Finite Group Databasebeta

← #6766329

Subgroups — #6766329

Order 512.

1693 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36187C211yesmaximal, characteristic
2#36129C211yesmaximal, characteristic, complemented
3#33048C211yesmaximal, characteristic, complemented
4#32126C214yesmaximal, complemented
5#31402C214yesmaximal, complemented
6#30205C211yesmaximal, characteristic, complemented
7#29807C211yesmaximal, characteristic, complemented
8#29218C211yesmaximal, characteristic, complemented
9#28613C211yesmaximal, characteristic, complemented
10#27889C211yesmaximal, characteristic, complemented
11#27876C211yesmaximal, characteristic, complemented
12#27445C214yesmaximal, complemented
13#26741C214yesmaximal, complemented
14#25903C211yesmaximal, characteristic, complemented
15#25598C211yesmaximal, characteristic, complemented
16#22219C211yesmaximal, characteristic, complemented
17#21833C211yesmaximal, characteristic, complemented
18#21409C211yesmaximal, characteristic, complemented
19#21102C211yesmaximal, characteristic, complemented
20C2×#555—21no—
21C2×#533C2211yescharacteristic
22C22×C4⋊Q8C2211yescharacteristic
23C2×#492C2211yescharacteristic
24C2×#486C2211yescharacteristic
25C2×#486C2211yescharacteristic
26C2×#431C2211yescharacteristic
27C2×C4×M16C2211yescharacteristic
28#2868C2211yescharacteristic
29#2862C2211yescharacteristic
30#2857C2211yescharacteristic
31#2857C2211yescharacteristic
32#2856C2211yescharacteristic
33#2856C2211yescharacteristic
34#2563—21no—
35#2550—21no—
36#2537—21no—
37#2537C2212yes—
38#2500—21no—
39#2500—21no—
40#2492C2212yes—
41#2491—21no—
42#2491—21no—
43#2491C2212yes—
44#2491C2212yes—
45#2451C2212yes—
46#2446—21no—
47#2442—21no—
48#2439—21no—
49#2429—21no—
50#2417C2212yes—
51#2409—21no—
52#2360C2212yes—
53#2354—21no—
54#2354C2212yes—
55#2352—21no—
56Q8×C22⋊C4—21no—
57C4×C4⋊Q8C2211yescharacteristic
58C4×#127C2211yescharacteristic
59#2285C2211yescharacteristic
60#2285C2211yescharacteristic
61C42×D4C2211yescharacteristic
62#2100C2214yes—
63#2077C2214yes—
64#2072C2214yes—
65#2055C2214yes—
66#2055C2214yes—
67#2035C2214yes—
68#2024C2214yes—
69#2023C2214yes—
70#2000C2214yes—
71#2000C2214yes—
72#1990C2211yescharacteristic
73#1990C2211yescharacteristic
74#1990C2211yescharacteristic
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1990C2211yescharacteristic
78#1988C2214yes—
79#1987C2214yes—
80#1957C2211yescharacteristic
81#1956C2211yescharacteristic
82#1956C2211yescharacteristic
83#1956C2211yescharacteristic
84#1936C2214yes—
85#1927C2214yes—
86#1926C2214yes—
87#1924C2212yes—
88#1919C2214yes—
89#1917C2212yes—
90#1895C2214yes—
91#1894C2214yes—
92#1880C2214yes—
93#1877C2214yes—
94#1874C2214yes—
95#1870C2212yes—
96#1864C2214yes—
97#1851C2212yes—
98#1844C2211yescharacteristic
99#1834C2211yescharacteristic
100#1834C2211yescharacteristic
101#1823C2214yes—
102C4×C4⋊C8C2211yescharacteristic
103#1763C2214yes—
104C4×C22⋊C8C2211yescharacteristic
105C4×C22⋊C8C2211yescharacteristic
106#1744C2211yescharacteristic
107C23×Q8—21no—
108C22×SD16C2314yes—
109C22×M16C2312yes—
110#555—48no—
111#533—24no—
112#533—42no—
113C2×C4⋊Q8—24no—
114C2×C4⋊Q8—21no—
115C2×C4⋊Q8—21no—
116C2×C4⋊Q8—21no—
117C2×C4⋊Q8—21no—
118C2×C4⋊Q8—42no—
119C2×C4⋊Q8C2311yescharacteristic
120C2×C4⋊Q8C2311yescharacteristic
121C2×C4⋊Q8C2312yes—
122C2×C4⋊Q8C2311yescharacteristic
123C2×C4⋊Q8C2312yes—
124C2×#127C2311yescharacteristic
125C2×#125—21no—
126C2×#124—22no—
127C2×#124—22no—
128C2×C22⋊Q8—21no—
129C2×C22⋊Q8—21no—
130C2×C22⋊Q8C2312yes—
131C2×C22⋊Q8C2312yes—
132C2×#121—22no—
133C2×#121—21no—
134C2×#121—21no—
135C2×#121—21no—
136C2×#121—21no—
137C2×#121C2312yes—
138C2×#121C2312yes—
139C2×C4×Q8—21no—
140C2×C4×Q8—21no—
141C2×C4×Q8C2312yes—
142C2×C4×D4—21no—
143C2×C4×D4—21no—
144C2×C4×D4D411yescharacteristic
145C2×C4×D4D411yescharacteristic
146C2×C4×D4C2312yes—
147C2×C4×D4C2311yescharacteristic
148C2×#117—21no—
149C2×#117—21no—
150C2×#117—21no—
151C2×#117—22no—
152C22×C4⋊C4—21no—
153C22×C4⋊C4C2312yes—
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156#492—42no—
157#486—24no—
158#486—42no—
159#431—42no—
160C2×#106C2314yes—
161C2×C4⋊C8C2312yes—
162C2×C4⋊C8C2312yes—
163C2×#103C2314yes—
164C2×#103C2314yes—
165C2×#103C2314yes—
166C2×#102C2314yes—
167C2×#102C2314yes—
168C2×#102C2314yes—
169C2×C22⋊C8C2312yes—
170C2×C22⋊C8C2312yes—
171C2×C22⋊C8C2312yes—
172C4×M16—42no—
173C2×#97C2312yes—
174C2×C4×C8C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178#400—22no—
179#398—22no—
180#398—22no—
181#396—22no—
182#395—22no—
183#394—22no—
184#394—22no—
185#394—22no—
186#394—22no—
187#393—22no—
188#393—22no—
189#393—22no—
190#391—21no—
191#391—21no—
192#391—21no—
193#391—21no—
194#391—22no—
195#391—22no—
196#391C2312yes—
197#391C2312yes—
198#391C2312yes—
199#390—21no—
200#390—21no—
201#390—21no—
202#390—21no—
203#390—21no—
204#390—21no—
205#390C2312yes—
206#390C2312yes—
207#390C2312yes—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—21no—
212#389—22no—
213#389C2312yes—
214#389C2312yes—
215#388—22no—
216#388—22no—
217#388—22no—
218#388—22no—
219#388—22no—
220#387—22no—
221#387—22no—
222#386—22no—
223#385—22no—
224#384—21no—
225#384—21no—
226#384C2311yescharacteristic
227#384C2311yescharacteristic
228#384C2312yes—
229#384C2311yescharacteristic
230#384C2311yescharacteristic
231#382—21no—
232#382—21no—
233#382—21no—
234#382—21no—
235#380—21no—
236#380—21no—
237#380—21no—
238#380—21no—
239#380—21no—
240#380—22no—
241#380—22no—
242#380—22no—
243#380C2312yes—
244#380C2312yes—
245#380C2312yes—
246C4×C4⋊C4—21no—
247C4×C4⋊C4—21no—
248C4×C4⋊C4—21no—
249C4×C4⋊C4D411yescharacteristic
250C4×C4⋊C4D411yescharacteristic
251C4×C4⋊C4C2312yes—
252C4×C4⋊C4C2312yes—
253C4×C4⋊C4C2312yes—
254C4×C4⋊C4C2311yescharacteristic
255C4×C22⋊C4—22no—
256C4×C22⋊C4D411yescharacteristic
257C4×C22⋊C4D411yescharacteristic
258C4×C22⋊C4D411yescharacteristic
259C4×C22⋊C4D411yescharacteristic
260C4×C22⋊C4C2311yescharacteristic
261C4×C22⋊C4C2311yescharacteristic
262C43C2311yescharacteristic
263#340C2314yes—
264#340C2314yes—
265#340C2314yes—
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#336C2312yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276C22×Q8—21no—
277C22×Q8—21no—
278C22×Q8—22no—
279C22×Q8—22no—
280C22×Q8—44no—
281C22×Q8—44no—
282C22×Q8—82no—
283C22×Q8C2412yes—
284C22×D4—22no—
285C22×D4—22no—
286C22×D4—21no—
287C22×D4—21no—
288C22×D4C2×D411yescharacteristic
289C22×D4C2412yes—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4C2×D411yescharacteristic
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2411yescharacteristic
297C23×C4C2411yescharacteristic
298C2×SD16—44no—
299C2×SD16—44no—
300C2×SD16—44no—
301C2×M16—42no—
302C2×M16—42no—
303C2×M16—42no—
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—42no—
315C4⋊Q8—44no—
316C4⋊Q8—44no—
317C4⋊Q8—44no—
318C4⋊Q8—44no—
319C4⋊Q8—82no—
320C4⋊Q8#4114yes—
321#127—22no—
322#127—22no—
323#125—44no—
324#124—48no—
325#124—48no—
326C22⋊Q8—24no—
327C22⋊Q8—44no—
328C22⋊Q8—42no—
329C22⋊Q8—44no—
330C22⋊Q8—82no—
331#121—44no—
332#121—48no—
333#121—44no—
334#121—44no—
335#121—44no—
336#121—82no—
337#121—82no—
338C4×Q8—24no—
339C4×Q8—42no—
340C4×Q8—44no—
341C4×Q8—82no—
342C4×D4—24no—
343C4×D4—24no—
344C4×D4—44no—
345C4×D4—42no—
346C4×D4—44no—
347C4×D4—44no—
348#117—44no—
349#117—48no—
350#117—44no—
351#117—44no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—42no—
376C2×C4⋊C4—44no—
377C2×C4⋊C4C2×D411yescharacteristic
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2412yes—
384C2×C4⋊C4C2412yes—
385C2×C4⋊C4C2412yes—
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⋊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⋊C4C2×D411yescharacteristic
401C2×C22⋊C4C2×D411yescharacteristic
402C2×C22⋊C4C2×D411yescharacteristic
403C2×C22⋊C4C2×D411yescharacteristic
404C2×C22⋊C4C2×D411yescharacteristic
405C2×C22⋊C4C2×D411yescharacteristic
406C2×C42—22no—
407C2×C42—22no—
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—
428C4⋊C8—42no—
429C4⋊C8—42no—
430#103—44no—
431#103—44no—
432#103—44no—
433#102—28no—
434#102—44no—
435#102—44no—
436C22⋊C8—42no—
437C22⋊C8—42no—
438C22⋊C8—42no—
439#97—42no—
440C4×C8—22no—
441C4×C8—22no—
442C4×C8—22no—
443C4×C8—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#95C2×D411yescharacteristic
459#95C2×D411yescharacteristic
460#95C2×D411yescharacteristic
461#95C2×D411yescharacteristic
462#95C2×D411yescharacteristic
463#95C2×D411yescharacteristic
464C24—22no—
465C24C22×D411yescharacteristic
466C24C22×D411yescharacteristic
467C2×Q8—24no—
468C2×Q8—22no—
469C2×Q8—22no—
470C2×Q8—24no—
471C2×Q8—24no—
472C2×Q8—44no—
473C2×Q8—44no—
474C2×Q8—42no—
475C2×Q8—42no—
476C2×Q8—44no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—82no—
481C2×Q8—82no—
482C2×Q8—82no—
483C2×Q8—816no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—41no—
491C2×D4—44no—
492C2×D4—44no—
493C2×D4—42no—
494C2×D4—42no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—82no—
500C2×D4—82no—
501C2×D4—82no—
502C2×D4—82no—
503C22×C4—22no—
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—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—44no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—82no—
535C22×C4AGL(1,ℤ/8)14yes—
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
549SD16—88no—
550M16—48no—
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—
562C2×C8—22no—
563C4⋊C4—24no—
564C4⋊C4—22no—
565C4⋊C4—22no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—24no—
573C4⋊C4—41no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
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—
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—82no—
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—21no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—22no—
628C42—22no—
629C42—44no—
630C42—44no—
631C42—44no—
632C42—82no—
633C42#13714yes—
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—21no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23C2×AGL(1,ℤ/8)12yes—
657C23C23×D411yescharacteristic
658Q8—48no—
659Q8—44no—
660Q8—44no—
661Q8—88no—
662Q8—84no—
663Q8—164no—
664D4—44no—
665D4—44no—
666D4—44no—
667D4—84no—
668D4—84no—
669D4—164no—
670D4—164no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—28no—
678C2×C4—21no—
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—42no—
701C2×C4—42no—
702C2×C4—44no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—44no—
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—42no—
727C2×C4—88no—
728C2×C4—88no—
729C2×C4#54612yes—
730C2×C4#54612yes—
731C2×C4C2×AGL(1,ℤ/8)12yes—
732C2×C4C2×AGL(1,ℤ/8)12yes—
733C2×C4C2×#13712yes—
734C2×C4C2×#13712yes—
735C2×C4C2×#13712yes—
736C2×C4#57712yes—
737C2×C4#57712yes—
738C2×C4C22×#4111yescharacteristic
739C2×C4C2×H(5,𝔽2)11yescharacteristic
740C2×C4#58512yes—
741C2×C4#58512yes—
742C8—42no—
743C8—42no—
744C8—42no—
745C8—42no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22—82no—
765C22—82no—
766C22—82no—
767C22#344911yescharacteristic
768C22C2×#54611yescharacteristic
769C22#350011yescharacteristic
770C22C22×AGL(1,ℤ/8)11yescharacteristic
771C22C22×#13711yescharacteristic
772C22C2×#57711yescharacteristic
773C22C2×#57711yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—41no—
778C4—41no—
779C4—41no—
780C4—44no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—82no—
786C4—82no—
787C4—82no—
788C4—82no—
789C4—82no—
790C4—82no—
791C4#330614yes—
792C4#332914yes—
793C4#352412yes—
794C4#354012yes—
795C2—42no—
796C2—81no—
797C2—162no—
798C2#3809511yescharacteristic
799C2#6096911yescharacteristic
800C2#6101511yescharacteristic
801C2C2×#330611yescharacteristic
802C2C2×#332911yescharacteristic
803C2#6253911yescharacteristic
804C2#6254211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36187C2
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. #36129C2semidirect
3. #33048C2semidirect
4. #32126C2semidirect
5. #31402C2semidirect
6. #30205C2semidirect
7. #29807C2semidirect
8. #29218C2semidirect
9. #28613C2semidirect
10. #27889C2semidirect
11. #27876C2semidirect
12. #27445C2semidirect
13. #26741C2semidirect
14. #25903C2semidirect
15. #25598C2semidirect
16. #22219C2semidirect
17. #21833C2semidirect
18. #21409C2semidirect
19. #21102C2semidirect

Maximal subgroups

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

subgroupindex
#361872
#361292
#330482
#321262
#314022
#302052
#298072
#292182
#286132
#278892
#278762
#274452
#267412
#259032
#255982
#222192
#218332
#214092
#211022