Finite Group Databasebeta

← #6625728

Subgroups — #6625728

Order 512.

1834 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3385C211yesmaximal, characteristic, complemented
2C2×Q8×SD16C211yesmaximal, characteristic, complemented
3#39618C211yesmaximal, characteristic
4#34335C211yesmaximal, characteristic, complemented
5#33204C212yesmaximal, complemented
6#33202C211yesmaximal, characteristic, complemented
7#28696C212yesmaximal, complemented
8#28688C211yesmaximal, characteristic, complemented
9#28290C212yesmaximal
10#28280C211yesmaximal, characteristic
11#25461C212yesmaximal, complemented
12#25452C212yesmaximal, complemented
13#25451C211yesmaximal, characteristic, complemented
14#25450C211yesmaximal, characteristic, complemented
15#24828C212yesmaximal, complemented
16#24819C212yesmaximal, complemented
17#24814C211yesmaximal, characteristic, complemented
18#24813C211yesmaximal, characteristic, complemented
19#22721C211yesmaximal, characteristic, complemented
20#22523C211yesmaximal, characteristic, complemented
21#22519C211yesmaximal, characteristic, complemented
22#21515C212yesmaximal
23C4×#460C211yesmaximal, characteristic
24C2×Q82C2211yescharacteristic
25C2×#554C2211yescharacteristic
26C2×D4×Q8C2211yescharacteristic
27#3385—28no—
28Q8×SD16—28no—
29C2×#501C2212yes—
30C2×#500C2211yescharacteristic
31C2×#498C2211yescharacteristic
32C2×#498C2212yes—
33C2×#479C2212yes—
34C2×#477C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#475C2212yes—
37C2×#476C2211yescharacteristic
38C2×#476C2211yescharacteristic
39C2×#476C2212yes—
40C2×#474C2212yes—
41C2×#460C2211yescharacteristic
42C2×#446C2211yescharacteristic
43C2×C8×Q8C2211yescharacteristic
44C2×#440C2212yes—
45C2×C4×SD16C2212yes—
46C2×C4×SD16C2211yescharacteristic
47C2×C4×SD16C2211yescharacteristic
48#2862C2211yescharacteristic
49#2692—22no—
50#2692—22no—
51#2660C2212yes—
52#2566C2212yes—
53#2563C2211yescharacteristic
54#2563C2212yes—
55#2542C2211yescharacteristic
56#2417—21no—
57#2417—21no—
58#2409—21no—
59#2409—21no—
60#2369—21no—
61#2369C2211yescharacteristic
62#2365—22no—
63#2365C2212yes—
64#2355—21no—
65#2355C2211yescharacteristic
66#2351C2212yes—
67Q8×C4⋊C4C2211yescharacteristic
68#2331—22no—
69#2331C2212yes—
70#2328C2212yes—
71C4×C4⋊Q8—21no—
72C4×C4⋊Q8C2211yescharacteristic
73C4×#127C2211yescharacteristic
74#2295—21no—
75#2295C2211yescharacteristic
76#2276C2212yes—
77C42×Q8C2211yescharacteristic
78#2085C2212yes—
79#2085C2212yes—
80#2085C2212yes—
81#2085C2212yes—
82#2084C2212yes—
83#2084C2212yes—
84#2067C2212yes—
85#2067C2212yes—
86#2065C2212yes—
87#2065C2212yes—
88#2065C2212yes—
89#2065C2212yes—
90#1993C2212yes—
91#1991C2212yes—
92#1990C2211yescharacteristic
93#1990C2211yescharacteristic
94#1989C2212yes—
95#1988C2211yescharacteristic
96#1987C2211yescharacteristic
97#1987C2212yes—
98#1982C2212yes—
99#1982C2211yescharacteristic
100#1949C2212yes—
101#1949C2212yes—
102#1949C2212yes—
103#1949C2212yes—
104#1949C2212yes—
105#1948C2211yescharacteristic
106#1948C2212yes—
107#1948C2212yes—
108#1940C2212yes—
109#1939C2211yescharacteristic
110#1939C2211yescharacteristic
111#1939C2212yes—
112#1926C2212yes—
113#1926C2211yescharacteristic
114#1926C2211yescharacteristic
115#1925C2212yes—
116#1880C2212yes—
117#1880C2212yes—
118#1880C2211yescharacteristic
119#1880C2211yescharacteristic
120#1843C2212yes—
121#1842C2211yescharacteristic
122#1805C2212yes—
123#1805C2212yes—
124#1805C2212yes—
125#1804C2212yes—
126#1804C2212yes—
127#1803C2211yescharacteristic
128#1803C2212yes—
129#1802C2211yescharacteristic
130#1802C2211yescharacteristic
131#1768C2212yes—
132C4×C4⋊C8C2211yescharacteristic
133#1762C2212yes—
134C4×#102C2212yes—
135C4×#102C2211yescharacteristic
136C4×#102C2211yescharacteristic
137C23×Q8—21no—
138C22×SD16C2311yescharacteristic
139C22×SD16C2311yescharacteristic
140Q82—24no—
141Q82D418yescomplemented
142#554—24no—
143#554—24no—
144D4×Q8—24no—
145D4×Q8—24no—
146C2×C4⋊Q8—21no—
147C2×C4⋊Q8—22no—
148C2×C4⋊Q8C2312yes—
149C2×C4⋊Q8C2311yescharacteristic
150C2×C4⋊Q8C2311yescharacteristic
151C2×C4⋊Q8C2311yescharacteristic
152C2×C4⋊Q8C2312yes—
153C2×#127C2311yescharacteristic
154C2×#125C2312yes—
155C2×C22⋊Q8—21no—
156C2×C22⋊Q8—21no—
157C2×C22⋊Q8—22no—
158C2×C22⋊Q8—22no—
159C2×C22⋊Q8—21no—
160C2×C22⋊Q8—21no—
161C2×C4×Q8—21no—
162C2×C4×Q8—22no—
163C2×C4×Q8—21no—
164C2×C4×Q8C2312yes—
165C2×C4×Q8C2311yescharacteristic
166C2×C4×Q8C2311yescharacteristic
167C2×C4×Q8C2312yes—
168C2×C4×Q8C2311yescharacteristic
169C2×C4×Q8C2311yescharacteristic
170C2×C4×D4—21no—
171C2×C4×D4—21no—
172C2×C4×D4C2311yescharacteristic
173C2×C4×D4C2311yescharacteristic
174C2×C4×D4C2312yes—
175C2×C4×D4C2312yes—
176C22×C4⋊C4—21no—
177#501—28no—
178#500—24no—
179#498—28no—
180#498—24no—
181#479—28no—
182#477—24no—
183#476—28no—
184#476—24no—
185#476—24no—
186#475—24no—
187#475—28no—
188#474—28no—
189#460Q818yescomplemented
190#446—24no—
191C8×Q8—24no—
192#440—28no—
193C4×SD16—24no—
194C4×SD16—28no—
195C4×SD16—24no—
196C2×#107C2312yes—
197C2×#107C2312yes—
198C2×#107C2312yes—
199C2×#106C2312yes—
200C2×#106C2312yes—
201C2×#106C2312yes—
202C2×#106C2312yes—
203C2×#106C2311yescharacteristic
204C2×#106C2312yes—
205C2×#106C2311yescharacteristic
206C2×C4⋊C8C2311yescharacteristic
207C2×C4⋊C8C2312yes—
208C2×C4⋊C8C2311yescharacteristic
209C2×C4⋊C8C2312yes—
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2312yes—
212C2×C4⋊C8C2312yes—
213C2×C4⋊C8C2312yes—
214C2×C4⋊C8C2312yes—
215C2×C4⋊C8C2311yescharacteristic
216C2×#103C2312yes—
217C2×#103C2311yescharacteristic
218C2×#103C2312yes—
219C2×#103C2311yescharacteristic
220C2×#102C2311yescharacteristic
221C2×#102C2312yes—
222C2×#102C2312yes—
223C2×#102C2311yescharacteristic
224C2×#102C2312yes—
225C2×#102C2312yes—
226C2×#102C2311yescharacteristic
227C2×#102C2311yescharacteristic
228C2×#102C2311yescharacteristic
229C2×#102C2311yescharacteristic
230C2×#97C2312yes—
231C2×C4×C8C2311yescharacteristic
232C2×C4×C8C2312yes—
233C2×C4×C8C2311yescharacteristic
234#399—22no—
235#398—22no—
236#398—22no—
237#396—22no—
238#396—22no—
239#395—22no—
240#395—22no—
241#393—22no—
242#393—22no—
243#393—22no—
244#391—21no—
245#391—22no—
246#391—21no—
247#391—21no—
248#391—21no—
249#391—21no—
250#391—21no—
251#391—22no—
252#391—22no—
253#391—22no—
254#391D411yescharacteristic
255#391D411yescharacteristic
256#390—21no—
257#390—21no—
258#390C2311yescharacteristic
259#390C2311yescharacteristic
260#390C2312yes—
261#390C2312yes—
262#389—22no—
263#389—22no—
264#389—21no—
265#389—21no—
266#389—22no—
267#389D411yescharacteristic
268#389D411yescharacteristic
269#389C2312yes—
270#389C2312yes—
271#389C2312yes—
272#387—22no—
273#387—22no—
274#387—22no—
275#387—22no—
276#387—22no—
277#387D412yes—
278#387D412yes—
279#386—22no—
280#386—22no—
281#386—22no—
282#386—22no—
283#385—22no—
284#385—22no—
285#384—21no—
286#384C2311yescharacteristic
287#384C2311yescharacteristic
288#384C2312yes—
289#382—22no—
290#382C2312yes—
291#382C2312yes—
292#382C2312yes—
293#382C2312yes—
294#380—21no—
295#380—21no—
296#380—22no—
297#380—22no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—21no—
301C4×C4⋊C4—21no—
302C4×C4⋊C4—21no—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4—22no—
306C4×C4⋊C4—22no—
307C4×C4⋊C4—22no—
308C4×C4⋊C4—22no—
309C4×C4⋊C4C2312yes—
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2312yes—
312C4×C4⋊C4C2311yescharacteristic
313C4×C4⋊C4C2311yescharacteristic
314C4×C4⋊C4C2312yes—
315C4×C4⋊C4C2312yes—
316C4×C4⋊C4C2311yescharacteristic
317#376—22no—
318#376C2312yes—
319C43—21no—
320C43C2311yescharacteristic
321#340C2312yes—
322#340C2312yes—
323#340C2312yes—
324#340C2311yescharacteristic
325#340C2311yescharacteristic
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2311yescharacteristic
332#340C2312yes—
333#340C2311yescharacteristic
334#340C2312yes—
335#336C2312yes—
336#336C2312yes—
337#336C2311yescharacteristic
338#336C2311yescharacteristic
339C22×Q8—22no—
340C22×Q8—21no—
341C22×Q8—21no—
342C22×Q8—21no—
343C22×Q8—22no—
344C22×Q8—44no—
345C22×Q8—82no—
346C22×Q8—82no—
347C22×Q8C2×D411yescharacteristic
348C22×Q8C2411yescharacteristic
349C22×D4—21no—
350C22×D4—21no—
351C22×D4C2411yescharacteristic
352C22×D4C2411yescharacteristic
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—22no—
356C23×C4—22no—
357C2×SD16—22no—
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16—22no—
361C2×SD16C2×Q814yes—
362C2×SD16C2×Q814yescomplemented
363C22×C8C2412yes—
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2412yes—
367C22×C8C2411yescharacteristic
368C22×C8C2411yescharacteristic
369C4⋊Q8—28no—
370C4⋊Q8—216no—
371C4⋊Q8—22no—
372C4⋊Q8—24no—
373C4⋊Q8—22no—
374C4⋊Q8—24no—
375C4⋊Q8—22no—
376C4⋊Q8—24no—
377C4⋊Q8—22no—
378C4⋊Q8—22no—
379C4⋊Q8C2×D418yes—
380C4⋊Q8C2×D414yes—
381#127—22no—
382#127C2×Q814yes—
383#125—24no—
384#125—24no—
385C22⋊Q8—44no—
386C22⋊Q8—44no—
387C22⋊Q8—48no—
388C22⋊Q8—48no—
389C22⋊Q8—82no—
390C22⋊Q8—82no—
391C4×Q8—28no—
392C4×Q8—24no—
393C4×Q8—22no—
394C4×Q8—22no—
395C4×Q8—24no—
396C4×Q8—22no—
397C4×Q8—42no—
398C4×Q8—41no—
399C4×Q8—82no—
400C4×Q8—84no—
401C4×Q8C2×D414yes—
402C4×Q8C2×D418yes—
403C4×Q8C2×D414yes—
404C4×Q8C2×Q814yescomplemented
405C4×Q8#4114yes—
406C4×D4—22no—
407C4×D4—24no—
408C4×D4—22no—
409C4×D4—24no—
410C4×D4—24no—
411C4×D4—22no—
412C4×D4—24no—
413C4×D4—22no—
414C4×D4—82no—
415C4×D4—82no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—44no—
438C2×C4⋊C4C2×D411yescharacteristic
439C2×C4⋊C4C2×D411yescharacteristic
440C2×C4⋊C4C2×D412yes—
441C2×C4⋊C4C2×D412yes—
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2×D412yes—
444C2×C4⋊C4C2411yescharacteristic
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2412yes—
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C22⋊C4—22no—
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—21no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—22no—
463C2×C22⋊C4—22no—
464C2×C22⋊C4—22no—
465C2×C42—21no—
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—22no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—22no—
474C2×C42—22no—
475C2×C42—21no—
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2411yescharacteristic
481C2×C42C2412yes—
482C2×C42C2412yes—
483C2×C42C2411yescharacteristic
484C2×C42C2411yescharacteristic
485#107—24no—
486#107—24no—
487#107—24no—
488#106—24no—
489#106—22no—
490#106—22no—
491#106—24no—
492#106—24no—
493#106—24no—
494#106—24no—
495C4⋊C8—22no—
496C4⋊C8—24no—
497C4⋊C8—24no—
498C4⋊C8—22no—
499C4⋊C8—22no—
500C4⋊C8—24no—
501C4⋊C8—42no—
502C4⋊C8—42no—
503C4⋊C8—42no—
504C4⋊C8C2×Q814yescomplemented
505#103—24no—
506#103—22no—
507#103—22no—
508#103—24no—
509#102—22no—
510#102—24no—
511#102—22no—
512#102—24no—
513#102—42no—
514#102—42no—
515#102—41no—
516#102—41no—
517#102C2×Q814yes—
518#102C2×Q814yescomplemented
519#97—24no—
520C4×C8—22no—
521C4×C8—24no—
522C4×C8—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95C2×D412yes—
541#95C2×D412yes—
542#95C2×D412yes—
543#95C2×D412yes—
544#95C2×D412yes—
545#95C2×D412yes—
546#95C2×D412yes—
547C24—21no—
548C24—21no—
549C2×Q8—24no—
550C2×Q8—28no—
551C2×Q8—22no—
552C2×Q8—22no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—44no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—42no—
561C2×Q8—81no—
562C2×Q8—82no—
563C2×Q8—81no—
564C2×Q8—82no—
565C2×Q8—82no—
566C2×Q8—82no—
567C2×Q8—81no—
568C2×Q8—81no—
569C2×Q8—816no—
570C2×Q8#12114yes—
571C2×Q8C22×D412yes—
572C2×Q8C22×Q812yes—
573C2×Q82−1+412yes—
574C2×D4—24no—
575C2×D4—24no—
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×D4—21no—
585C2×D4—21no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4C22×Q812yes—
591C2×D4C22×Q812yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—44no—
610C22×C4—82no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D412yes—
616C22×C4C22×D412yes—
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C2511yescharacteristic
625SD16—28no—
626SD16—28no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—22no—
633C2×C8—21no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—22no—
637C2×C8—21no—
638C2×C8—22no—
639C2×C8—22no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—22no—
643C2×C8C22×Q812yes—
644C2×C8C22×Q812yes—
645C4⋊C4—28no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—28no—
649C4⋊C4—24no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—21no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—22no—
667C4⋊C4—42no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—42no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—44no—
677C4⋊C4—42no—
678C4⋊C4—82no—
679C4⋊C4—81no—
680C4⋊C4—81no—
681C4⋊C4—81no—
682C4⋊C4—82no—
683C4⋊C4—82no—
684C4⋊C4—82no—
685C4⋊C4#12114yes—
686C4⋊C4#12118yes—
687C4⋊C4C22×D412yes—
688C4⋊C4C22×D414yes—
689C4⋊C4C22×Q812yes—
690C22⋊C4—42no—
691C22⋊C4—44no—
692C22⋊C4—42no—
693C22⋊C4—44no—
694C22⋊C4—82no—
695C22⋊C4—82no—
696C22⋊C4—81no—
697C22⋊C4—81no—
698C22⋊C4—81no—
699C22⋊C4—81no—
700C22⋊C4—82no—
701C22⋊C4—82no—
702C42—28no—
703C42—24no—
704C42—24no—
705C42—22no—
706C42—22no—
707C42—21no—
708C42—22no—
709C42—21no—
710C42—22no—
711C42—41no—
712C42—41no—
713C42—42no—
714C42—44no—
715C42—42no—
716C42—42no—
717C42—81no—
718C42—82no—
719C42—82no—
720C42—82no—
721C42C22×D412yes—
722C42C22×D414yes—
723C42C22×Q812yes—
724C42C2×#4114yes—
725C42C2×#4112yes—
726C422−1+412yes—
727C23—22no—
728C23—22no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23C23×D411yescharacteristic
742Q8—22no—
743Q8—22no—
744Q8—22no—
745Q8—28no—
746Q8—88no—
747Q8—84no—
748Q8—88no—
749Q8—84no—
750Q8—162no—
751Q8D4×Q814yes—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—22no—
756D4—41no—
757D4—41no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4—84no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—24no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—42no—
802C2×C4—41no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—88no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—164no—
818C2×C4C2×#12114yes—
819C2×C4C2×#12112yes—
820C2×C4C2×#12114yes—
821C2×C4C2×#12112yes—
822C2×C4D4×Q812yes—
823C2×C4D4×Q812yes—
824C2×C4#57712yes—
825C2×C4#57712yes—
826C2×C4C23×D411yescharacteristic
827C2×C4C23×Q811yescharacteristic
828C2×C4C22×#4111yescharacteristic
829C2×C4C2×2−1+411yescharacteristic
830C2×C4C2×2−1+411yescharacteristic
831C2×C4#58511yescharacteristic
832C8—22no—
833C8—22no—
834C8—41no—
835C8—42no—
836C8—41no—
837C8—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—42no—
843C22—42no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22—81no—
852C22C22×#12111yescharacteristic
853C22C2×D4×Q811yescharacteristic
854C22#348911yescharacteristic
855C22C2×#57711yescharacteristic
856C22C2×#57711yescharacteristic
857C22#358411yescharacteristic
858C22#358511yescharacteristic
859C4—24no—
860C4—24no—
861C4—22no—
862C4—22no—
863C4—24no—
864C4—22no—
865C4—41no—
866C4—42no—
867C4—42no—
868C4—44no—
869C4—42no—
870C4—41no—
871C4—42no—
872C4—81no—
873C4—81no—
874C4—82no—
875C4—81no—
876C4—82no—
877C4—82no—
878C4#304314yes—
879C4C2×D4×Q811yescharacteristic
880C4Q8×#4111yescharacteristic
881C4#349711yescharacteristic
882C4#352311yescharacteristic
883C2—82no—
884C2—82no—
885C2Q8×#12111yescharacteristic
886C2C2×#304311yescharacteristic
887C2#6043011yescharacteristic
888C2#6137111yescharacteristic
889C2#6138211yescharacteristic
890C2#6219411yescharacteristic
891C2#6221911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
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
1. C2×#3385C2semidirect
2. C2×Q8×SD16C2semidirect
4. #34335C2semidirect
5. #33204C2semidirect
6. #33202C2semidirect
7. #28696C2semidirect
8. #28688C2semidirect
11. #25461C2semidirect
12. #25452C2semidirect
13. #25451C2semidirect
14. #25450C2semidirect
15. #24828C2semidirect
16. #24819C2semidirect
17. #24814C2semidirect
18. #24813C2semidirect
19. #22721C2semidirect
20. #22523C2semidirect
21. #22519C2semidirect
141. Q82D4semidirect
189. #460Q8semidirect
362. C2×SD16C2×Q8semidirect
404. C4×Q8C2×Q8semidirect
504. C4⋊C8C2×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×#33852
C2×Q8×SD162
#396182
#343352
#332042
#332022
#286962
#286882
#282902
#282802
#254612
#254522
#254512
#254502
#248282
#248192
#248142
#248132
#227212
#225232
#225192
#215152
C4×#4602