Finite Group Databasebeta

← #6486795

Subgroups — #6486795

Order 512.

1926 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36631C211yesmaximal, characteristic, complemented
2C4×#532C211yesmaximal, characteristic, complemented
3#33080C214yesmaximal, complemented
4#30014C214yesmaximal, complemented
5#29536C214yesmaximal, complemented
6#29412C214yesmaximal, complemented
7#29190C211yesmaximal, characteristic, complemented
8#29176C211yesmaximal, characteristic, complemented
9#28655C211yesmaximal, characteristic, complemented
10#28615C211yesmaximal, characteristic, complemented
11#27890C211yesmaximal, characteristic, complemented
12#27876C211yesmaximal, characteristic, complemented
13#25673C211yesmaximal, characteristic, complemented
14#25599C211yesmaximal, characteristic
15#22269C211yesmaximal, characteristic, complemented
16#22248C211yesmaximal, characteristic, complemented
17#22219C211yesmaximal, characteristic, complemented
18#22219C211yesmaximal, characteristic, complemented
19#20777C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#529—21no—
22C2×C4×#41—21no—
23C2×#500C2211yescharacteristic
24C2×#493C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#486C2211yescharacteristic
27#2861—21no—
28#2860—21no—
29#2860C2212yes—
30#2859C2211yescharacteristic
31#2858C2211yescharacteristic
32#2857C2211yescharacteristic
33#2856C2211yescharacteristic
34#2854—21no—
35#2854C2212yes—
36#2850—21no—
37C4×C4⋊Q8C2211yescharacteristic
38C4×C4⋊Q8C2211yescharacteristic
39C4×C4⋊Q8C2211yescharacteristic
40C4×#127C2211yescharacteristic
41C4×#127C2211yescharacteristic
42C4×#127C2211yescharacteristic
43C4×#124—21no—
44C4×#124—21no—
45C4×#124—21no—
46C4×#121—21no—
47C4×#121—21no—
48C4×#121—21no—
49C4×#121C2212yes—
50C4×#121C2212yes—
51C4×#121C2212yes—
52#2297—21no—
53#2293—21no—
54#2293—21no—
55#2293C2212yes—
56#2293C2212yes—
57#2285C2211yescharacteristic
58C42×D4—21no—
59C42×D4C2212yes—
60C2×C43C2211yescharacteristic
61#2088C2214yes—
62#2077C2214yes—
63#2067C2214yes—
64#2065C2214yes—
65#2054C2214yes—
66#2034C2214yes—
67#2033C2214yes—
68#1999C2214yes—
69#1990C2211yescharacteristic
70#1990C2211yescharacteristic
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1957C2211yescharacteristic
74#1957C2211yescharacteristic
75#1957C2211yescharacteristic
76#1957C2211yescharacteristic
77#1926C2214yes—
78#1926C2214yes—
79#1926C2214yes—
80#1925C2214yes—
81#1921C2214yes—
82#1921C2214yes—
83#1920C2214yes—
84#1919C2214yes—
85#1879C2214yes—
86#1879C2214yes—
87#1879C2214yes—
88#1879C2214yes—
89#1864C2214yes—
90#1864C2214yes—
91#1864C2214yes—
92#1862C2214yes—
93#1844C2211yescharacteristic
94#1844C2211yescharacteristic
95#1839C2212yes—
96#1834C2211yescharacteristic
97#1834C2211yescharacteristic
98#1831C2212yes—
99#1817C2212yes—
100#1797C2212yes—
101C4×C4⋊C8C2211yescharacteristic
102C4×C4⋊C8C2211yescharacteristic
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105#1744C2211yescharacteristic
106#1744C2211yescharacteristic
107C22×#41—21no—
108C22×D8C2314yes—
109#532—24no—
110#532—24no—
111C2×C4⋊Q8C2311yescharacteristic
112C2×C4⋊Q8C2311yescharacteristic
113C2×#127C2311yescharacteristic
114C2×#127C2311yescharacteristic
115#529—48no—
116C2×#126—22no—
117C2×#125—21no—
118C2×#124—21no—
119C2×#124—21no—
120C2×#124—21no—
121C2×#123—22no—
122C2×C22⋊Q8—21no—
123C2×#121—21no—
124C2×#121—21no—
125C2×#121—21no—
126C2×#121C2312yes—
127C2×#121C2312yes—
128C4×#41—48no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×Q8—21no—
132C2×C4×D4—22no—
133C2×C4×D4—22no—
134C2×C4×D4—22no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4—21no—
139C2×C4×D4—21no—
140C2×C4×D4—21no—
141C2×C4×D4—21no—
142C2×C4×D4C2312yes—
143C2×C4×D4C2312yes—
144C2×C4×D4C2312yes—
145C2×C4×D4C2312yes—
146C2×#117—21no—
147C2×#117—22no—
148C2×#117—22no—
149C22×C42—22no—
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#500—24no—
158#493—24no—
159#486—24no—
160#486—24no—
161C2×#107C2314yes—
162C2×#106C2314yes—
163C2×#106C2314yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178#391—21no—
179#391—21no—
180#391—21no—
181#391—21no—
182#390—21no—
183#390—21no—
184#390—21no—
185#390—21no—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390—21no—
191#390—21no—
192#390C2312yes—
193#390C2312yes—
194#390C2312yes—
195#390C2312yes—
196#390C2312yes—
197#390C2312yes—
198#389—21no—
199#389—21no—
200#389—21no—
201#389—21no—
202#389—21no—
203#389—21no—
204#389C2312yes—
205#389C2312yes—
206#389C2312yes—
207#389C2312yes—
208#389C2312yes—
209#389C2312yes—
210#388—22no—
211#388—22no—
212#388—22no—
213#388—22no—
214#388—22no—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#388—22no—
221#388—22no—
222#386—22no—
223#386—22no—
224#386—22no—
225#386—22no—
226#384C2311yescharacteristic
227#384C2311yescharacteristic
228#384C2311yescharacteristic
229#384C2311yescharacteristic
230#382—21no—
231#382—21no—
232#380—21no—
233#380—21no—
234#380C2312yes—
235#380C2312yes—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4C2312yes—
241C4×C4⋊C4C2312yes—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C22⋊C4—22no—
245C4×C22⋊C4—22no—
246C4×C22⋊C4—22no—
247C4×C22⋊C4—22no—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C43D411yescharacteristic
253C43D411yescharacteristic
254C43D411yescharacteristic
255C43D411yescharacteristic
256C43C2311yescharacteristic
257C43C2311yescharacteristic
258C43C2311yescharacteristic
259C43C2311yescharacteristic
260#340C2314yes—
261#340C2314yes—
262#340C2314yes—
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#336C2312yes—
267#336C2312yes—
268#336C2312yes—
269#336C2312yes—
270#336C2312yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274C2×#41—28no—
275C2×#41—44no—
276C2×#41—44no—
277C22×Q8—21no—
278C22×Q8—21no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—21no—
282C22×D4—21no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4C2412yes—
286C22×D4C2412yes—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2411yescharacteristic
298C2×D8—28no—
299C2×D8—44no—
300C2×D8—44no—
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C4⋊Q8—22no—
306C4⋊Q8—22no—
307C4⋊Q8—22no—
308C4⋊Q8#4114yes—
309#127—22no—
310#127—22no—
311#127—22no—
312#127#4114yes—
313#126—48no—
314#125—44no—
315#124—28no—
316#124—44no—
317#124—44no—
318#123—48no—
319C22⋊Q8—44no—
320#121—28no—
321#121—24no—
322#121—24no—
323#121—44no—
324#121—44no—
325#121—44no—
326C4×Q8—44no—
327C4×Q8—44no—
328C4×Q8—44no—
329C4×D4—28no—
330C4×D4—24no—
331C4×D4—24no—
332C4×D4—44no—
333C4×D4—44no—
334C4×D4—44no—
335C4×D4—44no—
336C4×D4—44no—
337C4×D4—44no—
338C4×D4—48no—
339C4×D4—48no—
340C4×D4—48no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344#117—48no—
345#117—48no—
346#117—44no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4C2412yes—
364C2×C4⋊C4C2412yes—
365C2×C4⋊C4C2412yes—
366C2×C4⋊C4C2412yes—
367C2×C4⋊C4C2412yes—
368C2×C4⋊C4C2412yes—
369C2×C22⋊C4—22no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—22no—
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×C42—24no—
390C2×C42—24no—
391C2×C42—24no—
392C2×C42—22no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—42no—
399C2×C42—42no—
400C2×C42—42no—
401C2×C42—48no—
402C2×C42C2×D411yescharacteristic
403C2×C42C2×D411yescharacteristic
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
415C2×C42C2×D411yescharacteristic
416C2×C42C2×D411yescharacteristic
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—28no—
431#106—44no—
432#106—44no—
433C4⋊C8—42no—
434C4⋊C8—42no—
435#102—28no—
436#102—28no—
437#102—44no—
438#102—44no—
439#102—44no—
440#102—44no—
441C22⋊C8—42no—
442C22⋊C8—42no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—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—
459C24—22no—
460C24—22no—
461C24C22×D411yescharacteristic
462#41—432no—
463C2×Q8—24no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8—42no—
467C2×Q8—42no—
468C2×Q8—42no—
469C2×D4—28no—
470C2×D4—24no—
471C2×D4—24no—
472C2×D4—22no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—24no—
476C2×D4—24no—
477C2×D4—24no—
478C2×D4—24no—
479C2×D4—44no—
480C2×D4—44no—
481C2×D4—44no—
482C2×D4—44no—
483C2×D4—44no—
484C2×D4—42no—
485C2×D4—42no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4C2×#4114yes—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—28no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—41no—
520C22×C4—41no—
521C22×C4—41no—
522C22×C4—41no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—44no—
528C22×C4—44no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4AGL(1,ℤ/8)14yes—
535C22×C4C22×D411yescharacteristic
536C22×C4C22×D411yescharacteristic
537C22×C4C22×D411yescharacteristic
538C22×C4C22×D411yescharacteristic
539C22×C4C22×D411yescharacteristic
540C22×C4C22×D411yescharacteristic
541C22×C4C22×D411yescharacteristic
542C22×C4C22×D411yescharacteristic
543C22×C4C22×D411yescharacteristic
544C22×C4C22×D411yescharacteristic
545C22×C4C22×D411yescharacteristic
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C2511yescharacteristic
549D8—88no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C2×C8—22no—
556C2×C8—22no—
557C2×C8—22no—
558C2×C8—22no—
559C2×C8—22no—
560C2×C8—22no—
561C2×C8—22no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4C2×#4114yes—
586C22⋊C4—28no—
587C22⋊C4—28no—
588C22⋊C4—44no—
589C22⋊C4—44no—
590C22⋊C4—44no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C22⋊C4—44no—
600C22⋊C4—44no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—44no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—22no—
617C42—22no—
618C42—22no—
619C42—22no—
620C42—21no—
621C42—21no—
622C42—22no—
623C42—22no—
624C42—22no—
625C42—22no—
626C42—41no—
627C42—41no—
628C42—41no—
629C42—41no—
630C42—41no—
631C42—41no—
632C42—44no—
633C42—44no—
634C42—44no—
635C42—44no—
636C42#13514yes—
637C42AGL(1,ℤ/8)14yes—
638C42C2×#4112yes—
639C42C2×#4112yes—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—24no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23C2×AGL(1,ℤ/8)12yes—
661C23C23×D411yescharacteristic
662Q8—48no—
663Q8—84no—
664D4—28no—
665D4—416no—
666D4—48no—
667D4—48no—
668D4—44no—
669D4—44no—
670D4—44no—
671D4—88no—
672D4—84no—
673D4—84no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—28no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—24no—
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—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—416no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
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—42no—
729C2×C4—88no—
730C2×C4—88no—
731C2×C4—88no—
732C2×C4#52512yes—
733C2×C4#52512yes—
734C2×C4C2×#13512yes—
735C2×C4C2×#13512yes—
736C2×C4C2×#13512yes—
737C2×C4C2×AGL(1,ℤ/8)12yes—
738C2×C4C2×AGL(1,ℤ/8)12yes—
739C2×C4C2×AGL(1,ℤ/8)12yes—
740C2×C4C2×AGL(1,ℤ/8)12yes—
741C2×C4C2×AGL(1,ℤ/8)12yes—
742C2×C4#57512yes—
743C2×C4C22×#4111yescharacteristic
744C2×C4C22×#4111yescharacteristic
745C2×C4#58512yes—
746C2×C4#58512yes—
747C8—42no—
748C8—42no—
749C8—42no—
750C8—42no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22C2×#52511yescharacteristic
773C22#344911yescharacteristic
774C22#344911yescharacteristic
775C22C22×#13511yescharacteristic
776C22C22×AGL(1,ℤ/8)11yescharacteristic
777C22C22×AGL(1,ℤ/8)11yescharacteristic
778C22C2×#57511yescharacteristic
779C4—22no—
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—44no—
790C4—41no—
791C4—82no—
792C4—82no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4#310214yes—
797C4#310914yes—
798C4#352112yes—
799C4#352412yes—
800C2—42no—
801C2—84no—
802C2—162no—
803C2#3521111yescharacteristic
804C2C2×#310211yescharacteristic
805C2C2×#310911yescharacteristic
806C2#6094611yescharacteristic
807C2#6094611yescharacteristic
808C2#6096511yescharacteristic
809C2#6096511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25599C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #36631C2semidirect
2. C4×#532C2semidirect
3. #33080C2semidirect
4. #30014C2semidirect
5. #29536C2semidirect
6. #29412C2semidirect
7. #29190C2semidirect
8. #29176C2semidirect
9. #28655C2semidirect
10. #28615C2semidirect
11. #27890C2semidirect
12. #27876C2semidirect
13. #25673C2semidirect
15. #22269C2semidirect
16. #22248C2semidirect
17. #22219C2semidirect
18. #22219C2semidirect
19. #20777C2semidirect

Maximal subgroups

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

subgroupindex
#366312
C4×#5322
#330802
#300142
#295362
#294122
#291902
#291762
#286552
#286152
#278902
#278762
#256732
#255992
#222692
#222482
#222192
#207772