Finite Group Databasebeta

← #6376551

Subgroups — #6376551

Order 512.

2124 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3182C211yesmaximal, characteristic
2C4×#533C211yesmaximal, characteristic, complemented
3C4×#532C211yesmaximal, characteristic
4#22268C211yesmaximal, characteristic, complemented
5#22268C211yesmaximal, characteristic, complemented
6#22248C211yesmaximal, characteristic, complemented
7#22247C211yesmaximal, characteristic, complemented
8#22221C211yesmaximal, characteristic, complemented
9#22220C211yesmaximal, characteristic, complemented
10#22219C211yesmaximal, characteristic, complemented
11#22218C211yesmaximal, characteristic, complemented
12#22191C214yesmaximal, complemented
13#22186C214yesmaximal, complemented
14#21410C211yesmaximal, characteristic
15#21409C211yesmaximal, characteristic, complemented
16#21124C214yesmaximal, complemented
17#21121C214yesmaximal, complemented
18#20824C211yesmaximal, characteristic, complemented
19#20364C211yesmaximal, characteristic, complemented
20C2×#533C2211yescharacteristic
21C2×#532C2211yescharacteristic
22C2×C4×#41—21no—
23#3182C4116yescomplemented
24C2×#500C2211yescharacteristic
25C2×#492C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#486C2211yescharacteristic
28C2×#468C2214yes—
29C2×#440C2214yes—
30C2×C4×M16C2211yescharacteristic
31C2×C4×M16C2211yescharacteristic
32C4×C4⋊Q8C2211yescharacteristic
33C4×C4⋊Q8C2211yescharacteristic
34C4×C4⋊Q8C2211yescharacteristic
35C4×C4⋊Q8C2211yescharacteristic
36C4×C4⋊Q8C2211yescharacteristic
37C4×C4⋊Q8C2211yescharacteristic
38C4×#127C2211yescharacteristic
39C4×#127C2211yescharacteristic
40C4×#125—21no—
41C4×#125—21no—
42C4×#124—21no—
43C4×#124—21no—
44C4×C22⋊Q8—21no—
45C4×C22⋊Q8—21no—
46C4×C22⋊Q8C2212yes—
47C4×C22⋊Q8C2212yes—
48C4×#121—21no—
49C4×#121—21no—
50C4×#121C2212yes—
51C4×#121C2212yes—
52#2297—21no—
53#2296—21no—
54#2295—21no—
55#2295C2212yes—
56#2293—21no—
57#2293C2212yes—
58#2285C2211yescharacteristic
59#2285C2211yescharacteristic
60C42×Q8—21no—
61C42×Q8C2212yes—
62C42×D4—21no—
63C42×D4C2212yes—
64C4×#117—21no—
65C2×C43C2211yescharacteristic
66#1990C2211yescharacteristic
67#1990C2211yescharacteristic
68#1990C2211yescharacteristic
69#1990C2211yescharacteristic
70#1957C2211yescharacteristic
71#1957C2211yescharacteristic
72#1956C2211yescharacteristic
73#1956C2211yescharacteristic
74#1928C2214yes—
75#1927C2214yes—
76#1926C2214yes—
77#1925C2214yes—
78#1921C2214yes—
79#1921C2214yes—
80#1918C2214yes—
81#1918C2214yes—
82#1895C2214yes—
83#1894C2214yes—
84#1880C2214yes—
85#1880C2214yes—
86#1877C2214yes—
87#1877C2214yes—
88#1865C2214yes—
89#1864C2214yes—
90#1863C2214yes—
91#1862C2214yes—
92#1845C2211yescharacteristic
93#1844C2211yescharacteristic
94#1834C2211yescharacteristic
95#1834C2211yescharacteristic
96#1809C2214yes—
97#1776C2214yes—
98#1763C2214yes—
99#1762C2214yes—
100#1745C2212yes—
101#1745C2212yes—
102#1744C2211yescharacteristic
103#1744C2211yescharacteristic
104#1744C2211yescharacteristic
105#1744C2211yescharacteristic
106#1728C2212yes—
107#1728C2212yes—
108C22×#41—21no—
109C22×SD16C2314yes—
110C22×M16C2312yes—
111C22×M16C2312yes—
112#533—24no—
113#533C2×C418yescomplemented
114#532—24no—
115#532C2×C418yes—
116C2×C4⋊Q8C2311yescharacteristic
117C2×C4⋊Q8C2311yescharacteristic
118C2×C4⋊Q8C2311yescharacteristic
119C2×#127C2311yescharacteristic
120C2×#125—21no—
121C2×#124—21no—
122C2×C22⋊Q8—21no—
123C2×C22⋊Q8C2312yes—
124C2×#121—21no—
125C2×#121C2312yes—
126C4×#41—48no—
127C2×C4×Q8—21no—
128C2×C4×Q8—21no—
129C2×C4×Q8—21no—
130C2×C4×Q8—21no—
131C2×C4×Q8—21no—
132C2×C4×Q8C2312yes—
133C2×C4×Q8C2312yes—
134C2×C4×Q8C2312yes—
135C2×C4×D4—22no—
136C2×C4×D4—22no—
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×#117—21no—
146C2×#117—21no—
147C2×#117—21no—
148C2×#117—22no—
149C22×C42—22no—
150C22×C42D411yescharacteristic
151C22×C42D411yescharacteristic
152C22×C42D411yescharacteristic
153C22×C42D411yescharacteristic
154C22×C42C2311yescharacteristic
155C22×C42C2311yescharacteristic
156C22×C42C2311yescharacteristic
157#500C2×C418yescomplemented
158#492C2×C418yescomplemented
159#487C2×C418yescomplemented
160#486C2×C418yescomplemented
161#468C2×C4132yescomplemented
162#440C2×C4132yescomplemented
163C2×#107C2314yes—
164C2×#107C2314yes—
165C2×#106C2314yes—
166C2×#103C2314yes—
167C2×#103C2314yes—
168C2×#103C2314yes—
169C2×#102C2314yes—
170C2×#102C2314yes—
171C2×#102C2314yes—
172C4×M16—24no—
173C4×M16C2×C418yescomplemented
174C2×#97C2312yes—
175C2×#97C2312yes—
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2311yescharacteristic
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180#391—21no—
181#391—21no—
182#391—21no—
183#391—21no—
184#391C2312yes—
185#391C2312yes—
186#390—21no—
187#390—21no—
188#390—21no—
189#390—21no—
190#390C2312yes—
191#390C2312yes—
192#389—21no—
193#389—21no—
194#389—21no—
195#389—21no—
196#389—21no—
197#389—21no—
198#389—21no—
199#389—21no—
200#389C2312yes—
201#389C2312yes—
202#389C2312yes—
203#389C2312yes—
204#388—22no—
205#388—22no—
206#388—22no—
207#388—22no—
208#387—22no—
209#387—22no—
210#387—22no—
211#387—22no—
212#386—22no—
213#386—22no—
214#385—22no—
215#385—22no—
216#384C2311yescharacteristic
217#384C2311yescharacteristic
218#384C2311yescharacteristic
219#384C2311yescharacteristic
220#382—21no—
221#382—21no—
222#380—21no—
223#380—21no—
224#380C2312yes—
225#380C2312yes—
226C4×C4⋊C4—21no—
227C4×C4⋊C4—21no—
228C4×C4⋊C4—21no—
229C4×C4⋊C4—21no—
230C4×C4⋊C4—22no—
231C4×C4⋊C4—22no—
232C4×C4⋊C4—22no—
233C4×C4⋊C4—22no—
234C4×C4⋊C4—21no—
235C4×C4⋊C4—21no—
236C4×C4⋊C4—21no—
237C4×C4⋊C4—21no—
238C4×C4⋊C4—21no—
239C4×C4⋊C4—21no—
240C4×C4⋊C4—22no—
241C4×C4⋊C4—22no—
242C4×C4⋊C4C2312yes—
243C4×C4⋊C4C2312yes—
244C4×C4⋊C4C2312yes—
245C4×C4⋊C4C2312yes—
246C4×C4⋊C4C2312yes—
247C4×C4⋊C4C2312yes—
248C4×C22⋊C4—22no—
249C4×C22⋊C4—22no—
250C4×C22⋊C4—22no—
251C4×C22⋊C4—22no—
252C4×C22⋊C4—22no—
253C4×C22⋊C4—22no—
254C4×C22⋊C4—22no—
255C4×C22⋊C4—22no—
256#376—22no—
257C43—22no—
258C43D411yescharacteristic
259C43D411yescharacteristic
260C43D411yescharacteristic
261C43D411yescharacteristic
262C43C2311yescharacteristic
263C43C2311yescharacteristic
264C43C2311yescharacteristic
265C43C2311yescharacteristic
266#340C2314yes—
267#340C2314yes—
268#340C2314yes—
269#340C2314yes—
270#340C2314yes—
271#340C2314yes—
272#336C2312yes—
273#336C2312yes—
274#336C2312yes—
275#336C2312yes—
276#336C2312yes—
277#336C2312yes—
278#336C2312yes—
279#336C2312yes—
280C2×#41—28no—
281C2×#41—44no—
282C2×#41—44no—
283C22×Q8—21no—
284C22×Q8—21no—
285C22×Q8C2412yes—
286C22×D4—22no—
287C22×D4—21no—
288C22×D4—21no—
289C22×D4C2412yes—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4C2×D411yescharacteristic
294C23×C4C2×D411yescharacteristic
295C23×C4C2×D411yescharacteristic
296C23×C4C2×D411yescharacteristic
297C23×C4C2×D411yescharacteristic
298C23×C4C2×D411yescharacteristic
299C23×C4C2411yescharacteristic
300C2×SD16—44no—
301C2×SD16—44no—
302C2×SD16C22×C4116yes—
303C2×M16—24no—
304C2×M16—42no—
305C2×M16—42no—
306C2×M16—42no—
307C2×M16—42no—
308C2×M16C22×C418yes—
309C22×C8C2412yes—
310C22×C8C2412yes—
311C22×C8C2412yes—
312C22×C8C2412yes—
313C4⋊Q8—22no—
314C4⋊Q8—22no—
315C4⋊Q8—22no—
316C4⋊Q8C22×C414yes—
317C4⋊Q8C22×C414yes—
318C4⋊Q8C22×C414yes—
319#127—22no—
320#127C22×C414yes—
321#125—28no—
322#124—28no—
323C22⋊Q8—28no—
324C22⋊Q8—24no—
325C22⋊Q8C22×C418yes—
326#121—28no—
327#121—24no—
328#121C22×C418yes—
329C4×Q8—28no—
330C4×Q8—24no—
331C4×Q8—44no—
332C4×Q8—44no—
333C4×Q8—44no—
334C4×Q8—44no—
335C4×Q8—44no—
336C4×Q8—44no—
337C4×Q8C22×C418yes—
338C4×D4—28no—
339C4×D4—24no—
340C4×D4—44no—
341C4×D4—44no—
342C4×D4—44no—
343C4×D4—44no—
344C4×D4—48no—
345C4×D4—48no—
346C4×D4—44no—
347C4×D4—44no—
348C4×D4C22×C418yes—
349#117—28no—
350#117—48no—
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—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4C2412yes—
374C2×C4⋊C4C2412yes—
375C2×C4⋊C4C2412yes—
376C2×C4⋊C4C2412yes—
377C2×C4⋊C4C2412yes—
378C2×C4⋊C4C2412yes—
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×C22⋊C4—22no—
390C2×C42—22no—
391C2×C42—24no—
392C2×C42—24no—
393C2×C42—22no—
394C2×C42—22no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42—22no—
399C2×C42—22no—
400C2×C42—22no—
401C2×C42—42no—
402C2×C42—42no—
403C2×C42—42no—
404C2×C42—42no—
405C2×C42—48no—
406C2×C42C22×C414yes—
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×C42C2×D411yescharacteristic
425C2×C42C2×D411yescharacteristic
426C2×C42C2×D411yescharacteristic
427C2×C42C2×D411yescharacteristic
428C2×C42C2×D411yescharacteristic
429C2×C42#4114yes—
430C2×C42C2411yescharacteristic
431C2×C42C2411yescharacteristic
432C2×C42C2411yescharacteristic
433C2×C42C2411yescharacteristic
434C2×C42C2411yescharacteristic
435C2×C42C2411yescharacteristic
436#107—44no—
437#107C22×C4116yes—
438#106—44no—
439#103—44no—
440#103—44no—
441#103C22×C4116yes—
442#102—44no—
443#102—44no—
444#102C22×C4116yes—
445#97—24no—
446#97C22×C418yes—
447C4×C8—22no—
448C4×C8—22no—
449C4×C8C22×C414yes—
450C4×C8C22×C414yes—
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#95—22no—
467C24—22no—
468C24C22×D411yescharacteristic
469#41—432no—
470C2×Q8—24no—
471C2×Q8—24no—
472C2×Q8—22no—
473C2×Q8—24no—
474C2×Q8—24no—
475C2×Q8—42no—
476C2×Q8—42no—
477C2×Q8—42no—
478C2×Q8—42no—
479C2×Q8C23×C414yes—
480C2×D4—28no—
481C2×D4—24no—
482C2×D4—24no—
483C2×D4—22no—
484C2×D4—24no—
485C2×D4—24no—
486C2×D4—44no—
487C2×D4—44no—
488C2×D4—42no—
489C2×D4—42no—
490C2×D4—42no—
491C2×D4—42no—
492C2×D4C23×C414yes—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—28no—
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—41no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4—41no—
516C22×C4—41no—
517C22×C4—41no—
518C22×C4—41no—
519C22×C4—44no—
520C22×C4—44no—
521C22×C4—44no—
522C22×C4—44no—
523C22×C4—44no—
524C22×C4—44no—
525C22×C4—44no—
526C22×C4—44no—
527C22×C4C4×D414yes—
528C22×C4C4×D414yes—
529C22×C4C23×C412yes—
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×C4C22×D411yescharacteristic
543C22×C4C2×#4112yes—
544C22×C4C2511yescharacteristic
545SD16—416no—
546M16—48no—
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×C8C23×C414yes—
559C2×C8C23×C414yes—
560C4⋊C4—24no—
561C4⋊C4—24no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—28no—
565C4⋊C4—28no—
566C4⋊C4—22no—
567C4⋊C4—22no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—24no—
571C4⋊C4—24no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—44no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4C23×C414yes—
587C4⋊C4C23×C414yes—
588C22⋊C4—28no—
589C22⋊C4—28no—
590C22⋊C4—28no—
591C22⋊C4—44no—
592C22⋊C4—44no—
593C22⋊C4—44no—
594C22⋊C4—44no—
595C22⋊C4—44no—
596C22⋊C4—44no—
597C22⋊C4—44no—
598C22⋊C4—44no—
599C42—28no—
600C42—22no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—22no—
605C42—22no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—22no—
612C42—22no—
613C42—22no—
614C42—41no—
615C42—41no—
616C42—41no—
617C42—41no—
618C42—41no—
619C42—41no—
620C42—41no—
621C42—41no—
622C42—44no—
623C42—44no—
624C42—44no—
625C42—44no—
626C42—44no—
627C42—44no—
628C42—44no—
629C42—44no—
630C42C4×D414yes—
631C42C4×D414yes—
632C42AGL(1,ℤ/8)14yes—
633C42#13714yes—
634C42C23×C412yes—
635C42C23×C412yes—
636C42C2×#4112yes—
637C42C2×#4112yes—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23C2×C4×D412yes—
652C23C23×D411yescharacteristic
653Q8—28no—
654Q8—44no—
655Q8—48no—
656Q8—48no—
657D4—28no—
658D4—416no—
659D4—44no—
660D4—48no—
661D4—48no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—28no—
679C2×C4—28no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—21no—
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—44no—
696C2×C4—44no—
697C2×C4—44no—
698C2×C4—416no—
699C2×C4—44no—
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—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—88no—
719C2×C4—88no—
720C2×C4C2×C4×D412yes—
721C2×C4C2×C4×D412yes—
722C2×C4C2×C4×D412yes—
723C2×C4C2×C4×D412yes—
724C2×C4C2×C4×D412yes—
725C2×C4C2×AGL(1,ℤ/8)12yes—
726C2×C4C2×AGL(1,ℤ/8)12yes—
727C2×C4C2×AGL(1,ℤ/8)12yes—
728C2×C4C2×#13712yes—
729C2×C4C2×#13712yes—
730C2×C4C2×#13712yes—
731C2×C4#57512yes—
732C2×C4#57512yes—
733C2×C4C24×C411yescharacteristic
734C2×C4C22×#4111yescharacteristic
735C2×C4#58512yes—
736C2×C4#58512yes—
737C8—24no—
738C8—24no—
739C8—42no—
740C8—42no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—44no—
749C22—44no—
750C22—44no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22C22×C4×D411yescharacteristic
756C22#344911yescharacteristic
757C22#344911yescharacteristic
758C22C22×AGL(1,ℤ/8)11yescharacteristic
759C22C22×#13711yescharacteristic
760C22C2×#57511yescharacteristic
761C22C2×#57511yescharacteristic
762C4—22no—
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—22no—
769C4—44no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—44no—
775C4—44no—
776C4—82no—
777C4—82no—
778C4—82no—
779C4—82no—
780C4C4×AGL(1,ℤ/8)14yes—
781C4C4×#13714yes—
782C4#342812yes—
783C4#345512yes—
784C2—42no—
785C2—84no—
786C2#3407011yescharacteristic
787C2C2×C4×AGL(1,ℤ/8)11yescharacteristic
788C2C2×C4×#13711yescharacteristic
789C2#6096511yescharacteristic
790C2#6096611yescharacteristic
791C2#6096911yescharacteristic
792C2#6097211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutatorC2×C4C24×C4
Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C2×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
2. C4×#533C2semidirect
4. #22268C2semidirect
5. #22268C2semidirect
6. #22248C2semidirect
7. #22247C2semidirect
8. #22221C2semidirect
9. #22220C2semidirect
10. #22219C2semidirect
11. #22218C2semidirect
12. #22191C2semidirect
13. #22186C2semidirect
15. #21409C2semidirect
16. #21124C2semidirect
17. #21121C2semidirect
18. #20824C2semidirect
19. #20364C2semidirect
23. #3182C4semidirect
113. #533C2×C4semidirect
157. #500C2×C4semidirect
158. #492C2×C4semidirect
159. #487C2×C4semidirect
160. #486C2×C4semidirect
161. #468C2×C4semidirect
162. #440C2×C4semidirect
173. C4×M16C2×C4semidirect

Maximal subgroups

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

subgroupindex
C2×#31822
C4×#5332
C4×#5322
#222682
#222482
#222472
#222212
#222202
#222192
#222182
#221912
#221862
#214102
#214092
#211242
#211212
#208242
#203642