Finite Group Databasebeta

← C2×#62457 #10579215

Subgroups — C2×#62457 #10579215

Order 512.

7218 conjugacy classes of subgroups.

The subgroup lattice has 1209 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3543C211yesmaximal, characteristic, complemented
2C2×#3561C211yesmaximal, characteristic, complemented
3#62457C2132yesmaximal, direct product factor
4C2×#3401C212yesmaximal, complemented
5C2×#3397C212yesmaximal, complemented
6C2×D4×SD16C212yesmaximal, complemented
7C2×#3280C212yesmaximal, complemented
8C2×#3271C212yesmaximal, complemented
9C2×#3266C212yesmaximal, complemented
10C2×#3265C212yesmaximal, complemented
11C2×#3264C212yesmaximal, complemented
12C2×#3221C212yesmaximal, complemented
13C2×#3224C212yesmaximal, complemented
14C2×#3211C211yesmaximal, characteristic, complemented
15C2×#3208C211yesmaximal, characteristic, complemented
16C2×#3181C211yesmaximal, characteristic, complemented
17C2×#3179C212yesmaximal, complemented
18C2×#3154C212yesmaximal, complemented
19C22×#496C211yesmaximal, characteristic, complemented
20C2×#2968C211yesmaximal, characteristic, complemented
21C22×#137C2212yescomplemented
22C22×AGL(1,ℤ/8)C2212yescomplemented
23C22×#135C2212yescomplemented
24C23×SD16C2212yescomplemented
25C23×SD16C2212yescomplemented
26C23×D8C2212yescomplemented
27#3561—28no—
28#3561C22116yescomplemented
29#3543—28no—
30#3543C22116yescomplemented
31C2×#563—21no—
32C2×#562—21no—
33C2×#560—22no—
34C2×#559C2211yescharacteristic, complemented
35C2×#556C2212yescomplemented
36C2×#551—22no—
37C2×#550C2211yescharacteristic, complemented
38C2×#550C2211yescharacteristic, complemented
39C2×D4×Q8C2212yescomplemented
40C2×#548C2212yescomplemented
41C2×#546—21no—
42C2×#546C2212yes—
43C2×#546C2212yescomplemented
44C2×D42—21no—
45C2×D42C2212yes—
46C2×D42C2211yescharacteristic, complemented
47C2×#543—21no—
48C2×#542—22no—
49C2×#542C2212yescomplemented
50C2×#540—21no—
51C2×#540C2212yescomplemented
52C2×#538—21no—
53C2×#536C2212yescomplemented
54C2×#535—21no—
55C2×#535C2212yescomplemented
56C2×#534—22no—
57C2×#533C2211yescharacteristic, complemented
58C22×#127C2211yescharacteristic
59C2×#529C2211yescharacteristic
60C2×#529C2211yescharacteristic
61C22×#124C2211yescharacteristic, complemented
62#3401C22132yescomplemented
63#3397C22132yescomplemented
64D4×SD16C22132yescomplemented
65#3280C22132yescomplemented
66#3271C22132yescomplemented
67#3266C22132yescomplemented
68#3265C22132yescomplemented
69#3264C22132yescomplemented
70#3224C22132yescomplemented
71#3221C22132yescomplemented
72#3211C22116yescomplemented
73#3208C22116yescomplemented
74#3181C22116yescomplemented
75#3179C22132yescomplemented
76C2×#501C2211yescharacteristic, complemented
77#3154C22132yescomplemented
78C2×#497C2211yescharacteristic, complemented
79C2×#497C2212yescomplemented
80C2×#496C2212yes—
81C2×#496C2212yescomplemented
82C2×#496C2212yescomplemented
83C2×#496C2212yescomplemented
84C2×#496C2212yescomplemented
85C2×#496C22116yescomplemented
86C2×#495C2212yescomplemented
87C2×#495C2212yescomplemented
88C2×#492C2212yescomplemented
89C2×#492C2212yescomplemented
90C2×#491C2211yescharacteristic, complemented
91C2×#489C2211yescharacteristic, complemented
92C2×#488C2212yescomplemented
93C2×#486C2212yescomplemented
94C2×#469C2212yescomplemented
95C2×#468C2212yescomplemented
96C2×#467C2212yescomplemented
97C2×#466C2212yescomplemented
98C2×#465C2212yes—
99C2×#465C2212yescomplemented
100C2×#464C2212yescomplemented
101C2×#464C2212yescomplemented
102C2×#460C2212yescomplemented
103C2×#460C2212yescomplemented
104C2×#460C2212yescomplemented
105C2×#463C2212yescomplemented
106C2×#463C2212yescomplemented
107C2×#463C2212yescomplemented
108C2×#463C2212yescomplemented
109C2×#461C2212yescomplemented
110C2×#461C2212yescomplemented
111C2×#459C2212yescomplemented
112C2×#452C2212yescomplemented
113C2×#449C2212yescomplemented
114C2×#449C2212yescomplemented
115C2×#449C2212yescomplemented
116C2×#451C2211yescharacteristic, complemented
117C2×#448C2211yescharacteristic
118C2×#448C2212yescomplemented
119C2×#448C2212yescomplemented
120C2×#450C2212yescomplemented
121C2×#450C2212yescomplemented
122C2×#450C2212yescomplemented
123C2×#450C2211yescharacteristic, complemented
124C2×#447C2211yescharacteristic
125C2×#447C2212yescomplemented
126#2968C22116yescomplemented
127C2×#446C2212yescomplemented
128C2×#442C2212yescomplemented
129C2×#441C2212yescomplemented
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×#41C2312yes—
143C22×#41C2312yes—
144C23×Q8C2311yescharacteristic
145C23×Q8C2312yes—
146C23×D4—22no—
147C23×D4—21no—
148C23×D4—21no—
149C23×D4—21no—
150C23×D4C2311yescharacteristic
151C23×D4C2312yes—
152C23×D4C2312yes—
153C2×#137—48no—
154C2×#137C23116yescomplemented
155C2×AGL(1,ℤ/8)—48no—
156C2×AGL(1,ℤ/8)C23116yescomplemented
157C2×#135—48no—
158C2×#135C23116yescomplemented
159C22×Q16C2312yes—
160C22×Q16C2312yes—
161C22×SD16—48no—
162C22×SD16—48no—
163C22×SD16C2312yes—
164C22×SD16C2312yes—
165C22×SD16C2312yes—
166C22×SD16C2312yes—
167C22×SD16C2312yes—
168C22×SD16C2312yes—
169C22×SD16C2312yes—
170C22×SD16C2312yes—
171C22×SD16C2312yes—
172C22×SD16C2312yes—
173C22×SD16C2312yes—
174C22×SD16C23116yescomplemented
175C22×SD16C23116yescomplemented
176C22×D8—48no—
177C22×D8C2312yes—
178C22×D8C2312yes—
179C22×D8C2312yes—
180C22×D8C2312yes—
181C22×D8C2312yes—
182C22×D8C23116yescomplemented
183C22×M16C2312yes—
184C23×C8C2312yes—
185C23×C8C2312yes—
186#563—216no—
187#562—216no—
188#560—232no—
189#559—24no—
190#559C2318yescomplemented
191#556—28no—
192#556C23116yescomplemented
193#551—232no—
194#550—24no—
195#550—24no—
196#550C2318yescomplemented
197#550C2318yescomplemented
198D4×Q8—28no—
199D4×Q8C23116yescomplemented
200#548—28no—
201#548C23116yescomplemented
202#546—216no—
203#546—28no—
204#546—28no—
205#546C23116yes—
206#546C23116yescomplemented
207D42—216no—
208D42—28no—
209D42—24no—
210D42C23116yes—
211D42C2318yescomplemented
212#543—216no—
213#542—232no—
214#542—28no—
215#542C23116yescomplemented
216#540—216no—
217#540—28no—
218#540C23116yescomplemented
219#538—216no—
220#536—28no—
221#536C23116yescomplemented
222#535—216no—
223#535—28no—
224#535C23116yescomplemented
225#534—232no—
226#533—24no—
227#533C2318yescomplemented
228C2×C4⋊Q8—22no—
229C2×C4⋊Q8C2311yescharacteristic
230C2×C4⋊Q8C2312yes—
231C2×C4⋊Q8C2311yescharacteristic
232C2×#127—21no—
233C2×#127—21no—
234C2×#127—21no—
235C2×#127—24no—
236C2×#127C2312yes—
237C2×#127C2312yes—
238C2×#127C2311yescharacteristic
239C2×#127C2318yes—
240C2×#127C2311yescharacteristic
241#529—24no—
242#529D418yes—
243#529C2318yes—
244#529C2318yes—
245C2×#126—22no—
246C2×#126—22no—
247C2×#126—22no—
248C2×#126—21no—
249C2×#126D412yes—
250C2×#125—21no—
251C2×#125D411yescharacteristic
252C2×#125C2311yescharacteristic
253C2×#124—21no—
254C2×#124—22no—
255C2×#124—22no—
256C2×#124—21no—
257C2×#124—21no—
258C2×#124—24no—
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—21no—
278C2×C22⋊Q8—22no—
279C2×C22⋊Q8—22no—
280C2×C22⋊Q8—22no—
281C2×C22⋊Q8—22no—
282C2×C22⋊Q8—22no—
283C2×C22⋊Q8—22no—
284C2×C22⋊Q8D411yescharacteristic
285C2×C22⋊Q8C2311yescharacteristic
286C2×C22⋊Q8C2312yes—
287C2×C22⋊Q8C2312yes—
288C2×#121—22no—
289C2×#121—22no—
290C2×#121—22no—
291C2×#121—22no—
292C2×#121—21no—
293C2×#121—22no—
294C2×#121—21no—
295C2×#121—22no—
296C2×#121—22no—
297C2×#121—22no—
298C2×#121—22no—
299C2×#121—22no—
300C2×#121D411yescharacteristic
301C2×#121C2311yescharacteristic
302C2×#121C2312yes—
303C2×#121C2312yes—
304C2×#121C2312yes—
305C2×#120—22no—
306C2×#120—22no—
307C2×#120—22no—
308C2×#120—22no—
309C2×#120—22no—
310C2×#120—22no—
311C2×#120—22no—
312C2×C4×Q8—21no—
313C2×C4×Q8C2311yescharacteristic
314C2×C4×Q8C2312yes—
315C2×C4×Q8C2312yes—
316C2×C4×Q8C2311yescharacteristic
317C2×C4×D4—22no—
318C2×C4×D4—21no—
319C2×C4×D4—21no—
320C2×C4×D4—21no—
321C2×C4×D4—22no—
322C2×C4×D4C2311yescharacteristic
323C2×C4×D4C2312yes—
324C2×C4×D4C2312yes—
325C2×C4×D4C2312yes—
326C2×C4×D4C2312yes—
327C2×C4×D4C2311yescharacteristic
328C2×#117—21no—
329C2×#117—22no—
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#497C23116yescomplemented
339#497C2318yescomplemented
340#496C23116yes—
341#496C23116yescomplemented
342#496C23116yescomplemented
343#496C23116yescomplemented
344#496C23116yescomplemented
345#495C23116yescomplemented
346#495C23116yescomplemented
347#492C23116yescomplemented
348#492C23116yescomplemented
349#491C2318yescomplemented
350#489C2318yescomplemented
351#488C23116yescomplemented
352#486C23116yescomplemented
353#469C23116yescomplemented
354#468C23116yescomplemented
355#467C23116yescomplemented
356#466C23116yescomplemented
357#465C23116yes—
358#465C23116yescomplemented
359#464C23116yescomplemented
360#464C23116yescomplemented
361#463C23116yescomplemented
362#463C23116yescomplemented
363#463C23116yescomplemented
364#463C23116yescomplemented
365#461C23116yescomplemented
366#461C23116yescomplemented
367#460C23116yescomplemented
368#460C23116yescomplemented
369#460C23116yescomplemented
370#459C23116yescomplemented
371#452C23116yescomplemented
372#451C2318yescomplemented
373#450C23116yescomplemented
374#450C23116yescomplemented
375#450C2318yescomplemented
376#450C23116yescomplemented
377#449C23116yescomplemented
378#449C23116yescomplemented
379#449C23116yescomplemented
380#448C2318yes—
381#448C23116yescomplemented
382#448C23116yescomplemented
383#447C2318yes—
384#447C23116yescomplemented
385#446C23116yescomplemented
386#442C23116yescomplemented
387#441C23116yescomplemented
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×#103C2312yes—
406C2×#103C2312yes—
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—
429C2×#41—28no—
430C2×#41—24no—
431C2×#41—24no—
432C2×#41—44no—
433C2×#41—44no—
434C2×#41—44no—
435C2×#41—44no—
436C2×#41—84no—
437C2×#41C2418yes—
438C2×#41C2418yes—
439C22×Q8—21no—
440C22×Q8—22no—
441C22×Q8—21no—
442C22×Q8—22no—
443C22×Q8—24no—
444C22×Q8—44no—
445C22×Q8—44no—
446C22×Q8—44no—
447C22×Q8C2×D411yescharacteristic
448C22×Q8C2411yescharacteristic
449C22×Q8C2412yes—
450C22×Q8C2412yes—
451C22×Q8C2414yes—
452C22×Q8C2418yes—
453C22×D4—21no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—22no—
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—216no—
460C22×D4—28no—
461C22×D4—21no—
462C22×D4—21no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—21no—
466C22×D4—22no—
467C22×D4—22no—
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—22no—
473C22×D4—24no—
474C22×D4—28no—
475C22×D4—28no—
476C22×D4—24no—
477C22×D4—44no—
478C22×D4—44no—
479C22×D4—44no—
480C22×D4—44no—
481C22×D4—44no—
482C22×D4—84no—
483C22×D4—84no—
484C22×D4—84no—
485C22×D4—88no—
486C22×D4C2×D412yes—
487C22×D4C2×D411yescharacteristic
488C22×D4C2412yes—
489C22×D4C2412yes—
490C22×D4C2411yescharacteristic
491C22×D4C2412yes—
492C22×D4C2414yes—
493C22×D4C2418yes—
494C22×D4C2418yes—
495C23×C4—21no—
496C23×C4—22no—
497C23×C4—21no—
498C23×C4—22no—
499C23×C4—22no—
500C23×C4—22no—
501C23×C4—22no—
502C23×C4—22no—
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2412yes—
506C23×C4C2411yescharacteristic
507#137—432no—
508AGL(1,ℤ/8)—432no—
509#135—432no—
510C2×Q16—28no—
511C2×Q16—44no—
512C2×Q16C2418yes—
513C2×Q16C2418yes—
514C2×SD16—28no—
515C2×SD16—28no—
516C2×SD16—28no—
517C2×SD16—432no—
518C2×SD16—432no—
519C2×SD16—44no—
520C2×SD16—44no—
521C2×SD16—44no—
522C2×SD16—44no—
523C2×SD16—44no—
524C2×SD16—44no—
525C2×SD16—44no—
526C2×SD16—44no—
527C2×SD16C2418yes—
528C2×SD16C2418yes—
529C2×SD16C2418yes—
530C2×SD16C2418yes—
531C2×SD16C2418yes—
532C2×SD16C2418yes—
533C2×SD16C2418yes—
534C2×SD16C2418yes—
535C2×SD16C2418yes—
536C2×SD16C2418yes—
537C2×SD16C2418yes—
538C2×D8—28no—
539C2×D8—28no—
540C2×D8—432no—
541C2×D8—44no—
542C2×D8—44no—
543C2×D8—44no—
544C2×D8C2418yes—
545C2×D8C2418yes—
546C2×D8C2418yes—
547C2×D8C2418yes—
548C2×D8C2418yes—
549C2×M16—28no—
550C2×M16C2418yes—
551C22×C8—28no—
552C22×C8—28no—
553C22×C8C2412yes—
554C22×C8C2418yes—
555C22×C8C2412yes—
556C22×C8C2418yes—
557C22×C8C2412yes—
558C22×C8C2412yes—
559C4⋊Q8—216no—
560C4⋊Q8—22no—
561C4⋊Q8—22no—
562C4⋊Q8—24no—
563C4⋊Q8C2414yes—
564C4⋊Q8C2418yes—
565C4⋊Q8C2414yes—
566#127—28no—
567#127—28no—
568#127—24no—
569#127—22no—
570#127—22no—
571#127—28no—
572#127—24no—
573#127C2418yes—
574#127C2414yes—
575#127C2414yes—
576#127C2418yes—
577#126—216no—
578#126—216no—
579#126—216no—
580#126—28no—
581#126C2×D4116yes—
582#125—28no—
583#125—22no—
584#125C2×D418yes—
585#125C2414yes—
586#124—28no—
587#124—216no—
588#124—216no—
589#124—24no—
590#124—24no—
591#124—28no—
592#124—28no—
593#124—22no—
594#124—24no—
595#124—24no—
596#124C2×D418yes—
597#124C2418yes—
598#124C2418yes—
599#124C2414yes—
600#124C2418yes—
601#124C2418yes—
602#123—28no—
603#123—216no—
604#123—216no—
605#123—216no—
606#123—216no—
607#123—216no—
608#123—216no—
609#123—216no—
610#123—216no—
611#123C2×D4116yes—
612C22⋊Q8—216no—
613C22⋊Q8—28no—
614C22⋊Q8—22no—
615C22⋊Q8—24no—
616C22⋊Q8—24no—
617C22⋊Q8—216no—
618C22⋊Q8—216no—
619C22⋊Q8—216no—
620C22⋊Q8—216no—
621C22⋊Q8—216no—
622C22⋊Q8—216no—
623C22⋊Q8C2×D418yes—
624C22⋊Q8C2414yes—
625C22⋊Q8C2418yes—
626C22⋊Q8C2418yes—
627#121—216no—
628#121—22no—
629#121—24no—
630#121—24no—
631#121—24no—
632#121—216no—
633#121—216no—
634#121—216no—
635#121—28no—
636#121—216no—
637#121—28no—
638#121—216no—
639#121—216no—
640#121—216no—
641#121—216no—
642#121—216no—
643#121C2×D418yes—
644#121C2414yes—
645#121C2418yes—
646#121C2418yes—
647#121C2418yes—
648#120—216no—
649#120—216no—
650#120—216no—
651#120—216no—
652#120—216no—
653#120—216no—
654#120—216no—
655C4×Q8—28no—
656C4×Q8—22no—
657C4×Q8—24no—
658C4×Q8—24no—
659C4×Q8C2×D414yes—
660C4×Q8C2414yes—
661C4×Q8C2418yes—
662C4×Q8C2418yes—
663C4×Q8C2414yes—
664C4×D4—216no—
665C4×D4—28no—
666C4×D4—28no—
667C4×D4—28no—
668C4×D4—216no—
669C4×D4—22no—
670C4×D4—24no—
671C4×D4—24no—
672C4×D4—24no—
673C4×D4C2×D418yes—
674C4×D4C2×D414yes—
675C4×D4C2414yes—
676C4×D4C2418yes—
677C4×D4C2418yes—
678C4×D4C2418yes—
679C4×D4C2418yes—
680C4×D4C2414yes—
681#117—28no—
682#117—216no—
683#117—28no—
684#117C2×D418yes—
685#117C2418yes—
686C2×C4⋊C4—21no—
687C2×C4⋊C4—21no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—21no—
690C2×C4⋊C4—21no—
691C2×C4⋊C4—21no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—21no—
696C2×C4⋊C4—21no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4C2×D412yes—
700C2×C4⋊C4C2×D412yes—
701C2×C4⋊C4C2×D412yes—
702C2×C4⋊C4C2×D411yescharacteristic
703C2×C4⋊C4C2×D411yescharacteristic
704C2×C4⋊C4C2×D412yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2411yescharacteristic
707C2×C4⋊C4C2412yes—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
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—22no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—21no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—216no—
732C2×C22⋊C4—216no—
733C2×C22⋊C4C2×D412yes—
734C2×C22⋊C4C2×D412yes—
735C2×C22⋊C4C2×D412yes—
736C2×C22⋊C4C2×D412yes—
737C2×C22⋊C4C2×D412yes—
738C2×C42—22no—
739C2×C42—21no—
740C2×C42—22no—
741C2×C42C2×D411yescharacteristic
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D414yes—
744C2×C42C2411yescharacteristic
745C2×C42C2412yes—
746C2×C42C2411yescharacteristic
747C2×C42C2414yes—
748#107C2418yes—
749#106C2418yes—
750C4⋊C8C2418yes—
751C4⋊C8C2418yes—
752C4⋊C8C2418yes—
753#103C2418yes—
754#103C2418yes—
755#103C2418yes—
756#103C2418yes—
757#103C2418yes—
758#102C2418yes—
759#102C2418yes—
760#102C2418yes—
761#102C2418yes—
762#102C2418yes—
763#102C2418yes—
764#102C2418yes—
765C22⋊C8C2414yes—
766C22⋊C8C2414yes—
767C22⋊C8C2418yes—
768C22⋊C8C2418yes—
769#97C2414yes—
770#97C2414yes—
771#97C2418yes—
772#97C2418yes—
773C4×C8C2418yes—
774C4×C8C2418yes—
775C24—22no—
776C24—21no—
777C24—22no—
778C24—22no—
779C24—24no—
780C24—28no—
781C24—28no—
782C24—48no—
783C24—44no—
784C24—82no—
785C24—84no—
786C24—84no—
787C24—84no—
788C24—84no—
789C24—84no—
790C24—82no—
791C24C22×D412yes—
792C24C22×D411yescharacteristic
793#41—48no—
794#41—48no—
795#41—48no—
796#41—48no—
797#41—88no—
798#41—88no—
799#41—816no—
800C2×Q8—21no—
801C2×Q8—22no—
802C2×Q8—22no—
803C2×Q8—24no—
804C2×Q8—28no—
805C2×Q8—24no—
806C2×Q8—24no—
807C2×Q8—24no—
808C2×Q8—24no—
809C2×Q8—24no—
810C2×Q8—24no—
811C2×Q8—42no—
812C2×Q8—48no—
813C2×Q8—48no—
814C2×Q8—48no—
815C2×Q8—82no—
816C2×Q8—84no—
817C2×Q8—82no—
818C2×Q8—84no—
819C2×Q8—88no—
820C2×Q8C22×D414yes—
821C2×Q8C2512yes—
822C2×Q8C2514yes—
823C2×Q8C2514yes—
824C2×D4—28no—
825C2×D4—24no—
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—24no—
835C2×D4—22no—
836C2×D4—24no—
837C2×D4—28no—
838C2×D4—28no—
839C2×D4—24no—
840C2×D4—28no—
841C2×D4—28no—
842C2×D4—28no—
843C2×D4—28no—
844C2×D4—24no—
845C2×D4—24no—
846C2×D4—24no—
847C2×D4—24no—
848C2×D4—24no—
849C2×D4—24no—
850C2×D4—24no—
851C2×D4—24no—
852C2×D4—24no—
853C2×D4—48no—
854C2×D4—48no—
855C2×D4—48no—
856C2×D4—48no—
857C2×D4—48no—
858C2×D4—42no—
859C2×D4—44no—
860C2×D4—44no—
861C2×D4—44no—
862C2×D4—88no—
863C2×D4—84no—
864C2×D4—88no—
865C2×D4—84no—
866C2×D4—82no—
867C2×D4—84no—
868C2×D4—84no—
869C2×D4—82no—
870C2×D4—84no—
871C2×D4—82no—
872C2×D4—816no—
873C2×D4—84no—
874C2×D4—84no—
875C2×D4—816no—
876C2×D4—816no—
877C2×D4—84no—
878C2×D4—84no—
879C2×D4—84no—
880C2×D4—84no—
881C2×D4—84no—
882C2×D4—832no—
883C2×D4C22×D418yes—
884C2×D4C22×D414yes—
885C2×D4C2514yes—
886C2×D4C2514yes—
887C2×D4C2512yes—
888C2×D4C2514yes—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—22no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—21no—
897C22×C4—22no—
898C22×C4—21no—
899C22×C4—24no—
900C22×C4—28no—
901C22×C4—24no—
902C22×C4—28no—
903C22×C4—28no—
904C22×C4—28no—
905C22×C4—28no—
906C22×C4—28no—
907C22×C4—42no—
908C22×C4—44no—
909C22×C4—84no—
910C22×C4—84no—
911C22×C4—84no—
912C22×C4—84no—
913C22×C4—84no—
914C22×C4—84no—
915C22×C4—82no—
916C22×C4C22×D412yes—
917C22×C4C22×D414yes—
918C22×C4C22×D414yes—
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D412yes—
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D412yes—
926C22×C4C22×D412yes—
927C22×C4C22×D414yes—
928C22×C4C2512yes—
929C22×C4C2514yes—
930C22×C4C2511yescharacteristic
931Q16—216no—
932Q16—48no—
933SD16—216no—
934SD16—216no—
935SD16—216no—
936SD16—48no—
937SD16—48no—
938SD16—48no—
939SD16—48no—
940SD16—48no—
941SD16—48no—
942SD16—48no—
943SD16—48no—
944D8—216no—
945D8—216no—
946D8—48no—
947D8—48no—
948D8—48no—
949M16—216no—
950C2×C8—24no—
951C2×C8—24no—
952C2×C8—24no—
953C2×C8—216no—
954C2×C8—216no—
955C2×C8H(5,𝔽2)18yes—
956C2×C8C2514yes—
957C2×C8C2514yes—
958C2×C8C2514yes—
959C2×C8C2514yes—
960C4⋊C4—24no—
961C4⋊C4—24no—
962C4⋊C4—28no—
963C4⋊C4—24no—
964C4⋊C4—24no—
965C4⋊C4—24no—
966C4⋊C4—28no—
967C4⋊C4—28no—
968C4⋊C4—28no—
969C4⋊C4—24no—
970C4⋊C4—24no—
971C4⋊C4—28no—
972C4⋊C4—28no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—22no—
976C4⋊C4C22×D418yes—
977C4⋊C4C22×D418yes—
978C4⋊C4C22×D418yes—
979C4⋊C4C22×D414yes—
980C4⋊C4C22×D414yes—
981C4⋊C4C22×D418yes—
982C4⋊C4C2514yes—
983C4⋊C4C2512yes—
984C4⋊C4C2512yes—
985C22⋊C4—24no—
986C22⋊C4—28no—
987C22⋊C4—28no—
988C22⋊C4—28no—
989C22⋊C4—28no—
990C22⋊C4—28no—
991C22⋊C4—28no—
992C22⋊C4—28no—
993C22⋊C4—28no—
994C22⋊C4—28no—
995C22⋊C4—28no—
996C22⋊C4—24no—
997C22⋊C4—24no—
998C22⋊C4—28no—
999C22⋊C4—24no—
1000C22⋊C4—28no—
1001C22⋊C4—28no—
1002C22⋊C4—24no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4C22×D418yes—
1007C22⋊C4C22×D418yes—
1008C22⋊C4C22×D418yes—
1009C22⋊C4C22×D418yes—
1010C22⋊C4C22×D418yes—
1011C42—28no—
1012C42—24no—
1013C42—28no—
1014C42C22×D414yes—
1015C42C22×D412yes—
1016C42C22×D412yes—
1017C42C22×D414yes—
1018C42C22×D414yes—
1019C42C2512yes—
1020C42C2514yes—
1021C42C2512yes—
1022C23—22no—
1023C23—22no—
1024C23—24no—
1025C23—24no—
1026C23—24no—
1027C23—24no—
1028C23—24no—
1029C23—22no—
1030C23—24no—
1031C23—42no—
1032C23—44no—
1033C23—44no—
1034C23—44no—
1035C23—44no—
1036C23—44no—
1037C23—44no—
1038C23—42no—
1039C23—44no—
1040C23—42no—
1041C23—44no—
1042C23—44no—
1043C23—416no—
1044C23—48no—
1045C23—84no—
1046C23—88no—
1047C23—88no—
1048C23—88no—
1049C23—88no—
1050C23—88no—
1051C23—84no—
1052C23—168no—
1053C23—1616no—
1054C23—1616no—
1055C23#57714yes—
1056C23C23×D414yes—
1057C23C23×D412yes—
1058C23C23×D411yescharacteristic
1059Q8—24no—
1060Q8—24no—
1061Q8—24no—
1062Q8—24no—
1063Q8—24no—
1064Q8—44no—
1065Q8—44no—
1066Q8—44no—
1067Q8—42no—
1068Q8—88no—
1069Q8—84no—
1070Q8—84no—
1071D4—216no—
1072D4—24no—
1073D4—24no—
1074D4—24no—
1075D4—24no—
1076D4—24no—
1077D4—24no—
1078D4—24no—
1079D4—44no—
1080D4—48no—
1081D4—48no—
1082D4—48no—
1083D4—44no—
1084D4—42no—
1085D4—44no—
1086D4—44no—
1087D4—88no—
1088D4—84no—
1089D4—88no—
1090D4—84no—
1091D4—88no—
1092D4—84no—
1093D4—88no—
1094D4—88no—
1095D4—88no—
1096D4—88no—
1097D4—88no—
1098D4—88no—
1099D4—88no—
1100D4—88no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—24no—
1104C2×C4—24no—
1105C2×C4—22no—
1106C2×C4—28no—
1107C2×C4—22no—
1108C2×C4—22no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—24no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—22no—
1117C2×C4—24no—
1118C2×C4—22no—
1119C2×C4—24no—
1120C2×C4—22no—
1121C2×C4—44no—
1122C2×C4—48no—
1123C2×C4—42no—
1124C2×C4—44no—
1125C2×C4—42no—
1126C2×C4—44no—
1127C2×C4—44no—
1128C2×C4—42no—
1129C2×C4—88no—
1130C2×C4—88no—
1131C2×C4—88no—
1132C2×C4—88no—
1133C2×C4—88no—
1134C2×C4—88no—
1135C2×C4—84no—
1136C2×C4C23×D412yes—
1137C2×C4C23×D412yes—
1138C2×C4C23×D414yes—
1139C2×C4C23×D412yes—
1140C2×C4C23×D412yes—
1141C2×C4C23×D412yes—
1142C2×C4C23×D414yes—
1143C2×C4C23×D414yes—
1144C2×C4C23×D411yescharacteristic
1145C2×C4C2×H(5,𝔽2)14yes—
1146C2×C4C2611yescharacteristic
1147C8—24no—
1148C8—24no—
1149C8—24no—
1150C8C2×H(5,𝔽2)18yes—
1151C22—22no—
1152C22—22no—
1153C22—28no—
1154C22—24no—
1155C22—24no—
1156C22—24no—
1157C22—48no—
1158C22—44no—
1159C22—44no—
1160C22—44no—
1161C22—42no—
1162C22—44no—
1163C22—42no—
1164C22—44no—
1165C22—44no—
1166C22—42no—
1167C22—44no—
1168C22—44no—
1169C22—44no—
1170C22—88no—
1171C22—88no—
1172C22—84no—
1173C22—88no—
1174C22—168no—
1175C22—1616no—
1176C22—1616no—
1177C22#349812yes—
1178C22C2×#57714yes—
1179C22C2×#57712yes—
1180C22#358512yes—
1181C22C24×D411yescharacteristic
1182C4—24no—
1183C4—22no—
1184C4—22no—
1185C4—22no—
1186C4—24no—
1187C4—22no—
1188C4—22no—
1189C4—24no—
1190C4—42no—
1191C4—44no—
1192C4—44no—
1193C4—42no—
1194C4—42no—
1195C4—44no—
1196C4#349812yes—
1197C4C22×H(5,𝔽2)12yes—
1198C2—24no—
1199C2—44no—
1200C2—84no—
1201C2—84no—
1202C2—84no—
1203C2—82no—
1204C2#6245714yesdirect product factor
1205C2C2×#349811yescharacteristic
1206C2C22×#57711yescharacteristic
1207C2C2×#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×#3561C2semidirect
3. #62457C2direct (N × H)
4. C2×#3401C2semidirect
5. C2×#3397C2semidirect
6. C2×D4×SD16C2semidirect
7. C2×#3280C2semidirect
8. C2×#3271C2semidirect
9. C2×#3266C2semidirect
10. C2×#3265C2semidirect
11. C2×#3264C2semidirect
12. C2×#3221C2semidirect
13. C2×#3224C2semidirect
14. C2×#3211C2semidirect
15. C2×#3208C2semidirect
16. C2×#3181C2semidirect
17. C2×#3179C2semidirect
18. C2×#3154C2semidirect
19. C22×#496C2semidirect
20. C2×#2968C2semidirect
21. C22×#137C22semidirect
22. C22×AGL(1,ℤ/8)C22semidirect
23. C22×#135C22semidirect
24. C23×SD16C22semidirect
25. C23×SD16C22semidirect
26. C23×D8C22semidirect
28. #3561C22semidirect
30. #3543C22semidirect
34. C2×#559C22semidirect
35. C2×#556C22semidirect
37. C2×#550C22semidirect
38. C2×#550C22semidirect
39. C2×D4×Q8C22semidirect
40. C2×#548C22semidirect
43. C2×#546C22semidirect
46. C2×D42C22semidirect
49. C2×#542C22semidirect
51. C2×#540C22semidirect
53. C2×#536C22semidirect
55. C2×#535C22semidirect
57. C2×#533C22semidirect
61. C22×#124C22semidirect
62. #3401C22semidirect
63. #3397C22semidirect
64. D4×SD16C22semidirect
65. #3280C22semidirect
66. #3271C22semidirect
67. #3266C22semidirect
68. #3265C22semidirect
69. #3264C22semidirect
70. #3224C22semidirect
71. #3221C22semidirect
72. #3211C22semidirect
73. #3208C22semidirect
74. #3181C22semidirect
75. #3179C22semidirect
76. C2×#501C22semidirect
77. #3154C22semidirect
78. C2×#497C22semidirect
79. C2×#497C22semidirect
81. C2×#496C22semidirect
82. C2×#496C22semidirect
83. C2×#496C22semidirect
84. C2×#496C22semidirect
85. C2×#496C22semidirect
86. C2×#495C22semidirect
87. C2×#495C22semidirect
88. C2×#492C22semidirect
89. C2×#492C22semidirect
90. C2×#491C22semidirect
91. C2×#489C22semidirect
92. C2×#488C22semidirect
93. C2×#486C22semidirect
94. C2×#469C22semidirect
95. C2×#468C22semidirect
96. C2×#467C22semidirect
97. C2×#466C22semidirect
99. C2×#465C22semidirect
100. C2×#464C22semidirect
101. C2×#464C22semidirect
102. C2×#460C22semidirect
103. C2×#460C22semidirect
104. C2×#460C22semidirect
105. C2×#463C22semidirect
106. C2×#463C22semidirect
107. C2×#463C22semidirect
108. C2×#463C22semidirect
109. C2×#461C22semidirect
110. C2×#461C22semidirect
111. C2×#459C22semidirect
112. C2×#452C22semidirect
113. C2×#449C22semidirect
114. C2×#449C22semidirect
115. C2×#449C22semidirect
116. C2×#451C22semidirect
118. C2×#448C22semidirect
119. C2×#448C22semidirect
120. C2×#450C22semidirect
121. C2×#450C22semidirect
122. C2×#450C22semidirect
123. C2×#450C22semidirect
125. C2×#447C22semidirect
126. #2968C22semidirect
127. C2×#446C22semidirect
128. C2×#442C22semidirect
129. C2×#441C22semidirect
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
154. C2×#137C23semidirect
156. C2×AGL(1,ℤ/8)C23semidirect
158. C2×#135C23semidirect
174. C22×SD16C23semidirect
175. C22×SD16C23semidirect
182. C22×D8C23semidirect
190. #559C23semidirect
192. #556C23semidirect
196. #550C23semidirect
197. #550C23semidirect
199. D4×Q8C23semidirect
201. #548C23semidirect
206. #546C23semidirect
211. D42C23semidirect
215. #542C23semidirect
218. #540C23semidirect
221. #536C23semidirect
224. #535C23semidirect
227. #533C23semidirect
265. C2×#124C23semidirect
337. #501C23semidirect
338. #497C23semidirect
339. #497C23semidirect
341. #496C23semidirect
342. #496C23semidirect
343. #496C23semidirect
344. #496C23semidirect
345. #495C23semidirect
346. #495C23semidirect
347. #492C23semidirect
348. #492C23semidirect
349. #491C23semidirect
350. #489C23semidirect
351. #488C23semidirect
352. #486C23semidirect
353. #469C23semidirect
354. #468C23semidirect
355. #467C23semidirect
356. #466C23semidirect
358. #465C23semidirect
359. #464C23semidirect
360. #464C23semidirect
361. #463C23semidirect
362. #463C23semidirect
363. #463C23semidirect
364. #463C23semidirect
365. #461C23semidirect
366. #461C23semidirect
367. #460C23semidirect
368. #460C23semidirect
369. #460C23semidirect
370. #459C23semidirect
371. #452C23semidirect
372. #451C23semidirect
373. #450C23semidirect
374. #450C23semidirect
375. #450C23semidirect
376. #450C23semidirect
377. #449C23semidirect
378. #449C23semidirect
379. #449C23semidirect
381. #448C23semidirect
382. #448C23semidirect
384. #447C23semidirect
385. #446C23semidirect
386. #442C23semidirect
387. #441C23semidirect
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
1204. C2#62457direct (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×#35612
#624572
C2×#34012
C2×#33972
C2×D4×SD162
C2×#32802
C2×#32712
C2×#32662
C2×#32652
C2×#32642
C2×#32212
C2×#32242
C2×#32112
C2×#32082
C2×#31812
C2×#31792
C2×#31542
C22×#4962
C2×#29682