Finite Group Databasebeta

← #6537005

Subgroups — #6537005

Order 512.

1906 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3386C211yesmaximal, characteristic, complemented
2C2×#2983C211yesmaximal, characteristic, complemented
3#36545C211yesmaximal, characteristic, complemented
4Q8×#121C211yesmaximal, characteristic
5#29883C212yesmaximal, complemented
6#29876C211yesmaximal, characteristic, complemented
7#28685C212yesmaximal, complemented
8#28683C211yesmaximal, characteristic, complemented
9#28199C212yesmaximal, complemented
10#28195C211yesmaximal, characteristic, complemented
11#25486C212yesmaximal, complemented
12#25483C212yesmaximal, complemented
13#25479C211yesmaximal, characteristic, complemented
14#25478C211yesmaximal, characteristic, complemented
15#24711C212yesmaximal, complemented
16#24706C212yesmaximal
17#24703C211yesmaximal, characteristic, complemented
18#24700C211yesmaximal, characteristic
19#23710C212yesmaximal
20#23700C211yesmaximal, characteristic
21#22742C211yesmaximal, characteristic, complemented
22#22524C211yesmaximal, characteristic, complemented
23#22523C211yesmaximal, characteristic, complemented
24C2×#557C2211yescharacteristic
25C2×D4×Q8—21no—
26C2×D4×Q8C2211yescharacteristic
27C22×C4×Q8C2211yescharacteristic
28#3386—28no—
29C2×#501C2212yes—
30C2×#500C2211yescharacteristic
31C2×#477C2212yes—
32C2×#475C2211yescharacteristic
33C2×#478C2212yes—
34C2×#474C2211yescharacteristic
35#2983—28no—
36C2×#446C2211yescharacteristic
37C2×#446C2212yes—
38C2×#446C2211yescharacteristic
39C2×#446C2212yes—
40C2×#446C2211yescharacteristic
41C2×#446C2211yescharacteristic
42C2×#440C2212yes—
43C2×C4×SD16C2211yescharacteristic
44C2×#432C2212yes—
45C2×#432C2212yes—
46C2×#431C2211yescharacteristic
47C2×#431C2211yescharacteristic
48#2857C2211yescharacteristic
49#2857C2211yescharacteristic
50#2857C2212yes—
51#2851C2212yes—
52#2584C2212yes—
53#2582C2211yescharacteristic
54#2581C2212yes—
55#2546C2211yescharacteristic
56#2546C2211yescharacteristic
57#2546C2212yes—
58#2538C2211yescharacteristic
59#2538C2212yes—
60#2473—22no—
61#2462—22no—
62#2446—21no—
63#2434—21no—
64#2429—21no—
65#2429—22no—
66#2417—21no—
67#2417—22no—
68#2365—21no—
69#2360—21no—
70#2355C2211yescharacteristic
71Q8×C4⋊C4C2211yescharacteristic
72Q8×C22⋊C4—21no—
73C4×C22⋊Q8C2211yescharacteristic
74C4×C22⋊Q8C2212yes—
75C4×#121C2211yescharacteristic
76C4×#121C2212yes—
77#2088C2211yescharacteristic
78#2088C2212yes—
79#2088C2212yes—
80#2087C2212yes—
81#2087C2212yes—
82#2087C2212yes—
83#2086C2212yes—
84#2086C2212yes—
85#2077C2212yes—
86#2077C2211yescharacteristic
87#2075C2212yes—
88#2075C2212yes—
89#2075C2212yes—
90#2068C2212yes—
91#2066C2211yescharacteristic
92#2065C2212yes—
93#2065C2211yescharacteristic
94#2055C2212yes—
95#2055C2211yescharacteristic
96#2035C2212yes—
97#2035C2211yescharacteristic
98#2034C2211yescharacteristic
99#2033C2212yes—
100#2000C2211yescharacteristic
101#1993C2212yes—
102#1992C2212yes—
103#1990C2211yescharacteristic
104#1990C2211yescharacteristic
105#1989C2212yes—
106#1988C2211yescharacteristic
107#1988C2211yescharacteristic
108#1987C2212yes—
109#1949C2212yes—
110#1948C2211yescharacteristic
111#1948C2212yes—
112#1947C2211yescharacteristic
113#1944C2212yes—
114#1944C2212yes—
115#1944C2212yes—
116#1943C2212yes—
117#1942C2212yes—
118#1941C2212yes—
119#1936C2212yes—
120#1936C2212yes—
121#1935C2212yes—
122#1935C2212yes—
123#1934C2212yes—
124#1933C2212yes—
125#1836C2212yes—
126#1834C2211yescharacteristic
127#1804C2212yes—
128#1803C2211yescharacteristic
129#1803C2212yes—
130#1802C2211yescharacteristic
131#1776C2212yes—
132C4×#106C2211yescharacteristic
133#1763C2212yes—
134#1762C2212yes—
135C4×#103C2211yescharacteristic
136C4×#102C2211yescharacteristic
137C23×Q8—21no—
138C23×Q8D411yescharacteristic
139C22×SD16C2311yescharacteristic
140#557—24no—
141#557—24no—
142D4×Q8—24no—
143D4×Q8—24no—
144D4×Q8—48no—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—22no—
148C2×C4⋊Q8—21no—
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2312yes—
151C2×C4⋊Q8C2311yescharacteristic
152C2×#125—22no—
153C2×#125C2312yes—
154C2×C22⋊Q8—21no—
155C2×C22⋊Q8—22no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8—21no—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8—22no—
161C2×C22⋊Q8C2311yescharacteristic
162C2×#121C2311yescharacteristic
163C2×C4×Q8—24no—
164C2×C4×Q8—24no—
165C2×C4×Q8—21no—
166C2×C4×Q8—21no—
167C2×C4×Q8D411yescharacteristic
168C2×C4×Q8D411yescharacteristic
169C2×C4×Q8D412yes—
170C2×C4×Q8C2311yescharacteristic
171C2×C4×Q8C2312yes—
172C2×C4×Q8C2312yes—
173C2×C4×Q8C2311yescharacteristic
174C2×C4×Q8C2311yescharacteristic
175C2×C4×D4—22no—
176C2×C4×D4—21no—
177C2×C4×D4C2312yes—
178C2×C4×D4C2311yescharacteristic
179C22×C4⋊C4D411yescharacteristic
180C22×C4⋊C4D412yes—
181C22×C42C2312yes—
182C22×C42C2311yescharacteristic
183#501—28no—
184#500—24no—
185#478—28no—
186#477—28no—
187#475—24no—
188#474—24no—
189#446—24no—
190#446—28no—
191#446—24no—
192#446—28no—
193#446—24no—
194#446D418yescomplemented
195#440—28no—
196C4×SD16—24no—
197#432—28no—
198#432—28no—
199#431—24no—
200#431—24no—
201C2×#107C2312yes—
202C2×#107C2312yes—
203C2×#107C2312yes—
204C2×#107C2312yes—
205C2×#106C2312yes—
206C2×#106C2312yes—
207C2×#106C2311yescharacteristic
208C2×#106C2311yescharacteristic
209C2×#106C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2312yes—
212C2×C4⋊C8C2311yescharacteristic
213C2×C4⋊C8C2312yes—
214C2×C4⋊C8C2311yescharacteristic
215C2×C4⋊C8C2312yes—
216C2×C4⋊C8C2312yes—
217C2×C4⋊C8C2311yescharacteristic
218C2×#103C2312yes—
219C2×#103C2311yescharacteristic
220C2×#103C2312yes—
221C2×#103C2311yescharacteristic
222C2×#103C2311yescharacteristic
223C2×#102C2311yescharacteristic
224C2×#102C2312yes—
225C2×#102C2312yes—
226C2×#102C2311yescharacteristic
227C2×#102C2311yescharacteristic
228C2×C22⋊C8C2311yescharacteristic
229C2×C22⋊C8C2311yescharacteristic
230C2×C22⋊C8C2312yes—
231C2×#97C2312yes—
232C2×#97C2312yes—
233C2×#97C2312yes—
234C2×#97C2312yes—
235C2×C4×C8C2312yes—
236C2×C4×C8C2311yescharacteristic
237C2×C4×C8C2311yescharacteristic
238#400—22no—
239#398—22no—
240#398—22no—
241#398—22no—
242#398—22no—
243#398—22no—
244#398—22no—
245#396—22no—
246#396—22no—
247#396—22no—
248#395—22no—
249#395—22no—
250#391—21no—
251#391—21no—
252#391—21no—
253#391—22no—
254#391—21no—
255#391—21no—
256#391—22no—
257#391—21no—
258#391C2311yescharacteristic
259#391C2312yes—
260#390C2311yescharacteristic
261#390C2312yes—
262#389—21no—
263#389—22no—
264#389—22no—
265#389—21no—
266#389—22no—
267#389—22no—
268#389—21no—
269#389—21no—
270#389C2311yescharacteristic
271#389C2312yes—
272#389C2311yescharacteristic
273#389C2312yes—
274#389C2312yes—
275#389C2312yes—
276#389C2312yes—
277#389C2312yes—
278#389C2312yes—
279#389C2312yes—
280#388—22no—
281#388—21no—
282#387—22no—
283#387—22no—
284#387—22no—
285#387—22no—
286#387—22no—
287#387—22no—
288#387—21no—
289#386—22no—
290#386—21no—
291#385—22no—
292#385—22no—
293#385—22no—
294#385—21no—
295#384C2311yescharacteristic
296#384C2311yescharacteristic
297#384C2312yes—
298#382C2312yes—
299#380—22no—
300#380—21no—
301#380—21no—
302#380—21no—
303#380—22no—
304#380C2312yes—
305#380C2311yescharacteristic
306#380C2312yes—
307#380C2311yescharacteristic
308C4×C4⋊C4—21no—
309C4×C4⋊C4—21no—
310C4×C4⋊C4—22no—
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2312yes—
314C4×C4⋊C4C2311yescharacteristic
315C4×C22⋊C4—21no—
316C4×C22⋊C4—22no—
317C4×C22⋊C4—21no—
318C4×C22⋊C4—22no—
319#340C2312yes—
320#340C2311yescharacteristic
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2311yescharacteristic
329#340C2311yescharacteristic
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2311yescharacteristic
335#340C2312yes—
336#340C2312yes—
337#340C2311yescharacteristic
338#340C2311yescharacteristic
339C22×Q8—24no—
340C22×Q8—24no—
341C22×Q8—21no—
342C22×Q8—22no—
343C22×Q8—21no—
344C22×Q8—42no—
345C22×Q8—44no—
346C22×Q8—44no—
347C22×Q8—44no—
348C22×Q8C2×D411yescharacteristic
349C22×Q8C2×D412yes—
350C22×Q8C2×D411yescharacteristic
351C22×Q8C2411yescharacteristic
352C22×D4—21no—
353C22×D4C2411yescharacteristic
354C23×C4—22no—
355C23×C4—21no—
356C23×C4C2×D412yes—
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D412yes—
359C23×C4C2×D411yescharacteristic
360C23×C4C2411yescharacteristic
361C2×SD16—22no—
362C2×SD16—22no—
363C2×SD16—22no—
364C22×C8C2412yes—
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C22×C8C2411yescharacteristic
368C22×C8C2411yescharacteristic
369C22×C8C2412yes—
370C4⋊Q8—22no—
371C4⋊Q8—24no—
372C4⋊Q8—22no—
373C4⋊Q8—24no—
374C4⋊Q8—22no—
375C4⋊Q8—22no—
376C4⋊Q8—44no—
377C4⋊Q8—48no—
378C4⋊Q8—44no—
379C4⋊Q8—44no—
380#125—24no—
381#125—24no—
382#125—48no—
383C22⋊Q8—22no—
384C22⋊Q8—22no—
385C22⋊Q8—48no—
386C22⋊Q8—44no—
387C22⋊Q8—48no—
388C22⋊Q8—44no—
389C22⋊Q8—44no—
390C22⋊Q8—44no—
391C22⋊Q8—48no—
392#121—22no—
393#121—22no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×Q8—28no—
397C4×Q8—24no—
398C4×Q8—22no—
399C4×Q8—24no—
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—24no—
403C4×Q8—24no—
404C4×Q8—22no—
405C4×Q8—44no—
406C4×Q8—44no—
407C4×Q8C2×D414yes—
408C4×Q8#4114yes—
409C4×D4—22no—
410C4×D4—24no—
411C4×D4—24no—
412C4×D4—22no—
413C4×D4—48no—
414C4×D4—44no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—22no—
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D412yes—
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2×D412yes—
445C2×C4⋊C4C2×D412yes—
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2×D412yes—
448C2×C4⋊C4C2412yes—
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2412yes—
454C2×C4⋊C4C2412yes—
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2411yescharacteristic
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—22no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—22no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—22no—
470C2×C42—22no—
471C2×C42—24no—
472C2×C42—24no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—21no—
476C2×C42—22no—
477C2×C42—21no—
478C2×C42—21no—
479C2×C42—22no—
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D412yes—
482C2×C42C2×D412yes—
483C2×C42C2×D411yescharacteristic
484C2×C42C2411yescharacteristic
485C2×C42C2412yes—
486C2×C42C2412yes—
487C2×C42C2411yescharacteristic
488#107—24no—
489#107—24no—
490#107—24no—
491#107—24no—
492#106—22no—
493#106—24no—
494#106—24no—
495#106—22no—
496#106—22no—
497C4⋊C8—22no—
498C4⋊C8—22no—
499C4⋊C8—24no—
500C4⋊C8—24no—
501C4⋊C8—22no—
502C4⋊C8—24no—
503C4⋊C8C2×D414yes—
504C4⋊C8C2×D418yes—
505#103—24no—
506#103—22no—
507#103—22no—
508#103—24no—
509#103—22no—
510#102—24no—
511#102—22no—
512#102—22no—
513#102—24no—
514#102—22no—
515C22⋊C8—24no—
516C22⋊C8—22no—
517C22⋊C8—22no—
518#97—24no—
519#97—24no—
520#97—24no—
521#97C2×D418yes—
522C4×C8—24no—
523C4×C8—22no—
524C4×C8C2×D414yes—
525#95—21no—
526#95—22no—
527#95—21no—
528#95—22no—
529#95—21no—
530#95—22no—
531#95—21no—
532#95—22no—
533#95—21no—
534#95—22no—
535#95—22no—
536#95—21no—
537#95—22no—
538#95—21no—
539#95—22no—
540#95—22no—
541#95—21no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549C24—21no—
550C24C22×D411yescharacteristic
551C2×Q8—24no—
552C2×Q8—22no—
553C2×Q8—22no—
554C2×Q8—24no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×Q8—416no—
565C2×Q8—44no—
566C2×Q8—44no—
567C2×Q8—42no—
568C2×Q8—44no—
569C2×Q8—42no—
570C2×Q8—42no—
571C2×Q8—42no—
572C2×Q8—42no—
573C2×Q8—42no—
574C2×Q8—816no—
575C2×Q8#12114yes—
576C2×Q82−1+412yes—
577C2×D4—24no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—21no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D42−1+412yes—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—24no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—24no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—42no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—41no—
613C22×C4—41no—
614C22×C4—44no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4AGL(1,ℤ/8)14yes—
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D412yes—
625C22×C4C22×D412yes—
626C22×C4C22×D412yes—
627C22×C4C22×D411yescharacteristic
628C22×C4C22×D411yescharacteristic
629C22×C4C22×D411yescharacteristic
630C22×C4C2511yescharacteristic
631SD16—28no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—22no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—22no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8C22×D414yes—
648C2×C8C22×D412yes—
649C2×C8C22×D412yes—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—22no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4—22no—
660C4⋊C4—21no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—22no—
666C4⋊C4—21no—
667C4⋊C4—22no—
668C4⋊C4—22no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—22no—
672C4⋊C4—21no—
673C4⋊C4—22no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—42no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—42no—
685C4⋊C4—44no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—81no—
693C4⋊C4—82no—
694C4⋊C4—81no—
695C4⋊C4—81no—
696C4⋊C4—82no—
697C4⋊C4#12114yes—
698C4⋊C4#12118yes—
699C4⋊C42−1+412yes—
700C4⋊C42−1+412yes—
701C22⋊C4—24no—
702C22⋊C4—24no—
703C22⋊C4—44no—
704C22⋊C4—42no—
705C22⋊C4—44no—
706C22⋊C4—42no—
707C22⋊C4—44no—
708C22⋊C4—44no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—81no—
712C22⋊C4—82no—
713C42—22no—
714C42—24no—
715C42—22no—
716C42—24no—
717C42—21no—
718C42—22no—
719C42—21no—
720C42—22no—
721C42—44no—
722C42—44no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42—82no—
727C42C22×D412yes—
728C42C22×D414yes—
729C42C2×#4114yes—
730C42C2×#4112yes—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—22no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23C2×AGL(1,ℤ/8)12yes—
745C23C23×D411yescharacteristic
746Q8—28no—
747Q8—22no—
748Q8—22no—
749Q8—48no—
750Q8—41no—
751Q8—41no—
752Q8—44no—
753Q8—88no—
754Q8—84no—
755Q8—84no—
756D4—22no—
757D4—22no—
758D4—48no—
759D4—41no—
760D4—41no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—41no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—41no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—42no—
819C2×C4—41no—
820C2×C4—84no—
821C2×C4—82no—
822C2×C4—88no—
823C2×C4—84no—
824C2×C4C2×#12114yes—
825C2×C4C2×#12112yes—
826C2×C4C2×#12114yes—
827C2×C4C2×#12112yes—
828C2×C4C2×AGL(1,ℤ/8)12yes—
829C2×C4C2×AGL(1,ℤ/8)12yes—
830C2×C4#57512yes—
831C2×C4C23×D411yescharacteristic
832C2×C4C22×#4111yescharacteristic
833C2×C4C2×2−1+411yescharacteristic
834C2×C4C2×2−1+411yescharacteristic
835C2×C4C2×2−1+411yescharacteristic
836C2×C4C2×2−1+411yescharacteristic
837C8—22no—
838C8—22no—
839C8—24no—
840C8—42no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22C22×#12111yescharacteristic
858C22#348611yescharacteristic
859C22#348611yescharacteristic
860C22C22×AGL(1,ℤ/8)11yescharacteristic
861C22C2×#57511yescharacteristic
862C22#358611yescharacteristic
863C22#358611yescharacteristic
864C4—22no—
865C4—24no—
866C4—24no—
867C4—22no—
868C4—42no—
869C4—41no—
870C4—42no—
871C4—41no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—82no—
876C4—81no—
877C4—82no—
878C4—81no—
879C4—82no—
880C4—82no—
881C4—81no—
882C4—81no—
883C4#305514yes—
884C4#348611yescharacteristic
885C4#349911yescharacteristic
886C4#352311yescharacteristic
887C4#352311yescharacteristic
888C2—42no—
889C2—82no—
890C2#3570011yescharacteristic
891C2C2×#305511yescharacteristic
892C2#6046211yescharacteristic
893C2#6182711yescharacteristic
894C2#6182811yescharacteristic
895C2#6183411yescharacteristic
896C2#6183411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C4×Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3386C2semidirect
2. C2×#2983C2semidirect
3. #36545C2semidirect
5. #29883C2semidirect
6. #29876C2semidirect
7. #28685C2semidirect
8. #28683C2semidirect
9. #28199C2semidirect
10. #28195C2semidirect
11. #25486C2semidirect
12. #25483C2semidirect
13. #25479C2semidirect
14. #25478C2semidirect
15. #24711C2semidirect
17. #24703C2semidirect
21. #22742C2semidirect
22. #22524C2semidirect
23. #22523C2semidirect
194. #446D4semidirect

Maximal subgroups

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

subgroupindex
C2×#33862
C2×#29832
#365452
Q8×#1212
#298832
#298762
#286852
#286832
#281992
#281952
#254862
#254832
#254792
#254782
#247112
#247062
#247032
#247002
#237102
#237002
#227422
#225242
#225232