Finite Group Databasebeta

← #6574557

Subgroups — #6574557

Order 512.

2058 conjugacy classes of subgroups.

The subgroup lattice has 895 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3080C212yesmaximal, complemented
2D4×#125C211yesmaximal, characteristic, complemented
3C4×#547C211yesmaximal, characteristic
4#33199C211yesmaximal, characteristic, complemented
5#32961C212yesmaximal, complemented
6#28515C211yesmaximal, characteristic, complemented
7#28287C211yesmaximal, characteristic, complemented
8#26465C211yesmaximal, characteristic, complemented
9#26461C211yesmaximal, characteristic, complemented
10#26367C212yesmaximal, complemented
11#26365C212yesmaximal, complemented
12#26045C211yesmaximal, characteristic, complemented
13#26041C211yesmaximal, characteristic, complemented
14#25980C212yesmaximal, complemented
15#25972C212yesmaximal, complemented
16#24842C212yesmaximal, complemented
17#24307C212yesmaximal, complemented
18#22665C211yesmaximal, characteristic, complemented
19#22663C211yesmaximal, characteristic, complemented
20#22650C211yesmaximal, characteristic, complemented
21#22431C211yesmaximal, characteristic
22#22431C211yesmaximal, characteristic
23C4×#478C211yesmaximal, characteristic, complemented
24C2×#547C2211yescharacteristic
25C22×#125C2212yes—
26C2×C4×#41C2212yes—
27#3080—216no—
28C2×#479C2212yes—
29C2×#479C2212yes—
30C2×#479C2212yes—
31C2×#479C2212yes—
32C2×#479C2212yes—
33C2×#478C2212yes—
34C2×#478C2212yes—
35C2×#478C2212yes—
36C2×#478C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#436C2211yescharacteristic
39C2×#428C2212yes—
40C2×#428C2212yes—
41C2×#423C2212yes—
42C2×#417C2212yes—
43C2×#417C2212yes—
44#2859C2211yescharacteristic
45#2851C2212yes—
46#2552C2211yescharacteristic
47#2552C2211yescharacteristic
48#2506—21no—
49#2506—21no—
50#2473—22no—
51#2473—22no—
52#2442C2212yes—
53#2442C2212yes—
54#2365C2211yescharacteristic
55#2362C2212yes—
56#2361—21no—
57#2359—22no—
58#2354C2211yescharacteristic
59D4×C4⋊C4—21no—
60D4×C4⋊C4—21no—
61D4×C4⋊C4C2211yescharacteristic
62D4×C4⋊C4C2211yescharacteristic
63D4×C4⋊C4C2211yescharacteristic
64#2344—21no—
65#2339C2212yes—
66C4×C4⋊Q8C2211yescharacteristic
67C4×#125C2211yescharacteristic
68C4×C22⋊Q8C2212yes—
69C4×#123—22no—
70C4×#121—21no—
71C42×D4C2211yescharacteristic
72C42×D4C2211yescharacteristic
73C2×C4×C4⋊C4—21no—
74#2097C2212yes—
75#2097C2212yes—
76#2088C2212yes—
77#2087C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2066C2212yes—
81#2066C2212yes—
82#2059C2212yes—
83#2059C2212yes—
84#2026C2212yes—
85#2026C2212yes—
86#1989C2212yes—
87#1989C2211yescharacteristic
88#1981C2211yescharacteristic
89#1981C2211yescharacteristic
90#1956C2211yescharacteristic
91#1956C2211yescharacteristic
92#1949C2211yescharacteristic
93#1949C2212yes—
94#1948C2211yescharacteristic
95#1948C2211yescharacteristic
96#1947C2211yescharacteristic
97#1947C2211yescharacteristic
98#1939C2211yescharacteristic
99#1939C2211yescharacteristic
100#1921C2211yescharacteristic
101#1919C2211yescharacteristic
102#1894C2212yes—
103#1894C2212yes—
104#1872C2212yes—
105#1872C2212yes—
106#1865C2212yes—
107#1864C2211yescharacteristic
108#1864C2212yes—
109#1863C2212yes—
110#1862C2211yescharacteristic
111#1862C2212yes—
112#1854C2212yes—
113#1854C2212yes—
114#1853C2212yes—
115#1852C2212yes—
116#1851C2212yes—
117#1851C2212yes—
118#1845C2211yescharacteristic
119#1844C2211yescharacteristic
120#1842C2211yescharacteristic
121#1809C2212yes—
122#1809C2212yes—
123#1805C2212yes—
124#1804C2211yescharacteristic
125#1804C2212yes—
126#1802C2211yescharacteristic
127#1802C2211yescharacteristic
128#1797C2212yes—
129#1788C2212yes—
130#1788C2212yes—
131C4×#107C2211yescharacteristic
132C4×#106C2211yescharacteristic
133C4×C4⋊C8C2211yescharacteristic
134C4×#102C2211yescharacteristic
135C4×#102C2211yescharacteristic
136C22×#41C2312yes—
137C22×M16C2312yes—
138C22×M16C2312yes—
139#547—24no—
140#547Q818yes—
141C2×C4⋊Q8C2311yescharacteristic
142C2×#125—28no—
143C2×#125—22no—
144C2×#125—22no—
145C2×#125—44no—
146C2×#125C2312yes—
147C2×#125C2312yes—
148C2×#125C2312yes—
149C2×#125C2311yescharacteristic
150C2×#123—22no—
151C2×C22⋊Q8C2312yes—
152C2×#121—21no—
153C4×#41—28no—
154C4×#41—44no—
155C2×C4×Q8C2312yes—
156C2×C4×Q8C2312yes—
157C2×C4×D4—21no—
158C2×C4×D4—21no—
159C2×C4×D4—22no—
160C2×C4×D4—22no—
161C2×C4×D4D411yescharacteristic
162C2×C4×D4D411yescharacteristic
163C2×C4×D4C2312yes—
164C2×C4×D4C2311yescharacteristic
165C2×C4×D4C2311yescharacteristic
166C2×C4×D4C2311yescharacteristic
167C2×C4×D4C2311yescharacteristic
168C2×#117—22no—
169C2×#117C2312yes—
170C22×C4⋊C4—21no—
171C22×C4⋊C4—22no—
172C22×C4⋊C4—22no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4C2312yes—
175C22×C4⋊C4C2312yes—
176C22×C42—22no—
177C22×C42—21no—
178C22×C42C2312yes—
179#479—28no—
180#479—28no—
181#479—28no—
182#479—28no—
183#479—44no—
184#478—28no—
185#478—28no—
186#478—28no—
187#478D418yescomplemented
188#436—24no—
189#436—24no—
190#428—28no—
191#428—28no—
192C2×#107C2312yes—
193C2×#107C2312yes—
194C2×#107C2312yes—
195C2×#107C2312yes—
196C2×#107C2311yescharacteristic
197C2×#107C2311yescharacteristic
198C2×#106C2312yes—
199C2×#106C2312yes—
200C2×#106C2312yes—
201C2×#106C2312yes—
202C2×#106C2311yescharacteristic
203C2×#106C2311yescharacteristic
204#423—28no—
205C2×C4⋊C8C2312yes—
206C2×C4⋊C8C2312yes—
207C2×C4⋊C8C2312yes—
208C2×C4⋊C8C2311yescharacteristic
209C2×C4⋊C8C2311yescharacteristic
210C2×C4⋊C8C2311yescharacteristic
211C2×C4⋊C8C2312yes—
212C2×C4⋊C8C2311yescharacteristic
213#417—28no—
214#417—28no—
215C2×#103C2312yes—
216C2×#103C2312yes—
217C2×#103C2312yes—
218C2×#103C2312yes—
219C2×#103C2312yes—
220C2×#103C2312yes—
221C2×#103C2312yes—
222C2×#103C2312yes—
223C2×#102C2312yes—
224C2×#102C2312yes—
225C2×#102C2311yescharacteristic
226C2×#102C2311yescharacteristic
227C2×#102C2311yescharacteristic
228C2×#102C2311yescharacteristic
229C2×C22⋊C8C2312yes—
230C2×C22⋊C8C2312yes—
231C2×C4×C8C2311yescharacteristic
232C2×C4×C8C2311yescharacteristic
233#400—22no—
234#400—22no—
235#398—22no—
236#398—22no—
237#398—22no—
238#398—22no—
239#391C2312yes—
240#391C2312yes—
241#390—21no—
242#389—21no—
243#389—21no—
244#389—21no—
245#389—21no—
246#389—21no—
247#389—21no—
248#389—21no—
249#389—21no—
250#389—21no—
251#389—21no—
252#389—21no—
253#389C2311yescharacteristic
254#389C2311yescharacteristic
255#389C2312yes—
256#389C2312yes—
257#389C2312yes—
258#388—22no—
259#388—22no—
260#388—22no—
261#387—21no—
262#387—21no—
263#387—22no—
264#387—22no—
265#387—22no—
266#387—22no—
267#387—22no—
268#386—22no—
269#386—22no—
270#385—22no—
271#385—22no—
272#385—22no—
273#385—22no—
274#385—22no—
275#385—22no—
276#385—22no—
277#385—22no—
278#384—21no—
279#384—21no—
280#384C2311yescharacteristic
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#382C2311yescharacteristic
284#382C2312yes—
285#381—22no—
286#380—21no—
287#380—22no—
288#380—22no—
289#380C2312yes—
290#380C2312yes—
291#380C2312yes—
292C4×C4⋊C4—21no—
293C4×C4⋊C4—21no—
294C4×C4⋊C4—21no—
295C4×C4⋊C4—21no—
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—22no—
299C4×C4⋊C4—22no—
300C4×C4⋊C4D411yescharacteristic
301C4×C4⋊C4D411yescharacteristic
302C4×C4⋊C4C2311yescharacteristic
303C4×C4⋊C4C2311yescharacteristic
304C4×C4⋊C4C2311yescharacteristic
305C4×C4⋊C4C2311yescharacteristic
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C22⋊C4—22no—
309C4×C22⋊C4—21no—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4D412yes—
313C4×C22⋊C4D412yes—
314C4×C22⋊C4C2312yes—
315C2×#95—22no—
316C43C2311yescharacteristic
317#340C2312yes—
318#340C2312yes—
319#340C2311yescharacteristic
320#340C2311yescharacteristic
321#340C2312yes—
322#340C2312yes—
323#340C2311yescharacteristic
324#340C2311yescharacteristic
325#340C2312yes—
326#340C2312yes—
327#340C2311yescharacteristic
328#340C2311yescharacteristic
329#340C2311yescharacteristic
330#340C2311yescharacteristic
331#336C2312yes—
332#336C2312yes—
333#336C2311yescharacteristic
334#336C2311yescharacteristic
335C2×#41—24no—
336C2×#41—24no—
337C2×#41—24no—
338C2×#41—42no—
339C2×#41—42no—
340C2×#41C2×Q818yes—
341C22×Q8C2412yes—
342C22×D4—22no—
343C22×D4C2×D411yescharacteristic
344C22×D4C2411yescharacteristic
345C23×C4—21no—
346C23×C4—22no—
347C23×C4—21no—
348C23×C4—22no—
349C23×C4—22no—
350C23×C4—22no—
351C23×C4—21no—
352C23×C4C2×D412yes—
353C23×C4C2×D412yes—
354C23×C4C2412yes—
355C2×M16—24no—
356C2×M16—24no—
357C2×M16—24no—
358C2×M16—24no—
359C2×M16—42no—
360C2×M16—42no—
361C22×C8C2412yes—
362C22×C8C2412yes—
363C22×C8C2411yescharacteristic
364C22×C8C2411yescharacteristic
365C22×C8C2411yescharacteristic
366C22×C8C2411yescharacteristic
367C4⋊Q8—22no—
368C4⋊Q8C2×Q814yes—
369#125—24no—
370#125—24no—
371#125—24no—
372#125—22no—
373#125—24no—
374#125—42no—
375#125—42no—
376#125—48no—
377#125—48no—
378#125C2×D414yes—
379#123—216no—
380C22⋊Q8—24no—
381C22⋊Q8C2×Q818yes—
382#121—28no—
383C4×Q8—24no—
384C4×Q8—24no—
385C4×Q8—24no—
386C4×Q8—42no—
387C4×D4—24no—
388C4×D4—22no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—42no—
392C4×D4—42no—
393C4×D4—41no—
394C4×D4—42no—
395C4×D4—48no—
396C4×D4—48no—
397C4×D4—44no—
398C4×D4—44no—
399C4×D4C2×D414yes—
400C4×D4C2×Q814yes—
401C4×D4C2×Q814yes—
402C4×D4#4114yes—
403#117—24no—
404#117—48no—
405#117—42no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—28no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4—48no—
438C2×C4⋊C4—48no—
439C2×C4⋊C4—44no—
440C2×C4⋊C4C2×D411yescharacteristic
441C2×C4⋊C4C2×D411yescharacteristic
442C2×C4⋊C4C2×D411yescharacteristic
443C2×C4⋊C4C2412yes—
444C2×C4⋊C4C2412yes—
445C2×C4⋊C4C2412yes—
446C2×C4⋊C4C2411yescharacteristic
447C2×C4⋊C4C2411yescharacteristic
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2411yescharacteristic
451C2×C4⋊C4C2411yescharacteristic
452C2×C4⋊C4C2411yescharacteristic
453C2×C22⋊C4—22no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4C2×D412yes—
463C2×C22⋊C4C2×D412yes—
464C2×C22⋊C4C2×D412yes—
465C2×C42—24no—
466C2×C42—24no—
467C2×C42—22no—
468C2×C42—22no—
469C2×C42—22no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—21no—
475C2×C42—48no—
476C2×C42—44no—
477C2×C42C2×D412yes—
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
480C2×C42C2×D412yes—
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2412yes—
484C2×C42C2411yescharacteristic
485C2×C42C2411yescharacteristic
486C2×C42C2411yescharacteristic
487#107—24no—
488#107—24no—
489#107—24no—
490#107—41no—
491#107—42no—
492#107C2×D414yes—
493#106—24no—
494#106—24no—
495#106—24no—
496#106—41no—
497#106—42no—
498#106C2×D414yes—
499C4⋊C8—24no—
500C4⋊C8—24no—
501C4⋊C8—24no—
502C4⋊C8—22no—
503C4⋊C8—22no—
504C4⋊C8—22no—
505C4⋊C8—42no—
506C4⋊C8C2×D414yes—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—24no—
511#103—42no—
512#103—42no—
513#103—42no—
514#103—42no—
515#102—24no—
516#102—24no—
517#102—22no—
518#102—22no—
519#102C2×D414yes—
520#102C2×D414yes—
521C22⋊C8—24no—
522C22⋊C8—24no—
523C4×C8—22no—
524C4×C8—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—21no—
529#95—21no—
530#95—21no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—22no—
546#95C2×D412yes—
547#95C2×D412yes—
548#95C2×D412yes—
549C24—21no—
550C24C22×D412yes—
551#41—216no—
552#41—48no—
553#41—48no—
554#41—48no—
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8—22no—
559C2×Q8—22no—
560C2×Q8C22×Q814yes—
561C2×D4—28no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—44no—
568C2×D4—44no—
569C2×D4C22⋊Q814yes—
570C2×D4C22×D412yes—
571C2×D4C22×Q812yes—
572C2×D42−1+412yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—24no—
583C22×C4—28no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—24no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—44no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—44no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—81no—
612C22×C4—82no—
613C22×C4—82no—
614C22×C4—82no—
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D412yes—
618C22×C4C22×D412yes—
619C22×C4C22×D412yes—
620C22×C4C22×D411yescharacteristic
621C22×C4C22×D411yescharacteristic
622C22×C4C22×D411yescharacteristic
623C22×C4C22×D411yescharacteristic
624C22×C4C22×Q814yes—
625C22×C4C2×#4114yes—
626C22×C4C2511yescharacteristic
627M16—48no—
628M16—48no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8C22×D412yes—
646C2×C8C22×D412yes—
647C4⋊C4—24no—
648C4⋊C4—28no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—22no—
660C4⋊C4—22no—
661C4⋊C4—22no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—44no—
671C4⋊C4—44no—
672C4⋊C4—44no—
673C4⋊C4—44no—
674C4⋊C4—44no—
675C4⋊C4—44no—
676C4⋊C4—44no—
677C4⋊C4—44no—
678C4⋊C4—44no—
679C4⋊C4—44no—
680C4⋊C4—44no—
681C4⋊C4—42no—
682C4⋊C4—42no—
683C4⋊C4—42no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—81no—
688C4⋊C4—82no—
689C4⋊C4—81no—
690C4⋊C4—82no—
691C4⋊C4C22⋊Q814yes—
692C4⋊C4C22×D412yes—
693C4⋊C4C22×D412yes—
694C4⋊C4C22×D412yes—
695C4⋊C4C22×Q812yes—
696C22⋊C4—28no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C22⋊C4—44no—
703C22⋊C4—42no—
704C22⋊C4—44no—
705C22⋊C4—44no—
706C22⋊C4—82no—
707C22⋊C4C22⋊Q818yes—
708C42—24no—
709C42—24no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—21no—
716C42—41no—
717C42—41no—
718C42—44no—
719C42—44no—
720C42—42no—
721C42—42no—
722C42—44no—
723C42—42no—
724C42—42no—
725C42—42no—
726C42C22×D412yes—
727C42C22×Q812yes—
728C42C2×#4112yes—
729C42H(5,𝔽2)12yes—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23C2×C22⋊Q814yes—
744C23C23×D411yescharacteristic
745Q8—24no—
746Q8—24no—
747Q8—42no—
748Q8—42no—
749D4—28no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—416no—
754D4D4×Q814yes—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—24no—
764C2×C4—24no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—416no—
785C2×C4—48no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—48no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—42no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—84no—
816C2×C4—84no—
817C2×C4—88no—
818C2×C4—88no—
819C2×C4—88no—
820C2×C4—84no—
821C2×C4C2×C22⋊Q812yes—
822C2×C4C2×C22⋊Q814yes—
823C2×C4C2×C22⋊Q812yes—
824C2×C4D4212yes—
825C2×C4D4212yes—
826C2×C4#57512yes—
827C2×C4#57512yes—
828C2×C4C23×D411yescharacteristic
829C2×C4C23×Q811yescharacteristic
830C2×C4C22×#4111yescharacteristic
831C2×C4C2×H(5,𝔽2)11yescharacteristic
832C2×C4C2×2−1+411yescharacteristic
833C2×C4#58511yescharacteristic
834C8—22no—
835C8—22no—
836C8—42no—
837C8—42no—
838C8—41no—
839C8—41no—
840C22—24no—
841C22—24no—
842C22—24no—
843C22—24no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22C22×C22⋊Q811yescharacteristic
855C22C2×D4211yescharacteristic
856C22#348911yescharacteristic
857C22C2×#57511yescharacteristic
858C22C2×#57511yescharacteristic
859C22#358411yescharacteristic
860C22#358611yescharacteristic
861C4—22no—
862C4—22no—
863C4—22no—
864C4—24no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—41no—
872C4—41no—
873C4—44no—
874C4—82no—
875C4—82no—
876C4—82no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4#308014yescomplemented
881C4C2×D4×Q811yescharacteristic
882C4D4×#4111yescharacteristic
883C4#350111yescharacteristic
884C4#352011yescharacteristic
885C2—44no—
886C2—44no—
887C2D4×C22⋊Q811yescharacteristic
888C2C2×#308011yescharacteristic
889C2#6049911yescharacteristic
890C2#6103811yescharacteristic
891C2#6106711yescharacteristic
892C2#6212111yescharacteristic
893C2#6215211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#547C22
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
1. C2×#3080C2semidirect
2. D4×#125C2semidirect
4. #33199C2semidirect
5. #32961C2semidirect
6. #28515C2semidirect
7. #28287C2semidirect
8. #26465C2semidirect
9. #26461C2semidirect
10. #26367C2semidirect
11. #26365C2semidirect
12. #26045C2semidirect
13. #26041C2semidirect
14. #25980C2semidirect
15. #25972C2semidirect
16. #24842C2semidirect
17. #24307C2semidirect
18. #22665C2semidirect
19. #22663C2semidirect
20. #22650C2semidirect
23. C4×#478C2semidirect
187. #478D4semidirect
880. C4#3080semidirect

Maximal subgroups

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

subgroupindex
C2×#30802
D4×#1252
C4×#5472
#331992
#329612
#285152
#282872
#264652
#264612
#263672
#263652
#260452
#260412
#259802
#259722
#248422
#243072
#226652
#226632
#226502
#224312
C4×#4782