Finite Group Databasebeta

← #6625737

Subgroups — #6625737

Order 512.

1865 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3384C211yesmaximal, characteristic
2C2×Q8×SD16C211yesmaximal, characteristic, complemented
3#39617C211yesmaximal, characteristic, complemented
4#34334C211yesmaximal, characteristic, complemented
5#33205C212yesmaximal, complemented
6#33197C211yesmaximal, characteristic, complemented
7#28696C212yesmaximal, complemented
8#28687C211yesmaximal, characteristic, complemented
9#28289C212yesmaximal, complemented
10#28281C211yesmaximal, characteristic, complemented
11#25464C212yesmaximal, complemented
12#25453C211yesmaximal, characteristic, complemented
13#25452C211yesmaximal, characteristic, complemented
14#25451C212yesmaximal, complemented
15#24829C212yesmaximal
16#24822C212yesmaximal, complemented
17#24815C211yesmaximal, characteristic, complemented
18#24812C211yesmaximal, characteristic
19#22721C211yesmaximal, characteristic, complemented
20#22525C211yesmaximal, characteristic, complemented
21#22519C211yesmaximal, characteristic, complemented
22#21510C212yesmaximal
23C4×#463C211yesmaximal, characteristic
24C2×Q82C2211yescharacteristic
25C2×#554C2211yescharacteristic
26C2×D4×Q8C2211yescharacteristic
27#3384—28no—
28Q8×SD16—28no—
29C2×#501C2212yes—
30C2×#498C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#498C2212yes—
33C2×#475C2211yescharacteristic
34C2×#475C2212yes—
35C2×#478C2212yes—
36C2×#476C2212yes—
37C2×#476C2211yescharacteristic
38C2×#476C2212yes—
39C2×#476C2211yescharacteristic
40C2×#474C2211yescharacteristic
41C2×#463C2211yescharacteristic
42C2×#446C2211yescharacteristic
43C2×C8×Q8C2211yescharacteristic
44C2×#442C2212yes—
45C2×C4×SD16C2212yes—
46C2×C4×SD16C2211yescharacteristic
47C2×C4×D8C2211yescharacteristic
48#2868C2211yescharacteristic
49#2677—22no—
50#2677—22no—
51#2660C2212yes—
52#2567C2211yescharacteristic
53#2565C2212yes—
54#2563C2211yescharacteristic
55#2542C2212yes—
56#2440—21no—
57#2440—21no—
58#2423—21no—
59#2423—21no—
60#2369C2212yes—
61#2368—22no—
62#2365C2211yescharacteristic
63#2360—21no—
64#2355C2211yescharacteristic
65#2349C2212yes—
66D4×C4⋊C4C2211yescharacteristic
67Q8×C22⋊C4—21no—
68#2331C2212yes—
69#2329—22no—
70#2326C2212yes—
71C4×C4⋊Q8C2211yescharacteristic
72C4×#124C2211yescharacteristic
73C4×C22⋊Q8—21no—
74#2295C2211yescharacteristic
75C2×#391—21no—
76#2275C2212yes—
77C42×D4C2211yescharacteristic
78#2085C2212yes—
79#2085C2212yes—
80#2084C2212yes—
81#2084C2212yes—
82#2084C2212yes—
83#2084C2212yes—
84#2068C2212yes—
85#2066C2212yes—
86#2066C2212yes—
87#2065C2212yes—
88#2065C2212yes—
89#2065C2212yes—
90#1993C2212yes—
91#1991C2212yes—
92#1990C2211yescharacteristic
93#1990C2211yescharacteristic
94#1989C2212yes—
95#1988C2212yes—
96#1987C2211yescharacteristic
97#1987C2211yescharacteristic
98#1983C2212yes—
99#1983C2211yescharacteristic
100#1949C2211yescharacteristic
101#1949C2212yes—
102#1949C2212yes—
103#1948C2212yes—
104#1948C2212yes—
105#1948C2212yes—
106#1948C2212yes—
107#1948C2212yes—
108#1940C2212yes—
109#1939C2212yes—
110#1939C2211yescharacteristic
111#1939C2211yescharacteristic
112#1928C2211yescharacteristic
113#1927C2212yes—
114#1926C2212yes—
115#1926C2211yescharacteristic
116#1879C2212yes—
117#1879C2211yescharacteristic
118#1877C2212yes—
119#1877C2211yescharacteristic
120#1843C2212yes—
121#1842C2211yescharacteristic
122#1805C2212yes—
123#1804C2212yes—
124#1804C2211yescharacteristic
125#1804C2212yes—
126#1803C2211yescharacteristic
127#1802C2212yes—
128#1802C2211yescharacteristic
129#1802C2212yes—
130#1802C2212yes—
131#1768C2212yes—
132C4×C4⋊C8C2211yescharacteristic
133#1763C2212yes—
134C4×#103C2211yescharacteristic
135C4×#102C2212yes—
136C4×#102C2211yescharacteristic
137C23×Q8—21no—
138C22×SD16C2311yescharacteristic
139C22×D8C2311yescharacteristic
140Q82—24no—
141Q82—24no—
142#554—24no—
143#554—24no—
144D4×Q8—24no—
145D4×Q8D418yes—
146C2×C4⋊Q8—22no—
147C2×C4⋊Q8—21no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8—21no—
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2312yes—
153C2×C4⋊Q8C2311yescharacteristic
154C2×C4⋊Q8C2312yes—
155C2×#125C2312yes—
156C2×#124C2311yescharacteristic
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8—22no—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8—22no—
161C2×C22⋊Q8—22no—
162C2×C22⋊Q8—22no—
163C2×C4×Q8—21no—
164C2×C4×Q8—21no—
165C2×C4×Q8—21no—
166C2×C4×Q8C2312yes—
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2311yescharacteristic
169C2×C4×D4C2311yescharacteristic
170C2×C4×D4C2312yes—
171C2×C4×D4C2311yescharacteristic
172C2×C4×D4C2312yes—
173C2×C4×D4C2312yes—
174C2×C4×D4C2311yescharacteristic
175C2×C4×D4C2311yescharacteristic
176C22×C4⋊C4—21no—
177C22×C4⋊C4—21no—
178C22×C42—21no—
179#501—28no—
180#498—24no—
181#498—28no—
182#498—24no—
183#478—28no—
184#476—28no—
185#476—24no—
186#476—28no—
187#476—24no—
188#475—24no—
189#475—28no—
190#474—24no—
191#463Q818yescomplemented
192#446—24no—
193C8×Q8—24no—
194#442—28no—
195C4×SD16—24no—
196C4×SD16—28no—
197C4×D8—24no—
198C2×#107C2312yes—
199C2×#107C2311yescharacteristic
200C2×#106C2312yes—
201C2×#106C2312yes—
202C2×#106C2312yes—
203C2×#106C2312yes—
204C2×#106C2312yes—
205C2×#106C2311yescharacteristic
206C2×#106C2312yes—
207C2×#106C2312yes—
208C2×C4⋊C8C2312yes—
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2312yes—
211C2×C4⋊C8C2312yes—
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2311yescharacteristic
214C2×C4⋊C8C2312yes—
215C2×C4⋊C8C2312yes—
216C2×C4⋊C8C2312yes—
217C2×C4⋊C8C2311yescharacteristic
218C2×#103C2311yescharacteristic
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2311yescharacteristic
222C2×#103C2311yescharacteristic
223C2×#102C2311yescharacteristic
224C2×#102C2312yes—
225C2×#102C2312yes—
226C2×#102C2311yescharacteristic
227C2×#102C2311yescharacteristic
228C2×#102C2312yes—
229C2×#102C2312yes—
230C2×#102C2311yescharacteristic
231C2×#102C2311yescharacteristic
232C2×#97C2312yes—
233C2×C4×C8C2311yescharacteristic
234C2×C4×C8C2311yescharacteristic
235C2×C4×C8C2312yes—
236#399—22no—
237#399—22no—
238#398—22no—
239#398—22no—
240#398—22no—
241#398—22no—
242#395—22no—
243#395—22no—
244#395—22no—
245#393—22no—
246#391—21no—
247#391—21no—
248#391—21no—
249#391—22no—
250#391—22no—
251#391—22no—
252#391—22no—
253#391D411yescharacteristic
254#391D411yescharacteristic
255#391C2311yescharacteristic
256#391C2312yes—
257#390C2312yes—
258#390C2311yescharacteristic
259#389—21no—
260#389—21no—
261#389—22no—
262#389—21no—
263#389D411yescharacteristic
264#389D411yescharacteristic
265#389C2312yes—
266#389C2312yes—
267#389C2312yes—
268#388—21no—
269#388—21no—
270#388—22no—
271#388—22no—
272#387—22no—
273#387—22no—
274#387—22no—
275#387—22no—
276#387—22no—
277#387—22no—
278#387D412yes—
279#387D412yes—
280#385—22no—
281#385—22no—
282#385—22no—
283#385—22no—
284#385—22no—
285#384—21no—
286#384—21no—
287#384C2311yescharacteristic
288#384C2312yes—
289#384C2312yes—
290#384C2312yes—
291#382C2312yes—
292#382C2312yes—
293#382C2311yescharacteristic
294#380—21no—
295#380—21no—
296#380—21no—
297#380—22no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—22no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4C2312yes—
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2312yes—
305C4×C4⋊C4C2312yes—
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2312yes—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—22no—
315C4×C22⋊C4—22no—
316C4×C22⋊C4—22no—
317#376C2312yes—
318C2×#95—22no—
319C2×#95—22no—
320C43C2311yescharacteristic
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2311yescharacteristic
330#340C2311yescharacteristic
331#340C2312yes—
332#340C2311yescharacteristic
333#340C2312yes—
334#340C2311yescharacteristic
335#336C2311yescharacteristic
336#336C2311yescharacteristic
337#336C2312yes—
338#336C2312yes—
339C22×Q8—28no—
340C22×Q8—21no—
341C22×Q8—22no—
342C22×Q8—22no—
343C22×Q8—21no—
344C22×Q8—21no—
345C22×Q8—82no—
346C22×Q8—82no—
347C22×Q8C2×D411yescharacteristic
348C22×Q8C2411yescharacteristic
349C22×D4C2411yescharacteristic
350C22×D4C2411yescharacteristic
351C23×C4—21no—
352C23×C4—22no—
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—22no—
357C23×C4—22no—
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16C2×Q814yes—
361C2×D8—22no—
362C2×D8—22no—
363C2×D8C2×Q814yes—
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2412yes—
367C22×C8C2412yes—
368C22×C8C2411yescharacteristic
369C22×C8C2411yescharacteristic
370C4⋊Q8—22no—
371C4⋊Q8—22no—
372C4⋊Q8—24no—
373C4⋊Q8—24no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—24no—
377C4⋊Q8—22no—
378C4⋊Q8—44no—
379C4⋊Q8—48no—
380C4⋊Q8—82no—
381C4⋊Q8—82no—
382C4⋊Q8C2×D414yes—
383C4⋊Q8C2×D418yes—
384#125—24no—
385#125—24no—
386#124—22no—
387#124C2×Q814yescomplemented
388C22⋊Q8—28no—
389C22⋊Q8—216no—
390C22⋊Q8—44no—
391C22⋊Q8—48no—
392C22⋊Q8—84no—
393C22⋊Q8—84no—
394C4×Q8—22no—
395C4×Q8—24no—
396C4×Q8—24no—
397C4×Q8—22no—
398C4×Q8—44no—
399C4×Q8—82no—
400C4×Q8—82no—
401C4×Q8C2×D414yes—
402C4×Q8#4114yes—
403C4×D4—22no—
404C4×D4—24no—
405C4×D4—22no—
406C4×D4—24no—
407C4×D4—24no—
408C4×D4—22no—
409C4×D4—24no—
410C4×D4—22no—
411C4×D4—22no—
412C4×D4—41no—
413C4×D4—42no—
414C4×D4C2×D414yes—
415C4×D4C2×D418yes—
416C4×D4C2×Q814yes—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—22no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4—82no—
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D412yes—
442C2×C4⋊C4C2×D412yes—
443C2×C4⋊C4C2×D411yescharacteristic
444C2×C4⋊C4C2×D412yes—
445C2×C4⋊C4C2411yescharacteristic
446C2×C4⋊C4C2412yes—
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—22no—
466C2×C22⋊C4—22no—
467C2×C42—21no—
468C2×C42—22no—
469C2×C42—21no—
470C2×C42—22no—
471C2×C42—22no—
472C2×C42—22no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—82no—
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2412yes—
482C2×C42C2412yes—
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485#107—22no—
486#107—24no—
487#106—22no—
488#106—24no—
489#106—24no—
490#106—24no—
491#106—24no—
492#106—24no—
493#106—24no—
494#106—24no—
495C4⋊C8—22no—
496C4⋊C8—24no—
497C4⋊C8—22no—
498C4⋊C8—24no—
499C4⋊C8—24no—
500C4⋊C8—22no—
501C4⋊C8—42no—
502C4⋊C8—42no—
503C4⋊C8—42no—
504C4⋊C8C2×Q814yescomplemented
505#103—22no—
506#103—24no—
507#103—42no—
508#103—41no—
509#103C2×Q814yescomplemented
510#102—22no—
511#102—24no—
512#102—22no—
513#102—24no—
514#102—22no—
515#102—24no—
516#102—42no—
517#102—41no—
518#102C2×Q814yescomplemented
519#97—24no—
520C4×C8—22no—
521C4×C8—22no—
522C4×C8—24no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—21no—
530#95—21no—
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95C2×D412yes—
543#95C2×D412yes—
544#95C2×D412yes—
545#95C2×D412yes—
546#95C2×D412yes—
547#95C2×D412yes—
548#95C2×D412yes—
549C24—21no—
550C24—21no—
551C2×Q8—24no—
552C2×Q8—28no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—42no—
561C2×Q8—42no—
562C2×Q8—44no—
563C2×Q8—42no—
564C2×Q8—42no—
565C2×Q8—82no—
566C2×Q8—82no—
567C2×Q8—82no—
568C2×Q8—82no—
569C2×Q8—81no—
570C2×Q8—81no—
571C2×Q8—81no—
572C2×Q8—81no—
573C2×Q8—816no—
574C2×Q8#12114yes—
575C2×Q8C22×Q812yes—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4C22×D412yes—
585C2×D4C22×Q812yes—
586C2×D4C22×Q812yes—
587C2×D42−1+412yes—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—28no—
594C22×C4—24no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—42no—
602C22×C4—44no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—44no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—82no—
618C22×C4—82no—
619C22×C4C22×D412yes—
620C22×C4C22×D412yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D412yes—
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C2511yescharacteristic
630SD16—28no—
631D8—28no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—22no—
648C2×C8C22×Q812yes—
649C2×C8C22×Q812yes—
650C4⋊C4—24no—
651C4⋊C4—28no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—42no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—42no—
678C4⋊C4—44no—
679C4⋊C4—42no—
680C4⋊C4—44no—
681C4⋊C4—81no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4—82no—
686C4⋊C4—82no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4#12114yes—
690C4⋊C4#12118yes—
691C4⋊C4C22×D412yes—
692C4⋊C4C22×D414yes—
693C4⋊C4C22×Q812yes—
694C22⋊C4—24no—
695C22⋊C4—28no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—42no—
700C22⋊C4—44no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—44no—
704C22⋊C4—42no—
705C22⋊C4—82no—
706C22⋊C4—82no—
707C42—22no—
708C42—22no—
709C42—22no—
710C42—21no—
711C42—22no—
712C42—21no—
713C42—22no—
714C42—41no—
715C42—44no—
716C42—42no—
717C42—42no—
718C42—82no—
719C42—81no—
720C42—81no—
721C42—82no—
722C42—82no—
723C42C22×D412yes—
724C42C22×D414yes—
725C42C22×Q812yes—
726C42C2×#4114yes—
727C42C2×#4112yes—
728C422−1+412yes—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23C23×D411yescharacteristic
744Q8—28no—
745Q8—22no—
746Q8—22no—
747Q8—41no—
748Q8—41no—
749Q8—48no—
750Q8—88no—
751Q8—164no—
752Q8—162no—
753Q8—162no—
754D4—22no—
755D4—22no—
756D4—22no—
757D4—22no—
758D4—22no—
759D4—41no—
760D4—41no—
761D4D4×Q814yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—48no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—88no—
816C2×C4—84no—
817C2×C4—84no—
818C2×C4—164no—
819C2×C4—164no—
820C2×C4C2×#12114yes—
821C2×C4C2×#12112yes—
822C2×C4C2×#12114yes—
823C2×C4C2×#12112yes—
824C2×C4D4×Q812yes—
825C2×C4D4×Q812yes—
826C2×C4#57712yes—
827C2×C4#57712yes—
828C2×C4#57712yes—
829C2×C4C23×D411yescharacteristic
830C2×C4C23×Q811yescharacteristic
831C2×C4C22×#4111yescharacteristic
832C2×C4C2×2−1+411yescharacteristic
833C2×C4C2×2−1+411yescharacteristic
834C2×C4#58511yescharacteristic
835C8—22no—
836C8—22no—
837C8—41no—
838C8—41no—
839C8—42no—
840C8—42no—
841C22—24no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22C22×#12111yescharacteristic
856C22C2×D4×Q811yescharacteristic
857C22#348911yescharacteristic
858C22C2×#57711yescharacteristic
859C22C2×#57711yescharacteristic
860C22C2×#57711yescharacteristic
861C22#358511yescharacteristic
862C4—24no—
863C4—24no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—42no—
869C4—44no—
870C4—42no—
871C4—42no—
872C4—41no—
873C4—42no—
874C4—42no—
875C4—81no—
876C4—82no—
877C4—81no—
878C4—82no—
879C4—82no—
880C4—81no—
881C4#304214yes—
882C4C2×D4×Q811yescharacteristic
883C4Q8×#4111yescharacteristic
884C4#349711yescharacteristic
885C4#352311yescharacteristic
886C2—44no—
887C2—82no—
888C2Q8×#12111yescharacteristic
889C2C2×#304211yescharacteristic
890C2#6043111yescharacteristic
891C2#6137411yescharacteristic
892C2#6138211yescharacteristic
893C2#6217911yescharacteristic
894C2#6220211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D8C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×Q8×SD16C2semidirect
3. #39617C2semidirect
4. #34334C2semidirect
5. #33205C2semidirect
6. #33197C2semidirect
7. #28696C2semidirect
8. #28687C2semidirect
9. #28289C2semidirect
10. #28281C2semidirect
11. #25464C2semidirect
12. #25453C2semidirect
13. #25452C2semidirect
14. #25451C2semidirect
16. #24822C2semidirect
17. #24815C2semidirect
19. #22721C2semidirect
20. #22525C2semidirect
21. #22519C2semidirect
191. #463Q8semidirect
387. #124C2×Q8semidirect
504. C4⋊C8C2×Q8semidirect
509. #103C2×Q8semidirect
518. #102C2×Q8semidirect

Maximal subgroups

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

subgroupindex
C2×#33842
C2×Q8×SD162
#396172
#343342
#332052
#331972
#286962
#286872
#282892
#282812
#254642
#254532
#254522
#254512
#248292
#248222
#248152
#248122
#227212
#225252
#225192
#215102
C4×#4632