Finite Group Databasebeta

← #6798643

Subgroups — #6798643

Order 512.

1747 conjugacy classes of subgroups.

The subgroup lattice has 807 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36210C211yesmaximal, characteristic, complemented
2#36122C211yesmaximal, characteristic
3#33226C211yesmaximal, characteristic, complemented
4#31301C214yesmaximal, complemented
5#31296C214yesmaximal, complemented
6#29845C211yesmaximal, characteristic, complemented
7#29842C211yesmaximal, characteristic, complemented
8#28750C211yesmaximal, characteristic, complemented
9#28515C211yesmaximal, characteristic, complemented
10#27892C211yesmaximal, characteristic, complemented
11#27890C211yesmaximal, characteristic, complemented
12#25889C214yesmaximal, complemented
13#25857C211yesmaximal, characteristic, complemented
14#25856C211yesmaximal, characteristic, complemented
15#25282C214yesmaximal, complemented
16#21805C211yesmaximal, characteristic, complemented
17#21804C211yesmaximal, characteristic, complemented
18C4×#487C211yesmaximal, characteristic, complemented
19#21264C211yesmaximal, characteristic, complemented
20C2×#548C2212yes—
21C2×#532C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#488C2214yes—
24C2×#487C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#486C2211yescharacteristic
27C2×#479C2214yes—
28C2×#431C2211yescharacteristic
29C2×#431C2211yescharacteristic
30#2859C2211yescharacteristic
31#2858C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2856C2211yescharacteristic
36#2562C2212yes—
37#2545C2212yes—
38#2514—21no—
39#2509—21no—
40#2495C2212yes—
41#2494—21no—
42#2494C2212yes—
43#2491—21no—
44#2491—21no—
45#2485—21no—
46#2452—21no—
47#2452—21no—
48#2436C2212yes—
49#2432C2212yes—
50#2421—21no—
51#2416—21no—
52#2416—21no—
53#2415—21no—
54#2370C2212yes—
55#2362—21no—
56#2361—21no—
57#2361—21no—
58#2347—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61#2285C2211yescharacteristic
62#2285C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2097C2214yes—
65#2067C2214yes—
66#2066C2214yes—
67#2043C2214yes—
68#2042C2214yes—
69#2042C2214yes—
70#2036C2214yes—
71#2035C2214yes—
72#2034C2214yes—
73#2033C2214yes—
74#1990C2211yescharacteristic
75#1983C2214yes—
76#1983C2214yes—
77#1981C2214yes—
78#1958C2214yes—
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1956C2211yescharacteristic
87#1956C2211yescharacteristic
88#1954C2212yes—
89#1939C2212yes—
90#1933C2214yes—
91#1928C2214yes—
92#1926C2214yes—
93#1923C2212yes—
94#1923C2212yes—
95#1845C2211yescharacteristic
96#1844C2211yescharacteristic
97#1834C2211yescharacteristic
98#1788C2214yes—
99#1788C2214yes—
100#1787C2214yes—
101#1787C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103C4×#103C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C42×C8C2211yescharacteristic
107C22×#41C2312yes—
108C23×Q8C2312yes—
109#548—48no—
110#532—24no—
111#532—42no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—42no—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2312yes—
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#125C2312yes—
122C2×#124—22no—
123C2×#124C2312yes—
124C2×#124C2312yes—
125C2×#124C2312yes—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8—22no—
129C2×C22⋊Q8C2312yes—
130C2×#121—22no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121C2312yes—
136C2×C4×Q8—21no—
137C2×C4×Q8C2312yes—
138C2×C4×D4—22no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4D411yescharacteristic
142C2×C4×D4D411yescharacteristic
143C2×C4×D4C2311yescharacteristic
144C2×#117—21no—
145C2×#117—21no—
146C22×C4⋊C4—21no—
147C22×C4⋊C4—21no—
148C22×C42C2311yescharacteristic
149C22×C42C2311yescharacteristic
150#488—48no—
151#487—24no—
152#487—42no—
153#486—42no—
154#479—48no—
155#431—42no—
156#431—42no—
157C2×#107C2314yes—
158C2×#106C2314yes—
159C2×C4⋊C8C2312yes—
160C2×C4⋊C8C2312yes—
161C2×C4⋊C8C2312yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×#102C2314yes—
173C2×#102C2314yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×C22⋊C8C2312yes—
177C2×C22⋊C8C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2312yes—
182C2×C4×C8C2311yescharacteristic
183C2×C4×C8C2312yes—
184#401—22no—
185#400—22no—
186#400—22no—
187#397—22no—
188#397—22no—
189#396—22no—
190#396—22no—
191#394—22no—
192#394—22no—
193#394—22no—
194#393—22no—
195#393—22no—
196#391—21no—
197#391—21no—
198#391—21no—
199#391C2312yes—
200#391C2312yes—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390—21no—
206#390—21no—
207#390C2312yes—
208#389—22no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389—21no—
219#389—21no—
220#389C2312yes—
221#389C2312yes—
222#389C2312yes—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#388—22no—
229#387—22no—
230#387—22no—
231#387—22no—
232#386—22no—
233#386—22no—
234#385—22no—
235#385—22no—
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#384C2311yescharacteristic
240#383—22no—
241#382—21no—
242#382—21no—
243#382C2312yes—
244#380—21no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380C2312yes—
251#380C2312yes—
252#380C2312yes—
253#380C2312yes—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—21no—
256C4×C4⋊C4—21no—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—22no—
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2312yes—
264C4×C4⋊C4C2312yes—
265C4×C4⋊C4C2311yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4D411yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271C4×C22⋊C4C2311yescharacteristic
272C43C2311yescharacteristic
273#340C2314yes—
274#340C2314yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C2×#41—24no—
279C2×#41—42no—
280C2×#41—44no—
281C2×#41—44no—
282C22×Q8—21no—
283C22×Q8—22no—
284C22×Q8—24no—
285C22×Q8—42no—
286C22×Q8—44no—
287C22×Q8—44no—
288C22×Q8C2412yes—
289C22×Q8C2412yes—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C2×D411yescharacteristic
295C22×D4C2412yes—
296C23×C4—22no—
297C23×C4—22no—
298C23×C4C2×D411yescharacteristic
299C23×C4C2×D411yescharacteristic
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2411yescharacteristic
303C23×C4C2411yescharacteristic
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C4⋊Q8—24no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—44no—
315C4⋊Q8—44no—
316C4⋊Q8—42no—
317C4⋊Q8#4114yes—
318#127—22no—
319#127—22no—
320#125—28no—
321#124—24no—
322#124—28no—
323#124—42no—
324#124—44no—
325#124—48no—
326C22⋊Q8—44no—
327C22⋊Q8—48no—
328C22⋊Q8—44no—
329C22⋊Q8—82no—
330#121—44no—
331#121—44no—
332#121—44no—
333#121—44no—
334#121—48no—
335#121—44no—
336C4×Q8—28no—
337C4×Q8—82no—
338C4×D4—24no—
339C4×D4—24no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—42no—
343C4×D4—48no—
344#117—44no—
345#117—82no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—44no—
369C2×C4⋊C4—44no—
370C2×C4⋊C4C2×D411yescharacteristic
371C2×C4⋊C4C2×D411yescharacteristic
372C2×C4⋊C4C2×D411yescharacteristic
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—22no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—22no—
385C2×C22⋊C4—22no—
386C2×C22⋊C4—22no—
387C2×C22⋊C4—22no—
388C2×C22⋊C4—22no—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4C2×D411yescharacteristic
393C2×C22⋊C4C2×D411yescharacteristic
394C2×C22⋊C4C2×D411yescharacteristic
395C2×C22⋊C4C2×D411yescharacteristic
396C2×C22⋊C4C2×D411yescharacteristic
397C2×C22⋊C4C2×D411yescharacteristic
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2×D411yescharacteristic
409C2×C42C2×D411yescharacteristic
410C2×C42C2×D411yescharacteristic
411C2×C42C2×D411yescharacteristic
412C2×C42C2×D411yescharacteristic
413C2×C42C2×D411yescharacteristic
414C2×C42C2411yescharacteristic
415C2×C42C2411yescharacteristic
416C2×C42C2411yescharacteristic
417C2×C42C2411yescharacteristic
418C2×C42C2411yescharacteristic
419#107—44no—
420#106—44no—
421C4⋊C8—24no—
422C4⋊C8—42no—
423C4⋊C8—42no—
424#103—28no—
425#103—44no—
426#103—44no—
427#103—44no—
428#103—44no—
429#103—44no—
430#103—44no—
431#103—44no—
432#102—44no—
433#102—44no—
434#102—44no—
435#102—44no—
436C22⋊C8—42no—
437C22⋊C8—42no—
438C22⋊C8—42no—
439C22⋊C8—42no—
440C4×C8—22no—
441C4×C8—22no—
442C4×C8—22no—
443C4×C8—22no—
444C4×C8—24no—
445C4×C8—42no—
446#95—22no—
447#95—22no—
448#95—22no—
449#95—22no—
450#95—22no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468C24—22no—
469C24C22×D411yescharacteristic
470C24C22×D411yescharacteristic
471#41—88no—
472#41—88no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—24no—
477C2×Q8—22no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—82no—
486C2×Q8—88no—
487C2×Q8—88no—
488C2×Q8C2×#4114yes—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—24no—
493C2×D4—22no—
494C2×D4—24no—
495C2×D4—41no—
496C2×D4—44no—
497C2×D4—44no—
498C2×D4—44no—
499C2×D4—44no—
500C2×D4—44no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—42no—
507C2×D4—82no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—44no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4—44no—
538C22×C4—82no—
539C22×C4—82no—
540C22×C4#13514yes—
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C2511yescharacteristic
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C2×C8—22no—
563C2×C8—22no—
564C2×C8—22no—
565C2×C8—22no—
566C4⋊C4—22no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—24no—
573C4⋊C4—24no—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—41no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—44no—
582C4⋊C4—44no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—44no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—82no—
596C4⋊C4—82no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—41no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C22⋊C4—44no—
607C22⋊C4—44no—
608C22⋊C4—44no—
609C22⋊C4—44no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—82no—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C22⋊C4—82no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—22no—
621C42—22no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—22no—
630C42—44no—
631C42—44no—
632C42—82no—
633C42—82no—
634C42C2×#4112yes—
635C42H(5,𝔽2)14yes—
636C42H(5,𝔽2)12yes—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C2×#13512yes—
658C23C23×D411yescharacteristic
659Q8—28no—
660Q8—44no—
661Q8—44no—
662Q8—44no—
663Q8—88no—
664Q8—84no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—88no—
669D4—88no—
670D4—84no—
671D4—84no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—28no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—24no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—88no—
729C2×C4—88no—
730C2×C4#53512yes—
731C2×C4#53512yes—
732C2×C4#54612yes—
733C2×C4#54612yes—
734C2×C4C2×#13512yes—
735C2×C4C2×#13512yes—
736C2×C4#57512yes—
737C2×C4#57712yes—
738C2×C4#57812yes—
739C2×C4C22×#4111yescharacteristic
740C2×C4C2×H(5,𝔽2)12yes—
741C2×C4C2×H(5,𝔽2)11yescharacteristic
742C2×C4#58512yes—
743C8—42no—
744C8—42no—
745C8—42no—
746C8—42no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22C2×#53511yescharacteristic
769C22C2×#54611yescharacteristic
770C22#350011yescharacteristic
771C22C22×#13511yescharacteristic
772C22C2×#57511yescharacteristic
773C22C2×#57711yescharacteristic
774C22C2×#57811yescharacteristic
775C4—22no—
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—44no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—41no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4—82no—
792C4#330114yes—
793C4#332714yes—
794C4#351412yes—
795C4#354612yes—
796C2—42no—
797C2—81no—
798C2—162no—
799C2#3895711yescharacteristic
800C2#6078211yescharacteristic
801C2#6082411yescharacteristic
802C2C2×#330111yescharacteristic
803C2C2×#332711yescharacteristic
804C2#6252811yescharacteristic
805C2#6254311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36122C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×D4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36210C2semidirect
3. #33226C2semidirect
4. #31301C2semidirect
5. #31296C2semidirect
6. #29845C2semidirect
7. #29842C2semidirect
8. #28750C2semidirect
9. #28515C2semidirect
10. #27892C2semidirect
11. #27890C2semidirect
12. #25889C2semidirect
13. #25857C2semidirect
14. #25856C2semidirect
15. #25282C2semidirect
16. #21805C2semidirect
17. #21804C2semidirect
18. C4×#487C2semidirect
19. #21264C2semidirect

Maximal subgroups

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

subgroupindex
#362102
#361222
#332262
#313012
#312962
#298452
#298422
#287502
#285152
#278922
#278902
#258892
#258572
#258562
#252822
#218052
#218042
C4×#4872
#212642