Finite Group Databasebeta

← C2×#62459 #10579217

Subgroups — C2×#62459 #10579217

Order 512.

7434 conjugacy classes of subgroups.

The subgroup lattice has 1237 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3543C211yesmaximal, characteristic, complemented
2C2×#3558C211yesmaximal, characteristic, complemented
3#62459C2132yesmaximal, direct product factor
4C2×#3403C212yesmaximal, complemented
5C2×#3399C212yesmaximal, complemented
6C2×#3282C212yesmaximal, complemented
7C2×D4×D8C212yesmaximal, complemented
8C2×#3268C212yesmaximal, complemented
9C2×#3265C212yesmaximal, complemented
10C2×#3264C212yesmaximal, complemented
11C2×#3264C212yesmaximal, complemented
12C2×#3224C212yesmaximal, complemented
13C2×#3220C212yesmaximal, complemented
14C2×#3211C211yesmaximal, characteristic, complemented
15C2×#3205C211yesmaximal, characteristic, complemented
16C2×#3180C211yesmaximal, characteristic, complemented
17C2×#3179C212yesmaximal, complemented
18C2×#3155C212yesmaximal, complemented
19C22×#496C211yesmaximal, characteristic, complemented
20C2×#2968C211yesmaximal, characteristic, complemented
21C22×AGL(1,ℤ/8)C2212yescomplemented
22C22×AGL(1,ℤ/8)C2212yescomplemented
23C22×#135C2212yescomplemented
24C23×SD16C2212yescomplemented
25C23×D8C2212yescomplemented
26C23×D8C2212yescomplemented
27#3558—28no—
28#3558C22116yescomplemented
29#3543—28no—
30#3543C22116yescomplemented
31C2×#562—21no—
32C2×H(3,𝔽4)—21no—
33C2×#560—22no—
34C2×#559C2212yescomplemented
35C2×#559C2211yescharacteristic, complemented
36C2×#550C2211yescharacteristic, complemented
37C2×#550C2211yescharacteristic, complemented
38C2×#548C2212yescomplemented
39C2×#546—22no—
40C2×#546—21no—
41C2×#546C2212yescomplemented
42C2×#546C2212yescomplemented
43C2×D42—21no—
44C2×D42C2212yescomplemented
45C2×D42C2211yescharacteristic, complemented
46C2×D42C2212yescomplemented
47C2×#542C2212yescomplemented
48C2×#540—21no—
49C2×#540C2212yescomplemented
50C2×#538—22no—
51C2×#538—21no—
52C2×#535—21no—
53C2×#535C2212yescomplemented
54C2×#535C2212yescomplemented
55C2×#534—22no—
56C2×#534—21no—
57C2×#532C2211yescharacteristic, complemented
58C22×#127C2211yescharacteristic, complemented
59C2×#529C2211yescharacteristic
60C2×#529C2211yescharacteristic, complemented
61C22×#124C2211yescharacteristic, complemented
62#3403C22132yescomplemented
63#3399C22132yescomplemented
64#3282C22132yescomplemented
65D4×D8C22132yescomplemented
66#3268C22132yescomplemented
67#3265C22132yescomplemented
68#3264C22132yescomplemented
69#3264C22132yescomplemented
70#3224C22132yescomplemented
71#3220C22132yescomplemented
72#3211C22116yescomplemented
73#3205C22116yescomplemented
74#3180C22116yescomplemented
75#3179C22132yescomplemented
76C2×#501C2211yescharacteristic, complemented
77#3155C22132yescomplemented
78C2×#496C2212yescomplemented
79C2×#496C2211yescharacteristic, complemented
80C2×#496C2212yescomplemented
81C2×#496C2212yescomplemented
82C2×#496C2212yescomplemented
83C2×#496C2212yescomplemented
84C2×#496C2212yescomplemented
85C2×#496C22116yescomplemented
86C2×#495C2212yescomplemented
87C2×#495C2212yescomplemented
88C2×#493C2212yescomplemented
89C2×#493C2212yescomplemented
90C2×#490C2211yescharacteristic, complemented
91C2×#489C2211yescharacteristic, complemented
92C2×#488C2212yescomplemented
93C2×#486C2212yescomplemented
94C2×#469C2212yescomplemented
95C2×#468C2212yescomplemented
96C2×#466C2212yescomplemented
97C2×#466C2212yescomplemented
98C2×#465C2212yescomplemented
99C2×#465C2212yescomplemented
100C2×#464C2212yescomplemented
101C2×#464C2212yescomplemented
102C2×#460C2212yescomplemented
103C2×#463C2212yescomplemented
104C2×#463C2212yescomplemented
105C2×#463C2212yescomplemented
106C2×#463C2212yescomplemented
107C2×#459C2212yescomplemented
108C2×#459C2212yescomplemented
109C2×#459C2212yescomplemented
110C2×#459C2212yescomplemented
111C2×#459C2212yescomplemented
112C2×#452C2212yescomplemented
113C2×#449C2212yescomplemented
114C2×#449C2212yescomplemented
115C2×#449C2212yescomplemented
116C2×#451C2211yescharacteristic, complemented
117C2×#448C2211yescharacteristic, complemented
118C2×#450C2211yescharacteristic, complemented
119C2×#450C2212yescomplemented
120C2×#447C2211yescharacteristic
121C2×#447C2212yescomplemented
122C2×#447C2212yescomplemented
123C2×#447C2212yescomplemented
124C2×#447C2212yescomplemented
125C2×#447C2212yescomplemented
126#2968C22116yescomplemented
127C2×#446C2212yescomplemented
128C2×#442C2212yescomplemented
129C2×#442C2212yescomplemented
130C2×#440C2212yescomplemented
131C2×#440C2212yescomplemented
132C2×C4×SD16C2212yescomplemented
133C2×C4×D8C2212yescomplemented
134C2×#435C2212yescomplemented
135C2×#435C2212yescomplemented
136C2×C8×D4C2212yescomplemented
137C2×#433C2212yescomplemented
138C2×#431C2211yescharacteristic, complemented
139C2×#405C2212yescomplemented
140C22×#97C2211yescharacteristic, complemented
141C22×#41—21no—
142C22×#41—21no—
143C22×#41C2312yes—
144C22×#41C2312yes—
145C23×Q8C2311yescharacteristic
146C23×D4—22no—
147C23×D4—22no—
148C23×D4—21no—
149C23×D4—21no—
150C23×D4—21no—
151C23×D4C2311yescharacteristic
152C23×D4C2312yes—
153C23×D4C2312yes—
154C23×D4C2312yes—
155C2×AGL(1,ℤ/8)—48no—
156C2×AGL(1,ℤ/8)—48no—
157C2×AGL(1,ℤ/8)C23116yescomplemented
158C2×AGL(1,ℤ/8)C23116yescomplemented
159C2×#135—48no—
160C2×#135C23116yescomplemented
161C22×Q16C2312yes—
162C22×SD16—48no—
163C22×SD16C2312yes—
164C22×SD16C2312yes—
165C22×SD16C2312yes—
166C22×SD16C2312yes—
167C22×SD16C2312yes—
168C22×SD16C2312yes—
169C22×SD16C2312yes—
170C22×SD16C23116yescomplemented
171C22×D8—48no—
172C22×D8—48no—
173C22×D8C2312yes—
174C22×D8C2312yes—
175C22×D8C2312yes—
176C22×D8C2312yes—
177C22×D8C2312yes—
178C22×D8C2312yes—
179C22×D8C2312yes—
180C22×D8C2312yes—
181C22×D8C2312yes—
182C22×D8C2312yes—
183C22×D8C23116yescomplemented
184C22×D8C23116yescomplemented
185C22×M16C2312yes—
186C23×C8C2312yes—
187C23×C8C2312yes—
188#562—216no—
189H(3,𝔽4)—216no—
190#560—232no—
191#559—24no—
192#559—28no—
193#559C23116yescomplemented
194#559C2318yescomplemented
195#550—24no—
196#550—24no—
197#550C2318yescomplemented
198#550C2318yescomplemented
199#548—28no—
200#548C23116yescomplemented
201#546—232no—
202#546—216no—
203#546—28no—
204#546—28no—
205#546C23116yescomplemented
206#546C23116yescomplemented
207D42—216no—
208D42—24no—
209D42—28no—
210D42—28no—
211D42C2318yescomplemented
212D42C23116yescomplemented
213D42C23116yescomplemented
214#542—28no—
215#542C23116yescomplemented
216#540—216no—
217#540—28no—
218#540C23116yescomplemented
219#538—232no—
220#538—216no—
221#535—216no—
222#535—28no—
223#535—28no—
224#535C23116yescomplemented
225#535C23116yescomplemented
226#534—232no—
227#534—216no—
228#532—24no—
229#532C2318yescomplemented
230C2×C4⋊Q8C2311yescharacteristic
231C2×#127—21no—
232C2×#127—21no—
233C2×#127—21no—
234C2×#127—24no—
235C2×#127C2312yes—
236C2×#127C2311yescharacteristic
237C2×#127C2312yes—
238C2×#127C2312yes—
239C2×#127C2311yescharacteristic
240C2×#127C2311yescharacteristic
241C2×#127C2318yescomplemented
242#529—24no—
243#529D418yes—
244#529C2318yes—
245#529C2318yescomplemented
246C2×#126—22no—
247C2×#126—21no—
248C2×#126D412yes—
249C2×#125D411yescharacteristic
250C2×#125C2311yescharacteristic
251C2×#124—21no—
252C2×#124—22no—
253C2×#124—22no—
254C2×#124—22no—
255C2×#124—21no—
256C2×#124—21no—
257C2×#124—24no—
258C2×#124—21no—
259C2×#124D411yescharacteristic
260C2×#124C2312yes—
261C2×#124C2311yescharacteristic
262C2×#124C2312yes—
263C2×#124C2312yes—
264C2×#124C2312yes—
265C2×#124C2318yescomplemented
266C2×#123—21no—
267C2×#123—22no—
268C2×#123—22no—
269C2×#123—22no—
270C2×#123—22no—
271C2×#123—22no—
272C2×#123—22no—
273C2×#123—22no—
274C2×#123—22no—
275C2×#123D412yes—
276C2×C22⋊Q8—22no—
277C2×C22⋊Q8—22no—
278C2×C22⋊Q8D411yescharacteristic
279C2×C22⋊Q8C2311yescharacteristic
280C2×C22⋊Q8C2312yes—
281C2×#121—22no—
282C2×#121—21no—
283C2×#121—22no—
284C2×#121—22no—
285C2×#121—22no—
286C2×#121—22no—
287C2×#121—22no—
288C2×#121—22no—
289C2×#121—21no—
290C2×#121—21no—
291C2×#121—22no—
292C2×#121—22no—
293C2×#121—22no—
294C2×#121—22no—
295C2×#121—22no—
296C2×#121—22no—
297C2×#121D411yescharacteristic
298C2×#121C2311yescharacteristic
299C2×#121C2312yes—
300C2×#121C2312yes—
301C2×#121C2312yes—
302C2×#121C2312yes—
303C2×#120—22no—
304C2×#120—22no—
305C2×#120—22no—
306C2×#120—22no—
307C2×#120—22no—
308C2×#120—22no—
309C2×#120—22no—
310C2×#120—22no—
311C2×#120—22no—
312C2×#120—22no—
313C2×#120—22no—
314C2×C4×Q8C2311yescharacteristic
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×D4—21no—
318C2×C4×D4—22no—
319C2×C4×D4—21no—
320C2×C4×D4—21no—
321C2×C4×D4—22no—
322C2×C4×D4—21no—
323C2×C4×D4C2311yescharacteristic
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2312yes—
328C2×C4×D4C2312yes—
329C2×C4×D4C2311yescharacteristic
330C2×#117—21no—
331C2×#117C2312yes—
332C22×C22⋊C4—21no—
333C22×C22⋊C4—21no—
334C22×C22⋊C4—22no—
335C22×C22⋊C4—22no—
336C22×C42C2311yescharacteristic
337#501C2318yescomplemented
338#496C23116yescomplemented
339#496C23116yescomplemented
340#496C23116yescomplemented
341#496C23116yescomplemented
342#496C23116yescomplemented
343#496C23116yescomplemented
344#496C2318yescomplemented
345#495C23116yescomplemented
346#495C23116yescomplemented
347#493C23116yescomplemented
348#493C23116yescomplemented
349#490C2318yescomplemented
350#489C2318yescomplemented
351#488C23116yescomplemented
352#486C23116yescomplemented
353#469C23116yescomplemented
354#468C23116yescomplemented
355#466C23116yescomplemented
356#466C23116yescomplemented
357#465C23116yescomplemented
358#465C23116yescomplemented
359#464C23116yescomplemented
360#464C23116yescomplemented
361#463C23116yescomplemented
362#463C23116yescomplemented
363#463C23116yescomplemented
364#463C23116yescomplemented
365#460C23116yescomplemented
366#459C23116yescomplemented
367#459C23116yescomplemented
368#459C23116yescomplemented
369#459C23116yescomplemented
370#459C23116yescomplemented
371#452C23116yescomplemented
372#451C2318yescomplemented
373#450C2318yescomplemented
374#450C23116yescomplemented
375#449C23116yescomplemented
376#449C23116yescomplemented
377#449C23116yescomplemented
378#448C2318yescomplemented
379#447C2318yes—
380#447C23116yescomplemented
381#447C23116yescomplemented
382#447C23116yescomplemented
383#447C23116yescomplemented
384#447C23116yescomplemented
385#446C23116yescomplemented
386#442C23116yescomplemented
387#442C23116yescomplemented
388#440C23116yescomplemented
389#440C23116yescomplemented
390C4×SD16C23116yescomplemented
391C4×D8C23116yescomplemented
392#435C23116yescomplemented
393#435C23116yescomplemented
394C8×D4C23116yescomplemented
395#433C23116yescomplemented
396#431C2318yescomplemented
397C2×#107C2312yes—
398C2×#106C2312yes—
399C2×C4⋊C8C2312yes—
400C2×C4⋊C8C2312yes—
401C2×C4⋊C8C2312yes—
402C2×#103C2312yes—
403C2×#103C2312yes—
404C2×#103C2312yes—
405C2×#102C2312yes—
406C2×#102C2312yes—
407C2×#102C2312yes—
408C2×#102C2312yes—
409C2×#102C2312yes—
410C2×#102C2312yes—
411C2×#102C2312yes—
412C2×#102C2312yes—
413C2×#102C2312yes—
414C2×C22⋊C8C2311yescharacteristic
415C2×C22⋊C8C2311yescharacteristic
416C2×C22⋊C8C2312yes—
417C2×C22⋊C8C2312yes—
418#405C23116yescomplemented
419C2×#97C2311yescharacteristic
420C2×#97C2311yescharacteristic
421C2×#97C2312yes—
422C2×#97C2312yes—
423C2×#97C2318yescomplemented
424C2×C4×C8C2312yes—
425C2×C4×C8C2312yes—
426C25—21no—
427C25—22no—
428C25—22no—
429C25—22no—
430C2×#41—28no—
431C2×#41—28no—
432C2×#41—24no—
433C2×#41—24no—
434C2×#41—44no—
435C2×#41—44no—
436C2×#41—44no—
437C2×#41—44no—
438C2×#41—84no—
439C2×#41—84no—
440C2×#41C2418yes—
441C2×#41C2418yes—
442C22×Q8—21no—
443C22×Q8—21no—
444C22×Q8—22no—
445C22×Q8—44no—
446C22×Q8C2×D411yescharacteristic
447C22×Q8C2412yes—
448C22×Q8C2411yescharacteristic
449C22×Q8C2414yes—
450C22×D4—21no—
451C22×D4—22no—
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—216no—
458C22×D4—216no—
459C22×D4—28no—
460C22×D4—21no—
461C22×D4—21no—
462C22×D4—22no—
463C22×D4—21no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—21no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4—22no—
475C22×D4—21no—
476C22×D4—22no—
477C22×D4—24no—
478C22×D4—28no—
479C22×D4—28no—
480C22×D4—24no—
481C22×D4—24no—
482C22×D4—44no—
483C22×D4—44no—
484C22×D4—44no—
485C22×D4—44no—
486C22×D4—44no—
487C22×D4—44no—
488C22×D4—44no—
489C22×D4—84no—
490C22×D4—84no—
491C22×D4—84no—
492C22×D4—88no—
493C22×D4—88no—
494C22×D4C2×D412yes—
495C22×D4C2×D411yescharacteristic
496C22×D4C2412yes—
497C22×D4C2412yes—
498C22×D4C2412yes—
499C22×D4C2411yescharacteristic
500C22×D4C2412yes—
501C22×D4C2414yes—
502C22×D4C2418yes—
503C22×D4C2418yes—
504C22×D4C2418yes—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—22no—
508C23×C4—22no—
509C23×C4—22no—
510C23×C4—22no—
511C23×C4—22no—
512C23×C4—22no—
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2412yes—
516C23×C4C2411yescharacteristic
517AGL(1,ℤ/8)—432no—
518AGL(1,ℤ/8)—432no—
519#135—432no—
520C2×Q16—44no—
521C2×Q16C2418yes—
522C2×SD16—28no—
523C2×SD16—28no—
524C2×SD16—28no—
525C2×SD16—432no—
526C2×SD16—44no—
527C2×SD16—44no—
528C2×SD16—44no—
529C2×SD16—44no—
530C2×SD16C2418yes—
531C2×SD16C2418yes—
532C2×SD16C2418yes—
533C2×SD16C2418yes—
534C2×SD16C2418yes—
535C2×SD16C2418yes—
536C2×SD16C2418yes—
537C2×D8—28no—
538C2×D8—28no—
539C2×D8—28no—
540C2×D8—432no—
541C2×D8—432no—
542C2×D8—44no—
543C2×D8—44no—
544C2×D8—44no—
545C2×D8—44no—
546C2×D8—44no—
547C2×D8—44no—
548C2×D8—44no—
549C2×D8C2418yes—
550C2×D8C2418yes—
551C2×D8C2418yes—
552C2×D8C2418yes—
553C2×D8C2418yes—
554C2×D8C2418yes—
555C2×D8C2418yes—
556C2×D8C2418yes—
557C2×D8C2418yes—
558C2×D8C2418yes—
559C2×M16—28no—
560C2×M16C2418yes—
561C22×C8—28no—
562C22×C8—28no—
563C22×C8C2412yes—
564C22×C8C2412yes—
565C22×C8C2418yes—
566C22×C8C2418yes—
567C22×C8C2412yes—
568C22×C8C2412yes—
569C4⋊Q8—22no—
570C4⋊Q8C2414yes—
571#127—28no—
572#127—24no—
573#127—22no—
574#127—22no—
575#127—28no—
576#127—28no—
577#127—22no—
578#127—24no—
579#127—24no—
580#127C2418yes—
581#127C2414yes—
582#127C2414yes—
583#127C2414yes—
584#127C2418yes—
585#127C2418yes—
586#126—216no—
587#126—28no—
588#126C2×D4116yes—
589#125—22no—
590#125C2×D418yes—
591#125C2414yes—
592#124—28no—
593#124—216no—
594#124—216no—
595#124—216no—
596#124—24no—
597#124—24no—
598#124—28no—
599#124—28no—
600#124—28no—
601#124—22no—
602#124—24no—
603#124—24no—
604#124C2×D418yes—
605#124C2418yes—
606#124C2418yes—
607#124C2414yes—
608#124C2418yes—
609#124C2418yes—
610#123—28no—
611#123—216no—
612#123—216no—
613#123—216no—
614#123—216no—
615#123—216no—
616#123—216no—
617#123—216no—
618#123—216no—
619#123C2×D4116yes—
620C22⋊Q8—22no—
621C22⋊Q8—24no—
622C22⋊Q8—216no—
623C22⋊Q8—216no—
624C22⋊Q8C2×D418yes—
625C22⋊Q8C2414yes—
626C22⋊Q8C2418yes—
627#121—216no—
628#121—28no—
629#121—22no—
630#121—24no—
631#121—24no—
632#121—24no—
633#121—24no—
634#121—216no—
635#121—216no—
636#121—216no—
637#121—216no—
638#121—216no—
639#121—216no—
640#121—28no—
641#121—28no—
642#121—216no—
643#121—216no—
644#121—216no—
645#121—216no—
646#121—216no—
647#121—216no—
648#121C2×D418yes—
649#121C2414yes—
650#121C2418yes—
651#121C2418yes—
652#121C2418yes—
653#121C2418yes—
654#120—216no—
655#120—216no—
656#120—216no—
657#120—216no—
658#120—216no—
659#120—216no—
660#120—216no—
661#120—216no—
662#120—216no—
663#120—216no—
664#120—216no—
665C4×Q8—22no—
666C4×Q8—24no—
667C4×Q8C2×D414yes—
668C4×Q8C2414yes—
669C4×Q8C2418yes—
670C4×Q8C2414yes—
671C4×D4—28no—
672C4×D4—216no—
673C4×D4—28no—
674C4×D4—28no—
675C4×D4—216no—
676C4×D4—28no—
677C4×D4—22no—
678C4×D4—24no—
679C4×D4—24no—
680C4×D4—24no—
681C4×D4—24no—
682C4×D4C2×D418yes—
683C4×D4C2×D414yes—
684C4×D4C2414yes—
685C4×D4C2418yes—
686C4×D4C2418yes—
687C4×D4C2418yes—
688C4×D4C2418yes—
689C4×D4C2418yes—
690C4×D4C2414yes—
691#117—28no—
692#117C2×D418yes—
693#117C2418yes—
694C2×C4⋊C4—21no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—21no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4C2×D412yes—
702C2×C4⋊C4C2×D412yes—
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2×D411yescharacteristic
705C2×C4⋊C4C2×D412yes—
706C2×C4⋊C4C2×D412yes—
707C2×C4⋊C4C2411yescharacteristic
708C2×C4⋊C4C2411yescharacteristic
709C2×C4⋊C4C2412yes—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—28no—
720C2×C22⋊C4—28no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—21no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—216no—
735C2×C22⋊C4—216no—
736C2×C22⋊C4C2×D412yes—
737C2×C22⋊C4C2×D412yes—
738C2×C22⋊C4C2×D412yes—
739C2×C22⋊C4C2×D412yes—
740C2×C22⋊C4C2×D412yes—
741C2×C42—21no—
742C2×C42—22no—
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D414yes—
746C2×C42C2411yescharacteristic
747C2×C42C2412yes—
748C2×C42C2411yescharacteristic
749C2×C42C2414yes—
750#107C2418yes—
751#106C2418yes—
752C4⋊C8C2418yes—
753C4⋊C8C2418yes—
754C4⋊C8C2418yes—
755#103C2418yes—
756#103C2418yes—
757#103C2418yes—
758#102C2418yes—
759#102C2418yes—
760#102C2418yes—
761#102C2418yes—
762#102C2418yes—
763#102C2418yes—
764#102C2418yes—
765#102C2418yes—
766#102C2418yes—
767C22⋊C8C2414yes—
768C22⋊C8C2414yes—
769C22⋊C8C2418yes—
770C22⋊C8C2418yes—
771#97C2414yes—
772#97C2414yes—
773#97C2418yes—
774#97C2418yes—
775C4×C8C2418yes—
776C4×C8C2418yes—
777C24—22no—
778C24—22no—
779C24—21no—
780C24—22no—
781C24—22no—
782C24—24no—
783C24—28no—
784C24—28no—
785C24—28no—
786C24—44no—
787C24—48no—
788C24—84no—
789C24—82no—
790C24—84no—
791C24—84no—
792C24—84no—
793C24—84no—
794C24—84no—
795C24—84no—
796C24—82no—
797C24—84no—
798C24C22×D412yes—
799C24C22×D411yescharacteristic
800#41—48no—
801#41—48no—
802#41—48no—
803#41—48no—
804#41—816no—
805#41—88no—
806#41—88no—
807#41—816no—
808C2×Q8—22no—
809C2×Q8—21no—
810C2×Q8—24no—
811C2×Q8—24no—
812C2×Q8—24no—
813C2×Q8—24no—
814C2×Q8—24no—
815C2×Q8—42no—
816C2×Q8—48no—
817C2×Q8—82no—
818C2×Q8—82no—
819C2×Q8—84no—
820C2×Q8C22×D414yes—
821C2×Q8C2514yes—
822C2×Q8C2512yes—
823C2×D4—28no—
824C2×D4—24no—
825C2×D4—28no—
826C2×D4—28no—
827C2×D4—28no—
828C2×D4—28no—
829C2×D4—28no—
830C2×D4—28no—
831C2×D4—22no—
832C2×D4—21no—
833C2×D4—22no—
834C2×D4—22no—
835C2×D4—24no—
836C2×D4—22no—
837C2×D4—24no—
838C2×D4—28no—
839C2×D4—24no—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—24no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—28no—
846C2×D4—28no—
847C2×D4—28no—
848C2×D4—28no—
849C2×D4—28no—
850C2×D4—28no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—24no—
854C2×D4—24no—
855C2×D4—24no—
856C2×D4—24no—
857C2×D4—24no—
858C2×D4—24no—
859C2×D4—24no—
860C2×D4—24no—
861C2×D4—48no—
862C2×D4—48no—
863C2×D4—48no—
864C2×D4—48no—
865C2×D4—48no—
866C2×D4—48no—
867C2×D4—48no—
868C2×D4—42no—
869C2×D4—44no—
870C2×D4—44no—
871C2×D4—44no—
872C2×D4—48no—
873C2×D4—84no—
874C2×D4—88no—
875C2×D4—88no—
876C2×D4—88no—
877C2×D4—82no—
878C2×D4—84no—
879C2×D4—84no—
880C2×D4—84no—
881C2×D4—84no—
882C2×D4—82no—
883C2×D4—84no—
884C2×D4—82no—
885C2×D4—82no—
886C2×D4—84no—
887C2×D4—816no—
888C2×D4—84no—
889C2×D4—84no—
890C2×D4—84no—
891C2×D4—82no—
892C2×D4—816no—
893C2×D4—816no—
894C2×D4—84no—
895C2×D4—84no—
896C2×D4—84no—
897C2×D4—84no—
898C2×D4—84no—
899C2×D4—832no—
900C2×D4—832no—
901C2×D4C22×D418yes—
902C2×D4C22×D414yes—
903C2×D4C2514yes—
904C2×D4C2514yes—
905C2×D4C2514yes—
906C2×D4C2512yes—
907C2×D4C2514yes—
908C22×C4—24no—
909C22×C4—24no—
910C22×C4—24no—
911C22×C4—24no—
912C22×C4—21no—
913C22×C4—22no—
914C22×C4—21no—
915C22×C4—22no—
916C22×C4—21no—
917C22×C4—24no—
918C22×C4—24no—
919C22×C4—28no—
920C22×C4—28no—
921C22×C4—28no—
922C22×C4—28no—
923C22×C4—28no—
924C22×C4—28no—
925C22×C4—42no—
926C22×C4—44no—
927C22×C4—84no—
928C22×C4—84no—
929C22×C4—84no—
930C22×C4—84no—
931C22×C4—84no—
932C22×C4—84no—
933C22×C4—82no—
934C22×C4C22×D412yes—
935C22×C4C22×D414yes—
936C22×C4C22×D414yes—
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D412yes—
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D412yes—
944C22×C4C22×D412yes—
945C22×C4C22×D414yes—
946C22×C4C2512yes—
947C22×C4C2514yes—
948C22×C4C2511yescharacteristic
949Q16—48no—
950SD16—216no—
951SD16—216no—
952SD16—216no—
953SD16—48no—
954SD16—48no—
955SD16—48no—
956SD16—48no—
957D8—216no—
958D8—216no—
959D8—216no—
960D8—48no—
961D8—48no—
962D8—48no—
963D8—48no—
964D8—48no—
965D8—48no—
966D8—48no—
967M16—216no—
968C2×C8—24no—
969C2×C8—24no—
970C2×C8—24no—
971C2×C8—216no—
972C2×C8—216no—
973C2×C8H(5,𝔽2)18yes—
974C2×C8C2514yes—
975C2×C8C2514yes—
976C2×C8C2514yes—
977C2×C8C2514yes—
978C4⋊C4—24no—
979C4⋊C4—24no—
980C4⋊C4—24no—
981C4⋊C4—28no—
982C4⋊C4—24no—
983C4⋊C4—24no—
984C4⋊C4—28no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—22no—
988C4⋊C4C22×D418yes—
989C4⋊C4C22×D418yes—
990C4⋊C4C22×D414yes—
991C4⋊C4C22×D414yes—
992C4⋊C4C22×D418yes—
993C4⋊C4C22×D418yes—
994C4⋊C4C2514yes—
995C4⋊C4C2512yes—
996C4⋊C4C2512yes—
997C22⋊C4—24no—
998C22⋊C4—28no—
999C22⋊C4—28no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—24no—
1007C22⋊C4—24no—
1008C22⋊C4—24no—
1009C22⋊C4—28no—
1010C22⋊C4—28no—
1011C22⋊C4—28no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—24no—
1015C22⋊C4—28no—
1016C22⋊C4—28no—
1017C22⋊C4—28no—
1018C22⋊C4—28no—
1019C22⋊C4C22×D418yes—
1020C22⋊C4C22×D418yes—
1021C22⋊C4C22×D418yes—
1022C22⋊C4C22×D418yes—
1023C22⋊C4C22×D418yes—
1024C42—24no—
1025C42—28no—
1026C42C22×D414yes—
1027C42C22×D412yes—
1028C42C22×D412yes—
1029C42C22×D414yes—
1030C42C22×D414yes—
1031C42C2512yes—
1032C42C2514yes—
1033C42C2512yes—
1034C23—22no—
1035C23—22no—
1036C23—24no—
1037C23—24no—
1038C23—24no—
1039C23—24no—
1040C23—24no—
1041C23—24no—
1042C23—22no—
1043C23—24no—
1044C23—42no—
1045C23—44no—
1046C23—44no—
1047C23—44no—
1048C23—44no—
1049C23—44no—
1050C23—44no—
1051C23—44no—
1052C23—44no—
1053C23—42no—
1054C23—44no—
1055C23—44no—
1056C23—44no—
1057C23—42no—
1058C23—44no—
1059C23—48no—
1060C23—416no—
1061C23—88no—
1062C23—84no—
1063C23—88no—
1064C23—88no—
1065C23—88no—
1066C23—88no—
1067C23—88no—
1068C23—88no—
1069C23—84no—
1070C23—88no—
1071C23—1616no—
1072C23—168no—
1073C23—1616no—
1074C23—1616no—
1075C23#57614yes—
1076C23C23×D414yes—
1077C23C23×D412yes—
1078C23C23×D411yescharacteristic
1079Q8—24no—
1080Q8—24no—
1081Q8—24no—
1082Q8—44no—
1083Q8—44no—
1084Q8—42no—
1085Q8—84no—
1086Q8—84no—
1087D4—216no—
1088D4—24no—
1089D4—24no—
1090D4—24no—
1091D4—24no—
1092D4—24no—
1093D4—24no—
1094D4—24no—
1095D4—24no—
1096D4—24no—
1097D4—44no—
1098D4—48no—
1099D4—48no—
1100D4—48no—
1101D4—416no—
1102D4—44no—
1103D4—44no—
1104D4—42no—
1105D4—44no—
1106D4—44no—
1107D4—88no—
1108D4—88no—
1109D4—88no—
1110D4—84no—
1111D4—84no—
1112D4—88no—
1113D4—84no—
1114D4—84no—
1115D4—88no—
1116D4—88no—
1117D4—88no—
1118D4—88no—
1119D4—84no—
1120D4—88no—
1121D4—88no—
1122D4—88no—
1123D4—88no—
1124D4—88no—
1125D4—88no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—28no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—24no—
1137C2×C4—24no—
1138C2×C4—24no—
1139C2×C4—28no—
1140C2×C4—22no—
1141C2×C4—24no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—44no—
1146C2×C4—48no—
1147C2×C4—42no—
1148C2×C4—42no—
1149C2×C4—44no—
1150C2×C4—42no—
1151C2×C4—44no—
1152C2×C4—88no—
1153C2×C4—88no—
1154C2×C4—88no—
1155C2×C4—88no—
1156C2×C4—88no—
1157C2×C4—88no—
1158C2×C4—84no—
1159C2×C4C23×D412yes—
1160C2×C4C23×D414yes—
1161C2×C4C23×D412yes—
1162C2×C4C23×D412yes—
1163C2×C4C23×D412yes—
1164C2×C4C23×D412yes—
1165C2×C4C23×D414yes—
1166C2×C4C23×D414yes—
1167C2×C4C23×D411yescharacteristic
1168C2×C4C2×H(5,𝔽2)14yes—
1169C2×C4C2611yescharacteristic
1170C8—24no—
1171C8—24no—
1172C8—24no—
1173C8C2×H(5,𝔽2)18yes—
1174C22—22no—
1175C22—22no—
1176C22—28no—
1177C22—24no—
1178C22—24no—
1179C22—24no—
1180C22—48no—
1181C22—44no—
1182C22—44no—
1183C22—44no—
1184C22—44no—
1185C22—42no—
1186C22—44no—
1187C22—44no—
1188C22—44no—
1189C22—42no—
1190C22—44no—
1191C22—42no—
1192C22—44no—
1193C22—44no—
1194C22—44no—
1195C22—44no—
1196C22—88no—
1197C22—88no—
1198C22—84no—
1199C22—88no—
1200C22—88no—
1201C22—1616no—
1202C22—168no—
1203C22—1616no—
1204C22—1616no—
1205C22#349812yes—
1206C22C2×#57614yes—
1207C22C2×#57612yes—
1208C22#358512yes—
1209C22C24×D411yescharacteristic
1210C4—24no—
1211C4—22no—
1212C4—22no—
1213C4—22no—
1214C4—24no—
1215C4—22no—
1216C4—22no—
1217C4—24no—
1218C4—42no—
1219C4—44no—
1220C4—42no—
1221C4—44no—
1222C4—42no—
1223C4#349812yes—
1224C4C22×H(5,𝔽2)12yes—
1225C2—24no—
1226C2—44no—
1227C2—84no—
1228C2—84no—
1229C2—84no—
1230C2—84no—
1231C2—82no—
1232C2#6245914yesdirect product factor
1233C2C2×#349811yescharacteristic
1234C2C22×#57611yescharacteristic
1235C2C2×#358511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3543C2semidirect
2. C2×#3558C2semidirect
3. #62459C2direct (N × H)
4. C2×#3403C2semidirect
5. C2×#3399C2semidirect
6. C2×#3282C2semidirect
7. C2×D4×D8C2semidirect
8. C2×#3268C2semidirect
9. C2×#3265C2semidirect
10. C2×#3264C2semidirect
11. C2×#3264C2semidirect
12. C2×#3224C2semidirect
13. C2×#3220C2semidirect
14. C2×#3211C2semidirect
15. C2×#3205C2semidirect
16. C2×#3180C2semidirect
17. C2×#3179C2semidirect
18. C2×#3155C2semidirect
19. C22×#496C2semidirect
20. C2×#2968C2semidirect
21. C22×AGL(1,ℤ/8)C22semidirect
22. C22×AGL(1,ℤ/8)C22semidirect
23. C22×#135C22semidirect
24. C23×SD16C22semidirect
25. C23×D8C22semidirect
26. C23×D8C22semidirect
28. #3558C22semidirect
30. #3543C22semidirect
34. C2×#559C22semidirect
35. C2×#559C22semidirect
36. C2×#550C22semidirect
37. C2×#550C22semidirect
38. C2×#548C22semidirect
41. C2×#546C22semidirect
42. C2×#546C22semidirect
44. C2×D42C22semidirect
45. C2×D42C22semidirect
46. C2×D42C22semidirect
47. C2×#542C22semidirect
49. C2×#540C22semidirect
53. C2×#535C22semidirect
54. C2×#535C22semidirect
57. C2×#532C22semidirect
58. C22×#127C22semidirect
60. C2×#529C22semidirect
61. C22×#124C22semidirect
62. #3403C22semidirect
63. #3399C22semidirect
64. #3282C22semidirect
65. D4×D8C22semidirect
66. #3268C22semidirect
67. #3265C22semidirect
68. #3264C22semidirect
69. #3264C22semidirect
70. #3224C22semidirect
71. #3220C22semidirect
72. #3211C22semidirect
73. #3205C22semidirect
74. #3180C22semidirect
75. #3179C22semidirect
76. C2×#501C22semidirect
77. #3155C22semidirect
78. C2×#496C22semidirect
79. C2×#496C22semidirect
80. C2×#496C22semidirect
81. C2×#496C22semidirect
82. C2×#496C22semidirect
83. C2×#496C22semidirect
84. C2×#496C22semidirect
85. C2×#496C22semidirect
86. C2×#495C22semidirect
87. C2×#495C22semidirect
88. C2×#493C22semidirect
89. C2×#493C22semidirect
90. C2×#490C22semidirect
91. C2×#489C22semidirect
92. C2×#488C22semidirect
93. C2×#486C22semidirect
94. C2×#469C22semidirect
95. C2×#468C22semidirect
96. C2×#466C22semidirect
97. C2×#466C22semidirect
98. C2×#465C22semidirect
99. C2×#465C22semidirect
100. C2×#464C22semidirect
101. C2×#464C22semidirect
102. C2×#460C22semidirect
103. C2×#463C22semidirect
104. C2×#463C22semidirect
105. C2×#463C22semidirect
106. C2×#463C22semidirect
107. C2×#459C22semidirect
108. C2×#459C22semidirect
109. C2×#459C22semidirect
110. C2×#459C22semidirect
111. C2×#459C22semidirect
112. C2×#452C22semidirect
113. C2×#449C22semidirect
114. C2×#449C22semidirect
115. C2×#449C22semidirect
116. C2×#451C22semidirect
117. C2×#448C22semidirect
118. C2×#450C22semidirect
119. C2×#450C22semidirect
121. C2×#447C22semidirect
122. C2×#447C22semidirect
123. C2×#447C22semidirect
124. C2×#447C22semidirect
125. C2×#447C22semidirect
126. #2968C22semidirect
127. C2×#446C22semidirect
128. C2×#442C22semidirect
129. C2×#442C22semidirect
130. C2×#440C22semidirect
131. C2×#440C22semidirect
132. C2×C4×SD16C22semidirect
133. C2×C4×D8C22semidirect
134. C2×#435C22semidirect
135. C2×#435C22semidirect
136. C2×C8×D4C22semidirect
137. C2×#433C22semidirect
138. C2×#431C22semidirect
139. C2×#405C22semidirect
140. C22×#97C22semidirect
157. C2×AGL(1,ℤ/8)C23semidirect
158. C2×AGL(1,ℤ/8)C23semidirect
160. C2×#135C23semidirect
170. C22×SD16C23semidirect
183. C22×D8C23semidirect
184. C22×D8C23semidirect
193. #559C23semidirect
194. #559C23semidirect
197. #550C23semidirect
198. #550C23semidirect
200. #548C23semidirect
205. #546C23semidirect
206. #546C23semidirect
211. D42C23semidirect
212. D42C23semidirect
213. D42C23semidirect
215. #542C23semidirect
218. #540C23semidirect
224. #535C23semidirect
225. #535C23semidirect
229. #532C23semidirect
241. C2×#127C23semidirect
245. #529C23semidirect
265. C2×#124C23semidirect
337. #501C23semidirect
338. #496C23semidirect
339. #496C23semidirect
340. #496C23semidirect
341. #496C23semidirect
342. #496C23semidirect
343. #496C23semidirect
344. #496C23semidirect
345. #495C23semidirect
346. #495C23semidirect
347. #493C23semidirect
348. #493C23semidirect
349. #490C23semidirect
350. #489C23semidirect
351. #488C23semidirect
352. #486C23semidirect
353. #469C23semidirect
354. #468C23semidirect
355. #466C23semidirect
356. #466C23semidirect
357. #465C23semidirect
358. #465C23semidirect
359. #464C23semidirect
360. #464C23semidirect
361. #463C23semidirect
362. #463C23semidirect
363. #463C23semidirect
364. #463C23semidirect
365. #460C23semidirect
366. #459C23semidirect
367. #459C23semidirect
368. #459C23semidirect
369. #459C23semidirect
370. #459C23semidirect
371. #452C23semidirect
372. #451C23semidirect
373. #450C23semidirect
374. #450C23semidirect
375. #449C23semidirect
376. #449C23semidirect
377. #449C23semidirect
378. #448C23semidirect
380. #447C23semidirect
381. #447C23semidirect
382. #447C23semidirect
383. #447C23semidirect
384. #447C23semidirect
385. #446C23semidirect
386. #442C23semidirect
387. #442C23semidirect
388. #440C23semidirect
389. #440C23semidirect
390. C4×SD16C23semidirect
391. C4×D8C23semidirect
392. #435C23semidirect
393. #435C23semidirect
394. C8×D4C23semidirect
395. #433C23semidirect
396. #431C23semidirect
418. #405C23semidirect
423. C2×#97C23semidirect
1232. C2#62459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#35432
C2×#35582
#624592
C2×#34032
C2×#33992
C2×#32822
C2×D4×D82
C2×#32682
C2×#32652
C2×#32642
C2×#32242
C2×#32202
C2×#32112
C2×#32052
C2×#31802
C2×#31792
C2×#31552
C22×#4962
C2×#29682