Finite Group Databasebeta

← C2×#19146600 #25973298

Subgroups — C2×#19146600 #25973298

Order 11008.

2242 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583602C211yesmaximal, characteristic, complemented
2C2×#14583569C211yesmaximal, characteristic, complemented
3#19146600C2116yesmaximal, direct product factor
4C2×#14583221C211yesmaximal, characteristic, complemented
5C2×#14583211C211yesmaximal, characteristic, complemented
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583151C211yesmaximal, characteristic, complemented
8C2×#14583134C211yesmaximal, characteristic, complemented
9C2×#14583091C211yesmaximal, characteristic, complemented
10C2×#14583045C211yesmaximal, characteristic, complemented
11C2×#14583045C211yesmaximal, characteristic, complemented
12C2×#14583001C211yesmaximal, characteristic, complemented
13C2×#14582972C211yesmaximal, characteristic, complemented
14C2×#14582897C211yesmaximal, characteristic, complemented
15C2×#14582892C211yesmaximal, characteristic, complemented
16C2×C43×#490C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×#10621900C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×#10621872C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24#14583602—24no—
25#14583602C2218yescomplemented
26#14583569—24no—
27#14583569C2218yescomplemented
28C2×#13063321—21no—
29C2×#13063320—21no—
30C2×#13063310—21no—
31C2×#13063300—21no—
32C2×#13063300C2211yescharacteristic
33C2×#13063300C2211yescharacteristic
34C2×#13063297—21no—
35C2×#13063297—21no—
36C2×#13063296C2211yescharacteristic
37C2×#13063296C2211yescharacteristic
38C2×C4×Dic86C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×D4×Dic43—21no—
42C2×#13063287—21no—
43C2×#13063283C2211yescharacteristic
44C2×C4⋊C4×D43C2211yescharacteristic
45#14583221C2218yescomplemented
46#14583211C2218yescomplemented
47#14583203C2218yescomplemented
48#14583151C2218yescomplemented
49#14583134C2218yescomplemented
50#14583091C2218yescomplemented
51#14583045C2218yescomplemented
52#14583045C2218yescomplemented
53#14583001C2218yescomplemented
54#14582972C2218yescomplemented
55C2×#13063259C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59#14582897C2218yescomplemented
60#14582892C2218yescomplemented
61C2×#13063250C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063246C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#127×C43C2211yescharacteristic
70C2×#125×C43C2211yescharacteristic
71C43×#490C2218yescomplemented
72C2×#102×C43C2211yescharacteristic
73C2×#102×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—22no—
79C2×#10621900—24no—
80C2×#10621900—24no—
81C2×#10621900—42no—
82C2×#10621900—42no—
83C2×#10621900C2314yes—
84C2×#10621900C2314yes—
85C22×Dic86C2311yescharacteristic
86C22×D172—21no—
87C22×D172—21no—
88C22×D172D411yescharacteristic
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C22×C22⋊D43—21no—
94C23×Dic43—21no—
95C23×Dic43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43C2311yescharacteristic
99C22×C4×D43C2311yescharacteristic
100C2×#10621873—24no—
101C2×#10621873C2314yes—
102C2×#10621882—42no—
103C2×#10621882—42no—
104C2×#10621882C2314yes—
105C2×#10621882C2314yes—
106C2×#10621872—42no—
107C2×#10621872C2314yes—
108C22×C43⋊C8C2311yescharacteristic
109C22×C43⋊C8C2311yescharacteristic
110C2×C8×D43—42no—
111C2×C8×D43C2314yes—
112#13063321—28no—
113#13063320—28no—
114#13063310—28no—
115#13063300—28no—
116#13063300—22no—
117#13063300—22no—
118#13063300C2314yes—
119#13063300C2314yes—
120#13063297—28no—
121#13063297—28no—
122#13063296—22no—
123#13063296—22no—
124#13063296C2314yes—
125#13063296C2314yes—
126C4×Dic86—22no—
127C4×Dic86C2314yes—
128C4×D172—22no—
129C4×D172D414yes—
130C4×D172C2314yes—
131C4×D172C2314yes—
132D4×Dic43—28no—
133#13063287—28no—
134#13063283—22no—
135#13063283C2314yes—
136C2×C4⋊Dic43D411yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×C4⋊Dic43C2311yescharacteristic
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C4⋊C4×D43—22no—
142C4⋊C4×D43C2314yes—
143C2×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×(C2×D43)⋊C4D411yescharacteristic
151C2×C4×Dic43—21no—
152C2×C4×Dic43—21no—
153#13063259C2314yes—
154#13063258C2314yes—
155#13063256C2314yes—
156C4⋊(C43⋊C8)C2314yes—
157#13063250C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063247C2314yes—
161#13063246C2314yes—
162#13063246C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yes—
165C22×D4×C43—21no—
166C22×D4×C43—21no—
167C22×D4×C43C2311yescharacteristic
168C22×D4×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171#127×C43—22no—
172#127×C43C2314yes—
173#125×C43—22no—
174#125×C43C2314yes—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C42×C43C2311yescharacteristic
180#102×C43C2314yes—
181#102×C43C2314yes—
182#102×C43C2314yes—
183#102×C43C2314yes—
184#97×C43C2314yes—
185C24×C43—21no—
186C24×C43—21no—
187C23×D43—21no—
188C23×D43C2×D411yescharacteristic
189C23×D43C2×D411yescharacteristic
190C2×D4×C43—21no—
191C2×D4×C43—21no—
192C2×D4×C43—24no—
193C2×D4×C43—24no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43—22no—
197C2×D4×C43—22no—
198C2×D4×C43—44no—
199C2×D4×C43—82no—
200C2×D4×C43C2412yes—
201C2×D4×C43C2412yes—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43C2×D411yescharacteristic
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2411yescharacteristic
207C2×C22⋊D43—24no—
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—24no—
211C2×C22⋊D43—44no—
212C2×C22⋊D43—44no—
213C2×C22⋊D43—82no—
214C2×C22⋊D43—82no—
215C22×Dic43—24no—
216C22×Dic43—24no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43—44no—
221C22×Dic43—44no—
222C22×Dic43C2×D411yescharacteristic
223C22×Dic43C2×D411yescharacteristic
224#10621900—28no—
225#10621900—28no—
226#10621900—44no—
227#10621900—44no—
228#10621900—48no—
229#10621900—48no—
230C2×D172—21no—
231C2×D172—24no—
232C2×D172—24no—
233C2×D172—22no—
234C2×D172—22no—
235C2×D172—42no—
236C2×D172—44no—
237C2×D172—82no—
238C2×D172C2×D414yes—
239C2×D172C2412yes—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—22no—
243C2×C4×D43—22no—
244C2×C4×D43—24no—
245C2×C4×D43—24no—
246C2×C4×D43—82no—
247C2×C4×D43—82no—
248C2×C4×D43C2×D412yes—
249C2×C4×D43C2×D412yes—
250C2×C4×D43C2412yes—
251C2×C4×D43C2412yes—
252C2×Dic86—21no—
253C2×Dic86—22no—
254C2×Dic86#4114yes—
255C2×Dic86C2412yes—
256C2×C8×C43—22no—
257C2×C8×C43—22no—
258C2×C8×C43C2412yes—
259C2×C8×C43C2412yes—
260C4⋊C4×C43—24no—
261C4⋊C4×C43—24no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—21no—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C42×C43C2×D412yes—
267C42×C43C2412yes—
268C22⋊Dic43—24no—
269C22⋊Dic43—24no—
270#10621882—44no—
271#10621882—44no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4C2×D414yes—
277(C2×D43)⋊C4C2×D414yes—
278C4⋊Dic43—21no—
279C4⋊Dic43—21no—
280C4⋊Dic43C2×D414yes—
281C4⋊Dic43C2412yes—
282C4⋊Dic43C2412yes—
283Dic43⋊C4—24no—
284Dic43⋊C4—24no—
285C4×Dic43—24no—
286C4×Dic43—24no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291#10621873—28no—
292#10621872—44no—
293C8×D43—44no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43—42no—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43C22×D412yes—
314C22×D43C22×D412yes—
315D4×C43—22no—
316D4×C43—22no—
317D4×C43—22no—
318D4×C43—22no—
319D4×C43—48no—
320D4×C43—42no—
321D4×C43—42no—
322D4×C43—84no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—42no—
328C2×C4×C43—42no—
329C2×C4×C43C22×D412yes—
330C2×C4×C43C22×D412yes—
331C2×C4×C43C22×D411yescharacteristic
332C2×C4×C43C2×#4112yes—
333C2×C4×C43H(5,𝔽2)12yes—
334C2×C4×C43C2511yescharacteristic
335C22⋊D43—48no—
336C22⋊D43—48no—
337C22⋊D43—84no—
338C22⋊D43—84no—
339C2×Dic43—24no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—48no—
346C2×Dic43—48no—
347C2×Dic43—42no—
348C2×Dic43—42no—
349C2×Dic43C22×D412yes—
350C2×Dic43C22×D412yes—
351D172—22no—
352D172—22no—
353D172—44no—
354D172—48no—
355D172—42no—
356D172—84no—
357C4×D43—24no—
358C4×D43—24no—
359C4×D43—22no—
360C4×D43—22no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—84no—
364C4×D43—84no—
365Dic86—24no—
366Dic86—22no—
367Dic86C2×#4114yes—
368C8×C43—22no—
369C8×C43—22no—
370C43⋊C8—22no—
371C43⋊C8—22no—
372C2×#3309—431nomaximal, Sylow
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—84no—
380C22×C43—84no—
381C22×C43#54612yes—
382C22×C43#57512yes—
383C22×C43#57612yes—
384C22×C43C23×D411yescharacteristic
385C2×D43—22no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—22no—
390C2×D43—22no—
391C2×D43—44no—
392C2×D43—44no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—84no—
397C4×C43—22no—
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43#54612yes—
402C4×C43C22×#4111yescharacteristic
403C4×C43C2×H(5,𝔽2)11yescharacteristic
404Dic43—24no—
405Dic43—22no—
406Dic43—22no—
407Dic43—42no—
408Dic43—42no—
409C2×#553—431no—
410C2×#550—431no—
411#3309—4316no—
412C2×#490D4311yescharacteristic, complemented
413C2×#482—431no—
414C2×#480—431no—
415C2×#479—431no—
416C2×#469—431no—
417C2×#466—431no—
418C2×#459—431no—
419C2×#449—431no—
420C2×#449—431no—
421C2×#440—431no—
422C2×#435—431no—
423C2×#417—431no—
424C2×#416—431no—
425C2×C43—82no—
426C2×C43—82no—
427C2×C43#330914yescomplemented
428C2×C43C2×#54611yescharacteristic
429C2×C43C2×#57511yescharacteristic
430C2×C43C2×#57611yescharacteristic
431D43—42no—
432D43—42no—
433D43—82no—
434C22×#41—431no—
435C22×#41—431no—
436C22×SD16—431no—
437C22×D8—431no—
438C22×D8—431no—
439C22×M16—431no—
440C23×C8—431no—
441#553—438no—
442#553—864no—
443#550—438no—
444#550—864no—
445C2×#127—861no—
446C2×#127C2×D4311yescharacteristic
447C2×#126—861no—
448C2×#125C2×D4311yescharacteristic
449C2×#123—861no—
450C2×#121—431no—
451C2×#121—431no—
452C2×#121—431no—
453C2×#121—431no—
454C2×#121—861no—
455C2×#121—861no—
456C2×#121—861no—
457C2×C4×Q8—431no—
458C2×C4×D4—431no—
459C2×C4×D4—431no—
460C2×C4×D4—861no—
461C2×C4×D4—861no—
462C2×#117—431no—
463C22×C4⋊C4—431no—
464#490C2×D4318yescomplemented
465#482—438no—
466#480—438no—
467#479—438no—
468#469—438no—
469#466—438no—
470#459—438no—
471#449—438no—
472#449—438no—
473#440—438no—
474#435—438no—
475C2×#107—431no—
476C2×#107—431no—
477C2×#106—431no—
478C2×C4⋊C8—431no—
479#417—438no—
480#416—438no—
481C2×#103—431no—
482C2×#103—431no—
483C2×#103—431no—
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102C2×D4311yescharacteristic
488C2×#102C2×D4311yescharacteristic
489C2×#102C2×D4311yescharacteristic
490C2×#102C2×D4311yescharacteristic
491C2×C22⋊C8—431no—
492C2×C22⋊C8—431no—
493C2×#97C2×D4311yescharacteristic
494C43C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—434no—
496C2×#41—434no—
497C2×#41—862no—
498C2×#41—862no—
499C2×#41—864no—
500C2×#41—864no—
501C2×#41—1722no—
502C2×#41—1722no—
503C22×Q8—431no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—431no—
507C22×D4—431no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—861no—
511C22×D4—861no—
512C22×D4—861no—
513C22×D4—861no—
514C22×D4C22×D4311yescharacteristic
515C22×D4C22×D4311yescharacteristic
516C23×C4—431no—
517C23×C4—431no—
518C23×C4—861no—
519C23×C4—861no—
520C23×C4—861no—
521C23×C4—861no—
522C2×SD16—434no—
523C2×SD16—864no—
524C2×D8—434no—
525C2×D8—434no—
526C2×D8—1722no—
527C2×D8—1722no—
528C2×M16—434no—
529C2×M16—1722no—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—434no—
533C22×C8—1722no—
534C22×C8C22×D4311yescharacteristic
535C22×C8C22×D4311yescharacteristic
536#127—22no—
537#127—868no—
538#127C22×D4314yes—
539#126—868no—
540#125—22no—
541#125C22×D4314yes—
542#123—868no—
543#121—434no—
544#121—434no—
545#121—434no—
546#121—434no—
547#121—868no—
548#121—868no—
549#121—862no—
550#121—862no—
551#121—868no—
552#121—862no—
553#121—862no—
554C4×Q8—434no—
555C4×Q8—862no—
556C4×D4—434no—
557C4×D4—434no—
558C4×D4—434no—
559C4×D4—868no—
560C4×D4—868no—
561C4×D4—862no—
562#117—434no—
563#117—862no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—434no—
570C2×C4⋊C4—862no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4—861no—
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C4⋊C4C22×D4311yescharacteristic
575C2×C22⋊C4—431no—
576C2×C22⋊C4—431no—
577C2×C22⋊C4—861no—
578C2×C22⋊C4—861no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C42—861no—
584C2×C42—861no—
585C2×C42C22×D4311yescharacteristic
586#107—434no—
587#107—434no—
588#106—434no—
589C4⋊C8—434no—
590#103—434no—
591#103—434no—
592#103—434no—
593#102—434no—
594#102—434no—
595#102—434no—
596#102C22×D4314yes—
597#102C22×D4314yes—
598#102C22×D4314yes—
599#102C22×D4314yes—
600C22⋊C8—434no—
601C22⋊C8—434no—
602#97C22×D4314yes—
603C24—21no—
604C24—21no—
605C24—431no—
606C24—431no—
607C24—861no—
608#41—868no—
609#41—868no—
610#41—1724no—
611#41—1724no—
612#41—1728no—
613#41—1728no—
614C2×Q8—434no—
615C2×Q8—432no—
616C2×Q8—861no—
617C2×Q8—862no—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—24no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—22no—
625C2×D4—22no—
626C2×D4—44no—
627C2×D4—82no—
628C2×D4—434no—
629C2×D4—432no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—864no—
634C2×D4—864no—
635C2×D4—864no—
636C2×D4—861no—
637C2×D4—862no—
638C2×D4—862no—
639C2×D4—3442no—
640C2×D4—3442no—
641C2×D4—3442no—
642C2×D4—1722no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1724no—
646C2×D4C23×D4312yes—
647C2×D4C23×D4312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—431no—
651C22×C4—431no—
652C22×C4—432no—
653C22×C4—432no—
654C22×C4—432no—
655C22×C4—432no—
656C22×C4—864no—
657C22×C4—864no—
658C22×C4—864no—
659C22×C4—861no—
660C22×C4—862no—
661C22×C4—862no—
662C22×C4—862no—
663C22×C4—862no—
664C22×C4—861no—
665C22×C4—861no—
666C22×C4—864no—
667C22×C4—3442no—
668C22×C4—3442no—
669C22×C4—1724no—
670C22×C4—1724no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—868no—
675D8—1724no—
676D8—1724no—
677M16—1724no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—432no—
681C2×C8—432no—
682C2×C8—862no—
683C2×C8—862no—
684C2×C8—1724no—
685C2×C8C23×D4312yes—
686C2×C8C23×D4312yes—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—434no—
692C4⋊C4—432no—
693C4⋊C4—432no—
694C4⋊C4—864no—
695C4⋊C4—861no—
696C4⋊C4—861no—
697C4⋊C4—864no—
698C4⋊C4C23×D4312yes—
699C4⋊C4C23×D4312yes—
700C22⋊C4—434no—
701C22⋊C4—434no—
702C22⋊C4—864no—
703C22⋊C4—864no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C42—864no—
709C42—864no—
710C42D4×D4312yes—
711C42C23×D4312yes—
712C23—22no—
713C23—22no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—432no—
721C23—432no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—862no—
729C23—1722no—
730C23—1722no—
731C23—1722no—
732C23C2×D4×D4311yescharacteristic
733Q8—434no—
734Q8—862no—
735Q8—864no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—48no—
741D4—42no—
742D4—42no—
743D4—84no—
744D4—862no—
745D4—862no—
746D4—3444no—
747D4—3444no—
748D4—3444no—
749D4—1724no—
750D4—1728no—
751D4—1728no—
752D4—1728no—
753D4—1722no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—432no—
761C2×C4—432no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—864no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—864no—
771C2×C4—864no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—3444no—
775C2×C4—3444no—
776C2×C4—1728no—
777C2×C4—1728no—
778C2×C4—1722no—
779C2×C4—1722no—
780C2×C4C2×D4×D4312yes—
781C2×C4C2×D4×D4312yes—
782C2×C4C2×D4×D4311yescharacteristic
783C2×C4#41×D4312yes—
784C2×C4#1306337112yes—
785C2×C4C24×D4311yescharacteristic
786C8—22no—
787C8—22no—
788C8—862no—
789C8—862no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—84no—
797C22—84no—
798C22—862no—
799C22—862no—
800C22—862no—
801C22—862no—
802C22—862no—
803C22—862no—
804C22—3444no—
805C22—1722no—
806C22—1722no—
807C22—1722no—
808C22—1724no—
809C22—1724no—
810C22#1458354212yes—
811C22#1458369512yes—
812C22#1458370312yes—
813C22C22×D4×D4311yescharacteristic
814C4—22no—
815C4—22no—
816C4—42no—
817C4—42no—
818C4—862no—
819C4—862no—
820C4—864no—
821C4—1722no—
822C4—1722no—
823C4#1458354212yes—
824C4C2×#41×D4311yescharacteristic
825C4C2×#1306337111yescharacteristic
826C2—82no—
827C2—82no—
828C2—3442no—
829C2—1722no—
830C2—1722no—
831C2#1914660014yesdirect product factor
832C2C2×#1458354211yescharacteristic
833C2C2×#1458369511yescharacteristic
834C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#490C2
socleC23×C43C22×D4
hypercenterC2×#490D43
hypocenterC43C2×#3309
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#490

Complements

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

NH ≅ G/Ntype
1. C2×#14583602C2semidirect
2. C2×#14583569C2semidirect
3. #19146600C2direct (N × H)
4. C2×#14583221C2semidirect
5. C2×#14583211C2semidirect
6. C2×#14583203C2semidirect
7. C2×#14583151C2semidirect
8. C2×#14583134C2semidirect
9. C2×#14583091C2semidirect
10. C2×#14583045C2semidirect
11. C2×#14583045C2semidirect
12. C2×#14583001C2semidirect
13. C2×#14582972C2semidirect
14. C2×#14582897C2semidirect
15. C2×#14582892C2semidirect
16. C2×C43×#490C2semidirect
25. #14583602C22semidirect
27. #14583569C22semidirect
45. #14583221C22semidirect
46. #14583211C22semidirect
47. #14583203C22semidirect
48. #14583151C22semidirect
49. #14583134C22semidirect
50. #14583091C22semidirect
51. #14583045C22semidirect
52. #14583045C22semidirect
53. #14583001C22semidirect
54. #14582972C22semidirect
59. #14582897C22semidirect
60. #14582892C22semidirect
71. C43×#490C22semidirect
412. C2×#490D43semidirect
427. C2×C43#3309semidirect
464. #490C2×D43semidirect
494. C43C2×#3309semidirect
831. C2#19146600direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836022
C2×#145835692
#191466002
C2×#145832212
C2×#145832112
C2×#145832032
C2×#145831512
C2×#145831342
C2×#145830912
C2×#145830452
C2×#145830012
C2×#145829722
C2×#145828972
C2×#145828922
C2×C43×#4902
C2×#330943