Finite Group Databasebeta

← #6798679

Subgroups — #6798679

Order 512.

1700 conjugacy classes of subgroups.

The subgroup lattice has 783 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36210C211yesmaximal, characteristic
2D4×C4⋊Q8C211yesmaximal, characteristic
3#33232C211yesmaximal, characteristic, complemented
4#31316C214yesmaximal, complemented
5#31312C214yesmaximal, complemented
6#29845C211yesmaximal, characteristic, complemented
7#29844C211yesmaximal, characteristic, complemented
8#28748C211yesmaximal, characteristic, complemented
9#28515C211yesmaximal, characteristic, complemented
10#27892C211yesmaximal, characteristic, complemented
11#27889C211yesmaximal, characteristic, complemented
12#25894C214yesmaximal
13#25856C211yesmaximal, characteristic, complemented
14#25856C211yesmaximal, characteristic, complemented
15#25290C214yesmaximal, complemented
16#21804C211yesmaximal, characteristic, complemented
17#21804C211yesmaximal, characteristic, complemented
18#21647C211yesmaximal, characteristic, complemented
19#21265C211yesmaximal, characteristic
20C2×D4×Q8C2212yes—
21C22×C4⋊Q8C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#491C2214yes—
24C2×#487C2211yescharacteristic
25C2×#487C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#479C2214yes—
28C2×#431C2211yescharacteristic
29C2×#431C2211yescharacteristic
30#2868C2211yescharacteristic
31#2859C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2562C2212yes—
37#2551—21no—
38#2551—21no—
39#2546C2212yes—
40#2514—21no—
41#2509—21no—
42#2495C2212yes—
43#2494—21no—
44#2494C2212yes—
45#2485—21no—
46#2440—21no—
47#2440—21no—
48#2440—21no—
49#2440—21no—
50#2434C2212yes—
51#2434C2212yes—
52#2421—21no—
53#2415—21no—
54#2370C2212yes—
55#2362—21no—
56D4×C4⋊C4—21no—
57D4×C4⋊C4—21no—
58#2347—21no—
59C4×C4⋊Q8C2211yescharacteristic
60C4×C4⋊Q8C2211yescharacteristic
61#2285C2211yescharacteristic
62#2285C2211yescharacteristic
63C42×D4C2211yescharacteristic
64#2097C2214yes—
65#2068C2214yes—
66#2066C2214yes—
67#2043C2214yes—
68#2043C2214yes—
69#2043C2214yes—
70#2036C2214yes—
71#2036C2214yes—
72#2035C2214yes—
73#2035C2214yes—
74#1990C2211yescharacteristic
75#1981C2214yes—
76#1981C2214yes—
77#1981C2214yes—
78#1960C2214yes—
79#1956C2211yescharacteristic
80#1956C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1956C2211yescharacteristic
85#1956C2211yescharacteristic
86#1956C2211yescharacteristic
87#1956C2211yescharacteristic
88#1955C2212yes—
89#1940C2212yes—
90#1935C2214yes—
91#1928C2214yes—
92#1927C2214yes—
93#1924C2212yes—
94#1924C2212yes—
95#1845C2211yescharacteristic
96#1844C2211yescharacteristic
97#1834C2211yescharacteristic
98#1787C2214yes—
99#1787C2214yes—
100#1787C2214yes—
101#1787C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103#1763C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106C4×#97C2211yescharacteristic
107C23×Q8C2312yes—
108C23×Q8C2312yes—
109D4×Q8—48no—
110C2×C4⋊Q8—22no—
111C2×C4⋊Q8—24no—
112C2×C4⋊Q8—24no—
113C2×C4⋊Q8—21no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—42no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2312yes—
122C2×C4⋊Q8C2312yes—
123C2×C4⋊Q8C2312yes—
124C2×C4⋊Q8C2311yescharacteristic
125C2×C4⋊Q8C2312yes—
126C2×C4⋊Q8C2311yescharacteristic
127C2×#125C2312yes—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8—22no—
131C2×C22⋊Q8—22no—
132C2×C22⋊Q8C2312yes—
133C2×C22⋊Q8C2312yes—
134C2×C4×Q8—21no—
135C2×C4×Q8C2312yes—
136C2×C4×D4—22no—
137C2×C4×D4D411yescharacteristic
138C2×C4×D4D411yescharacteristic
139C2×C4×D4C2311yescharacteristic
140C2×#117—21no—
141C2×#117—21no—
142C22×C4⋊C4—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4—21no—
145C22×C4⋊C4—21no—
146C22×C42C2311yescharacteristic
147C22×C42C2311yescharacteristic
148#491—48no—
149#487—24no—
150#487—42no—
151#487—42no—
152#479—48no—
153#431—42no—
154#431—42no—
155C2×#107C2314yes—
156C2×#106C2314yes—
157C2×C4⋊C8C2312yes—
158C2×C4⋊C8C2312yes—
159C2×C4⋊C8C2312yes—
160C2×#103C2314yes—
161C2×#103C2314yes—
162C2×#103C2314yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#103C2314yes—
170C2×#103C2314yes—
171C2×#103C2314yes—
172C2×C22⋊C8C2312yes—
173C2×C22⋊C8C2312yes—
174C2×C22⋊C8C2312yes—
175C2×C22⋊C8C2312yes—
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2311yescharacteristic
182#401—22no—
183#400—22no—
184#400—22no—
185#398—22no—
186#398—22no—
187#397—22no—
188#397—22no—
189#395—22no—
190#395—22no—
191#395—22no—
192#395—22no—
193#394—22no—
194#391—21no—
195#391—21no—
196#391—21no—
197#391C2312yes—
198#391C2312yes—
199#391C2312yes—
200#389—22no—
201#389—22no—
202#389—22no—
203#389—21no—
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—21no—
216#389C2312yes—
217#389C2312yes—
218#389C2312yes—
219#388—22no—
220#388—22no—
221#388—22no—
222#388—22no—
223#387—22no—
224#387—22no—
225#387—22no—
226#385—22no—
227#385—22no—
228#385—22no—
229#385—22no—
230#384—21no—
231#384—21no—
232#384—21no—
233#384—21no—
234#384C2311yescharacteristic
235#384C2311yescharacteristic
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#383—22no—
239#382—21no—
240#382—21no—
241#382C2312yes—
242#380—21no—
243#380—21no—
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—
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—24no—
282C22×Q8—24no—
283C22×Q8—42no—
284C22×Q8—42no—
285C22×Q8—44no—
286C22×Q8—44no—
287C22×Q8—44no—
288C22×Q8—44no—
289C22×Q8C2412yes—
290C22×Q8C2412yes—
291C22×Q8C2412yes—
292C22×D4C2×D411yescharacteristic
293C23×C4—22no—
294C23×C4—22no—
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C23×C4C2411yescharacteristic
301C22×C8C2412yes—
302C22×C8C2412yes—
303C22×C8C2412yes—
304C22×C8C2412yes—
305C4⋊Q8—24no—
306C4⋊Q8—24no—
307C4⋊Q8—22no—
308C4⋊Q8—22no—
309C4⋊Q8—22no—
310C4⋊Q8—22no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—22no—
314C4⋊Q8—28no—
315C4⋊Q8—44no—
316C4⋊Q8—44no—
317C4⋊Q8—44no—
318C4⋊Q8—44no—
319C4⋊Q8—42no—
320C4⋊Q8—42no—
321C4⋊Q8—44no—
322C4⋊Q8—48no—
323C4⋊Q8#4114yes—
324#125—28no—
325C22⋊Q8—48no—
326C22⋊Q8—48no—
327C22⋊Q8—44no—
328C22⋊Q8—44no—
329C22⋊Q8—44no—
330C22⋊Q8—82no—
331C4×Q8—28no—
332C4×Q8—82no—
333C4×D4—24no—
334C4×D4—24no—
335C4×D4—24no—
336C4×D4—48no—
337#117—44no—
338#117—82no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—44no—
371C2×C4⋊C4—44no—
372C2×C4⋊C4—44no—
373C2×C4⋊C4—44no—
374C2×C4⋊C4C2×D411yescharacteristic
375C2×C4⋊C4C2×D411yescharacteristic
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
379C2×C4⋊C4C2412yes—
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
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⋊C4C2×D411yescharacteristic
389C2×C22⋊C4C2×D411yescharacteristic
390C2×C22⋊C4C2×D411yescharacteristic
391C2×C22⋊C4C2×D411yescharacteristic
392C2×C22⋊C4C2×D411yescharacteristic
393C2×C22⋊C4C2×D411yescharacteristic
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—22no—
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×C42C2411yescharacteristic
411C2×C42C2411yescharacteristic
412C2×C42C2411yescharacteristic
413C2×C42C2411yescharacteristic
414C2×C42C2411yescharacteristic
415#107—44no—
416#106—44no—
417C4⋊C8—24no—
418C4⋊C8—42no—
419C4⋊C8—42no—
420#103—28no—
421#103—44no—
422#103—44no—
423#103—44no—
424#103—44no—
425#103—44no—
426#103—44no—
427#103—44no—
428#103—44no—
429#103—44no—
430#103—44no—
431#103—44no—
432C22⋊C8—42no—
433C22⋊C8—42no—
434C22⋊C8—42no—
435C22⋊C8—42no—
436#97—24no—
437#97—42no—
438C4×C8—22no—
439C4×C8—22no—
440C4×C8—22no—
441C4×C8—22no—
442#95—22no—
443#95—22no—
444#95—22no—
445#95—22no—
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#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464#95C2×D411yescharacteristic
465#95C2×D411yescharacteristic
466C24C22×D411yescharacteristic
467C24C22×D411yescharacteristic
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—22no—
471C2×Q8—24no—
472C2×Q8—24no—
473C2×Q8—24no—
474C2×Q8—22no—
475C2×Q8—22no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—24no—
479C2×Q8—44no—
480C2×Q8—44no—
481C2×Q8—44no—
482C2×Q8—44no—
483C2×Q8—42no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8—82no—
487C2×Q8—82no—
488C2×Q8—88no—
489C2×Q8—88no—
490C2×Q8—88no—
491C2×Q8—88no—
492C2×Q8C2×#4114yes—
493C2×D4—22no—
494C2×D4—22no—
495C2×D4—22no—
496C22×C4—22no—
497C22×C4—22no—
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—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
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—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—82no—
527C22×C4—82no—
528C22×C4#13714yes—
529C22×C4#13714yes—
530C22×C4C22×D411yescharacteristic
531C22×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
543C2×C8—22no—
544C2×C8—22no—
545C2×C8—22no—
546C2×C8—22no—
547C2×C8—22no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—22no—
552C2×C8—22no—
553C2×C8—22no—
554C2×C8—22no—
555C4⋊C4—22no—
556C4⋊C4—24no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—44no—
567C4⋊C4—44no—
568C4⋊C4—44no—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4—42no—
589C4⋊C4—42no—
590C4⋊C4—42no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—44no—
604C22⋊C4—44no—
605C22⋊C4—82no—
606C22⋊C4—82no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—21no—
619C42—22no—
620C42—44no—
621C42—44no—
622C42—82no—
623C42—82no—
624C42C2×#4112yes—
625C42H(5,𝔽2)14yes—
626C42H(5,𝔽2)12yes—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23C2×#13712yes—
640C23C2×#13712yes—
641C23C23×D411yescharacteristic
642Q8—28no—
643Q8—44no—
644Q8—44no—
645Q8—44no—
646Q8—44no—
647Q8—44no—
648Q8—88no—
649Q8—88no—
650Q8—84no—
651D4—28no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—28no—
661C2×C4—28no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—24no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—88no—
711C2×C4—88no—
712C2×C4#53512yes—
713C2×C4#53512yes—
714C2×C4#54612yes—
715C2×C4#54612yes—
716C2×C4C2×#13712yes—
717C2×C4C2×#13712yes—
718C2×C4C2×#13712yes—
719C2×C4C2×#13712yes—
720C2×C4#57712yes—
721C2×C4#57812yes—
722C2×C4C22×#4111yescharacteristic
723C2×C4C2×H(5,𝔽2)12yes—
724C2×C4C2×H(5,𝔽2)11yescharacteristic
725C2×C4#58512yes—
726C8—42no—
727C8—42no—
728C8—42no—
729C8—42no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22C2×#53511yescharacteristic
745C22C2×#54611yescharacteristic
746C22#350011yescharacteristic
747C22C22×#13711yescharacteristic
748C22C22×#13711yescharacteristic
749C22C2×#57711yescharacteristic
750C22C2×#57811yescharacteristic
751C4—22no—
752C4—22no—
753C4—22no—
754C4—22no—
755C4—41no—
756C4—41no—
757C4—44no—
758C4—41no—
759C4—41no—
760C4—41no—
761C4—41no—
762C4—82no—
763C4—82no—
764C4—82no—
765C4—82no—
766C4—82no—
767C4—82no—
768C4—82no—
769C4#331214yes—
770C4#332014yes—
771C4#351412yes—
772C4#354612yes—
773C2—42no—
774C2—42no—
775C2#3895711yescharacteristic
776C2#6080011yescharacteristic
777C2#6082411yescharacteristic
778C2C2×#331211yescharacteristic
779C2C2×#332011yescharacteristic
780C2#6253611yescharacteristic
781C2#6254011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
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
3. #33232C2semidirect
4. #31316C2semidirect
5. #31312C2semidirect
6. #29845C2semidirect
7. #29844C2semidirect
8. #28748C2semidirect
9. #28515C2semidirect
10. #27892C2semidirect
11. #27889C2semidirect
13. #25856C2semidirect
14. #25856C2semidirect
15. #25290C2semidirect
16. #21804C2semidirect
17. #21804C2semidirect
18. #21647C2semidirect

Maximal subgroups

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

subgroupindex
#362102
D4×C4⋊Q82
#332322
#313162
#313122
#298452
#298442
#287482
#285152
#278922
#278892
#258942
#258562
#252902
#218042
#216472
#212652