438no—
502#447—438no—
503#447—438no—
504#433—438no—
505C2×C4⋊C8—431no—
506C2×C4⋊C8C2×D4311yescharacteristic, complemented
507C2×#103—431no—
508C2×#103C2×D4311yescharacteristic, complemented
509C2×#102—431no—
510C2×#102—431no—
511C2×#102—431no—
512C2×#102—431no—
513C2×#102—431no—
514C2×#102C2×D4311yescharacteristic
515C2×C22⋊C8—431no—
516C2×C22⋊C8—431no—
517C2×#97—431no—
518C2×C4×C8—431no—
519C43C2×#322011yescharacteristic, complemented, Sylow
520C25—861no—
521C2×#41—434no—
522C2×#41—862no—
523C2×#41—1722no—
524C2×#41—1722no—
525C22×Q8C22×D4311yescharacteristic
526C22×D4—434no—
527C22×D4—431no—
528C22×D4—431no—
529C22×D4—431no—
530C22×D4—861no—
531C22×D4—861no—
532C22×D4—862no—
533C22×D4—861no—
534C22×D4—861no—
535C22×D4—861no—
536C22×D4—861no—
537C22×D4—861no—
538C22×D4—861no—
539C22×D4—861no—
540C22×D4—861no—
541C22×D4—1722no—
542C22×D4—1722no—
543C22×D4C22×D4311yescharacteristic
544C22×D4C22×D4311yescharacteristic
545C23×C4—21no—
546C23×C4—431no—
547C23×C4—861no—
548C23×C4—861no—
549C2×SD16—42no—
550C2×SD16—434no—
551C2×SD16—1722no—
552C2×SD16C22×D4314yescomplemented
553C2×D8—42no—
554C2×D8—434no—
555C2×D8—434no—
556C2×D8—434no—
557C2×D8—434no—
558C2×D8—434no—
559C2×D8—1722no—
560C2×D8—1722no—
561C2×D8—1722no—
562C2×D8—1722no—
563C2×D8—1722no—
564C2×D8C22×D4314yes—
565C22×C8—431no—
566C22×C8—431no—
567C22×C8C22×D4311yescharacteristic
568C22×C8C22×D4311yescharacteristic
569#127—434no—
570#127—434no—
571#127—434no—
572#127—862no—
573#127—862no—
574#127—862no—
575#125—434no—
576#125—862no—
577#124—22no—
578#124—434no—
579#124—862no—
580#124C22×D4314yes—
581#123—868no—
582#123—868no—
583#121—434no—
584#121—434no—
585#121—868no—
586#121—868no—
587#121—868no—
588#121—868no—
589#121—862no—
590#121—862no—
591#120—868no—
592#120—868no—
593C4×D4—22no—
594C4×D4—434no—
595C4×D4—862no—
596C4×D4C22×D4314yescomplemented
597#117—434no—
598#117—434no—
599C2×C4⋊C4—431no—
600C2×C4⋊C4—431no—
601C2×C4⋊C4—431no—
602C2×C4⋊C4—861no—
603C2×C4⋊C4—861no—
604C2×C4⋊C4C22×D4311yescharacteristic
605C2×C22⋊C4—21no—
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×C22⋊C4—861no—
614C2×C22⋊C4—861no—
615C2×C42—431no—
616C2×C42C22×D4311yescharacteristic
617C4⋊C8—434no—
618C4⋊C8C22×D4314yescomplemented
619#103—434no—
620#103C22×D4314yescomplemented
621#102—434no—
622#102—434no—
623#102—434no—
624#102—434no—
625#102—434no—
626#102C22×D4314yes—
627C22⋊C8—434no—
628C22⋊C8—434no—
629#97—434no—
630C4×C8—434no—
631C24—21no—
632C24—21no—
633C24—431no—
634C24—864no—
635C24—861no—
636C24—861no—
637C24—861no—
638C24—3442no—
639C24—3442no—
640C24—1724no—
641#41—1724no—
642#41—1724no—
643#41—1728no—
644C2×Q8—21no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8C23×D4312yes—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—432no—
655C2×D4—432no—
656C2×D4—432no—
657C2×D4—864no—
658C2×D4—864no—
659C2×D4—864no—
660C2×D4—864no—
661C2×D4—864no—
662C2×D4—864no—
663C2×D4—864no—
664C2×D4—864no—
665C2×D4—864no—
666C2×D4—864no—
667C2×D4—861no—
668C2×D4—861no—
669C2×D4—861no—
670C2×D4—862no—
671C2×D4—862no—
672C2×D4—862no—
673C2×D4—862no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—3442no—
677C2×D4—3442no—
678C2×D4—3442no—
679C2×D4—3442no—
680C2×D4—3442no—
681C2×D4—3442no—
682C2×D4—3442no—
683C2×D4—3442no—
684C2×D4—1724no—
685C2×D4—1724no—
686C2×D4—1724no—
687C2×D4—1728no—
688C2×D4—1724no—
689C2×D4C23×D4312yes—
690C2×D4C23×D4312yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—24no—
694C22×C4—82no—
695C22×C4—431no—
696C22×C4—431no—
697C22×C4—431no—
698C22×C4—432no—
699C22×C4—432no—
700C22×C4—864no—
701C22×C4—862no—
702C22×C4—862no—
703C22×C4—861no—
704C22×C4—864no—
705C22×C4—3442no—
706C22×C4—1724no—
707C22×C4D4×D4311yescharacteristic
708C22×C4D4×D4311yescharacteristic
709C22×C4C23×D4311yescharacteristic
710SD16—44no—
711SD16—1724no—
712D8—44no—
713D8—1724no—
714D8—1724no—
715D8—1724no—
716D8—1724no—
717D8—1724no—
718C2×C8—22no—
719C2×C8—22no—
720C2×C8—432no—
721C2×C8—432no—
722C2×C8—862no—
723C2×C8—862no—
724C2×C8C23×D4312yes—
725C2×C8C23×D4312yes—
726C4⋊C4—21no—
727C4⋊C4—434no—
728C4⋊C4—434no—
729C4⋊C4—432no—
730C4⋊C4—864no—
731C4⋊C4—864no—
732C4⋊C4—861no—
733C4⋊C4C23×D4312yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—434no—
738C22⋊C4—434no—
739C22⋊C4—864no—
740C22⋊C4—864no—
741C22⋊C4—864no—
742C22⋊C4—864no—
743C22⋊C4—864no—
744C42—432no—
745C42—432no—
746C42D4×D4312yes—
747C42C23×D4312yes—
748C23—22no—
749C23—22no—
750C23—42no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—432no—
757C23—862no—
758C23—862no—
759C23—862no—
760C23—862no—
761C23—862no—
762C23—862no—
763C23—3444no—
764C23—3444no—
765C23—34416no—
766C23—1728no—
767C23—1722no—
768C23—1722no—
769C23—1722no—
770C23—1722no—
771C23—1722no—
772C23—1722no—
773C23—1722no—
774C23—1722no—
775C23—1722no—
776C23C2×D4×D4311yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—42no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—42no—
785D4—42no—
786D4—862no—
787D4—862no—
788D4—862no—
789D4—862no—
790D4—862no—
791D4—862no—
792D4—3444no—
793D4—3444no—
794D4—3444no—
795D4—3444no—
796D4—3444no—
797D4—3444no—
798D4—3444no—
799D4—3444no—
800D4—1728no—
801D4—1728no—
802D4—1722no—
803D4—1722no—
804D4—1722no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—84no—
812C2×C4—432no—
813C2×C4—432no—
814C2×C4—432no—
815C2×C4—862no—
816C2×C4—862no—
817C2×C4—862no—
818C2×C4—864no—
819C2×C4—862no—
820C2×C4—862no—
821C2×C4—862no—
822C2×C4—3444no—
823C2×C4—1728no—
824C2×C4—1722no—
825C2×C4C2×D4×D4312yes—
826C2×C4C2×D4×D4312yes—
827C2×C4C2×D4×D4311yescharacteristic
828C2×C4#1306337012yes—
829C2×C4#1306337112yes—
830C2×C4C24×D4311yescharacteristic
831C8—22no—
832C8—22no—
833C8—862no—
834C8—862no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—84no—
842C22—84no—
843C22—862no—
844C22—862no—
845C22—862no—
846C22—34416no—
847C22—3444no—
848C22—3444no—
849C22—3444no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1722no—
854C22—1722no—
855C22—1722no—
856C22—1722no—
857C22—1722no—
858C22—1722no—
859C22—1724no—
860C22#1458346512yes—
861C22#1458370112yes—
862C22#1458370312yes—
863C22C22×D4×D4311yescharacteristic
864C4—22no—
865C4—22no—
866C4—42no—
867C4—42no—
868C4—862no—
869C4—862no—
870C4—862no—
871C4—1722no—
872C4#1458346512yes—
873C4C2×#1306337011yescharacteristic
874C4C2×#1306337111yescharacteristic
875C2—82no—
876C2—82no—
877C2—3442no—
878C2—3442no—
879C2—3442no—
880C2—1722no—
881C2#1914564214yesdirect product factor
882C2C2×#1458346511yescharacteristic
883C2C2×#1458370111yescharacteristic
884C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#463C2
socleC23×C43C22×D4
hypercenterC2×#463D43
hypocenterC43C2×#3220
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C2×#14583500C2semidirect
2. C2×#14583467C2semidirect
3. #19145642C2direct (N × H)
4. C2×#14583285C2semidirect
5. C2×#14583274C2semidirect
6. C2×#14583262C2semidirect
7. C2×#14583255C2semidirect
8. C2×#14583111C2semidirect
9. C2×#14583095C2semidirect
10. C2×#14583094C2semidirect
11. C2×#14583047C2semidirect
12. C2×#14583043C2semidirect
13. C2×#14583034C2semidirect
14. C2×#14583031C2semidirect
15. C2×#14582959C2semidirect
16. C2×C43×#463C2semidirect
19. C22×#10621884C22semidirect
21. C22×D344C22semidirect
24. C22×#10621882C22semidirect
26. #14583500C22semidirect
28. #14583467C22semidirect
31. C2×#13063321C22semidirect
32. C2×#13063316C22semidirect
44. C2×C4×D172C22semidirect
46. #14583285C22semidirect
47. #14583274C22semidirect
48. #14583262C22semidirect
49. #14583255C22semidirect
50. #14583111C22semidirect
51. #14583095C22semidirect
52. #14583094C22semidirect
53. #14583047C22semidirect
54. #14583043C22semidirect
55. #14583034C22semidirect
56. #14583031C22semidirect
57. #14582959C22semidirect
58. C2×C4⋊(C43⋊C8)C22semidirect
59. C2×#13063249C22semidirect
61. C2×#13063247C22semidirect
64. C2×#13063245C22semidirect
67. C2×#13063235C22semidirect
68. C2×C8×Dic43C22semidirect
69. C22×SD16×C43C22semidirect
72. C2×C4×D4×C43C22semidirect
73. C43×#463C22semidirect
74. C2×C4⋊C8×C43C22semidirect
75. C2×#103×C43C22semidirect
103. C2×#10621884C23semidirect
107. C2×D344C23semidirect
113. C2×#10621882C23semidirect
121. #13063321C23semidirect
123. #13063316C23semidirect
139. C4×D172C23semidirect
155. C4⋊(C43⋊C8)C23semidirect
156. #13063249C23semidirect
158. #13063247C23semidirect
161. #13063245C23semidirect
164. #13063235C23semidirect
165. C8×Dic43C23semidirect
171. C2×SD16×C43C23semidirect
179. C4×D4×C43C23semidirect
185. C4⋊C8×C43C23semidirect
186. #103×C43C23semidirect
441. C2×#463D43semidirect
451. C2×C43#3220semidirect
462. C22×SD16C2×D43semidirect
490. C2×C4×D4C2×D43semidirect
497. #463C2×D43semidirect
506. C2×C4⋊C8C2×D43semidirect
508. C2×#103C2×D43semidirect
519. C43C2×#3220semidirect
552. C2×SD16C22×D43semidirect
596. C4×D4C22×D43semidirect
618. C4⋊C8C22×D43semidirect
620. #103C22×D43semidirect
881. C2#19145642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835002
C2×#145834672
#191456422
C2×#145832852
C2×#145832742
C2×#145832622
C2×#145832552
C2×#145831112
C2×#145830952
C2×#145830942
C2×#145830472
C2×#145830432
C2×#145830342
C2×#145830312
C2×#145829592
C2×C43×#4632
C2×#322043