Finite Group Databasebeta

← C2×#19146733 #25973152

Subgroups — C2×#19146733 #25973152

Order 11008.

2642 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583602C211yesmaximal, characteristic, complemented
2C2×D4×D172C211yesmaximal, characteristic, complemented
3#19146733C2116yesmaximal, direct product factor
4C2×#14583265C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583226C211yesmaximal, characteristic, complemented
7C2×#14583153C211yesmaximal, characteristic, complemented
8C2×#14583136C211yesmaximal, characteristic, complemented
9C2×#14583095C211yesmaximal, characteristic, complemented
10C2×#14583034C211yesmaximal, characteristic, complemented
11C2×#14583034C211yesmaximal, characteristic, complemented
12C2×#14583009C211yesmaximal, characteristic, complemented
13C2×#14582969C211yesmaximal, characteristic, complemented
14C2×#14582902C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#478C211yesmaximal, characteristic, complemented
17C23×D172—21no—
18C22×D4×D43C2211yescharacteristic
19C22×D4×D43C2211yescharacteristic
20C22×D344C2211yescharacteristic, complemented
21C22×D344C2211yescharacteristic, complemented
22C22×#10621882C2211yescharacteristic
23C22×#10621872C2211yescharacteristic, complemented
24C22×C8×D43C2211yescharacteristic, complemented
25#14583602—24no—
26#14583602C2218yescomplemented
27D4×D172—24no—
28D4×D172C2218yescomplemented
29C2×#13063322C2211yescharacteristic
30C2×#13063320—21no—
31C2×#13063310—21no—
32C2×#13063300—21no—
33C2×#13063300C2211yescharacteristic
34C2×#13063300C2211yescharacteristic
35C2×#13063300C2211yescharacteristic, complemented
36C2×#13063300C2211yescharacteristic, complemented
37C2×#13063299—21no—
38C2×#13063295—21no—
39C2×#13063295—21no—
40C2×C4×D172C2211yescharacteristic
41C2×C4×D172C2211yescharacteristic, complemented
42C2×#13063287—21no—
43C2×#13063283C2211yescharacteristic, complemented
44C2×C4⋊C4×D43C2211yescharacteristic, complemented
45#14583265C2218yescomplemented
46#14583226C2218yescomplemented
47#14583219C2218yescomplemented
48#14583153C2218yescomplemented
49#14583136C2218yescomplemented
50#14583095C2218yescomplemented
51#14583034C2218yescomplemented
52#14583034C2218yescomplemented
53#14583009C2218yescomplemented
54#14582969C2218yescomplemented
55C2×#13063256C2211yescharacteristic, complemented
56#14582902C2218yescomplemented
57C2×#13063247C2211yescharacteristic, complemented
58C2×#13063247C2211yescharacteristic, complemented
59C2×#13063246C2211yescharacteristic
60C2×#13063245C2211yescharacteristic, complemented
61C2×#13063245C2211yescharacteristic, complemented
62C2×#13063245C2211yescharacteristic, complemented
63C2×#13063245C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic, complemented
65#102×D43C2218yescomplemented
66C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
67C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
68C2×#13063236C2211yescharacteristic, complemented
69C2×#125×C43C2211yescharacteristic, complemented
70C2×C4×D4×C43C2211yescharacteristic
71C43×#478C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×C4⋊C8×C43C2211yescharacteristic, complemented
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C24×D43—21no—
78C24×D43—21no—
79C22×D172—21no—
80C22×D172—21no—
81C22×D172—21no—
82C22×D172—21no—
83C22×D172—21no—
84C22×D172—21no—
85C22×D172—28no—
86C22×D172—48no—
87C22×D172D411yescharacteristic
88C22×D172C2311yescharacteristic
89C22×D172C2311yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C2×D4×D43—24no—
94C2×D4×D43—24no—
95C2×D4×D43—22no—
96C2×D4×D43—22no—
97C2×D4×D43—42no—
98C2×D4×D43—42no—
99C2×D4×D43C2314yes—
100C2×D4×D43C2314yes—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43C2311yescharacteristic
104C22×C4×D43C2311yescharacteristic
105C2×D344—42no—
106C2×D344—42no—
107C2×D344C2314yescomplemented
108C2×D344C2314yescomplemented
109C2×#10621882—24no—
110C2×#10621882C2314yes—
111C2×#10621872—42no—
112C2×#10621872C2314yescomplemented
113C22×C43⋊C8C2311yescharacteristic
114C22×C43⋊C8C2311yescharacteristic
115C2×C8×D43—42no—
116C2×C8×D43C2314yescomplemented
117#13063322—22no—
118#13063322C2314yes—
119#13063320—28no—
120#13063310—28no—
121#13063300—28no—
122#13063300—22no—
123#13063300—22no—
124#13063300—22no—
125#13063300—22no—
126#13063300C2314yes—
127#13063300C2314yes—
128#13063300C2314yescomplemented
129#13063300C2314yescomplemented
130#13063299—28no—
131#13063295—28no—
132#13063295—28no—
133C4×D172—22no—
134C4×D172D414yes—
135C4×D172C2314yes—
136C4×D172C2314yescomplemented
137#13063287—28no—
138#13063283—22no—
139#13063283C2314yescomplemented
140C2×C4⋊Dic43D411yescharacteristic
141C2×C4⋊Dic43C2311yescharacteristic
142C2×Dic43⋊C4—21no—
143C4⋊C4×D43—22no—
144C4⋊C4×D43C2314yescomplemented
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×(C2×D43)⋊C4D411yescharacteristic
152C2×(C2×D43)⋊C4D411yescharacteristic
153C2×C4×Dic43—21no—
154#13063256C2314yescomplemented
155#13063247C2314yescomplemented
156#13063247C2314yescomplemented
157#13063246C2314yes—
158#13063245C2314yescomplemented
159#13063245C2314yescomplemented
160#13063245C2314yescomplemented
161#13063245C2314yescomplemented
162#13063245C2314yescomplemented
163(C2×D43)⋊C8C2314yescomplemented
164(C2×D43)⋊C8C2314yescomplemented
165#13063236C2314yescomplemented
166C22×D4×C43C2311yescharacteristic
167C23×C4×C43—21no—
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170#125×C43—22no—
171#125×C43C2314yescomplemented
172C4×D4×C43—22no—
173C4×D4×C43C2314yes—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C22⋊C4×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#107×C43C2314yescomplemented
182#106×C43C2314yescomplemented
183C4⋊C8×C43C2314yescomplemented
184#102×C43C2314yes—
185#102×C43C2314yes—
186C24×C43—21no—
187C23×D43—21no—
188C23×D43—21no—
189C23×D43—21no—
190C23×D43—24no—
191C23×D43—24no—
192C23×D43—44no—
193C23×D43—44no—
194C23×D43—44no—
195C23×D43—44no—
196C23×D43—82no—
197C23×D43—82no—
198C23×D43C2×D411yescharacteristic
199C23×D43C2×D411yescharacteristic
200C2×D4×C43—21no—
201C2×D4×C43—22no—
202C2×D4×C43#4114yes—
203C2×D4×C43C2412yes—
204C22×C4×C43—24no—
205C22×C4×C43—21no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—44no—
209C22×C4×C43C2×D411yescharacteristic
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2411yescharacteristic
212C2×C22⋊D43—24no—
213C2×C22⋊D43—24no—
214C2×C22⋊D43—44no—
215C2×C22⋊D43—44no—
216C22×Dic43—21no—
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D411yescharacteristic
219D4×D43—28no—
220D4×D43—28no—
221D4×D43—44no—
222D4×D43—44no—
223D4×D43—48no—
224D4×D43—48no—
225C2×D172—21no—
226C2×D172—24no—
227C2×D172—21no—
228C2×D172—21no—
229C2×D172—24no—
230C2×D172—24no—
231C2×D172—24no—
232C2×D172—24no—
233C2×D172—24no—
234C2×D172—24no—
235C2×D172—22no—
236C2×D172—22no—
237C2×D172—22no—
238C2×D172—22no—
239C2×D172—22no—
240C2×D172—22no—
241C2×D172—44no—
242C2×D172—432no—
243C2×D172—44no—
244C2×D172—44no—
245C2×D172—44no—
246C2×D172—82no—
247C2×D172—82no—
248C2×D172C2×D414yes—
249C2×D172C2412yes—
250C2×D172C2412yes—
251C2×D172C2412yes—
252C2×C4×D43—22no—
253C2×C4×D43—22no—
254C2×C4×D43—22no—
255C2×C4×D43—22no—
256C2×C4×D43—24no—
257C2×C4×D43—24no—
258C2×C4×D43—82no—
259C2×C4×D43—82no—
260C2×C4×D43C2×D412yes—
261C2×C4×D43C2×D412yes—
262C2×C4×D43C2412yes—
263C2×C4×D43C2412yes—
264C2×C8×C43—22no—
265C2×C8×C43—22no—
266C2×C8×C43C2412yes—
267C2×C8×C43C2412yes—
268C4⋊C4×C43—24no—
269C4⋊C4×C43—24no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43C2412yes—
274C4⋊C4×C43C2412yes—
275C4⋊C4×C43C2412yes—
276C22⋊C4×C43—24no—
277C42×C43C2×D412yes—
278C42×C43C2412yes—
279#10621882—28no—
280(C2×D43)⋊C4—24no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4C2×D414yes—
287(C2×D43)⋊C4C2×D414yes—
288C4⋊Dic43—21no—
289C4⋊Dic43C2×D414yes—
290C4⋊Dic43C2412yes—
291Dic43⋊C4—24no—
292C4×Dic43—24no—
293C2×C43⋊C8—22no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8C2412yes—
296C2×C43⋊C8C2412yes—
297D344—44no—
298D344—44no—
299#10621872—44no—
300C8×D43—44no—
301C23×C43—24no—
302C23×C43—22no—
303C23×C43—42no—
304C23×C43—42no—
305C23×C43C22×D411yescharacteristic
306C22×D43—22no—
307C22×D43—22no—
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—22no—
314C22×D43—48no—
315C22×D43—48no—
316C22×D43—48no—
317C22×D43—42no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43—42no—
321C22×D43—42no—
322C22×D43—42no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—42no—
326C22×D43—48no—
327C22×D43—84no—
328C22×D43—84no—
329C22×D43—816no—
330C22×D43—816no—
331C22×D43AGL(1,ℤ/8)14yes—
332C22×D43C22×D412yes—
333C22×D43C22×D412yes—
334D4×C43—24no—
335D4×C43—22no—
336D4×C43C2×#4114yes—
337C2×C4×C43—22no—
338C2×C4×C43—22no—
339C2×C4×C43—22no—
340C2×C4×C43—22no—
341C2×C4×C43—22no—
342C2×C4×C43—48no—
343C2×C4×C43—42no—
344C2×C4×C43—42no—
345C2×C4×C43—42no—
346C2×C4×C43C22×D412yes—
347C2×C4×C43C22×D412yes—
348C2×C4×C43C22×D411yescharacteristic
349C2×C4×C43C2×#4112yes—
350C2×C4×C43H(5,𝔽2)12yes—
351C2×C4×C43C2511yescharacteristic
352C22⋊D43—48no—
353C22⋊D43—48no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—42no—
358C2×Dic43C22×D412yes—
359C2×Dic43C22×D412yes—
360D172—28no—
361D172—22no—
362D172—22no—
363D172—22no—
364D172—22no—
365D172—22no—
366D172—22no—
367D172—48no—
368D172—48no—
369D172—48no—
370D172—48no—
371D172—42no—
372D172—42no—
373D172—42no—
374D172—84no—
375D172—84no—
376C4×D43—24no—
377C4×D43—24no—
378C4×D43—22no—
379C4×D43—22no—
380C4×D43—22no—
381C4×D43—22no—
382C4×D43—84no—
383C4×D43—84no—
384C8×C43—22no—
385C8×C43—22no—
386C43⋊C8—22no—
387C43⋊C8—22no—
388C2×#3318—431nomaximal, Sylow
389C22×C43—24no—
390C22×C43—48no—
391C22×C43—42no—
392C22×C43—42no—
393C22×C43#54612yes—
394C22×C43C2×AGL(1,ℤ/8)12yes—
395C22×C43#57612yes—
396C22×C43C23×D411yescharacteristic
397C2×D43—22no—
398C2×D43—28no—
399C2×D43—22no—
400C2×D43—22no—
401C2×D43—22no—
402C2×D43—22no—
403C2×D43—44no—
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—42no—
413C2×D43—816no—
414C2×D43—816no—
415C2×D43—84no—
416C2×D43—84no—
417C2×D43—84no—
418C2×D43C2×AGL(1,ℤ/8)14yes—
419C4×C43—22no—
420C4×C43—22no—
421C4×C43—42no—
422C4×C43—42no—
423C4×C43—42no—
424C4×C43#54612yes—
425C4×C43C22×#4111yescharacteristic
426C4×C43C2×H(5,𝔽2)11yescharacteristic
427Dic43—22no—
428Dic43—22no—
429Dic43—42no—
430C2×#553—431no—
431C2×D42—431no—
432#3318—4316no—
433C2×#490—431no—
434C2×#481—431no—
435C2×#482—431no—
436C2×#478D4311yescharacteristic, complemented
437C2×#469—431no—
438C2×#466—431no—
439C2×#459—431no—
440C2×#447—431no—
441C2×#447—431no—
442C2×#442—431no—
443C2×#435—431no—
444C2×#418—431no—
445C22×#102—431no—
446C2×C43—44no—
447C2×C43#331814yescomplemented
448C2×C43C2×#54611yescharacteristic
449C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
450C2×C43C2×#57611yescharacteristic
451D43—24no—
452D43—42no—
453D43—82no—
454D43—82no—
455D43—82no—
456C23×D4—431no—
457C23×D4—431no—
458C23×D4—861no—
459C22×D8—431no—
460C22×D8—431no—
461C22×D8—431no—
462C22×M16—431no—
463C23×C8—431no—
464#553—438no—
465#553—864no—
466D42—438no—
467D42—864no—
468C2×#127—431no—
469C2×#126—861no—
470C2×#125C2×D4311yescharacteristic, complemented
471C2×#123—861no—
472C2×#121—431no—
473C2×#121—431no—
474C2×#121—431no—
475C2×#121—431no—
476C2×#121—861no—
477C2×#121—861no—
478C2×#120—861no—
479C2×#120—861no—
480C2×C4×D4—431no—
481C2×C4×D4—431no—
482C2×C4×D4—861no—
483C2×C4×D4C2×D4311yescharacteristic
484C2×#117—431no—
485C22×C4⋊C4—431no—
486#490—438no—
487#482—438no—
488#481—438no—
489#478C2×D4318yescomplemented
490#469—438no—
491#466—438no—
492#459—438no—
493#447—438no—
494#447—438no—
495#442—438no—
496#435—438no—
497C2×#107C2×D4311yescharacteristic, complemented
498C2×#106—431no—
499C2×#106C2×D4311yescharacteristic, complemented
500C2×C4⋊C8C2×D4311yescharacteristic, complemented
501#418—438no—
502C2×#102—431no—
503C2×#102—431no—
504C2×#102—431no—
505C2×#102—431no—
506C2×#102—431no—
507C2×#102—431no—
508C2×#102—431no—
509C2×#102—431no—
510C2×#102—438no—
511C2×#102C2×D4311yescharacteristic
512C2×#102C2×D4311yescharacteristic
513C2×C22⋊C8—431no—
514C2×C22⋊C8—431no—
515C2×#97—431no—
516C43C2×#331811yescharacteristic, complemented, Sylow
517C25—861no—
518C25—861no—
519C22×D4—434no—
520C22×D4—434no—
521C22×D4—431no—
522C22×D4—431no—
523C22×D4—431no—
524C22×D4—431no—
525C22×D4—868no—
526C22×D4—861no—
527C22×D4—861no—
528C22×D4—861no—
529C22×D4—861no—
530C22×D4—862no—
531C22×D4—862no—
532C22×D4—861no—
533C22×D4—861no—
534C22×D4—864no—
535C22×D4—864no—
536C22×D4—861no—
537C22×D4—861no—
538C22×D4—1728no—
539C22×D4—1722no—
540C22×D4—1722no—
541C22×D4C22×D4311yescharacteristic
542C23×C4—21no—
543C23×C4—431no—
544C23×C4—431no—
545C23×C4—861no—
546C23×C4—861no—
547C2×D8—434no—
548C2×D8—434no—
549C2×D8—434no—
550C2×D8—864no—
551C2×D8—1722no—
552C2×D8—1722no—
553C2×M16—434no—
554C2×M16—1722no—
555C22×C8—431no—
556C22×C8—431no—
557C22×C8—434no—
558C22×C8—1722no—
559C22×C8C22×D4311yescharacteristic
560C22×C8C22×D4311yescharacteristic
561#127—434no—
562#127—862no—
563#126—868no—
564#125—22no—
565#125C22×D4314yescomplemented
566#123—868no—
567#121—434no—
568#121—434no—
569#121—434no—
570#121—434no—
571#121—862no—
572#121—862no—
573#121—862no—
574#121—862no—
575#121—868no—
576#121—868no—
577#120—868no—
578#120—868no—
579C4×D4—22no—
580C4×D4—434no—
581C4×D4—434no—
582C4×D4—434no—
583C4×D4—868no—
584C4×D4—862no—
585C4×D4C22×D4314yes—
586#117—434no—
587#117—862no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—434no—
593C2×C4⋊C4—862no—
594C2×C4⋊C4—861no—
595C2×C4⋊C4C22×D4311yescharacteristic
596C2×C4⋊C4C22×D4311yescharacteristic
597C2×C4⋊C4C22×D4311yescharacteristic
598C2×C22⋊C4—21no—
599C2×C22⋊C4—431no—
600C2×C22⋊C4—431no—
601C2×C22⋊C4—861no—
602C2×C22⋊C4—861no—
603C2×C22⋊C4—861no—
604C2×C22⋊C4—861no—
605C2×C22⋊C4—861no—
606C2×C22⋊C4—861no—
607C2×C42—861no—
608C2×C42C22×D4311yescharacteristic
609#107C22×D4314yescomplemented
610#106—434no—
611#106C22×D4314yescomplemented
612C4⋊C8C22×D4314yescomplemented
613#102—434no—
614#102—434no—
615#102—434no—
616#102—434no—
617#102—434no—
618#102—434no—
619#102—434no—
620#102—434no—
621#102C22×D4314yes—
622#102C22×D4314yes—
623C22⋊C8—434no—
624C22⋊C8—434no—
625#97—434no—
626C24—21no—
627C24—431no—
628C24—431no—
629C24—864no—
630C24—864no—
631C24—861no—
632C24—861no—
633C24—861no—
634C24—3442no—
635C24—3442no—
636C24—1724no—
637C24—1724no—
638C24—1724no—
639C24—1724no—
640C2×D4—21no—
641C2×D4—22no—
642C2×D4—434no—
643C2×D4—432no—
644C2×D4—432no—
645C2×D4—432no—
646C2×D4—864no—
647C2×D4—864no—
648C2×D4—864no—
649C2×D4—864no—
650C2×D4—864no—
651C2×D4—864no—
652C2×D4—864no—
653C2×D4—868no—
654C2×D4—868no—
655C2×D4—864no—
656C2×D4—861no—
657C2×D4—864no—
658C2×D4—861no—
659C2×D4—861no—
660C2×D4—862no—
661C2×D4—862no—
662C2×D4—862no—
663C2×D4—862no—
664C2×D4—862no—
665C2×D4—862no—
666C2×D4—3442no—
667C2×D4—3442no—
668C2×D4—1724no—
669C2×D4—17232no—
670C2×D4—1724no—
671C2×D4—1724no—
672C2×D4—1724no—
673C2×D4—1724no—
674C2×D4—1724no—
675C2×D4—1728no—
676C2×D4—1728no—
677C2×D4—1724no—
678C2×D4—1724no—
679C2×D4#1062190214yes—
680C2×D4C23×D4312yes—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—44no—
686C22×C4—431no—
687C22×C4—431no—
688C22×C4—432no—
689C22×C4—432no—
690C22×C4—432no—
691C22×C4—432no—
692C22×C4—864no—
693C22×C4—862no—
694C22×C4—862no—
695C22×C4—862no—
696C22×C4—862no—
697C22×C4—861no—
698C22×C4—864no—
699C22×C4—3442no—
700C22×C4—3442no—
701C22×C4D4×D4311yescharacteristic
702C22×C4D4×D4311yescharacteristic
703C22×C4C23×D4311yescharacteristic
704D8—868no—
705D8—1724no—
706D8—1724no—
707M16—1724no—
708C2×C8—22no—
709C2×C8—22no—
710C2×C8—432no—
711C2×C8—432no—
712C2×C8—862no—
713C2×C8—862no—
714C2×C8—1724no—
715C2×C8C23×D4312yes—
716C2×C8C23×D4312yes—
717C4⋊C4—24no—
718C4⋊C4—24no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—434no—
723C4⋊C4—432no—
724C4⋊C4—864no—
725C4⋊C4—861no—
726C4⋊C4C23×D4312yes—
727C4⋊C4C23×D4312yes—
728C4⋊C4C23×D4312yes—
729C22⋊C4—24no—
730C22⋊C4—434no—
731C22⋊C4—434no—
732C22⋊C4—864no—
733C22⋊C4—864no—
734C22⋊C4—864no—
735C22⋊C4—864no—
736C22⋊C4—864no—
737C22⋊C4—864no—
738C42—864no—
739C42D4×D4312yes—
740C42C23×D4312yes—
741C23—22no—
742C23—24no—
743C23—42no—
744C23—42no—
745C23—434no—
746C23—432no—
747C23—432no—
748C23—862no—
749C23—862no—
750C23—862no—
751C23—862no—
752C23—862no—
753C23—862no—
754C23—862no—
755C23—862no—
756C23—34416no—
757C23—3444no—
758C23—3444no—
759C23—34416no—
760C23—1728no—
761C23—1728no—
762C23—1728no—
763C23—1728no—
764C23—1722no—
765C23—1722no—
766C23—1722no—
767C23—1722no—
768C23—1722no—
769C23—1722no—
770C23—1722no—
771C23—1722no—
772C23—1722no—
773C23C2×D4×D4311yescharacteristic
774D4—22no—
775D4—24no—
776D4—868no—
777D4—862no—
778D4—862no—
779D4—862no—
780D4—862no—
781D4—862no—
782D4—862no—
783D4—3444no—
784D4—3444no—
785D4—1728no—
786D4—1728no—
787D4—1728no—
788D4—1728no—
789D4—1728no—
790D4—1728no—
791D4—1722no—
792D4—1722no—
793D4—1722no—
794D4C2×#1062190214yes—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—48no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—432no—
805C2×C4—432no—
806C2×C4—862no—
807C2×C4—862no—
808C2×C4—862no—
809C2×C4—862no—
810C2×C4—862no—
811C2×C4—862no—
812C2×C4—864no—
813C2×C4—864no—
814C2×C4—862no—
815C2×C4—3444no—
816C2×C4—3444no—
817C2×C4—1722no—
818C2×C4C2×D4×D4312yes—
819C2×C4C2×D4×D4312yes—
820C2×C4C2×D4×D4311yescharacteristic
821C2×C4C2×#1062190212yes—
822C2×C4#1306337112yes—
823C2×C4C24×D4311yescharacteristic
824C8—22no—
825C8—22no—
826C8—862no—
827C8—862no—
828C22—24no—
829C22—42no—
830C22—42no—
831C22—48no—
832C22—434no—
833C22—862no—
834C22—862no—
835C22—868no—
836C22—862no—
837C22—862no—
838C22—862no—
839C22—34416no—
840C22—34416no—
841C22—3444no—
842C22—3444no—
843C22—3444no—
844C22—1722no—
845C22—1722no—
846C22—1722no—
847C22—1722no—
848C22—1722no—
849C22—1722no—
850C22—1722no—
851C22—1722no—
852C22—1722no—
853C22—1724no—
854C22#1458354012yes—
855C22AGL(1,ℤ/8)×D4312yes—
856C22#1458370112yes—
857C22C22×D4×D4311yescharacteristic
858C4—22no—
859C4—22no—
860C4—42no—
861C4—42no—
862C4—42no—
863C4—862no—
864C4—862no—
865C4—1722no—
866C4#1458354012yes—
867C4C22×#1062190211yescharacteristic
868C4C2×#1306337111yescharacteristic
869C2—44no—
870C2—864no—
871C2—3442no—
872C2—3442no—
873C2—3442no—
874C2—1722no—
875C2#1914673314yesdirect product factor
876C2C2×#1458354011yescharacteristic
877C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
878C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
hypercenterC2×#478D43
hypocenterC43C2×#3318
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#14583602C2semidirect
2. C2×D4×D172C2semidirect
3. #19146733C2direct (N × H)
4. C2×#14583265C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583226C2semidirect
7. C2×#14583153C2semidirect
8. C2×#14583136C2semidirect
9. C2×#14583095C2semidirect
10. C2×#14583034C2semidirect
11. C2×#14583034C2semidirect
12. C2×#14583009C2semidirect
13. C2×#14582969C2semidirect
14. C2×#14582902C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#478C2semidirect
20. C22×D344C22semidirect
21. C22×D344C22semidirect
23. C22×#10621872C22semidirect
24. C22×C8×D43C22semidirect
26. #14583602C22semidirect
28. D4×D172C22semidirect
35. C2×#13063300C22semidirect
36. C2×#13063300C22semidirect
41. C2×C4×D172C22semidirect
43. C2×#13063283C22semidirect
44. C2×C4⋊C4×D43C22semidirect
45. #14583265C22semidirect
46. #14583226C22semidirect
47. #14583219C22semidirect
48. #14583153C22semidirect
49. #14583136C22semidirect
50. #14583095C22semidirect
51. #14583034C22semidirect
52. #14583034C22semidirect
53. #14583009C22semidirect
54. #14582969C22semidirect
55. C2×#13063256C22semidirect
56. #14582902C22semidirect
57. C2×#13063247C22semidirect
58. C2×#13063247C22semidirect
60. C2×#13063245C22semidirect
61. C2×#13063245C22semidirect
62. C2×#13063245C22semidirect
63. C2×#13063245C22semidirect
64. C2×#13063245C22semidirect
65. #102×D43C22semidirect
66. C2×(C2×D43)⋊C8C22semidirect
67. C2×(C2×D43)⋊C8C22semidirect
68. C2×#13063236C22semidirect
69. C2×#125×C43C22semidirect
71. C43×#478C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×C4⋊C8×C43C22semidirect
107. C2×D344C23semidirect
108. C2×D344C23semidirect
112. C2×#10621872C23semidirect
116. C2×C8×D43C23semidirect
128. #13063300C23semidirect
129. #13063300C23semidirect
136. C4×D172C23semidirect
139. #13063283C23semidirect
144. C4⋊C4×D43C23semidirect
154. #13063256C23semidirect
155. #13063247C23semidirect
156. #13063247C23semidirect
158. #13063245C23semidirect
159. #13063245C23semidirect
160. #13063245C23semidirect
161. #13063245C23semidirect
162. #13063245C23semidirect
163. (C2×D43)⋊C8C23semidirect
164. (C2×D43)⋊C8C23semidirect
165. #13063236C23semidirect
171. #125×C43C23semidirect
181. #107×C43C23semidirect
182. #106×C43C23semidirect
183. C4⋊C8×C43C23semidirect
436. C2×#478D43semidirect
447. C2×C43#3318semidirect
470. C2×#125C2×D43semidirect
489. #478C2×D43semidirect
497. C2×#107C2×D43semidirect
499. C2×#106C2×D43semidirect
500. C2×C4⋊C8C2×D43semidirect
516. C43C2×#3318semidirect
565. #125C22×D43semidirect
609. #107C22×D43semidirect
611. #106C22×D43semidirect
612. C4⋊C8C22×D43semidirect
875. C2#19146733direct (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×D4×D1722
#191467332
C2×#145832652
C2×#145832192
C2×#145832262
C2×#145831532
C2×#145831362
C2×#145830952
C2×#145830342
C2×#145830092
C2×#145829692
C2×#145829022
C2×#102×D432
C2×C43×#4782
C2×#331843