Finite Group Databasebeta

← C2×#60460 #10574909

Subgroups — C2×#60460 #10574909

Order 512.

10598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#577C211yesmaximal, characteristic, complemented
2C22×#568C211yesmaximal, characteristic, complemented
3C2×#3489C211yesmaximal, characteristic, complemented
4C2×#3488C211yesmaximal, characteristic, complemented
5#60460C2132yesmaximal, direct product factor
6C2×#3063C213yesmaximal, complemented
7C2×#3062C213yesmaximal, complemented
8C2×#3061C213yesmaximal, complemented
9C2×#3057C213yesmaximal, complemented
10C2×#3056C213yesmaximal, complemented
11C2×#3055C213yesmaximal, complemented
12C2×#3054C213yesmaximal, complemented
13C22×#468C213yesmaximal, complemented
14C2×#2913C211yesmaximal, characteristic, complemented
15C2×#2898C211yesmaximal, characteristic, complemented
16C2×#2897C211yesmaximal, characteristic, complemented
17C22×2−1+4C2211yescharacteristic
18C22×H(5,𝔽2)C2211yescharacteristic
19C23×#41C2211yescharacteristic
20C2×#577—216no—
21C2×#577C22116yescomplemented
22C22×#137C2213yescomplemented
23C22×AGL(1,ℤ/8)C2213yescomplemented
24C22×#135C2213yescomplemented
25C23×SD16C2213yescomplemented
26C2×#568—216no—
27C2×#568C22116yescomplemented
28C22×#131C2211yescharacteristic
29C22×#131C2211yescharacteristic
30C22×#131C2213yescomplemented
31C22×#131C2213yescomplemented
32C23×M16C2213yescomplemented
33C23×M16C2213yescomplemented
34#3489—28no—
35#3489C22116yescomplemented
36#3488—28no—
37#3488C22116yescomplemented
38C2×#550—21no—
39C2×D4×Q8—21no—
40C2×#548—21no—
41C2×#548—21no—
42C2×#547—23no—
43C2×#546—23no—
44C2×#546—23no—
45C2×D42—23no—
46C2×#537C2213yes—
47C2×#537C2213yescomplemented
48C2×#536C2213yescomplemented
49C2×#535C2213yes—
50C2×#525C2213yes—
51C2×#525C2213yescomplemented
52C22×C22⋊Q8C2213yescomplemented
53C22×#121C2213yes—
54C2×#520C2211yescharacteristic
55C2×#520C2211yescharacteristic
56#3063C22148yescomplemented
57#3062C22148yescomplemented
58#3061C22148yescomplemented
59#3057C22148yescomplemented
60#3056C22148yescomplemented
61#3055C22148yescomplemented
62#3054C22148yescomplemented
63C2×#470C2213yescomplemented
64C2×#470C2213yescomplemented
65C2×#469C2213yescomplemented
66C2×#469C2213yescomplemented
67C2×#468C2213yescomplemented
68C2×#468C2216yescomplemented
69C2×#468C2216yescomplemented
70C2×#468C2216yescomplemented
71C2×#468C2211yescharacteristic, complemented
72C2×#468C2213yescomplemented
73C2×#468C2213yescomplemented
74C2×#468C22148yescomplemented
75C2×#467C2216yescomplemented
76C2×#466C2216yescomplemented
77C2×#465C2216yescomplemented
78C2×#465C2216yescomplemented
79#2913C22116yescomplemented
80C2×#428C2213yescomplemented
81C2×#428C2213yescomplemented
82C2×#427C2213yescomplemented
83C22×#107C2213yescomplemented
84#2898C22116yescomplemented
85#2897C22116yescomplemented
86C2×#417C2213yescomplemented
87C2×#417C2213yescomplemented
88C2×#419C2213yescomplemented
89C2×#418C2213yescomplemented
90C2×#416C2213yescomplemented
91C2×#416C2213yescomplemented
92C22×#103C2213yescomplemented
93C22×#102C2213yescomplemented
94C2×2−1+4—24no—
95C2×2−1+4—28no—
96C2×2−1+4—28no—
97C2×2−1+4C2318yes—
98C2×H(5,𝔽2)—24no—
99C2×H(5,𝔽2)—28no—
100C2×H(5,𝔽2)—28no—
101C2×H(5,𝔽2)C2318yes—
102C22×#41—28no—
103C22×#41—28no—
104C22×#41—21no—
105C22×#41—23no—
106C22×#41D413yes—
107C22×#41D411yescharacteristic
108C22×#41D418yes—
109C22×#41C2313yes—
110C22×#41C2313yes—
111C22×#41C2313yes—
112C22×#41C2318yes—
113C22×#41C2311yescharacteristic
114C23×Q8—21no—
115C23×Q8D411yescharacteristic
116C23×Q8C2313yes—
117C23×D4—23no—
118C23×D4—23no—
119C23×D4D413yes—
120C23×D4C2313yes—
121C24×C4C2313yes—
122#577—2128no—
123C2×#137—224no—
124C2×#137C23124yescomplemented
125C2×AGL(1,ℤ/8)—224no—
126C2×AGL(1,ℤ/8)C23124yescomplemented
127C2×#135—224no—
128C2×#135C23124yescomplemented
129C22×Q16C2313yes—
130C22×SD16—224no—
131C22×SD16C2316yes—
132C22×SD16C2313yes—
133C22×SD16C2311yescharacteristic
134C22×SD16C23124yescomplemented
135C22×D8C2313yes—
136#568—2128no—
137C2×#131—28no—
138C2×#131—224no—
139C2×#131—224no—
140C2×#131D4116yescomplemented
141C2×#131C2318yes—
142C2×#131C2318yes—
143C2×#131C23124yescomplemented
144C2×#131C23124yescomplemented
145C22×M16—224no—
146C22×M16—224no—
147C22×M16C2313yes—
148C22×M16C2311yescharacteristic
149C22×M16C2313yes—
150C22×M16C2313yes—
151C22×M16C2313yes—
152C22×M16C2313yes—
153C22×M16C23124yescomplemented
154C22×M16C23124yescomplemented
155C23×C8C2313yes—
156C23×C8C2316yes—
157C23×C8C2313yes—
158#550—216no—
159D4×Q8—216no—
160#548—216no—
161#548—216no—
162#547—248no—
163#546—248no—
164#546—248no—
165D42—248no—
166#537—212no—
167#537—212no—
168#537C23124yes—
169#537C23124yescomplemented
170#536—212no—
171#536C23124yescomplemented
172#535—212no—
173#535C23124yes—
174C2×C4⋊Q8—23no—
175C2×#127—23no—
176C2×#124—23no—
177C2×#124—23no—
178#525—212no—
179#525—212no—
180#525C23124yes—
181#525C23124yescomplemented
182C2×#123—26no—
183C2×#123—23no—
184C2×#123—23no—
185C2×C22⋊Q8—23no—
186C2×C22⋊Q8—23no—
187C2×C22⋊Q8—23no—
188C2×C22⋊Q8—23no—
189C2×C22⋊Q8—212no—
190C2×C22⋊Q8C2313yes—
191C2×C22⋊Q8C2316yes—
192C2×C22⋊Q8C2311yescharacteristic
193C2×C22⋊Q8C2313yes—
194C2×C22⋊Q8C2313yes—
195C2×C22⋊Q8C23124yescomplemented
196C2×#121—26no—
197C2×#121—23no—
198C2×#121—26no—
199C2×#121—23no—
200C2×#121—23no—
201C2×#121—23no—
202C2×#121—212no—
203C2×#121C2313yes—
204C2×#121C2316yes—
205C2×#121C23124yes—
206C2×#121C2313yes—
207C2×#121C2311yescharacteristic
208C2×#121C2313yes—
209C2×#120—23no—
210C2×#120—23no—
211C2×#120—26no—
212#520—24no—
213#520—24no—
214#520C2318yes—
215#520C2318yes—
216C2×C4×Q8—21no—
217C2×C4×Q8—21no—
218C2×C4×D4—23no—
219C2×C4×D4—23no—
220C2×C4×D4—23no—
221C2×C4×D4—23no—
222C2×C4×D4—23no—
223C2×C4×D4—23no—
224C2×#117C2313yes—
225C2×#117C2313yes—
226C22×C4⋊C4—23no—
227C22×C4⋊C4C2313yes—
228C22×C4⋊C4C2313yes—
229C22×C22⋊C4—23no—
230C22×C22⋊C4—23no—
231#470C23124yescomplemented
232#470C23124yescomplemented
233#469C23124yescomplemented
234#469C23124yescomplemented
235#468C23124yescomplemented
236#468C23148yescomplemented
237#468C23148yescomplemented
238#468C23148yescomplemented
239#468C2318yescomplemented
240#468C23124yescomplemented
241#468C23124yescomplemented
242#467C23148yescomplemented
243#466C23148yescomplemented
244#465C23148yescomplemented
245#465C23148yescomplemented
246#428C23124yescomplemented
247#428C23124yescomplemented
248#427C23124yescomplemented
249C2×#107C2313yes—
250C2×#107C2316yes—
251C2×#107C2311yescharacteristic
252C2×#107C23124yescomplemented
253C2×#106C2313yes—
254C2×#106C2313yes—
255#419C23124yescomplemented
256#418C23124yescomplemented
257#417C23124yescomplemented
258#417C23124yescomplemented
259#416C23124yescomplemented
260#416C23124yescomplemented
261C2×#103C2313yes—
262C2×#103C2316yes—
263C2×#103C2311yescharacteristic
264C2×#103C2313yes—
265C2×#103C2313yes—
266C2×#103C23124yescomplemented
267C2×#102C2313yes—
268C2×#102C2316yes—
269C2×#102C2311yescharacteristic
270C2×#102C2313yes—
271C2×#102C2313yes—
272C2×#102C23124yescomplemented
273C25—23no—
274C25C2×D413yes—
2752−1+4—232no—
2762−1+4—232no—
2772−1+4—432no—
278H(5,𝔽2)—232no—
279H(5,𝔽2)—232no—
280H(5,𝔽2)—432no—
281C2×#41—264no—
282C2×#41—232no—
283C2×#41—232no—
284C2×#41—28no—
285C2×#41—28no—
286C2×#41—224no—
287C2×#41—224no—
288C2×#41—212no—
289C2×#41—26no—
290C2×#41—26no—
291C2×#41—212no—
292C2×#41—212no—
293C2×#41—212no—
294C2×#41—212no—
295C2×#41—212no—
296C2×#41—48no—
297C2×#41—424no—
298C2×#41C2×D418yes—
299C2×#41C2×D4112yes—
300C2×#41C2×D4124yes—
301C2×#41C2×D418yes—
302C2×#41C2×D414yes—
303C2×#41#4118yes—
304C2×#41C24112yes—
305C2×#41C24112yes—
306C2×#41C24112yes—
307C2×#41C2414yes—
308C22×Q8—28no—
309C22×Q8—28no—
310C22×Q8—23no—
311C22×Q8—26no—
312C22×Q8—212no—
313C22×Q8—212no—
314C22×Q8—48no—
315C22×Q8C2×D413yes—
316C22×Q8C2×D418yes—
317C22×Q8C2×D411yescharacteristic
318C22×Q8C2413yes—
319C22×Q8C2411yescharacteristic
320C22×Q8C24112yes—
321C22×D4—224no—
322C22×D4—21no—
323C22×D4—23no—
324C22×D4—23no—
325C22×D4—23no—
326C22×D4—23no—
327C22×D4—23no—
328C22×D4—26no—
329C22×D4—224no—
330C22×D4—224no—
331C22×D4—212no—
332C22×D4—23no—
333C22×D4—26no—
334C22×D4—212no—
335C22×D4—424no—
336C22×D4—812no—
337C22×D4C2×D416yes—
338C22×D4C2×D413yes—
339C22×D4C2×D4124yes—
340C22×D4C2×D413yes—
341C22×D4C2411yescharacteristic
342C22×D4C2413yes—
343C22×D4C24112yes—
344C23×C4—212no—
345C23×C4—212no—
346C23×C4—23no—
347C23×C4—23no—
348C23×C4—23no—
349C23×C4—23no—
350C23×C4—23no—
351C23×C4C2×D413yes—
352C23×C4C2×D413yes—
353C23×C4C2×D413yes—
354C23×C4C2×D4112yes—
355C23×C4C2413yes—
356C23×C4C2411yescharacteristic
357C23×C4C24112yes—
358C23×C4C2413yes—
359#137—296no—
360AGL(1,ℤ/8)—296no—
361#135—296no—
362C2×Q16—212no—
363C2×Q16C24112yes—
364C2×SD16—212no—
365C2×SD16—224no—
366C2×SD16—24no—
367C2×SD16—296no—
368C2×SD16C24112yes—
369C2×SD16C24124yes—
370C2×SD16C2414yes—
371C2×D8—212no—
372C2×D8C24112yes—
373#131—232no—
374#131—296no—
375#131—296no—
376#131C2×D4164yescomplemented
377C2×M16—212no—
378C2×M16—296no—
379C2×M16—212no—
380C2×M16—24no—
381C2×M16—212no—
382C2×M16—212no—
383C2×M16—296no—
384C2×M16C2×D4124yescomplemented
385C2×M16C2414yes—
386C2×M16C24112yes—
387C2×M16C24112yes—
388C2×M16C24112yes—
389C2×M16C24112yes—
390C2×M16C24112yes—
391C22×C8—212no—
392C22×C8—224no—
393C22×C8C2×D4124yescomplemented
394C22×C8C2411yescharacteristic
395C22×C8C2413yes—
396C22×C8C24112yes—
397C22×C8C24124yes—
398C22×C8C2413yes—
399C22×C8C2411yescharacteristic
400C22×C8C24112yes—
401C4⋊Q8—224no—
402#127—224no—
403#124—224no—
404#124—224no—
405#123—248no—
406#123—224no—
407#123—224no—
408C22⋊Q8—224no—
409C22⋊Q8—224no—
410C22⋊Q8—26no—
411C22⋊Q8—212no—
412C22⋊Q8—224no—
413C22⋊Q8—224no—
414C22⋊Q8—22no—
415C22⋊Q8—26no—
416C22⋊Q8—26no—
417C22⋊Q8C24112yes—
418C22⋊Q8C24124yes—
419C22⋊Q8C2414yes—
420C22⋊Q8C24112yes—
421C22⋊Q8C24112yes—
422#121—248no—
423#121—224no—
424#121—248no—
425#121—224no—
426#121—26no—
427#121—212no—
428#121—224no—
429#121—224no—
430#121—22no—
431#121—26no—
432#121—26no—
433#121C24112yes—
434#121C24124yes—
435#121C24112yes—
436#121C2414yes—
437#121C24112yes—
438#120—224no—
439#120—224no—
440#120—248no—
441C4×Q8—28no—
442C4×Q8—28no—
443C4×D4—224no—
444C4×D4—224no—
445C4×D4—224no—
446C4×D4—224no—
447C4×D4—224no—
448C4×D4—224no—
449#117—26no—
450#117—26no—
451#117C24112yes—
452#117C24112yes—
453C2×C4⋊C4—23no—
454C2×C4⋊C4—26no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—23no—
457C2×C4⋊C4—23no—
458C2×C4⋊C4—26no—
459C2×C4⋊C4—26no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—23no—
462C2×C4⋊C4—23no—
463C2×C4⋊C4C2413yes—
464C2×C4⋊C4C2413yes—
465C2×C4⋊C4C24112yes—
466C2×C4⋊C4C24112yes—
467C2×C4⋊C4C2411yescharacteristic
468C2×C4⋊C4C2411yescharacteristic
469C2×C22⋊C4—23no—
470C2×C22⋊C4—26no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—23no—
473C2×C22⋊C4—23no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—23no—
476C2×C22⋊C4—23no—
477C2×C22⋊C4—23no—
478C2×C22⋊C4—26no—
479C2×C22⋊C4—224no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—23no—
482C2×C22⋊C4—23no—
483C2×C42—23no—
484C2×C42—23no—
485#107C24112yes—
486#107C24124yes—
487#107C2414yes—
488#106C24112yes—
489#106C24112yes—
490#103C24112yes—
491#103C24124yes—
492#103C2414yes—
493#103C24112yes—
494#103C24112yes—
495#102C24112yes—
496#102C24124yes—
497#102C2414yes—
498#102C24112yes—
499#102C24112yes—
500C24—212no—
501C24—21no—
502C24—23no—
503C24—212no—
504C24—46no—
505C24—46no—
506C24—412no—
507C24—86no—
508C24—86no—
509C24C22×D411yescharacteristic
510C24C22×D413yes—
511C24C22×D413yes—
512C24C22×D4112yes—
513#41—232no—
514#41—296no—
515#41—248no—
516#41—224no—
517#41—224no—
518#41—224no—
519#41—224no—
520#41—224no—
521#41—224no—
522#41—432no—
523#41—496no—
524#41—424no—
525#41—424no—
526#41#121132yes—
527#41C22×D4116yes—
528#41C2×#41116yes—
529C2×Q8—232no—
530C2×Q8—212no—
531C2×Q8—23no—
532C2×Q8—21no—
533C2×Q8—212no—
534C2×Q8—26no—
535C2×Q8—224no—
536C2×Q8—22no—
537C2×Q8—26no—
538C2×Q8—224no—
539C2×Q8—22no—
540C2×Q8—432no—
541C2×Q8—412no—
542C2×Q8—424no—
543C2×Q8#12118yes—
544C2×Q8C22×D4112yes—
545C2×Q8C22×D414yes—
546C2×Q8C2516yes—
547C2×Q8C2512yes—
548C2×D4—224no—
549C2×D4—296no—
550C2×D4—24no—
551C2×D4—212no—
552C2×D4—212no—
553C2×D4—212no—
554C2×D4—212no—
555C2×D4—212no—
556C2×D4—224no—
557C2×D4—212no—
558C2×D4—22no—
559C2×D4—26no—
560C2×D4—224no—
561C2×D4—23no—
562C2×D4—21no—
563C2×D4—212no—
564C2×D4—26no—
565C2×D4—224no—
566C2×D4—22no—
567C2×D4—44no—
568C2×D4—412no—
569C2×D4—412no—
570C2×D4—412no—
571C2×D4—496no—
572C2×D4—412no—
573C2×D4—424no—
574C2×D4—86no—
575C2×D4—86no—
576C2×D4—812no—
577C2×D4—848no—
578C2×D4#121124yes—
579C2×D4C22×D4124yes—
580C2×D4C22×D4112yes—
581C2×D4C22×D4112yes—
582C2×D4C2512yes—
583C2×D4C2516yes—
584C22×C4—212no—
585C22×C4—212no—
586C22×C4—212no—
587C22×C4—248no—
588C22×C4—26no—
589C22×C4—22no—
590C22×C4—224no—
591C22×C4—22no—
592C22×C4—26no—
593C22×C4—224no—
594C22×C4—212no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—23no—
598C22×C4—23no—
599C22×C4—21no—
600C22×C4—23no—
601C22×C4—212no—
602C22×C4—212no—
603C22×C4—212no—
604C22×C4—212no—
605C22×C4—412no—
606C22×C4—412no—
607C22×C4—412no—
608C22×C4—86no—
609C22×C4—86no—
610C22×C4C22×D4112yes—
611C22×C4C22×D4112yes—
612C22×C4C22×D4112yes—
613C22×C4C22×D412yes—
614C22×C4C22×D416yes—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D413yes—
617C22×C4C22×D416yes—
618C22×C4C22×D413yes—
619C22×C4C22×D4112yes—
620C22×C4C2×#41112yes—
621C22×C4C2516yes—
622C22×C4C2512yes—
623C22×C4C2516yes—
624C22×C4C2511yescharacteristic
625Q16—224no—
626SD16—224no—
627SD16—248no—
628SD16—28no—
629D8—224no—
630M16—224no—
631M16—224no—
632M16—28no—
633M16—224no—
634M16—224no—
635M16C22×D4148yescomplemented
636C2×C8—22no—
637C2×C8—26no—
638C2×C8—224no—
639C2×C8—248no—
640C2×C8C22×D4112yes—
641C2×C8C22×D414yes—
642C2×C8C22×D4148yescomplemented
643C2×C8C2512yes—
644C2×C8C2516yes—
645C2×C8C2516yes—
646C2×C8C2512yes—
647C4⋊C4—212no—
648C4⋊C4—23no—
649C4⋊C4—23no—
650C4⋊C4—224no—
651C4⋊C4—212no—
652C4⋊C4—212no—
653C4⋊C4—24no—
654C4⋊C4—212no—
655C4⋊C4—212no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4C2512yes—
659C4⋊C4C2516yes—
660C4⋊C4C2512yes—
661C4⋊C4C2516yes—
662C22⋊C4—212no—
663C22⋊C4—224no—
664C22⋊C4—212no—
665C22⋊C4—212no—
666C22⋊C4—24no—
667C22⋊C4—212no—
668C22⋊C4—212no—
669C22⋊C4—212no—
670C22⋊C4—224no—
671C22⋊C4—24no—
672C22⋊C4—212no—
673C22⋊C4—212no—
674C42—212no—
675C42—212no—
676C23—26no—
677C23—26no—
678C23—22no—
679C23—26no—
680C23—22no—
681C23—26no—
682C23—22no—
683C23—26no—
684C23—224no—
685C23—22no—
686C23—26no—
687C23—412no—
688C23—412no—
689C23—46no—
690C23—42no—
691C23—42no—
692C23—46no—
693C23—42no—
694C23—46no—
695C23—424no—
696C23—824no—
697C23—812no—
698C23—812no—
699C23—1624no—
700C23C2×#121112yes—
701C23C23×D412yes—
702C23C23×D416yes—
703C23C23×D416yes—
704C23C23×D411yescharacteristic
705Q8—224no—
706Q8—26no—
707Q8—22no—
708Q8—26no—
709Q8—22no—
710Q8—46no—
711Q8—424no—
712Q8—42no—
713Q8C2×#121116yes—
714D4—248no—
715D4—22no—
716D4—26no—
717D4—26no—
718D4—22no—
719D4—224no—
720D4—48no—
721D4—424no—
722D4—424no—
723D4—424no—
724D4—46no—
725D4—424no—
726D4—42no—
727D4—812no—
728D4—812no—
729D4—824no—
730D4C2×#121148yes—
731C2×C4—22no—
732C2×C4—26no—
733C2×C4—224no—
734C2×C4—26no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—26no—
738C2×C4—24no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—212no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—26no—
745C2×C4—26no—
746C2×C4—22no—
747C2×C4—26no—
748C2×C4—46no—
749C2×C4—46no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—46no—
754C2×C4—424no—
755C2×C4—424no—
756C2×C4—424no—
757C2×C4—812no—
758C2×C4—812no—
759C2×C4C2×#121112yes—
760C2×C4C2×#121124yes—
761C2×C4C23×D412yes—
762C2×C4C23×D416yes—
763C2×C4C23×D412yes—
764C2×C4C23×D4112yes—
765C2×C4C23×D416yes—
766C2×C4C23×D411yescharacteristic
767C2×C4C22×#4112yes—
768C2×C4C22×#41112yes—
769C2×C4C2611yescharacteristic
770C8—22no—
771C8—26no—
772C8C23×D4112yes—
773C8C23×D414yes—
774C22—224no—
775C22—26no—
776C22—26no—
777C22—22no—
778C22—26no—
779C22—22no—
780C22—26no—
781C22—22no—
782C22—26no—
783C22—412no—
784C22—44no—
785C22—46no—
786C22—42no—
787C22—42no—
788C22—46no—
789C22—42no—
790C22—46no—
791C22—824no—
792C22—84no—
793C22—812no—
794C22—1624no—
795C22C22×#121112yes—
796C22C22×#12112yes—
797C22#358512yes—
798C22#358612yes—
799C22C24×D411yescharacteristic
800C4—22no—
801C4—26no—
802C4—46no—
803C4—46no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—46no—
808C4C22×#12112yes—
809C4C22×#121112yes—
810C4C24×D411yescharacteristic
811C4C23×#4111yescharacteristic
812C2—212no—
813C2—46no—
814C2—42no—
815C2—82no—
816C2—86no—
817C2#6046014yesdirect product factor
818C2C23×#12111yescharacteristic
819C2C2×#358511yescharacteristic
820C2C2×#358611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC2×C4C26
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×#41 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C22×#577C2semidirect
2. C22×#568C2semidirect
3. C2×#3489C2semidirect
4. C2×#3488C2semidirect
5. #60460C2direct (N × H)
6. C2×#3063C2semidirect
7. C2×#3062C2semidirect
8. C2×#3061C2semidirect
9. C2×#3057C2semidirect
10. C2×#3056C2semidirect
11. C2×#3055C2semidirect
12. C2×#3054C2semidirect
13. C22×#468C2semidirect
14. C2×#2913C2semidirect
15. C2×#2898C2semidirect
16. C2×#2897C2semidirect
21. C2×#577C22semidirect
22. C22×#137C22semidirect
23. C22×AGL(1,ℤ/8)C22semidirect
24. C22×#135C22semidirect
25. C23×SD16C22semidirect
27. C2×#568C22semidirect
30. C22×#131C22semidirect
31. C22×#131C22semidirect
32. C23×M16C22semidirect
33. C23×M16C22semidirect
35. #3489C22semidirect
37. #3488C22semidirect
47. C2×#537C22semidirect
48. C2×#536C22semidirect
51. C2×#525C22semidirect
52. C22×C22⋊Q8C22semidirect
56. #3063C22semidirect
57. #3062C22semidirect
58. #3061C22semidirect
59. #3057C22semidirect
60. #3056C22semidirect
61. #3055C22semidirect
62. #3054C22semidirect
63. C2×#470C22semidirect
64. C2×#470C22semidirect
65. C2×#469C22semidirect
66. C2×#469C22semidirect
67. C2×#468C22semidirect
68. C2×#468C22semidirect
69. C2×#468C22semidirect
70. C2×#468C22semidirect
71. C2×#468C22semidirect
72. C2×#468C22semidirect
73. C2×#468C22semidirect
74. C2×#468C22semidirect
75. C2×#467C22semidirect
76. C2×#466C22semidirect
77. C2×#465C22semidirect
78. C2×#465C22semidirect
79. #2913C22semidirect
80. C2×#428C22semidirect
81. C2×#428C22semidirect
82. C2×#427C22semidirect
83. C22×#107C22semidirect
84. #2898C22semidirect
85. #2897C22semidirect
86. C2×#417C22semidirect
87. C2×#417C22semidirect
88. C2×#419C22semidirect
89. C2×#418C22semidirect
90. C2×#416C22semidirect
91. C2×#416C22semidirect
92. C22×#103C22semidirect
93. C22×#102C22semidirect
124. C2×#137C23semidirect
126. C2×AGL(1,ℤ/8)C23semidirect
128. C2×#135C23semidirect
134. C22×SD16C23semidirect
140. C2×#131D4semidirect
143. C2×#131C23semidirect
144. C2×#131C23semidirect
153. C22×M16C23semidirect
154. C22×M16C23semidirect
169. #537C23semidirect
171. #536C23semidirect
181. #525C23semidirect
195. C2×C22⋊Q8C23semidirect
231. #470C23semidirect
232. #470C23semidirect
233. #469C23semidirect
234. #469C23semidirect
235. #468C23semidirect
236. #468C23semidirect
237. #468C23semidirect
238. #468C23semidirect
239. #468C23semidirect
240. #468C23semidirect
241. #468C23semidirect
242. #467C23semidirect
243. #466C23semidirect
244. #465C23semidirect
245. #465C23semidirect
246. #428C23semidirect
247. #428C23semidirect
248. #427C23semidirect
252. C2×#107C23semidirect
255. #419C23semidirect
256. #418C23semidirect
257. #417C23semidirect
258. #417C23semidirect
259. #416C23semidirect
260. #416C23semidirect
266. C2×#103C23semidirect
272. C2×#102C23semidirect
376. #131C2×D4semidirect
384. C2×M16C2×D4semidirect
393. C22×C8C2×D4semidirect
635. M16C22×D4semidirect
642. C2×C8C22×D4semidirect
817. C2#60460direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#5772
C22×#5682
C2×#34892
C2×#34882
#604602
C2×#30632
C2×#30622
C2×#30612
C2×#30572
C2×#30562
C2×#30552
C2×#30542
C22×#4682
C2×#29132
C2×#28982
C2×#28972