Finite Group Databasebeta

← C2×#19146496 #25973019

Subgroups — C2×#19146496 #25973019

Order 11008.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583602C211yesmaximal, characteristic, complemented
2C2×#14583557C211yesmaximal, characteristic, complemented
3#19146496C2116yesmaximal, direct product factor
4C2×#14583216C211yesmaximal, characteristic, complemented
5C2×#14583238C211yesmaximal, characteristic, complemented
6C2×#14583203C211yesmaximal, characteristic, complemented
7C2×#14583134C211yesmaximal, characteristic, complemented
8C2×#14583131C211yesmaximal, characteristic, complemented
9C2×#14583111C211yesmaximal, characteristic, complemented
10C2×#14583045C211yesmaximal, characteristic, complemented
11C2×#14583039C211yesmaximal, characteristic, complemented
12C2×C4×#10621873C211yesmaximal, characteristic, complemented
13C2×C8×D172C211yesmaximal, characteristic, complemented
14C2×#14582892C211yesmaximal, characteristic, complemented
15C2×#103×D43C211yesmaximal, characteristic, complemented
16C2×C43×#488C211yesmaximal, characteristic, complemented
17C22×#10621900C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621884C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic
24#14583602—24no—
25#14583602C2218yescomplemented
26#14583557—24no—
27#14583557C2218yescomplemented
28C2×#13063320—21no—
29C2×#13063311—21no—
30C2×#13063310—21no—
31C2×#13063302—21no—
32C2×#13063301C2211yescharacteristic
33C2×#13063300—21no—
34C2×#13063300C2211yescharacteristic
35C2×#13063300C2211yescharacteristic
36C2×#13063298—21no—
37C2×#13063296C2211yescharacteristic
38C2×C4×Dic86C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic
41C2×#13063287—21no—
42C2×(C22⋊D43)⋊C4—21no—
43C2×#13063283C2211yescharacteristic
44C2×C4⋊C4×D43C2211yescharacteristic
45#14583238C2218yescomplemented
46#14583216C2218yescomplemented
47#14583203C2218yescomplemented
48#14583134C2218yescomplemented
49#14583131C2218yescomplemented
50#14583111C2218yescomplemented
51#14583045C2218yescomplemented
52#14583039C2218yescomplemented
53C4×#10621873C2218yescomplemented
54C8×D172C2218yescomplemented
55C2×#13063258C2211yescharacteristic
56C2×#13063257C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×C4⋊(C43⋊C8)C2211yescharacteristic
59#14582892C2218yescomplemented
60C2×#13063250C2211yescharacteristic
61C2×#13063249C2211yescharacteristic
62C2×#13063248C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64#103×D43C2218yescomplemented
65C2×#13063247C2211yescharacteristic
66C2×#13063246C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×#124×C43C2211yescharacteristic
71C43×#488C2218yescomplemented
72C2×#103×C43C2211yescharacteristic
73C2×#103×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C2×#10621900—22no—
78C2×#10621900—24no—
79C2×#10621900—42no—
80C2×#10621900C2314yes—
81C22×Dic86—21no—
82C22×Dic86C2311yescharacteristic
83C2×Q8×D43—22no—
84C2×Q8×D43—24no—
85C2×Q8×D43—42no—
86C2×Q8×D43C2314yes—
87C22×D172—21no—
88C22×D172—21no—
89C22×D172D411yescharacteristic
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C22×C22⋊D43—21no—
93C23×Dic43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43C2311yescharacteristic
98C22×C4×D43C2311yescharacteristic
99C2×#10621873—24no—
100C2×#10621873C2314yes—
101C2×#10621884—42no—
102C2×#10621884C2314yes—
103C2×#10621882—42no—
104C2×#10621882C2314yes—
105C22×C43⋊C8C2311yescharacteristic
106C22×C43⋊C8C2311yescharacteristic
107C2×C8×D43—42no—
108C2×C8×D43—42no—
109C2×C8×D43C2314yes—
110C2×C8×D43C2314yes—
111#13063320—28no—
112#13063311—28no—
113#13063310—28no—
114#13063302—28no—
115#13063301—22no—
116#13063301C2314yes—
117#13063300—28no—
118#13063300—22no—
119#13063300—22no—
120#13063300C2314yes—
121#13063300C2314yes—
122#13063298—28no—
123#13063296—22no—
124#13063296C2314yes—
125C4×Dic86—22no—
126C4×Dic86C2314yes—
127C4×D172—22no—
128C4×D172D414yes—
129C4×D172C2314yes—
130C4×D172C2314yes—
131#13063287—28no—
132(C22⋊D43)⋊C4—28no—
133#13063283—22no—
134#13063283C2314yes—
135C2×C4⋊Dic43D411yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C4⋊C4×D43—22no—
142C4⋊C4×D43C2314yes—
143C2×C22⋊Dic43—21no—
144C2×(C2×D43)⋊C4—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#13063258C2314yes—
154#13063257C2314yes—
155#13063256C2314yes—
156C4⋊(C43⋊C8)C2314yes—
157#13063250C2314yes—
158#13063249C2314yes—
159#13063248C2314yes—
160#13063248C2314yes—
161#13063247C2314yes—
162#13063246C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yes—
165C22×Q8×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169#125×C43—22no—
170#125×C43C2314yes—
171#124×C43—22no—
172#124×C43C2314yes—
173C2×C4⋊C4×C43—21no—
174C2×C4⋊C4×C43—21no—
175C2×C4⋊C4×C43C2311yescharacteristic
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C22⋊C4×C43—21no—
178C2×C22⋊C4×C43—21no—
179C2×C42×C43C2311yescharacteristic
180#103×C43C2314yes—
181#103×C43C2314yes—
182#102×C43C2314yes—
183#102×C43C2314yes—
184C4×C8×C43C2314yes—
185C24×C43—21no—
186C23×D43—21no—
187C23×D43C2×D411yescharacteristic
188C23×D43C2×D411yescharacteristic
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—22no—
192C2×Q8×C43C2412yes—
193C2×D4×C43—21no—
194C2×D4×C43—22no—
195C2×D4×C43—22no—
196C2×D4×C43C2412yes—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43C2×D411yescharacteristic
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2411yescharacteristic
203C2×C22⋊D43—24no—
204C2×C22⋊D43—24no—
205C2×C22⋊D43—44no—
206C2×C22⋊D43—44no—
207C22×Dic43—24no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—44no—
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214Q8×D43—28no—
215Q8×D43—44no—
216Q8×D43—48no—
217#10621900—28no—
218#10621900—44no—
219#10621900—48no—
220C2×D172—21no—
221C2×D172—24no—
222C2×D172—24no—
223C2×D172—24no—
224C2×D172—22no—
225C2×D172—22no—
226C2×D172—44no—
227C2×D172—82no—
228C2×D172C2×D414yes—
229C2×D172C2412yes—
230C2×C4×D43—22no—
231C2×C4×D43—22no—
232C2×C4×D43—22no—
233C2×C4×D43—22no—
234C2×C4×D43—24no—
235C2×C4×D43—24no—
236C2×C4×D43—24no—
237C2×C4×D43—44no—
238C2×C4×D43—82no—
239C2×C4×D43—82no—
240C2×C4×D43C2×D412yes—
241C2×C4×D43C2×D412yes—
242C2×C4×D43C2412yes—
243C2×C4×D43C2412yes—
244C2×Dic86—21no—
245C2×Dic86—22no—
246C2×Dic86—24no—
247C2×Dic86—44no—
248C2×Dic86#4114yes—
249C2×Dic86C2412yes—
250C2×C8×C43—22no—
251C2×C8×C43—22no—
252C2×C8×C43C2412yes—
253C2×C8×C43C2412yes—
254C4⋊C4×C43—24no—
255C4⋊C4×C43—24no—
256C4⋊C4×C43—21no—
257C4⋊C4×C43—21no—
258C4⋊C4×C43C2412yes—
259C4⋊C4×C43C2412yes—
260C22⋊C4×C43—24no—
261C22⋊C4×C43—24no—
262C42×C43C2×D412yes—
263C42×C43C2412yes—
264C22⋊Dic43—24no—
265#10621884—44no—
266#10621882—44no—
267(C2×D43)⋊C4—24no—
268(C2×D43)⋊C4—24no—
269(C2×D43)⋊C4—24no—
270(C2×D43)⋊C4—24no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4C2×D414yes—
273(C2×D43)⋊C4C2×D414yes—
274C4⋊Dic43—21no—
275C4⋊Dic43—21no—
276C4⋊Dic43C2×D414yes—
277C4⋊Dic43C2412yes—
278C4⋊Dic43C2412yes—
279Dic43⋊C4—24no—
280Dic43⋊C4—24no—
281Dic43⋊C4—24no—
282C4×Dic43—24no—
283C4×Dic43—24no—
284C2×C43⋊C8—22no—
285C2×C43⋊C8—22no—
286C2×C43⋊C8C2412yes—
287C2×C43⋊C8C2412yes—
288#10621873—28no—
289C8×D43—44no—
290C8×D43—44no—
291C23×C43—22no—
292C23×C43—42no—
293C23×C43—42no—
294C23×C43—42no—
295C23×C43C22×D411yescharacteristic
296C22×D43—22no—
297C22×D43—22no—
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43#13514yes—
306C22×D43C22×D412yes—
307C22×D43C22×D412yes—
308Q8×C43—22no—
309Q8×C43—22no—
310Q8×C43—42no—
311D4×C43—22no—
312D4×C43—22no—
313D4×C43—42no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—42no—
320C2×C4×C43—42no—
321C2×C4×C43—42no—
322C2×C4×C43C22×D412yes—
323C2×C4×C43C22×D412yes—
324C2×C4×C43C22×D411yescharacteristic
325C2×C4×C43C2×#4112yes—
326C2×C4×C43H(5,𝔽2)12yes—
327C2×C4×C43C2511yescharacteristic
328C22⋊D43—48no—
329C22⋊D43—48no—
330C2×Dic43—24no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—48no—
337C2×Dic43—42no—
338C2×Dic43—42no—
339C2×Dic43C22×D412yes—
340C2×Dic43C22×D412yes—
341D172—28no—
342D172—22no—
343D172—22no—
344D172—48no—
345D172—42no—
346D172—84no—
347C4×D43—24no—
348C4×D43—24no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—22no—
353C4×D43—48no—
354C4×D43—84no—
355C4×D43—84no—
356Dic86—24no—
357Dic86—22no—
358Dic86—48no—
359Dic86C2×#4114yes—
360C8×C43—22no—
361C8×C43—22no—
362C43⋊C8—22no—
363C43⋊C8—22no—
364C2×#3301—431nomaximal, Sylow
365C22×C43—42no—
366C22×C43—42no—
367C22×C43—42no—
368C22×C43—84no—
369C22×C43#54612yes—
370C22×C43C2×#13512yes—
371C22×C43#57712yes—
372C22×C43C23×D411yescharacteristic
373C2×D43—22no—
374C2×D43—28no—
375C2×D43—22no—
376C2×D43—22no—
377C2×D43—22no—
378C2×D43—22no—
379C2×D43—44no—
380C2×D43—42no—
381C2×D43—42no—
382C2×D43—42no—
383C2×D43—84no—
384C2×D43C2×#13514yes—
385C4×C43—22no—
386C4×C43—22no—
387C4×C43—42no—
388C4×C43—42no—
389C4×C43—42no—
390C4×C43#54612yes—
391C4×C43C22×#4111yescharacteristic
392C4×C43C2×H(5,𝔽2)11yescharacteristic
393Dic43—24no—
394Dic43—22no—
395Dic43—22no—
396Dic43—42no—
397Dic43—42no—
398C2×#553—431no—
399C2×#548—431no—
400#3301—4316no—
401C2×#488D4311yescharacteristic, complemented
402C2×#481—431no—
403C2×#485—431no—
404C2×#479—431no—
405C2×#466—431no—
406C2×#465—431no—
407C2×#463—431no—
408C2×#449—431no—
409C2×#448—431no—
410C2×C4×SD16—431no—
411C2×C8×D4—431no—
412C2×#416—431no—
413C22×#103—431no—
414C2×C43—82no—
415C2×C43#330114yescomplemented
416C2×C43C2×#54611yescharacteristic
417C2×C43C22×#13511yescharacteristic
418C2×C43C2×#57711yescharacteristic
419D43—24no—
420D43—42no—
421D43—82no—
422C22×#41—431no—
423C23×Q8—431no—
424C22×SD16—431no—
425C22×SD16—431no—
426C22×D8—431no—
427C23×C8—431no—
428C23×C8—431no—
429#553—438no—
430#553—864no—
431#548—438no—
432#548—864no—
433C2×#126—861no—
434C2×#125C2×D4311yescharacteristic
435C2×#124—861no—
436C2×#124C2×D4311yescharacteristic
437C2×#123—861no—
438C2×C22⋊Q8—431no—
439C2×C22⋊Q8—861no—
440C2×#121—431no—
441C2×#121—431no—
442C2×#121—431no—
443C2×#121—861no—
444C2×#121—861no—
445C2×C4×Q8—431no—
446C2×C4×D4—431no—
447C2×C4×D4—431no—
448C2×C4×D4—861no—
449C2×C4×D4—861no—
450C2×#117—431no—
451C22×C4⋊C4—431no—
452#488C2×D4318yescomplemented
453#485—438no—
454#481—438no—
455#479—438no—
456#466—438no—
457#465—438no—
458#463—438no—
459#449—438no—
460#448—438no—
461C4×SD16—438no—
462C8×D4—438no—
463C2×#107—431no—
464C2×#106—431no—
465C2×#106—431no—
466C2×C4⋊C8—431no—
467#416—438no—
468C2×#103—431no—
469C2×#103—431no—
470C2×#103—431no—
471C2×#103—431no—
472C2×#103—438no—
473C2×#103C2×D4311yescharacteristic
474C2×#103C2×D4311yescharacteristic
475C2×#102—431no—
476C2×#102—431no—
477C2×#102C2×D4311yescharacteristic
478C2×#102C2×D4311yescharacteristic
479C2×C22⋊C8—431no—
480C2×C22⋊C8—431no—
481C2×C4×C8C2×D4311yescharacteristic
482C43C2×#330111yescharacteristic, complemented, Sylow
483C2×#41—434no—
484C2×#41—862no—
485C2×#41—864no—
486C2×#41—1722no—
487C22×Q8—434no—
488C22×Q8—431no—
489C22×Q8—861no—
490C22×Q8—862no—
491C22×Q8—864no—
492C22×Q8—1722no—
493C22×Q8C22×D4311yescharacteristic
494C22×D4—431no—
495C22×D4—431no—
496C22×D4—861no—
497C22×D4—861no—
498C22×D4—861no—
499C22×D4—861no—
500C22×D4C22×D4311yescharacteristic
501C23×C4—431no—
502C23×C4—431no—
503C23×C4—861no—
504C23×C4—861no—
505C23×C4—861no—
506C23×C4—861no—
507C2×SD16—434no—
508C2×SD16—434no—
509C2×SD16—864no—
510C2×SD16—1722no—
511C2×D8—434no—
512C2×D8—1722no—
513C22×C8—431no—
514C22×C8—431no—
515C22×C8—434no—
516C22×C8—434no—
517C22×C8—1722no—
518C22×C8—1722no—
519C22×C8C22×D4311yescharacteristic
520C22×C8C22×D4311yescharacteristic
521#126—868no—
522#125—22no—
523#125C22×D4314yes—
524#124—22no—
525#124—868no—
526#124C22×D4314yes—
527#123—868no—
528C22⋊Q8—434no—
529C22⋊Q8—868no—
530C22⋊Q8—862no—
531#121—434no—
532#121—434no—
533#121—434no—
534#121—868no—
535#121—862no—
536#121—862no—
537#121—868no—
538#121—862no—
539C4×Q8—434no—
540C4×Q8—862no—
541C4×D4—434no—
542C4×D4—434no—
543C4×D4—434no—
544C4×D4—868no—
545C4×D4—868no—
546C4×D4—862no—
547#117—434no—
548#117—862no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—431no—
552C2×C4⋊C4—431no—
553C2×C4⋊C4—431no—
554C2×C4⋊C4—434no—
555C2×C4⋊C4—862no—
556C2×C4⋊C4—861no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4C22×D4311yescharacteristic
560C2×C4⋊C4C22×D4311yescharacteristic
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—431no—
564C2×C22⋊C4—431no—
565C2×C22⋊C4—861no—
566C2×C22⋊C4—861no—
567C2×C22⋊C4—861no—
568C2×C22⋊C4—861no—
569C2×C22⋊C4—861no—
570C2×C22⋊C4—861no—
571C2×C42—861no—
572C2×C42—861no—
573C2×C42C22×D4311yescharacteristic
574#107—434no—
575#106—434no—
576#106—434no—
577C4⋊C8—434no—
578#103—434no—
579#103—434no—
580#103—434no—
581#103—434no—
582#103C22×D4314yes—
583#103C22×D4314yes—
584#102—434no—
585#102—434no—
586#102C22×D4314yes—
587#102C22×D4314yes—
588C22⋊C8—434no—
589C22⋊C8—434no—
590C4×C8C22×D4314yes—
591C24—21no—
592C24—431no—
593C24—431no—
594C24—861no—
595#41—868no—
596#41—1724no—
597#41—1728no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—434no—
602C2×Q8—432no—
603C2×Q8—864no—
604C2×Q8—861no—
605C2×Q8—862no—
606C2×Q8—868no—
607C2×Q8—1724no—
608C2×Q8—1724no—
609C2×Q8—1728no—
610C2×Q8C23×D4312yes—
611C2×D4—21no—
612C2×D4—22no—
613C2×D4—22no—
614C2×D4—434no—
615C2×D4—432no—
616C2×D4—864no—
617C2×D4—864no—
618C2×D4—864no—
619C2×D4—864no—
620C2×D4—864no—
621C2×D4—861no—
622C2×D4—862no—
623C2×D4—862no—
624C2×D4—3442no—
625C2×D4—1724no—
626C2×D4—1724no—
627C2×D4—1724no—
628C2×D4C23×D4312yes—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—864no—
639C22×C4—864no—
640C22×C4—864no—
641C22×C4—861no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—862no—
646C22×C4—861no—
647C22×C4—861no—
648C22×C4—864no—
649C22×C4—3442no—
650C22×C4—3442no—
651C22×C4—1724no—
652C22×C4—1724no—
653C22×C4D4×D4311yescharacteristic
654C22×C4D4×D4311yescharacteristic
655C22×C4C23×D4311yescharacteristic
656SD16—868no—
657SD16—1724no—
658D8—1724no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—432no—
662C2×C8—432no—
663C2×C8—862no—
664C2×C8—862no—
665C2×C8—1724no—
666C2×C8—1724no—
667C2×C8C23×D4312yes—
668C2×C8C23×D4312yes—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—434no—
674C4⋊C4—432no—
675C4⋊C4—432no—
676C4⋊C4—864no—
677C4⋊C4—864no—
678C4⋊C4—861no—
679C4⋊C4—861no—
680C4⋊C4—864no—
681C4⋊C4C23×D4312yes—
682C4⋊C4C23×D4312yes—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—434no—
686C22⋊C4—434no—
687C22⋊C4—864no—
688C22⋊C4—864no—
689C22⋊C4—864no—
690C22⋊C4—864no—
691C22⋊C4—864no—
692C22⋊C4—864no—
693C42—864no—
694C42—864no—
695C42D4×D4312yes—
696C42C23×D4312yes—
697C23—22no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—434no—
702C23—432no—
703C23—432no—
704C23—862no—
705C23—862no—
706C23—862no—
707C23—862no—
708C23—862no—
709C23—862no—
710C23—1722no—
711C23—1722no—
712C23—1722no—
713C23C2×D4×D4311yescharacteristic
714Q8—22no—
715Q8—22no—
716Q8—42no—
717Q8—434no—
718Q8—862no—
719Q8—864no—
720Q8—1728no—
721D4—22no—
722D4—22no—
723D4—42no—
724D4—868no—
725D4—862no—
726D4—862no—
727D4—3444no—
728D4—1728no—
729D4—1728no—
730D4—1728no—
731D4—1722no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—432no—
741C2×C4—432no—
742C2×C4—862no—
743C2×C4—862no—
744C2×C4—862no—
745C2×C4—864no—
746C2×C4—862no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—864no—
751C2×C4—864no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—3444no—
755C2×C4—3444no—
756C2×C4—1728no—
757C2×C4—1728no—
758C2×C4—1722no—
759C2×C4—1722no—
760C2×C4C2×D4×D4312yes—
761C2×C4C2×D4×D4312yes—
762C2×C4C2×D4×D4311yescharacteristic
763C2×C4#41×D4312yes—
764C2×C4#1306337112yes—
765C2×C4C24×D4311yescharacteristic
766C8—22no—
767C8—22no—
768C8—862no—
769C8—862no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—84no—
774C22—434no—
775C22—868no—
776C22—862no—
777C22—862no—
778C22—862no—
779C22—862no—
780C22—862no—
781C22—3444no—
782C22—1722no—
783C22—1722no—
784C22—1722no—
785C22—1724no—
786C22#1458354212yes—
787C22#135×D4312yes—
788C22#1458370612yes—
789C22C22×D4×D4311yescharacteristic
790C4—22no—
791C4—22no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—862no—
796C4—862no—
797C4—864no—
798C4—1722no—
799C4—1722no—
800C4#1458354212yes—
801C4C2×#41×D4311yescharacteristic
802C4C2×#1306337111yescharacteristic
803C2—82no—
804C2—864no—
805C2—3442no—
806C2—1722no—
807C2#1914649614yesdirect product factor
808C2C2×#1458354211yescharacteristic
809C2C2×#135×D4311yescharacteristic
810C2C2×#1458370611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#488C2
socleC23×C43C22×D4
hypercenterC2×#488D43
hypocenterC43C2×#3301
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#488

Complements

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

NH ≅ G/Ntype
1. C2×#14583602C2semidirect
2. C2×#14583557C2semidirect
3. #19146496C2direct (N × H)
4. C2×#14583216C2semidirect
5. C2×#14583238C2semidirect
6. C2×#14583203C2semidirect
7. C2×#14583134C2semidirect
8. C2×#14583131C2semidirect
9. C2×#14583111C2semidirect
10. C2×#14583045C2semidirect
11. C2×#14583039C2semidirect
12. C2×C4×#10621873C2semidirect
13. C2×C8×D172C2semidirect
14. C2×#14582892C2semidirect
15. C2×#103×D43C2semidirect
16. C2×C43×#488C2semidirect
25. #14583602C22semidirect
27. #14583557C22semidirect
45. #14583238C22semidirect
46. #14583216C22semidirect
47. #14583203C22semidirect
48. #14583134C22semidirect
49. #14583131C22semidirect
50. #14583111C22semidirect
51. #14583045C22semidirect
52. #14583039C22semidirect
53. C4×#10621873C22semidirect
54. C8×D172C22semidirect
59. #14582892C22semidirect
64. #103×D43C22semidirect
71. C43×#488C22semidirect
401. C2×#488D43semidirect
415. C2×C43#3301semidirect
452. #488C2×D43semidirect
482. C43C2×#3301semidirect
807. C2#19146496direct (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×#145835572
#191464962
C2×#145832162
C2×#145832382
C2×#145832032
C2×#145831342
C2×#145831312
C2×#145831112
C2×#145830452
C2×#145830392
C2×C4×#106218732
C2×C8×D1722
C2×#145828922
C2×#103×D432
C2×C43×#4882
C2×#330143