Finite Group Databasebeta

← #6613946

Subgroups — #6613946

Order 512.

1841 conjugacy classes of subgroups.

The subgroup lattice has 815 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36189C211yesmaximal, characteristic, complemented
2#36149C211yesmaximal, characteristic
3#33278C211yesmaximal, characteristic, complemented
4#33176C211yesmaximal, characteristic, complemented
5#33049C211yesmaximal, characteristic, complemented
6#29190C211yesmaximal, characteristic, complemented
7#28886C214yesmaximal, complemented
8#28616C211yesmaximal, characteristic, complemented
9#27948C211yesmaximal, characteristic, complemented
10#27889C211yesmaximal, characteristic, complemented
11#26970C214yesmaximal, complemented
12#25719C211yesmaximal, characteristic, complemented
13#25597C211yesmaximal, characteristic, complemented
14#25135C214yesmaximal, complemented
15#22882C214yesmaximal, complemented
16C4×#492C211yesmaximal, characteristic, complemented
17#21410C211yesmaximal, characteristic, complemented
18#21200C211yesmaximal, characteristic, complemented
19C4×#436C211yesmaximal, characteristic, complemented
20C2×#532C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×#494C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#487C2211yescharacteristic
25C2×#470C2214yes—
26C2×#452C2214yes—
27C2×C4×SD16C2214yes—
28C2×#436C2212yes—
29C2×#417C2214yes—
30C2×C4×M16C2211yescharacteristic
31C2×C4×M16C2211yescharacteristic
32#2862C2211yescharacteristic
33#2859C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2857C2211yescharacteristic
37#2857C2211yescharacteristic
38#2570—21no—
39#2535—21no—
40#2511C2212yes—
41#2507—21no—
42#2497—21no—
43#2487—21no—
44#2447—21no—
45#2447C2212yes—
46#2442—21no—
47#2441—21no—
48#2427—21no—
49#2427C2212yes—
50#2423C2212yes—
51#2420—21no—
52#2420—21no—
53#2417C2212yes—
54#2407—21no—
55#2407C2212yes—
56#2360C2212yes—
57#2352—21no—
58#2349—21no—
59#2345—21no—
60#2339—21no—
61#2339C2212yes—
62C4×C4⋊Q8C2211yescharacteristic
63C4×#127C2211yescharacteristic
64#2285C2211yescharacteristic
65C2×#384C2211yescharacteristic
66C42×D4C2211yescharacteristic
67#2084C2214yes—
68#2065C2214yes—
69#2056C2214yes—
70#2035C2214yes—
71#2015C2214yes—
72#2000C2214yes—
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1971C2214yes—
77#1968C2214yes—
78#1959C2214yes—
79#1957C2211yescharacteristic
80#1957C2211yescharacteristic
81#1957C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1935C2214yes—
87#1933C2214yes—
88#1933C2214yes—
89#1927C2214yes—
90#1895C2214yes—
91#1894C2214yes—
92#1878C2214yes—
93#1877C2214yes—
94#1864C2214yes—
95#1853C2214yes—
96#1844C2211yescharacteristic
97#1844C2211yescharacteristic
98#1834C2211yescharacteristic
99#1770C2212yes—
100C4×C4⋊C8C2211yescharacteristic
101#1762C2214yes—
102#1753C2212yes—
103#1753C2212yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C42×C8C2211yescharacteristic
107C22×#41—21no—
108C22×#41C2312yes—
109C22×Q16C2314yes—
110C22×SD16C2314yes—
111C22×M16C2312yes—
112C22×M16C2312yes—
113#532—24no—
114#532—24no—
115#532—42no—
116#532—42no—
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×C4⋊Q8C2311yescharacteristic
120C2×#127C2311yescharacteristic
121C2×#125—21no—
122C2×#124—21no—
123C2×#124C2312yes—
124C2×C22⋊Q8—21no—
125C2×C22⋊Q8C2312yes—
126C2×C22⋊Q8C2312yes—
127C2×C22⋊Q8C2312yes—
128C2×#121—21no—
129C2×#121—21no—
130C2×#121—21no—
131C2×#121C2312yes—
132C2×C4×Q8C2312yes—
133C2×C4×D4—21no—
134C2×C4×D4—21no—
135C2×C4×D4—21no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4D411yescharacteristic
139C2×C4×D4D411yescharacteristic
140C2×C4×D4C2312yes—
141C2×C4×D4C2312yes—
142C2×C4×D4C2311yescharacteristic
143C2×#117—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C4⋊C4C2312yes—
147C22×C42C2311yescharacteristic
148C22×C42C2311yescharacteristic
149#494—42no—
150#492—24no—
151#487—42no—
152#470—48no—
153#452—216no—
154C4×SD16—48no—
155#436—28no—
156C2×#106C2314yes—
157C2×#106C2314yes—
158C2×C4⋊C8C2312yes—
159#417—48no—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#102C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×C22⋊C8C2312yes—
169C2×C22⋊C8C2312yes—
170C4×M16—42no—
171C4×M16—42no—
172C2×#97C2312yes—
173C2×#97C2312yes—
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2312yes—
179C2×C4×C8C2312yes—
180#400—22no—
181#400—22no—
182#399—22no—
183#398—22no—
184#398—22no—
185#397—22no—
186#397—22no—
187#397—22no—
188#396—22no—
189#394—22no—
190#394—22no—
191#392—22no—
192#391—21no—
193#391—21no—
194#391—21no—
195#391C2312yes—
196#391C2312yes—
197#391C2312yes—
198#391C2312yes—
199#391C2312yes—
200#391C2312yes—
201#390—21no—
202#390—21no—
203#390C2312yes—
204#389—21no—
205#389—21no—
206#389—21no—
207#389—21no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—21no—
213#389—21no—
214#389—21no—
215#389—22no—
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#388—22no—
220#387—22no—
221#387—22no—
222#387—22no—
223#387—22no—
224#386—22no—
225#386—22no—
226#386—22no—
227#386—22no—
228#386—22no—
229#385—22no—
230#385—22no—
231#385—22no—
232#384—21no—
233#384—21no—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2312yes—
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#382—21no—
240#382—21no—
241#382—21no—
242#382—21no—
243#381—22no—
244#381—22no—
245#380—21no—
246#380—21no—
247#380—21no—
248#380—21no—
249#380—21no—
250#380—21no—
251#380—21no—
252#380—21no—
253#380—22no—
254#380—22no—
255#380C2312yes—
256#380C2312yes—
257C4×C4⋊C4—21no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4D411yescharacteristic
261C4×C4⋊C4D411yescharacteristic
262C4×C4⋊C4C2312yes—
263C4×C4⋊C4C2311yescharacteristic
264C4×C22⋊C4—22no—
265C4×C22⋊C4D411yescharacteristic
266C4×C22⋊C4D411yescharacteristic
267C4×C22⋊C4D411yescharacteristic
268C4×C22⋊C4D411yescharacteristic
269C4×C22⋊C4C2311yescharacteristic
270C4×C22⋊C4C2311yescharacteristic
271C2×#95—22no—
272C43C2311yescharacteristic
273#340C2314yes—
274#340C2314yes—
275#340C2314yes—
276#340C2314yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C2×#41—24no—
281C2×#41—28no—
282C2×#41—42no—
283C2×#41—44no—
284C2×#41—44no—
285C2×#41—44no—
286C2×#41—82no—
287C22×Q8—21no—
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×C4—22no—
299C23×C4—22no—
300C23×C4C2×D411yescharacteristic
301C23×C4C2×D411yescharacteristic
302C23×C4C2×D411yescharacteristic
303C23×C4C2×D411yescharacteristic
304C23×C4C2411yescharacteristic
305C23×C4C2411yescharacteristic
306C2×Q16—28no—
307C2×Q16—44no—
308C2×Q16—44no—
309C2×SD16—28no—
310C2×SD16—28no—
311C2×SD16—44no—
312C2×M16—24no—
313C2×M16—24no—
314C2×M16—24no—
315C2×M16—24no—
316C2×M16—42no—
317C2×M16—42no—
318C22×C8C2412yes—
319C22×C8C2412yes—
320C22×C8C2412yes—
321C22×C8C2412yes—
322C4⋊Q8—22no—
323C4⋊Q8—22no—
324C4⋊Q8—22no—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327C4⋊Q8—22no—
328#127—22no—
329#127#4114yes—
330#125—82no—
331#124—24no—
332#124—42no—
333#124—44no—
334C22⋊Q8—28no—
335C22⋊Q8—44no—
336C22⋊Q8—44no—
337C22⋊Q8—82no—
338#121—24no—
339#121—42no—
340#121—44no—
341#121—44no—
342#121—44no—
343C4×Q8—44no—
344C4×D4—24no—
345C4×D4—24no—
346C4×D4—24no—
347C4×D4—42no—
348C4×D4—42no—
349C4×D4—44no—
350C4×D4—44no—
351C4×D4—44no—
352C4×D4—44no—
353C4×D4—44no—
354C4×D4—82no—
355#117—82no—
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⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—44no—
380C2×C4⋊C4—44no—
381C2×C4⋊C4—82no—
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D411yescharacteristic
384C2×C4⋊C4C2×D411yescharacteristic
385C2×C4⋊C4C2412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2412yes—
388C2×C4⋊C4C2412yes—
389C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C22⋊C4C2×D411yescharacteristic
407C2×C22⋊C4C2×D411yescharacteristic
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—22no—
413C2×C42—22no—
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×C42C2411yescharacteristic
423C2×C42C2411yescharacteristic
424C2×C42C2411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2411yescharacteristic
427#106—44no—
428#106—44no—
429C4⋊C8—24no—
430#103—28no—
431#103—28no—
432#103—28no—
433#103—44no—
434#103—44no—
435#102—28no—
436#102—28no—
437#102—44no—
438C22⋊C8—24no—
439C22⋊C8#4118yescomplemented
440#97—42no—
441#97—42no—
442C4×C8—24no—
443C4×C8—24no—
444C4×C8—22no—
445C4×C8—22no—
446C4×C8—22no—
447C4×C8—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#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95C2×D411yescharacteristic
467#95C2×D411yescharacteristic
468#95C2×D411yescharacteristic
469#95C2×D411yescharacteristic
470#95C2×D411yescharacteristic
471#95C2×D411yescharacteristic
472C24—22no—
473C24C22×D411yescharacteristic
474C24C22×D411yescharacteristic
475#41—416no—
476#41—88no—
477#41—816no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—22no—
481C2×Q8—22no—
482C2×Q8—24no—
483C2×Q8—24no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—42no—
489C2×D4—22no—
490C2×D4—24no—
491C2×D4—24no—
492C2×D4—22no—
493C2×D4—24no—
494C2×D4—24no—
495C2×D4—22no—
496C2×D4—41no—
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—82no—
506C2×D4—82no—
507C2×D4C2×#4114yes—
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—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
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—44no—
539C22×C4—44no—
540C22×C4—82no—
541C22×C4—82no—
542C22×C4—82no—
543C22×C4—82no—
544C22×C4—82no—
545C22×C4—82no—
546C22×C4C22×D411yescharacteristic
547C22×C4C22×D411yescharacteristic
548C22×C4C22×D411yescharacteristic
549C22×C4C22×D411yescharacteristic
550C22×C4C22×D411yescharacteristic
551C22×C4C22×D411yescharacteristic
552C22×C4C22×D411yescharacteristic
553C22×C4C22×D411yescharacteristic
554C22×C4C22×D411yescharacteristic
555C22×C4C22×D411yescharacteristic
556C22×C4C22×D411yescharacteristic
557C22×C4C22×D411yescharacteristic
558C22×C4C2×#4114yes—
559C22×C4C2511yescharacteristic
560Q16—88no—
561SD16—416no—
562M16—48no—
563M16—48no—
564C2×C8—22no—
565C2×C8—22no—
566C2×C8—22no—
567C2×C8—22no—
568C2×C8—22no—
569C2×C8—22no—
570C2×C8—22no—
571C2×C8—22no—
572C2×C8—22no—
573C2×C8C2×#4114yes—
574C2×C8C2×#4114yes—
575C2×C8H(5,𝔽2)14yes—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—24no—
579C4⋊C4—22no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—41no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—42no—
592C4⋊C4—42no—
593C4⋊C4—42no—
594C4⋊C4—42no—
595C4⋊C4—42no—
596C4⋊C4—42no—
597C4⋊C4—42no—
598C4⋊C4—42no—
599C4⋊C4—42no—
600C4⋊C4—82no—
601C4⋊C4—82no—
602C4⋊C4—82no—
603C4⋊C4—82no—
604C4⋊C4—82no—
605C4⋊C4—82no—
606C4⋊C4—82no—
607C4⋊C4—82no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—44no—
615C22⋊C4—44no—
616C22⋊C4—44no—
617C22⋊C4—44no—
618C22⋊C4—44no—
619C22⋊C4—44no—
620C22⋊C4—82no—
621C22⋊C4—82no—
622C22⋊C4—82no—
623C22⋊C4—82no—
624C22⋊C4—82no—
625C22⋊C4—82no—
626C42—22no—
627C42—22no—
628C42—22no—
629C42—22no—
630C42—22no—
631C42—22no—
632C42—22no—
633C42—22no—
634C42—21no—
635C42—21no—
636C42—22no—
637C42—21no—
638C42—21no—
639C42—82no—
640C42—82no—
641C42#13714yes—
642C42C2×#4112yes—
643C42H(5,𝔽2)12yes—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—24no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23#53212yes—
665C23C23×D411yescharacteristic
666Q8—44no—
667Q8—44no—
668Q8—44no—
669Q8—44no—
670Q8—84no—
671D4—28no—
672D4—44no—
673D4—48no—
674D4—44no—
675D4—48no—
676D4—88no—
677D4—88no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—24no—
685C2×C4—24no—
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—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—44no—
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—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—88no—
735C2×C4—88no—
736C2×C4—164no—
737C2×C4—164no—
738C2×C4#53212yes—
739C2×C4#54612yes—
740C2×C4#54612yes—
741C2×C4C2×#13712yes—
742C2×C4C2×#13712yes—
743C2×C4C2×#13712yes—
744C2×C4#57512yes—
745C2×C4#57712yes—
746C2×C4#57712yes—
747C2×C4C22×#4111yescharacteristic
748C2×C4C22×#4112yes—
749C2×C4C2×H(5,𝔽2)12yes—
750C2×C4C2×H(5,𝔽2)11yescharacteristic
751C8—24no—
752C8—24no—
753C8—24no—
754C8—42no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—44no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—44no—
769C22—41no—
770C22—41no—
771C22—44no—
772C22—82no—
773C22—82no—
774C22—82no—
775C22—82no—
776C22C2×#53211yescharacteristic
777C22C2×#54611yescharacteristic
778C22#349811yescharacteristic
779C22C22×#13711yescharacteristic
780C22C2×#57511yescharacteristic
781C22C2×#57711yescharacteristic
782C22C2×#57711yescharacteristic
783C4—22no—
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C4—82no—
794C4—82no—
795C4—82no—
796C4—82no—
797C4—82no—
798C4—82no—
799C4—82no—
800C4#332314yes—
801C4#333114yes—
802C4#348112yes—
803C4#351912yes—
804C2—42no—
805C2—81no—
806C2—84no—
807C2#3636211yescharacteristic
808C2#6070111yescharacteristic
809C2#6071611yescharacteristic
810C2C2×#332311yescharacteristic
811C2C2×#333111yescharacteristic
812C2#6242211yescharacteristic
813C2#6242711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36149C2
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. #36189C2semidirect
3. #33278C2semidirect
4. #33176C2semidirect
5. #33049C2semidirect
6. #29190C2semidirect
7. #28886C2semidirect
8. #28616C2semidirect
9. #27948C2semidirect
10. #27889C2semidirect
11. #26970C2semidirect
12. #25719C2semidirect
13. #25597C2semidirect
14. #25135C2semidirect
15. #22882C2semidirect
16. C4×#492C2semidirect
17. #21410C2semidirect
18. #21200C2semidirect
19. C4×#436C2semidirect
439. C22⋊C8#41semidirect

Maximal subgroups

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

subgroupindex
#361892
#361492
#332782
#331762
#330492
#291902
#288862
#286162
#279482
#278892
#269702
#257192
#255972
#251352
#228822
C4×#4922
#214102
#212002
C4×#4362