Finite Group Databasebeta

← C2×#19146444 #25972963

Subgroups — C2×#19146444 #25972963

Order 11008.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583602C211yesmaximal, characteristic, complemented
2C2×#14583542C211yesmaximal, characteristic, complemented
3#19146444C2116yesmaximal, direct product factor
4C2×#14583233C211yesmaximal, characteristic, complemented
5C2×#14583221C211yesmaximal, characteristic, complemented
6C2×#14583196C211yesmaximal, characteristic, complemented
7C2×#14583134C211yesmaximal, characteristic, complemented
8C2×#14583131C211yesmaximal, characteristic, complemented
9C2×#14583111C211yesmaximal, characteristic, complemented
10C2×#14583047C211yesmaximal, characteristic, complemented
11C2×#14583034C211yesmaximal, characteristic, complemented
12C2×C4×D344C211yesmaximal, characteristic, complemented
13C2×C8×D172C211yesmaximal, characteristic, complemented
14C2×#14582894C211yesmaximal, characteristic, complemented
15C2×#102×D43C211yesmaximal, characteristic, complemented
16C2×C43×#488C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×D4×D43C2211yescharacteristic
19C22×#10621884C2211yescharacteristic, complemented
20C22×D344C2211yescharacteristic
21C22×#10621882C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23C22×C8×D43C2211yescharacteristic, complemented
24#14583602—24no—
25#14583602C2218yescomplemented
26#14583542—24no—
27#14583542C2218yescomplemented
28C2×#13063320—21no—
29C2×#13063310—21no—
30C2×#13063307—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063300—21no—
33C2×#13063300C2211yescharacteristic
34C2×#13063300C2211yescharacteristic, complemented
35C2×#13063298—21no—
36C2×#13063296C2211yescharacteristic
37C2×#13063295—21no—
38C2×C4×D172C2211yescharacteristic
39C2×C4×D172C2211yescharacteristic
40C2×C4×D172C2211yescharacteristic, complemented
41C2×#13063287—21no—
42C2×#13063283C2211yescharacteristic, complemented
43C2×C4⋊C4×D43C2211yescharacteristic
44C2×C22⋊C4×D43—21no—
45#14583233C2218yescomplemented
46#14583221C2218yescomplemented
47#14583196C2218yescomplemented
48#14583134C2218yescomplemented
49#14583131C2218yescomplemented
50#14583111C2218yescomplemented
51#14583047C2218yescomplemented
52#14583034C2218yescomplemented
53C4×D344C2218yescomplemented
54C8×D172C2218yescomplemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
59#14582894C2218yescomplemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063247C2211yescharacteristic
62C2×#13063247C2211yescharacteristic, complemented
63C2×#13063246C2211yescharacteristic
64C2×#13063245C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66#102×D43C2218yescomplemented
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
69C2×#125×C43C2211yescharacteristic, complemented
70C2×#124×C43C2211yescharacteristic
71C43×#488C2218yescomplemented
72C2×#103×C43C2211yescharacteristic, complemented
73C2×#103×C43C2211yescharacteristic, complemented
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic, complemented
77C24×D43—21no—
78C2×#10621902—22no—
79C2×#10621902—24no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×D172—21no—
83C22×D172—21no—
84C22×D172—21no—
85C22×D172D411yescharacteristic
86C22×D172C2311yescharacteristic
87C22×D172C2311yescharacteristic
88C22×C22⋊D43—21no—
89C22×C22⋊D43—21no—
90C2×D4×D43—24no—
91C2×D4×D43—22no—
92C2×D4×D43—42no—
93C2×D4×D43C2314yes—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—21no—
98C22×C4×D43C2311yescharacteristic
99C22×C4×D43C2311yescharacteristic
100C2×#10621884—42no—
101C2×#10621884C2314yescomplemented
102C2×D344—24no—
103C2×D344C2314yes—
104C2×#10621882—42no—
105C2×#10621882C2314yes—
106C22×C43⋊C8C2311yescharacteristic
107C22×C43⋊C8C2311yescharacteristic
108C2×C8×D43—42no—
109C2×C8×D43—42no—
110C2×C8×D43C2314yes—
111C2×C8×D43C2314yescomplemented
112#13063320—28no—
113#13063310—28no—
114#13063307—28no—
115#13063301—22no—
116#13063301C2314yes—
117#13063300—28no—
118#13063300—22no—
119#13063300—22no—
120#13063300C2314yes—
121#13063300C2314yescomplemented
122#13063298—28no—
123#13063296—22no—
124#13063296C2314yes—
125#13063295—28no—
126C4×D172—22no—
127C4×D172—22no—
128C4×D172D414yes—
129C4×D172C2314yes—
130C4×D172C2314yes—
131C4×D172C2314yescomplemented
132#13063287—28no—
133#13063283—22no—
134#13063283C2314yescomplemented
135C2×C4⋊Dic43D411yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×C4⋊Dic43C2311yescharacteristic
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C4⋊C4×D43—22no—
141C4⋊C4×D43C2314yes—
142C2×C22⋊Dic43—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)⋊C4—21no—
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×(C2×D43)⋊C4D411yescharacteristic
151C22⋊C4×D43—28no—
152C2×C4×Dic43—21no—
153#13063259C2314yescomplemented
154#13063258C2314yescomplemented
155#13063256C2314yescomplemented
156C4⋊(C43⋊C8)C2314yescomplemented
157#13063249C2314yescomplemented
158#13063247C2314yes—
159#13063247C2314yescomplemented
160#13063246C2314yes—
161#13063245C2314yes—
162#13063245C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yescomplemented
165C22×Q8×C43C2311yescharacteristic
166C22×D4×C43C2311yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169#125×C43—22no—
170#125×C43C2314yescomplemented
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×C43C2314yescomplemented
181#103×C43C2314yescomplemented
182#102×C43C2314yes—
183#102×C43C2314yes—
184C4×C8×C43C2314yescomplemented
185C24×C43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C23×D43—24no—
189C23×D43—44no—
190C23×D43—44no—
191C23×D43—82no—
192C23×D43C2×D411yescharacteristic
193C23×D43C2×D411yescharacteristic
194C2×Q8×C43—21no—
195C2×Q8×C43—22no—
196C2×Q8×C43—22no—
197C2×Q8×C43C2412yes—
198C2×D4×C43—21no—
199C2×D4×C43—22no—
200C2×D4×C43—22no—
201C2×D4×C43C2412yes—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43C2×D411yescharacteristic
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2411yescharacteristic
208C2×C22⋊D43—24no—
209C2×C22⋊D43—24no—
210C2×C22⋊D43—44no—
211C2×C22⋊D43—82no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216#10621902—28no—
217#10621902—44no—
218#10621902—48no—
219D4×D43—28no—
220D4×D43—44no—
221D4×D43—48no—
222C2×D172—21no—
223C2×D172—22no—
224C2×D172—21no—
225C2×D172—24no—
226C2×D172—24no—
227C2×D172—24no—
228C2×D172—24no—
229C2×D172—22no—
230C2×D172—22no—
231C2×D172—44no—
232C2×D172—44no—
233C2×D172—82no—
234C2×D172C2×D414yes—
235C2×D172#4114yes—
236C2×D172C2412yes—
237C2×D172C2412yes—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43—22no—
241C2×C4×D43—22no—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43—24no—
245C2×C4×D43—24no—
246C2×C4×D43—44no—
247C2×C4×D43—82no—
248C2×C4×D43—82no—
249C2×C4×D43—82no—
250C2×C4×D43C2×D412yes—
251C2×C4×D43C2×D412yes—
252C2×C4×D43C2412yes—
253C2×C4×D43C2412yes—
254C2×C8×C43—22no—
255C2×C8×C43—22no—
256C2×C8×C43C2412yes—
257C2×C8×C43C2412yes—
258C4⋊C4×C43—24no—
259C4⋊C4×C43—24no—
260C4⋊C4×C43—21no—
261C4⋊C4×C43—21no—
262C4⋊C4×C43C2412yes—
263C4⋊C4×C43C2412yes—
264C22⋊C4×C43—24no—
265C22⋊C4×C43—24no—
266C42×C43C2×D412yes—
267C42×C43C2412yes—
268C22⋊Dic43—24no—
269#10621884—44no—
270#10621882—44no—
271(C2×D43)⋊C4—24no—
272(C2×D43)⋊C4—24no—
273(C2×D43)⋊C4—24no—
274(C2×D43)⋊C4—24no—
275(C2×D43)⋊C4—24no—
276(C2×D43)⋊C4—24no—
277(C2×D43)⋊C4C2×D414yes—
278(C2×D43)⋊C4C2×D414yes—
279C4⋊Dic43—21no—
280C4⋊Dic43—21no—
281C4⋊Dic43C2×D414yes—
282C4⋊Dic43C2412yes—
283C4⋊Dic43C2412yes—
284Dic43⋊C4—24no—
285Dic43⋊C4—24no—
286C4×Dic43—24no—
287C2×C43⋊C8—22no—
288C2×C43⋊C8—22no—
289C2×C43⋊C8C2412yes—
290C2×C43⋊C8C2412yes—
291D344—28no—
292C8×D43—44no—
293C8×D43—44no—
294C23×C43—22no—
295C23×C43—42no—
296C23×C43—42no—
297C23×C43—42no—
298C23×C43C22×D411yescharacteristic
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—24no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—22no—
306C22×D43—22no—
307C22×D43—48no—
308C22×D43—42no—
309C22×D43—42no—
310C22×D43—42no—
311C22×D43—42no—
312C22×D43—42no—
313C22×D43—48no—
314C22×D43—84no—
315C22×D43—816no—
316C22×D43#13514yes—
317C22×D43C22×D412yes—
318C22×D43C22×D412yes—
319Q8×C43—22no—
320Q8×C43—22no—
321Q8×C43—42no—
322D4×C43—22no—
323D4×C43—22no—
324D4×C43—42no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
329C2×C4×C43—22no—
330C2×C4×C43—42no—
331C2×C4×C43—42no—
332C2×C4×C43—42no—
333C2×C4×C43C22×D412yes—
334C2×C4×C43C22×D412yes—
335C2×C4×C43C22×D411yescharacteristic
336C2×C4×C43C2×#4112yes—
337C2×C4×C43H(5,𝔽2)12yes—
338C2×C4×C43C2511yescharacteristic
339C22⋊D43—48no—
340C22⋊D43—84no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—42no—
346C2×Dic43—42no—
347C2×Dic43C22×D412yes—
348C2×Dic43C22×D412yes—
349D172—28no—
350D172—24no—
351D172—22no—
352D172—22no—
353D172—22no—
354D172—48no—
355D172—48no—
356D172—42no—
357D172—84no—
358D172C2×#4114yes—
359C4×D43—24no—
360C4×D43—24no—
361C4×D43—22no—
362C4×D43—22no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—48no—
366C4×D43—84no—
367C4×D43—84no—
368C4×D43—84no—
369C8×C43—22no—
370C8×C43—22no—
371C43⋊C8—22no—
372C43⋊C8—22no—
373C2×#3297—431nomaximal, Sylow
374C22×C43—42no—
375C22×C43—42no—
376C22×C43—42no—
377C22×C43—84no—
378C22×C43#54612yes—
379C22×C43C2×#13512yes—
380C22×C43#57612yes—
381C22×C43C23×D411yescharacteristic
382C2×D43—22no—
383C2×D43—28no—
384C2×D43—22no—
385C2×D43—24no—
386C2×D43—22no—
387C2×D43—22no—
388C2×D43—22no—
389C2×D43—44no—
390C2×D43—48no—
391C2×D43—42no—
392C2×D43—42no—
393C2×D43—42no—
394C2×D43—42no—
395C2×D43—42no—
396C2×D43—816no—
397C2×D43—84no—
398C2×D43C2×#13514yes—
399C4×C43—22no—
400C4×C43—22no—
401C4×C43—42no—
402C4×C43—42no—
403C4×C43—42no—
404C4×C43#54612yes—
405C4×C43C22×#4111yescharacteristic
406C4×C43C2×H(5,𝔽2)11yescharacteristic
407Dic43—22no—
408Dic43—22no—
409Dic43—42no—
410Dic43—42no—
411C2×#553—431no—
412C2×#546—431no—
413#3297—4316no—
414C2×#488D4311yescharacteristic, complemented
415C2×#484—431no—
416C2×#482—431no—
417C2×#478—431no—
418C2×#466—431no—
419C2×#465—431no—
420C2×#463—431no—
421C2×#449—431no—
422C2×#447—431no—
423C2×C4×D8—431no—
424C2×C8×D4—431no—
425C2×#416—431no—
426C22×#102—431no—
427C2×C43—82no—
428C2×C43#329714yescomplemented
429C2×C43C2×#54611yescharacteristic
430C2×C43C22×#13511yescharacteristic
431C2×C43C2×#57611yescharacteristic
432D43—24no—
433D43—42no—
434D43—44no—
435D43—82no—
436C22×#41—431no—
437C23×D4—431no—
438C22×SD16—431no—
439C22×D8—431no—
440C22×D8—431no—
441C23×C8—431no—
442C23×C8—431no—
443#553—438no—
444#553—864no—
445#546—438no—
446#546—864no—
447C2×#126—861no—
448C2×#125C2×D4311yescharacteristic, complemented
449C2×#124C2×D4311yescharacteristic
450C2×#123—861no—
451C2×#123—861no—
452C2×C22⋊Q8—431no—
453C2×#121—431no—
454C2×#121—431no—
455C2×#121—431no—
456C2×#121—861no—
457C2×#121—861no—
458C2×#120—861no—
459C2×C4×D4—431no—
460C2×C4×D4—431no—
461C2×C4×D4—431no—
462C2×C4×D4—861no—
463C2×#117—431no—
464C22×C4⋊C4—431no—
465C22×C22⋊C4—861no—
466#488C2×D4318yescomplemented
467#484—438no—
468#482—438no—
469#478—438no—
470#466—438no—
471#465—438no—
472#463—438no—
473#449—438no—
474#447—438no—
475C4×D8—438no—
476C8×D4—438no—
477C2×#107—431no—
478C2×#107—431no—
479C2×#106—431no—
480C2×C4⋊C8—431no—
481#416—438no—
482C2×#103—431no—
483C2×#103C2×D4311yescharacteristic, complemented
484C2×#103C2×D4311yescharacteristic, complemented
485C2×#102—431no—
486C2×#102—431no—
487C2×#102—431no—
488C2×#102—431no—
489C2×#102—431no—
490C2×#102—438no—
491C2×#102C2×D4311yescharacteristic
492C2×#102C2×D4311yescharacteristic
493C2×C22⋊C8—431no—
494C2×C22⋊C8—431no—
495C2×C4×C8C2×D4311yescharacteristic, complemented
496C43C2×#329711yescharacteristic, complemented, Sylow
497C25—861no—
498C2×#41—434no—
499C2×#41—862no—
500C2×#41—864no—
501C2×#41—1722no—
502C22×Q8C22×D4311yescharacteristic
503C22×D4—434no—
504C22×D4—431no—
505C22×D4—431no—
506C22×D4—431no—
507C22×D4—861no—
508C22×D4—861no—
509C22×D4—861no—
510C22×D4—862no—
511C22×D4—861no—
512C22×D4—864no—
513C22×D4—861no—
514C22×D4—1722no—
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—1722no—
524C2×D8—434no—
525C2×D8—434no—
526C2×D8—864no—
527C2×D8—1722no—
528C22×C8—431no—
529C22×C8—431no—
530C22×C8—434no—
531C22×C8—434no—
532C22×C8—1722no—
533C22×C8—1722no—
534C22×C8C22×D4311yescharacteristic
535C22×C8C22×D4311yescharacteristic
536#126—868no—
537#125—22no—
538#125C22×D4314yescomplemented
539#124—22no—
540#124C22×D4314yes—
541#123—868no—
542#123—868no—
543C22⋊Q8—434no—
544C22⋊Q8—862no—
545#121—434no—
546#121—434no—
547#121—434no—
548#121—868no—
549#121—862no—
550#121—862no—
551#121—868no—
552#121—862no—
553#120—868no—
554C4×D4—434no—
555C4×D4—434no—
556C4×D4—434no—
557C4×D4—434no—
558C4×D4—868no—
559C4×D4—862no—
560C4×D4—862no—
561#117—434no—
562#117—862no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—431no—
566C2×C4⋊C4—431no—
567C2×C4⋊C4—431no—
568C2×C4⋊C4—434no—
569C2×C4⋊C4—862no—
570C2×C4⋊C4—861no—
571C2×C4⋊C4—861no—
572C2×C4⋊C4C22×D4311yescharacteristic
573C2×C4⋊C4C22×D4311yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—431no—
577C2×C22⋊C4—431no—
578C2×C22⋊C4—868no—
579C2×C22⋊C4—861no—
580C2×C22⋊C4—861no—
581C2×C22⋊C4—861no—
582C2×C22⋊C4—861no—
583C2×C22⋊C4—861no—
584C2×C22⋊C4—861no—
585C2×C22⋊C4—861no—
586C2×C42—861no—
587C2×C42C22×D4311yescharacteristic
588#107—434no—
589#107—434no—
590#106—434no—
591C4⋊C8—434no—
592#103—434no—
593#103C22×D4314yescomplemented
594#103C22×D4314yescomplemented
595#102—434no—
596#102—434no—
597#102—434no—
598#102—434no—
599#102—434no—
600#102C22×D4314yes—
601#102C22×D4314yes—
602C22⋊C8—434no—
603C22⋊C8—434no—
604C4×C8C22×D4314yescomplemented
605C24—21no—
606C24—431no—
607C24—431no—
608C24—864no—
609C24—861no—
610C24—861no—
611C24—3442no—
612C24—1724no—
613C24—1724no—
614#41—868no—
615#41—1724no—
616#41—1728no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D4312yes—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—434no—
625C2×D4—434no—
626C2×D4—432no—
627C2×D4—432no—
628C2×D4—864no—
629C2×D4—864no—
630C2×D4—864no—
631C2×D4—864no—
632C2×D4—864no—
633C2×D4—868no—
634C2×D4—864no—
635C2×D4—861no—
636C2×D4—861no—
637C2×D4—862no—
638C2×D4—862no—
639C2×D4—862no—
640C2×D4—3442no—
641C2×D4—3442no—
642C2×D4—1724no—
643C2×D4—1724no—
644C2×D4—1724no—
645C2×D4—1728no—
646C2×D4—1724no—
647C2×D4C23×D4312yes—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—431no—
652C22×C4—431no—
653C22×C4—432no—
654C22×C4—432no—
655C22×C4—432no—
656C22×C4—432no—
657C22×C4—864no—
658C22×C4—864no—
659C22×C4—862no—
660C22×C4—862no—
661C22×C4—862no—
662C22×C4—862no—
663C22×C4—861no—
664C22×C4—861no—
665C22×C4—864no—
666C22×C4—864no—
667C22×C4—3442no—
668C22×C4—3442no—
669C22×C4—3442no—
670C22×C4—1724no—
671C22×C4D4×D4311yescharacteristic
672C22×C4D4×D4311yescharacteristic
673C22×C4C23×D4311yescharacteristic
674SD16—1724no—
675D8—868no—
676D8—1724no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—432no—
680C2×C8—432no—
681C2×C8—862no—
682C2×C8—862no—
683C2×C8—1724no—
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—864no—
696C4⋊C4—861no—
697C4⋊C4—861no—
698C4⋊C4C23×D4312yes—
699C4⋊C4C23×D4312yes—
700C22⋊C4—24no—
701C22⋊C4—24no—
702C22⋊C4—434no—
703C22⋊C4—434no—
704C22⋊C4—864no—
705C22⋊C4—864no—
706C22⋊C4—864no—
707C22⋊C4—864no—
708C22⋊C4—864no—
709C22⋊C4—864no—
710C22⋊C4—864no—
711C42—864no—
712C42D4×D4312yes—
713C42C23×D4312yes—
714C23—22no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—434no—
719C23—432no—
720C23—432no—
721C23—862no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—864no—
728C23—862no—
729C23—3444no—
730C23—34416no—
731C23—1728no—
732C23—1728no—
733C23—1722no—
734C23—1722no—
735C23—1722no—
736C23—1722no—
737C23—1722no—
738C23C2×D4×D4311yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—22no—
743D4—22no—
744D4—42no—
745D4—434no—
746D4—868no—
747D4—862no—
748D4—862no—
749D4—862no—
750D4—864no—
751D4—3444no—
752D4—3444no—
753D4—1728no—
754D4—1728no—
755D4—1728no—
756D4—1722no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—432no—
766C2×C4—432no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—864no—
774C2×C4—864no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—3444no—
778C2×C4—3444no—
779C2×C4—3444no—
780C2×C4—1728no—
781C2×C4—1722no—
782C2×C4—1722no—
783C2×C4C2×D4×D4312yes—
784C2×C4C2×D4×D4312yes—
785C2×C4C2×D4×D4311yescharacteristic
786C2×C4#41×D4312yes—
787C2×C4#1306337112yes—
788C2×C4C24×D4311yescharacteristic
789C8—22no—
790C8—22no—
791C8—862no—
792C8—862no—
793C22—42no—
794C22—42no—
795C22—42no—
796C22—84no—
797C22—434no—
798C22—862no—
799C22—862no—
800C22—868no—
801C22—862no—
802C22—862no—
803C22—864no—
804C22—862no—
805C22—34416no—
806C22—3444no—
807C22—1722no—
808C22—1722no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—1724no—
813C22—1728no—
814C22#1458354212yes—
815C22#135×D4312yes—
816C22#1458370112yes—
817C22C22×D4×D4311yescharacteristic
818C4—22no—
819C4—22no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—862no—
824C4—862no—
825C4—1722no—
826C4—1722no—
827C4#1458354212yes—
828C4C2×#41×D4311yescharacteristic
829C4C2×#1306337111yescharacteristic
830C2—82no—
831C2—864no—
832C2—3442no—
833C2—1722no—
834C2—1724no—
835C2#1914644414yesdirect product factor
836C2C2×#1458354211yescharacteristic
837C2C2×#135×D4311yescharacteristic
838C2C2×#1458370111yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#488C2
socleC23×C43C22×D4
hypercenterC2×#488D43
hypocenterC43C2×#3297
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×#14583542C2semidirect
3. #19146444C2direct (N × H)
4. C2×#14583233C2semidirect
5. C2×#14583221C2semidirect
6. C2×#14583196C2semidirect
7. C2×#14583134C2semidirect
8. C2×#14583131C2semidirect
9. C2×#14583111C2semidirect
10. C2×#14583047C2semidirect
11. C2×#14583034C2semidirect
12. C2×C4×D344C2semidirect
13. C2×C8×D172C2semidirect
14. C2×#14582894C2semidirect
15. C2×#102×D43C2semidirect
16. C2×C43×#488C2semidirect
19. C22×#10621884C22semidirect
23. C22×C8×D43C22semidirect
25. #14583602C22semidirect
27. #14583542C22semidirect
34. C2×#13063300C22semidirect
40. C2×C4×D172C22semidirect
42. C2×#13063283C22semidirect
45. #14583233C22semidirect
46. #14583221C22semidirect
47. #14583196C22semidirect
48. #14583134C22semidirect
49. #14583131C22semidirect
50. #14583111C22semidirect
51. #14583047C22semidirect
52. #14583034C22semidirect
53. C4×D344C22semidirect
54. C8×D172C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063256C22semidirect
58. C2×C4⋊(C43⋊C8)C22semidirect
59. #14582894C22semidirect
60. C2×#13063249C22semidirect
62. C2×#13063247C22semidirect
66. #102×D43C22semidirect
68. C2×(C2×D43)⋊C8C22semidirect
69. C2×#125×C43C22semidirect
71. C43×#488C22semidirect
72. C2×#103×C43C22semidirect
73. C2×#103×C43C22semidirect
76. C2×C4×C8×C43C22semidirect
101. C2×#10621884C23semidirect
111. C2×C8×D43C23semidirect
121. #13063300C23semidirect
131. C4×D172C23semidirect
134. #13063283C23semidirect
153. #13063259C23semidirect
154. #13063258C23semidirect
155. #13063256C23semidirect
156. C4⋊(C43⋊C8)C23semidirect
157. #13063249C23semidirect
159. #13063247C23semidirect
164. (C2×D43)⋊C8C23semidirect
170. #125×C43C23semidirect
180. #103×C43C23semidirect
181. #103×C43C23semidirect
184. C4×C8×C43C23semidirect
414. C2×#488D43semidirect
428. C2×C43#3297semidirect
448. C2×#125C2×D43semidirect
466. #488C2×D43semidirect
483. C2×#103C2×D43semidirect
484. C2×#103C2×D43semidirect
495. C2×C4×C8C2×D43semidirect
496. C43C2×#3297semidirect
538. #125C22×D43semidirect
593. #103C22×D43semidirect
594. #103C22×D43semidirect
604. C4×C8C22×D43semidirect
835. C2#19146444direct (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×#145835422
#191464442
C2×#145832332
C2×#145832212
C2×#145831962
C2×#145831342
C2×#145831312
C2×#145831112
C2×#145830472
C2×#145830342
C2×C4×D3442
C2×C8×D1722
C2×#145828942
C2×#102×D432
C2×C43×#4882
C2×#329743