Finite Group Databasebeta

← #6615037

Subgroups — #6615037

Order 512.

1750 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36182C211yesmaximal, characteristic
2#36151C211yesmaximal, characteristic, complemented
3#33287C211yesmaximal, characteristic, complemented
4#33174C211yesmaximal, characteristic, complemented
5#33042C211yesmaximal, characteristic, complemented
6#29179C211yesmaximal, characteristic, complemented
7#29094C214yesmaximal, complemented
8#28987C214yesmaximal, complemented
9#28613C211yesmaximal, characteristic, complemented
10#28559C214yesmaximal, complemented
11#27972C211yesmaximal, characteristic, complemented
12#27877C211yesmaximal, characteristic, complemented
13#25905C211yesmaximal, characteristic, complemented
14#25598C211yesmaximal, characteristic, complemented
15#23141C214yesmaximal, complemented
16#21646C211yesmaximal, characteristic, complemented
17#21400C211yesmaximal, characteristic, complemented
18#21322C211yesmaximal, characteristic, complemented
19C4×#435C211yesmaximal, characteristic, complemented
20C2×#553—21no—
21C2×#533C2211yescharacteristic
22C2×#533C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#468C2214yes—
27C2×#435C2212yes—
28C2×C4×M16C2211yescharacteristic
29C22×C4×C8C2211yescharacteristic
30#2862C2211yescharacteristic
31#2859C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2856C2211yescharacteristic
35#2856C2211yescharacteristic
36#2566—21no—
37#2536—21no—
38#2512—21no—
39#2512C2212yes—
40#2504—21no—
41#2500—21no—
42#2489—21no—
43#2489C2212yes—
44#2453—21no—
45#2453C2212yes—
46#2422—21no—
47#2422C2212yes—
48#2421—21no—
49#2421—21no—
50#2416—21no—
51#2416C2212yes—
52#2415—21no—
53#2415C2212yes—
54#2362—21no—
55#2362C2212yes—
56#2361—21no—
57#2361C2212yes—
58#2351—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×#127C2211yescharacteristic
61#2285C2211yescharacteristic
62C2×#384C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2087C2214yes—
65#2075C2214yes—
66#2072C2214yes—
67#2055C2214yes—
68#2025C2214yes—
69#2000C2214yes—
70#1992C2214yes—
71#1990C2211yescharacteristic
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1973C2214yes—
78#1957C2211yescharacteristic
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1936C2214yes—
83#1935C2214yes—
84#1935C2214yes—
85#1934C2214yes—
86#1921C2214yes—
87#1918C2214yes—
88#1893C2214yes—
89#1892C2214yes—
90#1880C2214yes—
91#1877C2214yes—
92#1875C2214yes—
93#1872C2214yes—
94#1845C2211yescharacteristic
95#1834C2211yescharacteristic
96#1834C2211yescharacteristic
97#1771C2212yes—
98C4×C4⋊C8C2211yescharacteristic
99#1762C2214yes—
100C4×#103C2214yes—
101#1753C2212yes—
102#1752C2212yes—
103C4×C22⋊C8C2211yescharacteristic
104C4×C22⋊C8C2211yescharacteristic
105#1736C2214yes—
106C4×#97C2211yescharacteristic
107C22×SD16C2314yes—
108C22×M16C2312yes—
109C23×C8C2312yes—
110#553—48no—
111#533—24no—
112#533—24no—
113#533—42no—
114#533—42no—
115C2×C4⋊Q8C2311yescharacteristic
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×#127C2311yescharacteristic
119C2×#126—22no—
120C2×#125—21no—
121C2×#125—21no—
122C2×#125C2312yes—
123C2×#123—22no—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8—21no—
126C2×C22⋊Q8—21no—
127C2×C22⋊Q8—21no—
128C2×C22⋊Q8C2312yes—
129C2×C22⋊Q8C2312yes—
130C2×#121—22no—
131C2×#121—21no—
132C2×#121—21no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121C2312yes—
136C2×#121C2312yes—
137C2×C4×Q8—21no—
138C2×C4×Q8—21no—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8C2312yes—
142C2×C4×D4—22no—
143C2×C4×D4—21no—
144C2×C4×D4—21no—
145C2×C4×D4D411yescharacteristic
146C2×C4×D4D411yescharacteristic
147C2×C4×D4C2312yes—
148C2×C4×D4C2311yescharacteristic
149C2×#117—21no—
150C2×#117—21no—
151C2×#117C2312yes—
152C22×C4⋊C4—21no—
153C22×C4⋊C4—21no—
154C22×C4⋊C4C2312yes—
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#492—42no—
158#486—24no—
159#486—42no—
160#468—216no—
161#435—28no—
162C2×#107C2314yes—
163C2×C4⋊C8C2312yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×#102C2314yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C4×M16—42no—
173C2×#97C2312yes—
174C2×#97C2312yes—
175C2×#97C2312yes—
176C2×C4×C8—42no—
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2312yes—
182#400—22no—
183#400—22no—
184#398—22no—
185#397—22no—
186#397—22no—
187#397—22no—
188#397—22no—
189#396—22no—
190#396—22no—
191#394—22no—
192#394—22no—
193#394—22no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391—21no—
198#391C2312yes—
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#390C2312yes—
209#390C2312yes—
210#389—22no—
211#389—22no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—21no—
216#389—21no—
217#389—21no—
218#389C2312yes—
219#389C2312yes—
220#389C2312yes—
221#389C2312yes—
222#388—22no—
223#388—22no—
224#388—22no—
225#388—22no—
226#388—22no—
227#388—22no—
228#387—22no—
229#387—22no—
230#386—22no—
231#386—22no—
232#385—22no—
233#385—22no—
234#384—21no—
235#384—21no—
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#384C2312yes—
239#384C2311yescharacteristic
240#384C2311yescharacteristic
241#382—21no—
242#382—21no—
243#382—21no—
244#382—21no—
245#382—22no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380C2312yes—
251#380C2312yes—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—22no—
255C4×C4⋊C4D411yescharacteristic
256C4×C4⋊C4D411yescharacteristic
257C4×C4⋊C4C2312yes—
258C4×C4⋊C4C2312yes—
259C4×C4⋊C4C2311yescharacteristic
260C4×C22⋊C4D411yescharacteristic
261C4×C22⋊C4D411yescharacteristic
262C4×C22⋊C4D411yescharacteristic
263C4×C22⋊C4D411yescharacteristic
264C4×C22⋊C4C2311yescharacteristic
265C4×C22⋊C4C2311yescharacteristic
266C43C2311yescharacteristic
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#340C2314yes—
273#340C2314yes—
274#340C2314yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278C22×Q8—21no—
279C22×Q8—21no—
280C22×Q8C2412yes—
281C22×D4—22no—
282C22×D4—22no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4C2×D411yescharacteristic
286C22×D4C2412yes—
287C23×C4—22no—
288C23×C4—22no—
289C23×C4C2×D411yescharacteristic
290C23×C4C2×D411yescharacteristic
291C23×C4C2×D411yescharacteristic
292C23×C4C2×D411yescharacteristic
293C23×C4C2411yescharacteristic
294C23×C4C2411yescharacteristic
295C2×SD16—28no—
296C2×SD16—44no—
297C2×SD16—44no—
298C2×M16—42no—
299C2×M16—42no—
300C2×M16#4118yes—
301C22×C8—24no—
302C22×C8—42no—
303C22×C8—42no—
304C22×C8C2412yes—
305C22×C8C2412yes—
306C22×C8C2412yes—
307C22×C8C2412yes—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8#4114yes—
314#127—22no—
315#127—22no—
316#126—48no—
317#125—24no—
318#125—42no—
319#125—44no—
320#125—44no—
321#123—48no—
322C22⋊Q8—28no—
323C22⋊Q8—24no—
324C22⋊Q8—42no—
325C22⋊Q8—44no—
326C22⋊Q8—44no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329#121—28no—
330#121—44no—
331#121—44no—
332#121—48no—
333#121—44no—
334#121—44no—
335#121—82no—
336C4×Q8—24no—
337C4×Q8—42no—
338C4×Q8—44no—
339C4×Q8—44no—
340C4×Q8—44no—
341C4×Q8—44no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—42no—
345C4×D4—44no—
346C4×D4—44no—
347C4×D4—48no—
348C4×D4—82no—
349#117—24no—
350#117—42no—
351#117—44no—
352#117—44no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
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—21no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—44no—
378C2×C4⋊C4—44no—
379C2×C4⋊C4—82no—
380C2×C4⋊C4C2×D411yescharacteristic
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C22⋊C4—22no—
390C2×C22⋊C4—22no—
391C2×C22⋊C4—22no—
392C2×C22⋊C4—22no—
393C2×C22⋊C4—22no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—22no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—22no—
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C22⋊C4C2×D411yescharacteristic
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
414C2×C42—22no—
415C2×C42—22no—
416C2×C42—22no—
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D411yescharacteristic
420C2×C42C2×D411yescharacteristic
421C2×C42C2×D411yescharacteristic
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D411yescharacteristic
424C2×C42C2×D411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427C2×C42C2411yescharacteristic
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—28no—
431C4⋊C8—24no—
432#103—28no—
433#103—44no—
434#103—44no—
435#102—28no—
436#102—28no—
437#102—44no—
438C22⋊C8—24no—
439C22⋊C8—24no—
440#97—24no—
441#97—42no—
442#97—42no—
443C4×C8—22no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—42no—
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
471C2×Q8—24no—
472C2×Q8—24no—
473C2×Q8—22no—
474C2×Q8—22no—
475C2×Q8—24no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—42no—
481C2×D4—22no—
482C2×D4—22no—
483C2×D4—22no—
484C2×D4—24no—
485C2×D4—22no—
486C2×D4—24no—
487C2×D4—41no—
488C2×D4—44no—
489C2×D4—44no—
490C2×D4—44no—
491C2×D4—44no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—82no—
499C2×D4—82no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
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—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4—82no—
528C22×C4—82no—
529C22×C4—82no—
530C22×C4—82no—
531C22×C4AGL(1,ℤ/8)14yes—
532C22×C4C22×D411yescharacteristic
533C22×C4C22×D411yescharacteristic
534C22×C4C22×D411yescharacteristic
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×C4C2×#4114yes—
545C22×C4C2511yescharacteristic
546SD16—88no—
547M16—48no—
548C2×C8—22no—
549C2×C8—22no—
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—48no—
559C2×C8C2×#4114yes—
560C2×C8C2×#4114yes—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—41no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—44no—
581C4⋊C4—42no—
582C4⋊C4—42no—
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—82no—
594C4⋊C4—82no—
595C4⋊C4C2×#4114yes—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—41no—
601C22⋊C4—41no—
602C22⋊C4—44no—
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—82no—
613C22⋊C4—82no—
614C22⋊C4—82no—
615C22⋊C4—82no—
616C42—22no—
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—44no—
633C42—44no—
634C42C2×#4112yes—
635C42H(5,𝔽2)12yes—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23#53212yes—
656C23C2×AGL(1,ℤ/8)12yes—
657C23C23×D411yescharacteristic
658Q8—48no—
659Q8—44no—
660Q8—44no—
661Q8—84no—
662D4—44no—
663D4—44no—
664D4—44no—
665D4—88no—
666D4—84no—
667D4—84no—
668D4—164no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—28no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
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—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—42no—
709C2×C4—42no—
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—164no—
727C2×C4—164no—
728C2×C4#53212yes—
729C2×C4#54612yes—
730C2×C4#54612yes—
731C2×C4C2×AGL(1,ℤ/8)12yes—
732C2×C4C2×AGL(1,ℤ/8)12yes—
733C2×C4#57512yes—
734C2×C4#57712yes—
735C2×C4#57812yes—
736C2×C4C22×#4111yescharacteristic
737C2×C4C22×#4112yes—
738C2×C4C2×H(5,𝔽2)11yescharacteristic
739C2×C4#58512yes—
740C8—24no—
741C8—24no—
742C8—42no—
743C8—42no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22C2×#53211yescharacteristic
766C22C2×#54611yescharacteristic
767C22#350011yescharacteristic
768C22C22×AGL(1,ℤ/8)11yescharacteristic
769C22C2×#57511yescharacteristic
770C22C2×#57711yescharacteristic
771C22C2×#57811yescharacteristic
772C4—22no—
773C4—22no—
774C4—41no—
775C4—41no—
776C4—41no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—44no—
783C4—82no—
784C4—82no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4#330714yes—
790C4#330814yes—
791C4#348012yes—
792C4#350512yes—
793C2—42no—
794C2—42no—
795C2—162no—
796C2#3639611yescharacteristic
797C2#6070011yescharacteristic
798C2#6072311yescharacteristic
799C2C2×#330811yescharacteristic
800C2C2×#330711yescharacteristic
801C2#6253911yescharacteristic
802C2#6254511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36182C2
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
2. #36151C2semidirect
3. #33287C2semidirect
4. #33174C2semidirect
5. #33042C2semidirect
6. #29179C2semidirect
7. #29094C2semidirect
8. #28987C2semidirect
9. #28613C2semidirect
10. #28559C2semidirect
11. #27972C2semidirect
12. #27877C2semidirect
13. #25905C2semidirect
14. #25598C2semidirect
15. #23141C2semidirect
16. #21646C2semidirect
17. #21400C2semidirect
18. #21322C2semidirect
19. C4×#435C2semidirect

Maximal subgroups

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

subgroupindex
#361822
#361512
#332872
#331742
#330422
#291792
#290942
#289872
#286132
#285592
#279722
#278772
#259052
#255982
#231412
#216462
#214002
#213222
C4×#4352