Finite Group Databasebeta

← C2×#19146602 #25973300

Subgroups — C2×#19146602 #25973300

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×#14583597C211yesmaximal, characteristic, complemented
2C2×#14583568C211yesmaximal, characteristic, complemented
3#19146602C2116yesmaximal, direct product factor
4C2×#14583262C211yesmaximal, characteristic, complemented
5C2×#14583222C211yesmaximal, characteristic, complemented
6C2×#14583212C211yesmaximal, characteristic, complemented
7C2×#14583204C211yesmaximal, characteristic, complemented
8C2×#14583152C211yesmaximal, characteristic, complemented
9C2×#14583134C211yesmaximal, characteristic, complemented
10C2×#14583093C211yesmaximal, characteristic, complemented
11C2×#14583047C211yesmaximal, characteristic, complemented
12C2×#14583044C211yesmaximal, characteristic, complemented
13C2×#14583002C211yesmaximal, characteristic, complemented
14C2×#14582968C211yesmaximal, characteristic, complemented
15C2×#14582894C211yesmaximal, characteristic, complemented
16C2×C43×#417C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×D344C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×C8×D43C2211yescharacteristic
22#14583597—24no—
23#14583597C2218yescomplemented
24#14583568—24no—
25#14583568C2218yescomplemented
26C2×#13063321—21no—
27C2×#13063321C2211yescharacteristic
28C2×#13063320—21no—
29C2×#13063316C2211yescharacteristic
30C2×#13063310—21no—
31C2×#13063300C2211yescharacteristic
32C2×#13063299—21no—
33C2×#13063299—21no—
34C2×#13063299C2211yescharacteristic
35C2×#13063299C2211yescharacteristic
36C2×#13063296—21no—
37C2×#13063296C2211yescharacteristic
38C2×Q8×Dic43C2211yescharacteristic
39C2×#13063287C2211yescharacteristic
40C2×C4×C22⋊D43—21no—
41C2×C4×C22⋊D43—21no—
42C2×C4×C22⋊D43C2211yescharacteristic
43C2×#13063283C2211yescharacteristic
44#14583262C2218yescomplemented
45#14583222C2218yescomplemented
46#14583212C2218yescomplemented
47#14583204C2218yescomplemented
48#14583152C2218yescomplemented
49#14583134C2218yescomplemented
50#14583093C2218yescomplemented
51#14583047C2218yescomplemented
52#14583044C2218yescomplemented
53#14583002C2218yescomplemented
54#14582968C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063258C2211yescharacteristic
57C2×#13063257C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59#14582894C2218yescomplemented
60C2×#13063249C2211yescharacteristic
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×#41×C43C2211yescharacteristic
70C22×M16×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C43×#417C2218yescomplemented
73C2×#103×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C2×#10621902—22no—
78C2×#10621902—24no—
79C2×#10621902—42no—
80C2×#10621902C2314yes—
81C22×D172—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C22×C22⋊D43D411yescharacteristic
91C22×C4×D43—21no—
92C22×C4×D43—21no—
93C22×C4×D43C2311yescharacteristic
94C2×#10621884—24no—
95C2×#10621884C2314yes—
96C2×D344—42no—
97C2×D344C2314yes—
98C2×#10621882—42no—
99C2×#10621882C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—42no—
103C2×C8×D43C2314yes—
104#13063321—28no—
105#13063321—22no—
106#13063321C2314yes—
107#13063320—28no—
108#13063316—22no—
109#13063316C2314yes—
110#13063310—28no—
111#13063300—22no—
112#13063300C2314yes—
113#13063299—22no—
114#13063299—22no—
115#13063299—28no—
116#13063299—28no—
117#13063299C2314yes—
118#13063299C2314yes—
119#13063296—22no—
120#13063296—28no—
121#13063296C2314yes—
122Q8×Dic43—22no—
123Q8×Dic43C2314yes—
124#13063287—22no—
125#13063287C2314yes—
126C4×C22⋊D43—28no—
127C4×C22⋊D43—28no—
128C4×C22⋊D43D414yes—
129C4×C22⋊D43C2314yes—
130#13063283—22no—
131#13063283C2314yes—
132C2×C4⋊Dic43—21no—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×C4⋊Dic43C2311yescharacteristic
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4D411yescharacteristic
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43D411yescharacteristic
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4D411yescharacteristic
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063258C2314yes—
150#13063258C2314yes—
151#13063257C2314yes—
152Dic43⋊C8C2314yes—
153#13063249C2314yes—
154#13063247C2314yes—
155#13063247C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
158#13063245C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160(C2×D43)⋊C8C2314yes—
161#13063235C2314yes—
162C2×#41×C43—22no—
163C2×#41×C43—24no—
164C2×#41×C43—42no—
165C2×#41×C43C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×D4×C43—21no—
168C22×D4×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C2×M16×C43—42no—
173C2×M16×C43C2314yes—
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2311yescharacteristic
176C2×C4⋊C4×C43—22no—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2314yes—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181#103×C43C2314yes—
182#103×C43C2314yes—
183#102×C43C2314yes—
184#102×C43C2314yes—
185C24×C43—21no—
186C24×C43C2×D411yescharacteristic
187C23×D43—21no—
188C23×D43—21no—
189C23×D43C2×D411yescharacteristic
190#41×C43—28no—
191#41×C43—44no—
192#41×C43—48no—
193C2×Q8×C43—21no—
194C2×Q8×C43—22no—
195C2×Q8×C43#4114yes—
196C2×Q8×C43C2412yes—
197C2×D4×C43—21no—
198C2×D4×C43—24no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43—44no—
202C2×D4×C43C2412yes—
203C22×C4×C43—22no—
204C22×C4×C43—22no—
205C22×C4×C43—24no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—24no—
210C22×C4×C43—44no—
211C22×C4×C43—82no—
212C22×C4×C43C2×D411yescharacteristic
213C22×C4×C43C2×D412yes—
214C22×C4×C43C2412yes—
215C22×C4×C43C2411yescharacteristic
216C2×C22⋊D43—24no—
217C2×C22⋊D43—24no—
218C2×C22⋊D43—24no—
219C2×C22⋊D43—24no—
220C2×C22⋊D43—24no—
221C2×C22⋊D43—42no—
222C2×C22⋊D43—44no—
223C2×C22⋊D43—44no—
224C2×C22⋊D43—82no—
225C2×C22⋊D43—82no—
226C2×C22⋊D43—82no—
227C2×C22⋊D43C2×D414yes—
228C22×Dic43—21no—
229C22×Dic43—21no—
230C22×Dic43C2×D411yescharacteristic
231C22×Dic43C2×D411yescharacteristic
232C22×Dic43C2×D411yescharacteristic
233#10621902—28no—
234#10621902—44no—
235#10621902—48no—
236C2×D172—21no—
237C2×D172—21no—
238C2×D172—24no—
239C2×D172—24no—
240C2×D172—22no—
241C2×D172—22no—
242C2×D172—22no—
243C2×D172—22no—
244C2×D172—44no—
245C2×D172—82no—
246C2×D172C2412yes—
247C2×D172C2412yes—
248C2×C4×D43—22no—
249C2×C4×D43—22no—
250C2×C4×D43—24no—
251C2×C4×D43—24no—
252C2×C4×D43—44no—
253C2×C4×D43—82no—
254C2×C4×D43C2×D412yes—
255C2×C4×D43C2412yes—
256M16×C43—44no—
257C2×C8×C43—22no—
258C2×C8×C43—22no—
259C2×C8×C43C2412yes—
260C2×C8×C43C2412yes—
261C4⋊C4×C43—21no—
262C4⋊C4×C43—21no—
263C4⋊C4×C43—24no—
264C4⋊C4×C43C2412yes—
265C4⋊C4×C43C2412yes—
266C22⋊Dic43—24no—
267C22⋊Dic43C2×D414yes—
268#10621884—28no—
269#10621882—44no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4C2×D414yes—
276C4⋊Dic43—21no—
277C4⋊Dic43—21no—
278C4⋊Dic43—24no—
279C4⋊Dic43—24no—
280C4⋊Dic43C2412yes—
281C4⋊Dic43C2412yes—
282Dic43⋊C4—24no—
283Dic43⋊C4C2×D414yes—
284C4×Dic43—24no—
285C4×Dic43—24no—
286C4×Dic43C2×D412yes—
287C4×Dic43C2412yes—
288C2×C43⋊C8—22no—
289C2×C43⋊C8—22no—
290C2×C43⋊C8C2412yes—
291C2×C43⋊C8C2412yes—
292D344—44no—
293C8×D43—44no—
294C23×C43—22no—
295C23×C43—22no—
296C23×C43—22no—
297C23×C43—22no—
298C23×C43—42no—
299C23×C43—42no—
300C23×C43—42no—
301C23×C43C22×D412yes—
302C23×C43C22×D411yescharacteristic
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—42no—
314C22×D43C22×D412yes—
315Q8×C43—24no—
316Q8×C43—22no—
317Q8×C43C2×#4114yes—
318D4×C43—22no—
319D4×C43—22no—
320D4×C43—48no—
321D4×C43—42no—
322C2×C4×C43—24no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—24no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—48no—
331C2×C4×C43—42no—
332C2×C4×C43—42no—
333C2×C4×C43—84no—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4112yes—
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43C2511yescharacteristic
339C22⋊D43—44no—
340C22⋊D43—48no—
341C22⋊D43—48no—
342C22⋊D43—84no—
343C22⋊D43—84no—
344C22⋊D43—84no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—42no—
351C2×Dic43—42no—
352C2×Dic43C22×D412yes—
353C2×Dic43C22×D412yes—
354C2×Dic43C22×D412yes—
355D172—22no—
356D172—22no—
357D172—22no—
358D172—22no—
359D172—48no—
360D172—42no—
361D172—42no—
362D172—84no—
363C4×D43—24no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—48no—
367C4×D43—84no—
368C8×C43—22no—
369C8×C43—22no—
370C43⋊C8—22no—
371C43⋊C8—22no—
372C2×#3309—431nomaximal, Sylow
373C22×C43—22no—
374C22×C43—22no—
375C22×C43—22no—
376C22×C43—44no—
377C22×C43—42no—
378C22×C43—42no—
379C22×C43—42no—
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—44no—
389C2×D43—42no—
390C2×D43—42no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—84no—
396C2×D43—84no—
397C4×C43—24no—
398C4×C43—22no—
399C4×C43—42no—
400C4×C43—42no—
401C4×C43#54612yes—
402C4×C43C22×#4111yescharacteristic
403C4×C43C2×H(5,𝔽2)11yescharacteristic
404Dic43—22no—
405Dic43—22no—
406Dic43—22no—
407Dic43—42no—
408Dic43—42no—
409C2×#553—431no—
410C2×#550—431no—
411#3309—4316no—
412C2×#490—431no—
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×#417D4311yescharacteristic, complemented
424C2×#416—431no—
425C2×C43—42no—
426C2×C43—82no—
427C2×C43#330914yescomplemented
428C2×C43C2×#54611yescharacteristic
429C2×C43C2×#57511yescharacteristic
430C2×C43C2×#57611yescharacteristic
431D43—42no—
432D43—82no—
433D43—82no—
434C22×#41—431no—
435C22×#41C2×D4311yescharacteristic
436C22×SD16—431no—
437C22×D8—431no—
438C22×D8—431no—
439C22×M16C2×D4311yescharacteristic
440C23×C8—431no—
441#553—438no—
442#553—864no—
443#550—438no—
444#550—864no—
445C2×#127—431no—
446C2×#127—861no—
447C2×#126—861no—
448C2×#125—431no—
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⋊C4C2×D4311yescharacteristic
464#490—438no—
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#417C2×D4318yescomplemented
480#416—438no—
481C2×#103—431no—
482C2×#103C2×D4311yescharacteristic
483C2×#103C2×D4311yescharacteristic
484C2×#102—431no—
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102C2×D4311yescharacteristic
490C2×#102C2×D4311yescharacteristic
491C2×C22⋊C8—431no—
492C2×C22⋊C8—431no—
493C2×#97—431no—
494C43C2×#330911yescharacteristic, complemented, Sylow
495C2×#41—22no—
496C2×#41—24no—
497C2×#41—42no—
498C2×#41—434no—
499C2×#41—862no—
500C2×#41—864no—
501C2×#41—1722no—
502C2×#41C22×D4314yes—
503C22×Q8C22×D4311yescharacteristic
504C22×D4—21no—
505C22×D4—431no—
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×D4—861no—
515C22×D4C22×D4311yescharacteristic
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—431no—
519C23×C4—861no—
520C23×C4—861no—
521C23×C4C22×D4311yescharacteristic
522C2×SD16—434no—
523C2×SD16—864no—
524C2×D8—434no—
525C2×D8—434no—
526C2×D8—1722no—
527C2×D8—1722no—
528C2×M16—42no—
529C2×M16C22×D4314yes—
530C22×C8—431no—
531C22×C8—431no—
532C22×C8—434no—
533C22×C8—1722no—
534C22×C8C22×D4311yescharacteristic
535C22×C8C22×D4311yescharacteristic
536#127—434no—
537#127—862no—
538#127—868no—
539#126—868no—
540#125—434no—
541#125—862no—
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—868no—
551#121—862no—
552#121—862no—
553#121—862no—
554C4×Q8—434no—
555C4×Q8—862no—
556C4×D4—434no—
557C4×D4—434no—
558C4×D4—434no—
559C4×D4—862no—
560C4×D4—868no—
561C4×D4—868no—
562#117—434no—
563#117—862no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—431no—
569C2×C4⋊C4—861no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4C22×D4311yescharacteristic
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C4⋊C4C22×D4314yes—
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—431no—
584C2×C42—861no—
585C2×C42—861no—
586#107—434no—
587#107—434no—
588#106—434no—
589C4⋊C8—434no—
590#103—434no—
591#103C22×D4314yes—
592#103C22×D4314yes—
593#102—434no—
594#102—434no—
595#102—434no—
596#102—434no—
597#102—434no—
598#102C22×D4314yes—
599#102C22×D4314yes—
600C22⋊C8—434no—
601C22⋊C8—434no—
602#97—434no—
603C24—21no—
604C24—431no—
605C24—861no—
606C24—861no—
607C24D4×D4311yescharacteristic
608#41—28no—
609#41—44no—
610#41—48no—
611#41—868no—
612#41—1724no—
613#41—1728no—
614C2×Q8—21no—
615C2×Q8—22no—
616C2×Q8#1062189814yes—
617C2×Q8C23×D4312yes—
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—22no—
621C2×D4—22no—
622C2×D4—44no—
623C2×D4—434no—
624C2×D4—432no—
625C2×D4—432no—
626C2×D4—864no—
627C2×D4—864no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—861no—
634C2×D4—861no—
635C2×D4—862no—
636C2×D4—862no—
637C2×D4—862no—
638C2×D4—862no—
639C2×D4—3442no—
640C2×D4—3442no—
641C2×D4—3442no—
642C2×D4—3442no—
643C2×D4—1724no—
644C2×D4—1722no—
645C2×D4—1724no—
646C2×D4—1724no—
647C2×D4C23×D4312yes—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—24no—
655C22×C4—44no—
656C22×C4—82no—
657C22×C4—431no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—432no—
661C22×C4—432no—
662C22×C4—864no—
663C22×C4—864no—
664C22×C4—862no—
665C22×C4—862no—
666C22×C4—861no—
667C22×C4—861no—
668C22×C4—3442no—
669C22×C4—1724no—
670C22×C4D4×D4312yes—
671C22×C4D4×D4311yescharacteristic
672C22×C4C23×D4312yes—
673C22×C4C23×D4311yescharacteristic
674SD16—868no—
675D8—1724no—
676D8—1724no—
677M16—44no—
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—21no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—434no—
691C4⋊C4—432no—
692C4⋊C4—432no—
693C4⋊C4—864no—
694C4⋊C4—864no—
695C4⋊C4—864no—
696C4⋊C4—861no—
697C4⋊C4—861no—
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—432no—
709C42—432no—
710C42—864no—
711C42—864no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—42no—
717C23—42no—
718C23—42no—
719C23—432no—
720C23—862no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—1722no—
726C23—1722no—
727C23—1722no—
728C23—1722no—
729C23—1722no—
730C23—1722no—
731C23C2×D4×D4312yes—
732C23C2×D4×D4311yescharacteristic
733Q8—22no—
734Q8—24no—
735Q8C2×#1062189814yes—
736D4—22no—
737D4—22no—
738D4—48no—
739D4—42no—
740D4—862no—
741D4—862no—
742D4—862no—
743D4—862no—
744D4—3444no—
745D4—3444no—
746D4—3444no—
747D4—3444no—
748D4—1728no—
749D4—1724no—
750D4—1728no—
751D4—1728no—
752D4—1722no—
753D4—1722no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—24no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—48no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—84no—
766C2×C4—432no—
767C2×C4—432no—
768C2×C4—432no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—862no—
774C2×C4—864no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—3444no—
778C2×C4—1728no—
779C2×C4—1722no—
780C2×C4—1722no—
781C2×C4C2×D4×D4312yes—
782C2×C4C2×D4×D4311yescharacteristic
783C2×C4C2×#1062189812yes—
784C2×C4#1306337012yes—
785C2×C4C24×D4311yescharacteristic
786C8—22no—
787C8—22no—
788C8—862no—
789C8—862no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—44no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—84no—
798C22—862no—
799C22—862no—
800C22—862no—
801C22—3444no—
802C22—3444no—
803C22—1722no—
804C22—1722no—
805C22—1722no—
806C22—1722no—
807C22—1722no—
808C22—1722no—
809C22—1724no—
810C22#1458353912yes—
811C22#1458369812yes—
812C22#1458370312yes—
813C22C22×D4×D4311yescharacteristic
814C4—22no—
815C4—24no—
816C4—42no—
817C4—42no—
818C4—862no—
819C4—862no—
820C4—862no—
821C4—1722no—
822C4—1722no—
823C4#1458353912yes—
824C4C22×#1062189811yescharacteristic
825C4C2×#1306337011yescharacteristic
826C2—42no—
827C2—82no—
828C2—3442no—
829C2—3442no—
830C2—1722no—
831C2#1914660214yesdirect product factor
832C2C2×#1458353911yescharacteristic
833C2C2×#1458369811yescharacteristic
834C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#417C2
socleC23×C43C22×D4
hypercenterC2×#417D43
hypocenterC43C2×#3309
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. C2×#14583597C2semidirect
2. C2×#14583568C2semidirect
3. #19146602C2direct (N × H)
4. C2×#14583262C2semidirect
5. C2×#14583222C2semidirect
6. C2×#14583212C2semidirect
7. C2×#14583204C2semidirect
8. C2×#14583152C2semidirect
9. C2×#14583134C2semidirect
10. C2×#14583093C2semidirect
11. C2×#14583047C2semidirect
12. C2×#14583044C2semidirect
13. C2×#14583002C2semidirect
14. C2×#14582968C2semidirect
15. C2×#14582894C2semidirect
16. C2×C43×#417C2semidirect
23. #14583597C22semidirect
25. #14583568C22semidirect
44. #14583262C22semidirect
45. #14583222C22semidirect
46. #14583212C22semidirect
47. #14583204C22semidirect
48. #14583152C22semidirect
49. #14583134C22semidirect
50. #14583093C22semidirect
51. #14583047C22semidirect
52. #14583044C22semidirect
53. #14583002C22semidirect
54. #14582968C22semidirect
59. #14582894C22semidirect
72. C43×#417C22semidirect
423. C2×#417D43semidirect
427. C2×C43#3309semidirect
479. #417C2×D43semidirect
494. C43C2×#3309semidirect
831. C2#19146602direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835972
C2×#145835682
#191466022
C2×#145832622
C2×#145832222
C2×#145832122
C2×#145832042
C2×#145831522
C2×#145831342
C2×#145830932
C2×#145830472
C2×#145830442
C2×#145830022
C2×#145829682
C2×#145828942
C2×C43×#4172
C2×#330943