Finite Group Databasebeta

← C2×#19146033 #25969536

Subgroups — C2×#19146033 #25969536

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583505C211yesmaximal, characteristic, complemented
2C2×#14583500C211yesmaximal, characteristic, complemented
3#19146033C2116yesmaximal, direct product factor
4C2×#14583202C211yesmaximal, characteristic, complemented
5C2×#14583198C211yesmaximal, characteristic, complemented
6C2×#14583196C211yesmaximal, characteristic, complemented
7C2×#14583153C211yesmaximal, characteristic, complemented
8C2×#14583151C211yesmaximal, characteristic, complemented
9C2×#14583136C211yesmaximal, characteristic, complemented
10C2×#14583134C211yesmaximal, characteristic, complemented
11C2×#14583095C211yesmaximal, characteristic, complemented
12C2×#14583094C211yesmaximal, characteristic, complemented
13C2×#14583093C211yesmaximal, characteristic, complemented
14C2×#14583093C211yesmaximal, characteristic, complemented
15C2×#14582924C211yesmaximal, characteristic, complemented
16C2×C43×#478C211yesmaximal, characteristic, complemented
17C22×D344C2211yescharacteristic
18C22×D344C2211yescharacteristic
19C22×#10621882C2211yescharacteristic
20C22×#10621882C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583505—24no—
24#14583505C2218yescomplemented
25#14583500—24no—
26#14583500C2218yescomplemented
27C2×#13063322C2211yescharacteristic
28C2×#13063321C2211yescharacteristic
29C2×#13063316C2211yescharacteristic
30C2×#13063310—21no—
31C2×#13063310—21no—
32C2×#13063308—21no—
33C2×#13063307—21no—
34C2×#13063300—21no—
35C2×#13063300—21no—
36C2×#13063300C2211yescharacteristic
37C2×#13063300C2211yescharacteristic
38C2×#13063300C2211yescharacteristic
39C2×#13063299—21no—
40C2×#13063298—21no—
41C2×#13063296C2211yescharacteristic
42C2×C4×D172C2211yescharacteristic
43C2×#13063287C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583202C2218yescomplemented
47#14583198C2218yescomplemented
48#14583196C2218yescomplemented
49#14583153C2218yescomplemented
50#14583151C2218yescomplemented
51#14583136C2218yescomplemented
52#14583134C2218yescomplemented
53#14583095C2218yescomplemented
54#14583094C2218yescomplemented
55#14583093C2218yescomplemented
56#14583093C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063245C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C43×#478C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#102×C43C2211yescharacteristic
77C22×D172—21no—
78C22×D172—21no—
79C22×D172—21no—
80C22×D172—21no—
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C22⋊D43—21no—
86C22×C22⋊D43—21no—
87C22×C22⋊D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43—21no—
90C22×C4×D43—21no—
91C22×C4×D43C2311yescharacteristic
92C2×D344—42no—
93C2×D344—42no—
94C2×D344C2314yes—
95C2×D344C2314yes—
96C2×#10621882—42no—
97C2×#10621882—42no—
98C2×#10621882C2314yes—
99C2×#10621882C2314yes—
100C2×#10621872—42no—
101C2×#10621872C2314yes—
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104C2×C8×D43—42no—
105C2×C8×D43C2314yes—
106#13063322—22no—
107#13063322C2314yes—
108#13063321—22no—
109#13063321C2314yes—
110#13063316—22no—
111#13063316C2314yes—
112#13063310—28no—
113#13063310—28no—
114#13063308—28no—
115#13063307—28no—
116#13063300—22no—
117#13063300—22no—
118#13063300—22no—
119#13063300—28no—
120#13063300—28no—
121#13063300C2314yes—
122#13063300C2314yes—
123#13063300C2314yes—
124#13063299—28no—
125#13063298—28no—
126#13063296—22no—
127#13063296C2314yes—
128C4×D172—22no—
129C4×D172C2314yes—
130#13063287—22no—
131#13063287—22no—
132#13063287C2314yes—
133#13063287C2314yes—
134#13063282D414yes—
135#13063282C2314yes—
136C2×C4⋊Dic43—21no—
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4D411yescharacteristic
140C2×Dic43⋊C4D411yescharacteristic
141C2×C22⋊Dic43—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4D411yescharacteristic
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×C4×Dic43C2311yescharacteristic
151#13063258C2314yes—
152#13063256C2314yes—
153C4⋊(C43⋊C8)C2314yes—
154Dic43⋊C8C2314yes—
155Dic43⋊C8C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162C22×D4×C43C2311yescharacteristic
163C23×C4×C43—21no—
164C22×C8×C43C2311yescharacteristic
165C22×C8×C43C2311yescharacteristic
166#125×C43—22no—
167#125×C43C2314yes—
168C4×D4×C43—22no—
169C4×D4×C43C2314yes—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C22⋊C4×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#107×C43C2314yes—
178#106×C43C2314yes—
179C4⋊C8×C43C2314yes—
180#102×C43C2314yes—
181#102×C43C2314yes—
182C24×C43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43—21no—
186C23×D43C2×D411yescharacteristic
187C2×D4×C43—21no—
188C2×D4×C43—22no—
189C2×D4×C43—22no—
190C2×D4×C43C2412yes—
191C22×C4×C43—24no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43—21no—
195C22×C4×C43—82no—
196C22×C4×C43C2×D411yescharacteristic
197C22×C4×C43C2×D411yescharacteristic
198C22×C4×C43C2411yescharacteristic
199C2×C22⋊D43—24no—
200C2×C22⋊D43—24no—
201C2×C22⋊D43—24no—
202C2×C22⋊D43—82no—
203C2×C22⋊D43—82no—
204C2×C22⋊D43—82no—
205C22×Dic43—21no—
206C22×Dic43C2×D411yescharacteristic
207C22×Dic43C2×D411yescharacteristic
208C22×Dic43C2×D411yescharacteristic
209C2×D172—21no—
210C2×D172—21no—
211C2×D172—21no—
212C2×D172—24no—
213C2×D172—24no—
214C2×D172—24no—
215C2×D172—24no—
216C2×D172—24no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172—22no—
221C2×D172—22no—
222C2×D172—22no—
223C2×D172—82no—
224C2×D172—82no—
225C2×D172—82no—
226C2×D172—82no—
227C2×D172—82no—
228C2×D172C2412yes—
229C2×D172C2412yes—
230C2×D172C2412yes—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—24no—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—82no—
237C2×C4×D43—82no—
238C2×C4×D43—82no—
239C2×C4×D43C2×D412yes—
240C2×C4×D43C2412yes—
241C2×C8×C43—22no—
242C2×C8×C43—22no—
243C2×C8×C43C2412yes—
244C2×C8×C43C2412yes—
245C4⋊C4×C43—24no—
246C4⋊C4×C43—24no—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—21no—
250C4⋊C4×C43C2412yes—
251C4⋊C4×C43C2412yes—
252C4⋊C4×C43C2412yes—
253C22⋊C4×C43—24no—
254C42×C43C2×D412yes—
255C42×C43C2412yes—
256C22⋊Dic43—24no—
257#10621882—44no—
258#10621882—44no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264(C2×D43)⋊C4—24no—
265(C2×D43)⋊C4C2×D414yes—
266(C2×D43)⋊C4C2×D414yes—
267C4⋊Dic43—21no—
268C4⋊Dic43—24no—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4C2×D414yes—
272Dic43⋊C4C2×D414yes—
273C4×Dic43C2×D412yes—
274C4×Dic43C2412yes—
275C2×C43⋊C8—22no—
276C2×C43⋊C8—22no—
277C2×C43⋊C8C2412yes—
278C2×C43⋊C8C2412yes—
279D344—44no—
280D344—44no—
281#10621872—44no—
282C8×D43—44no—
283C23×C43—22no—
284C23×C43—42no—
285C23×C43—42no—
286C23×C43—42no—
287C23×C43C22×D411yescharacteristic
288C22×D43—22no—
289C22×D43—22no—
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298C22×D43—42no—
299C22×D43—42no—
300C22×D43—42no—
301C22×D43—42no—
302C22×D43—42no—
303C22×D43C22×D412yes—
304D4×C43—22no—
305D4×C43—22no—
306D4×C43—42no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—42no—
313C2×C4×C43—42no—
314C2×C4×C43—42no—
315C2×C4×C43—84no—
316C2×C4×C43C22×D412yes—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43H(5,𝔽2)12yes—
320C2×C4×C432−1+412yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—84no—
323C22⋊D43—84no—
324C22⋊D43—84no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—42no—
330C2×Dic43C22×D412yes—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333D172—22no—
334D172—22no—
335D172—22no—
336D172—22no—
337D172—22no—
338D172—22no—
339D172—42no—
340D172—42no—
341D172—42no—
342D172—84no—
343D172—84no—
344D172—84no—
345D172—84no—
346D172—84no—
347C4×D43—24no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—84no—
351C4×D43—84no—
352C4×D43—84no—
353C8×C43—22no—
354C8×C43—22no—
355C43⋊C8—22no—
356C43⋊C8—22no—
357C2×#3259—431nomaximal, Sylow
358C22×C43—42no—
359C22×C43—42no—
360C22×C43—42no—
361C22×C43—84no—
362C22×C43#53712yes—
363C22×C43#57612yes—
364C22×C43#57612yes—
365C22×C43C23×D411yescharacteristic
366C2×D43—22no—
367C2×D43—22no—
368C2×D43—22no—
369C2×D43—44no—
370C2×D43—42no—
371C2×D43—42no—
372C2×D43—42no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C2×D43—42no—
378C2×D43—42no—
379C2×D43—84no—
380C2×D43—84no—
381C2×D43—84no—
382C4×C43—22no—
383C4×C43—22no—
384C4×C43—42no—
385C4×C43—42no—
386C4×C43—42no—
387C4×C43#53712yes—
388C4×C43C2×H(5,𝔽2)11yescharacteristic
389C4×C43C2×2−1+411yescharacteristic
390Dic43—22no—
391Dic43—22no—
392Dic43—22no—
393Dic43—42no—
394C2×#540—431no—
395C2×#540—431no—
396#3259—4316no—
397C2×#478—431no—
398C2×#478—431no—
399C2×#478—431no—
400C2×#478D4311yescharacteristic, complemented
401C2×#469—431no—
402C2×#469—431no—
403C2×#466—431no—
404C2×#466—431no—
405C2×#459—431no—
406C2×#459—431no—
407C2×#459—431no—
408C2×#459—431no—
409C2×#424—431no—
410C2×C43—82no—
411C2×C43#325914yescomplemented
412C2×C43C2×#53711yescharacteristic
413C2×C43C2×#57611yescharacteristic
414C2×C43C2×#57611yescharacteristic
415D43—42no—
416D43—82no—
417D43—82no—
418D43—82no—
419C22×D8—431no—
420C22×D8—431no—
421C22×D8—431no—
422C22×D8—431no—
423C22×M16—431no—
424C23×C8—431no—
425#540—438no—
426#540—438no—
427#540—864no—
428#540—864no—
429C2×#127—431no—
430C2×#127—431no—
431C2×#125—431no—
432C2×#125C2×D4311yescharacteristic
433C2×#123—861no—
434C2×#123—861no—
435C2×#123—861no—
436C2×#123—861no—
437C2×#121—431no—
438C2×#121—431no—
439C2×#121—431no—
440C2×#121—431no—
441C2×#121—861no—
442C2×#121—861no—
443C2×#121—861no—
444C2×#121—861no—
445C2×C4×D4—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448C2×C4×D4C2×D4311yescharacteristic
449C2×#117—431no—
450#478—438no—
451#478—438no—
452#478—438no—
453#478C2×D4318yescomplemented
454#469—438no—
455#469—438no—
456#466—438no—
457#466—438no—
458#459—438no—
459#459—438no—
460#459—438no—
461#459—438no—
462C2×#107—431no—
463C2×#107C2×D4311yescharacteristic
464C2×#106—431no—
465C2×#106C2×D4311yescharacteristic
466#424—438no—
467C2×C4⋊C8—431no—
468C2×C4⋊C8—431no—
469C2×C4⋊C8—431no—
470C2×C4⋊C8C2×D4311yescharacteristic
471C2×#102—431no—
472C2×#102—431no—
473C2×#102—431no—
474C2×#102—431no—
475C2×#102—431no—
476C2×#102—431no—
477C2×#102C2×D4311yescharacteristic
478C2×#102C2×D4311yescharacteristic
479C43C2×#325911yescharacteristic, complemented, Sylow
480C22×D4—431no—
481C22×D4—431no—
482C22×D4—431no—
483C22×D4—861no—
484C22×D4—861no—
485C22×D4—861no—
486C22×D4—861no—
487C22×D4—861no—
488C22×D4—861no—
489C22×D4—861no—
490C22×D4—861no—
491C22×D4C22×D4311yescharacteristic
492C23×C4—21no—
493C23×C4—431no—
494C23×C4—861no—
495C23×C4—861no—
496C23×C4—861no—
497C2×D8—434no—
498C2×D8—434no—
499C2×D8—434no—
500C2×D8—434no—
501C2×D8—1722no—
502C2×D8—1722no—
503C2×D8—1722no—
504C2×D8—1722no—
505C2×M16—434no—
506C2×M16—1722no—
507C22×C8—431no—
508C22×C8—431no—
509C22×C8—434no—
510C22×C8—1722no—
511C22×C8C22×D4311yescharacteristic
512C22×C8C22×D4311yescharacteristic
513#127—434no—
514#127—434no—
515#127—862no—
516#127—862no—
517#125—22no—
518#125—434no—
519#125—862no—
520#125C22×D4314yes—
521#123—868no—
522#123—868no—
523#123—868no—
524#123—868no—
525#121—434no—
526#121—434no—
527#121—434no—
528#121—434no—
529#121—868no—
530#121—868no—
531#121—868no—
532#121—868no—
533#121—862no—
534#121—862no—
535#121—862no—
536#121—862no—
537C4×D4—22no—
538C4×D4—434no—
539C4×D4—434no—
540C4×D4—434no—
541C4×D4—862no—
542C4×D4—862no—
543C4×D4—862no—
544C4×D4C22×D4314yes—
545#117—434no—
546#117—434no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—431no—
550C2×C4⋊C4—431no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—861no—
553C2×C4⋊C4—861no—
554C2×C4⋊C4C22×D4311yescharacteristic
555C2×C4⋊C4C22×D4311yescharacteristic
556C2×C4⋊C4C22×D4311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—431no—
559C2×C22⋊C4—431no—
560C2×C22⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C42—431no—
568C2×C42C22×D4311yescharacteristic
569#107—434no—
570#107C22×D4314yes—
571#106—434no—
572#106C22×D4314yes—
573C4⋊C8—434no—
574C4⋊C8—434no—
575C4⋊C8—434no—
576C4⋊C8C22×D4314yes—
577#102—434no—
578#102—434no—
579#102—434no—
580#102—434no—
581#102—434no—
582#102—434no—
583#102C22×D4314yes—
584#102C22×D4314yes—
585C24—21no—
586C24—431no—
587C24—861no—
588C24—861no—
589C24—861no—
590C2×D4—21no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—432no—
594C2×D4—432no—
595C2×D4—432no—
596C2×D4—864no—
597C2×D4—864no—
598C2×D4—864no—
599C2×D4—864no—
600C2×D4—864no—
601C2×D4—864no—
602C2×D4—864no—
603C2×D4—864no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—862no—
608C2×D4—862no—
609C2×D4—862no—
610C2×D4—862no—
611C2×D4—862no—
612C2×D4—862no—
613C2×D4—3442no—
614C2×D4—3442no—
615C2×D4—3442no—
616C2×D4—3442no—
617C2×D4—3442no—
618C2×D4—3442no—
619C2×D4—3442no—
620C2×D4—3442no—
621C2×D4C23×D4312yes—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—24no—
626C22×C4—82no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—432no—
631C22×C4—432no—
632C22×C4—864no—
633C22×C4—864no—
634C22×C4—862no—
635C22×C4—862no—
636C22×C4—861no—
637C22×C4—864no—
638C22×C4—3442no—
639C22×C4—3442no—
640C22×C4—3442no—
641C22×C4D4×D4311yescharacteristic
642C22×C4D4×D4311yescharacteristic
643C22×C4C23×D4311yescharacteristic
644D8—1724no—
645D8—1724no—
646D8—1724no—
647D8—1724no—
648M16—1724no—
649C2×C8—22no—
650C2×C8—22no—
651C2×C8—432no—
652C2×C8—432no—
653C2×C8—862no—
654C2×C8—862no—
655C2×C8—1724no—
656C2×C8C23×D4312yes—
657C2×C8C23×D4312yes—
658C4⋊C4—24no—
659C4⋊C4—24no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—434no—
664C4⋊C4—434no—
665C4⋊C4—432no—
666C4⋊C4—864no—
667C4⋊C4—864no—
668C4⋊C4—861no—
669C4⋊C4C23×D4312yes—
670C4⋊C4C23×D4312yes—
671C4⋊C4C23×D4312yes—
672C22⋊C4—24no—
673C22⋊C4—434no—
674C22⋊C4—434no—
675C22⋊C4—864no—
676C22⋊C4—864no—
677C22⋊C4—864no—
678C22⋊C4—864no—
679C22⋊C4—864no—
680C22⋊C4—864no—
681C22⋊C4—864no—
682C42—432no—
683C42—432no—
684C42D4×D4312yes—
685C42C23×D4312yes—
686C23—22no—
687C23—42no—
688C23—42no—
689C23—42no—
690C23—432no—
691C23—862no—
692C23—862no—
693C23—862no—
694C23—862no—
695C23—862no—
696C23—862no—
697C23—1722no—
698C23—1722no—
699C23—1722no—
700C23—1722no—
701C23—1722no—
702C23—1722no—
703C23—1722no—
704C23—1722no—
705C23—1722no—
706C23C2×D4×D4311yescharacteristic
707D4—22no—
708D4—22no—
709D4—42no—
710D4—862no—
711D4—862no—
712D4—862no—
713D4—862no—
714D4—862no—
715D4—862no—
716D4—3444no—
717D4—3444no—
718D4—3444no—
719D4—3444no—
720D4—3444no—
721D4—3444no—
722D4—3444no—
723D4—3444no—
724D4—1722no—
725D4—1722no—
726D4—1722no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—84no—
736C2×C4—432no—
737C2×C4—432no—
738C2×C4—432no—
739C2×C4—862no—
740C2×C4—862no—
741C2×C4—862no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—864no—
745C2×C4—862no—
746C2×C4—3444no—
747C2×C4—3444no—
748C2×C4—3444no—
749C2×C4—1722no—
750C2×C4C2×D4×D4312yes—
751C2×C4C2×D4×D4312yes—
752C2×C4C2×D4×D4311yescharacteristic
753C2×C4#1306337112yes—
754C2×C4#1306337312yes—
755C2×C4C24×D4311yescharacteristic
756C8—22no—
757C8—22no—
758C8—862no—
759C8—862no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—84no—
764C22—862no—
765C22—862no—
766C22—862no—
767C22—3444no—
768C22—3444no—
769C22—3444no—
770C22—1722no—
771C22—1722no—
772C22—1722no—
773C22—1722no—
774C22—1722no—
775C22—1722no—
776C22—1722no—
777C22—1722no—
778C22—1722no—
779C22—1724no—
780C22#1458347912yes—
781C22#1458370112yes—
782C22#1458370312yes—
783C22C22×D4×D4311yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—862no—
790C4—862no—
791C4—862no—
792C4—1722no—
793C4#1458347912yes—
794C4C2×#1306337111yescharacteristic
795C4C2×#1306337311yescharacteristic
796C2—82no—
797C2—3442no—
798C2—3442no—
799C2—3442no—
800C2—1722no—
801C2#1914603314yesdirect product factor
802C2C2×#1458347911yescharacteristic
803C2C2×#1458370111yescharacteristic
804C2C2×#1458370311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#478C2
socleC23×C43C22×D4
hypercenterC2×#478D43
hypocenterC43C2×#3259
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×#14583505C2semidirect
2. C2×#14583500C2semidirect
3. #19146033C2direct (N × H)
4. C2×#14583202C2semidirect
5. C2×#14583198C2semidirect
6. C2×#14583196C2semidirect
7. C2×#14583153C2semidirect
8. C2×#14583151C2semidirect
9. C2×#14583136C2semidirect
10. C2×#14583134C2semidirect
11. C2×#14583095C2semidirect
12. C2×#14583094C2semidirect
13. C2×#14583093C2semidirect
14. C2×#14583093C2semidirect
15. C2×#14582924C2semidirect
16. C2×C43×#478C2semidirect
24. #14583505C22semidirect
26. #14583500C22semidirect
46. #14583202C22semidirect
47. #14583198C22semidirect
48. #14583196C22semidirect
49. #14583153C22semidirect
50. #14583151C22semidirect
51. #14583136C22semidirect
52. #14583134C22semidirect
53. #14583095C22semidirect
54. #14583094C22semidirect
55. #14583093C22semidirect
56. #14583093C22semidirect
59. #14582924C22semidirect
71. C43×#478C22semidirect
400. C2×#478D43semidirect
411. C2×C43#3259semidirect
453. #478C2×D43semidirect
479. C43C2×#3259semidirect
801. C2#19146033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835052
C2×#145835002
#191460332
C2×#145832022
C2×#145831982
C2×#145831962
C2×#145831532
C2×#145831512
C2×#145831362
C2×#145831342
C2×#145830952
C2×#145830942
C2×#145830932
C2×#145829242
C2×C43×#4782
C2×#325943