Finite Group Databasebeta

← #6560969

Subgroups — #6560969

Order 512.

1542 conjugacy classes of subgroups.

The subgroup lattice has 899 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36387C211yesmaximal, characteristic
2#36180C211yesmaximal, characteristic
3#30309C211yesmaximal, characteristic, complemented
4#30295C211yesmaximal, characteristic, complemented
5#30293C211yesmaximal, characteristic, complemented
6#29317C211yesmaximal, characteristic, complemented
7#29304C211yesmaximal, characteristic, complemented
8#29296C211yesmaximal, characteristic, complemented
9#28837C212yesmaximal, complemented
10#28804C212yesmaximal, complemented
11#28784C212yesmaximal, complemented
12#28776C212yesmaximal, complemented
13#28694C211yesmaximal, characteristic, complemented
14#27953C211yesmaximal, characteristic, complemented
15#27948C211yesmaximal, characteristic, complemented
16#26078C212yesmaximal, complemented
17#26071C212yesmaximal, complemented
18#23841C211yesmaximal, characteristic, complemented
19#23658C211yesmaximal, characteristic, complemented
20C2×#2083C211yesmaximal, characteristic, complemented
21#22711C212yesmaximal
22#22661C212yesmaximal
23#20556C211yesmaximal, characteristic
24C2×#554—21no—
25C2×#501C2212yes—
26C2×#435C2212yes—
27C2×#428C2212yes—
28C22×#107C2212yes—
29#2868C2211yescharacteristic
30#2864C2211yescharacteristic
31#2857C2211yescharacteristic
32#2857C2211yescharacteristic
33#2857C2211yescharacteristic
34#2851C2211yescharacteristic
35#2590—21no—
36#2589—21no—
37#2588—21no—
38#2587—21no—
39#2579—21no—
40#2570C2211yescharacteristic
41#2567—21no—
42#2564—21no—
43#2552—21no—
44#2552C2212yes—
45#2550C2211yescharacteristic
46#2502—21no—
47#2502—21no—
48#2442C2211yescharacteristic
49#2442C2211yescharacteristic
50#2441C2211yescharacteristic
51#2440—21no—
52#2440—21no—
53#2440C2212yes—
54#2440C2212yes—
55#2439C2211yescharacteristic
56#2368—21no—
57#2352C2211yescharacteristic
58#2352C2211yescharacteristic
59D4×C4⋊C4—21no—
60D4×C4⋊C4C2212yes—
61#2345—21no—
62C4×C4⋊Q8C2211yescharacteristic
63C4×#125C2211yescharacteristic
64#2296C2211yescharacteristic
65C2×#389C2211yescharacteristic
66C2×#384C2211yescharacteristic
67C2×#384C2211yescharacteristic
68C42×D4C2211yescharacteristic
69#2085C2212yes—
70#2085C2212yes—
71#2084C2211yescharacteristic
72#2084C2211yescharacteristic
73#2084C2211yescharacteristic
74#2084C2211yescharacteristic
75#2084C2211yescharacteristic
76#2084C2211yescharacteristic
77#2084C2212yes—
78#2084C2212yes—
79#2083C2211yescharacteristic
80#2083C2211yescharacteristic
81#2083C2211yescharacteristic
82#2083C2211yescharacteristic
83#2083C2211yescharacteristic
84#2083C2211yescharacteristic
85#2083C2212yes—
86#2083C2212yes—
87#2083C2212yes—
88#2059C2212yes—
89#2059C2212yes—
90#2058C2211yescharacteristic
91#2058C2212yes—
92#2058C2211yescharacteristic
93#2058C2212yes—
94#2057C2211yescharacteristic
95#2057C2211yescharacteristic
96#2057C2212yes—
97#1993C2212yes—
98#1992C2212yes—
99#1990C2212yes—
100#1949C2212yes—
101#1949C2212yes—
102#1948C2212yes—
103#1947C2212yes—
104#1944C2212yes—
105#1944C2212yes—
106#1943C2212yes—
107#1943C2212yes—
108#1942C2212yes—
109#1942C2212yes—
110#1854C2212yes—
111#1854C2212yes—
112#1853C2212yes—
113#1853C2212yes—
114#1853C2212yes—
115#1852C2212yes—
116#1852C2212yes—
117#1852C2212yes—
118#1847C2212yes—
119#1847C2212yes—
120#1844C2212yes—
121#1836C2212yes—
122#1809C2212yes—
123#1809C2212yes—
124#1807C2212yes—
125#1807C2212yes—
126#1776C2212yes—
127#1776C2212yes—
128#1771C2212yes—
129#1767C2211yescharacteristic
130#1753C2212yes—
131#1752C2212yes—
132#1749C2211yescharacteristic
133C4×C22⋊C8C2211yescharacteristic
134#1745C2211yescharacteristic
135#1736C2212yes—
136C2×#340C2212yes—
137#1728C2211yescharacteristic
138C2×#336C2211yescharacteristic
139C22×M16C2312yes—
140C23×C8C2312yes—
141#554—48no—
142C2×C4⋊Q8—21no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2312yes—
146C2×C4⋊Q8C2311yescharacteristic
147C2×#125—22no—
148C2×#125C2311yescharacteristic
149C2×#125C2311yescharacteristic
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—21no—
152C2×C22⋊Q8—21no—
153C2×C22⋊Q8—22no—
154C2×C22⋊Q8—22no—
155C2×C4×Q8—21no—
156C2×C4×D4—22no—
157C2×C4×D4D411yescharacteristic
158C2×C4×D4D411yescharacteristic
159C2×C4×D4C2311yescharacteristic
160C2×#117C2311yescharacteristic
161C2×#117C2311yescharacteristic
162C22×C4⋊C4—21no—
163C22×C4⋊C4—21no—
164C22×C4⋊C4—21no—
165C22×C4⋊C4—21no—
166C22×C4⋊C4—21no—
167C22×C4⋊C4C2311yescharacteristic
168C22×C4⋊C4C2312yes—
169C22×C4⋊C4C2312yes—
170C22×C4⋊C4C2311yescharacteristic
171C22×C42C2311yescharacteristic
172C22×C42C2311yescharacteristic
173#501—44no—
174#435Q8116yescomplemented
175#428—44no—
176C2×#107—44no—
177C2×#107C2312yes—
178C2×#107C2312yes—
179C2×#107C2312yes—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#107C2312yes—
184C2×#107C2312yes—
185C2×#106C2312yes—
186C2×#106C2312yes—
187C2×#106C2312yes—
188C2×#106C2312yes—
189C2×#106C2312yes—
190C2×#106C2312yes—
191C2×#106C2312yes—
192C2×#106C2312yes—
193C2×C4⋊C8C2312yes—
194C2×C22⋊C8C2312yes—
195C2×C22⋊C8C2312yes—
196C2×#97C2312yes—
197C2×#97C2312yes—
198C2×#97C2312yes—
199C2×C4×C8C2312yes—
200#400—21no—
201#400—21no—
202#400—21no—
203#399—21no—
204#398—21no—
205#398—21no—
206#398—21no—
207#398—21no—
208#398—22no—
209#398—22no—
210#398—22no—
211#398—22no—
212#396—21no—
213#396—21no—
214#395—21no—
215#395—22no—
216#395—22no—
217#393—21no—
218#391—21no—
219#391—21no—
220#391—21no—
221#391—21no—
222#391—21no—
223#391—21no—
224#389—22no—
225#389—22no—
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389—21no—
231#389—21no—
232#389—21no—
233#389—21no—
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2312yes—
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#389C2311yescharacteristic
241#389C2312yes—
242#389C2311yescharacteristic
243#389C2311yescharacteristic
244#389C2312yes—
245#389C2311yescharacteristic
246#389C2311yescharacteristic
247#388—21no—
248#388—21no—
249#387—21no—
250#387—21no—
251#387—21no—
252#387—21no—
253#387—21no—
254#387—21no—
255#387—21no—
256#387—21no—
257#387—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—21no—
263#386—21no—
264#386—21no—
265#385—21no—
266#385—21no—
267#385—21no—
268#385—21no—
269#385—21no—
270#385—21no—
271#385—22no—
272#385—22no—
273#385—22no—
274#385—22no—
275#384—21no—
276#384—21no—
277#384—21no—
278#384—21no—
279#384—21no—
280#384—21no—
281#384C2311yescharacteristic
282#384C2311yescharacteristic
283#384C2311yescharacteristic
284#384C2311yescharacteristic
285#384C2312yes—
286#384C2312yes—
287#384C2312yes—
288#382C2311yescharacteristic
289#382C2311yescharacteristic
290#382C2311yescharacteristic
291#382C2311yescharacteristic
292#380—21no—
293#380—21no—
294#380—21no—
295#380—21no—
296#380—21no—
297#380C2312yes—
298#380C2311yescharacteristic
299#380C2311yescharacteristic
300#380C2311yescharacteristic
301#380C2311yescharacteristic
302#380C2312yes—
303C4×C4⋊C4—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4—21no—
307C4×C4⋊C4—21no—
308C4×C4⋊C4D411yescharacteristic
309C4×C4⋊C4D411yescharacteristic
310C4×C4⋊C4C2311yescharacteristic
311C4×C4⋊C4C2311yescharacteristic
312C4×C4⋊C4C2312yes—
313C4×C4⋊C4C2311yescharacteristic
314C4×C22⋊C4—21no—
315C4×C22⋊C4—21no—
316C4×C22⋊C4D411yescharacteristic
317C4×C22⋊C4D411yescharacteristic
318C4×C22⋊C4D411yescharacteristic
319C4×C22⋊C4D411yescharacteristic
320C4×C22⋊C4C2311yescharacteristic
321C4×C22⋊C4C2311yescharacteristic
322C2×#95—21no—
323C43C2311yescharacteristic
324#340C2312yes—
325#340C2312yes—
326#340C2312yes—
327#340C2312yes—
328#340C2312yes—
329#340C2312yes—
330#340C2312yes—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#336C2312yes—
341#336C2311yescharacteristic
342#336C2311yescharacteristic
343#336C2311yescharacteristic
344#336C2311yescharacteristic
345#336C2312yes—
346#336C2312yes—
347C22×Q8—21no—
348C22×Q8—22no—
349C22×Q8—21no—
350C22×D4C2×D411yescharacteristic
351C23×C4—21no—
352C23×C4—22no—
353C23×C4—22no—
354C23×C4—21no—
355C23×C4C2×D411yescharacteristic
356C23×C4C2×D411yescharacteristic
357C23×C4C2×D411yescharacteristic
358C23×C4C2×D411yescharacteristic
359C23×C4C2411yescharacteristic
360C23×C4C2411yescharacteristic
361C2×M16—42no—
362C2×M16—42no—
363C2×M16C2×Q818yes—
364C22×C8—42no—
365C22×C8—42no—
366C22×C8C2×Q818yes—
367C22×C8C2412yes—
368C22×C8C2412yes—
369C22×C8C2412yes—
370C22×C8C2412yes—
371C4⋊Q8—42no—
372C4⋊Q8—42no—
373C4⋊Q8—42no—
374C4⋊Q8—42no—
375C4⋊Q8—44no—
376C4⋊Q8—82no—
377#125—22no—
378#125—41no—
379#125—42no—
380#125—48no—
381C22⋊Q8—48no—
382C22⋊Q8—48no—
383C22⋊Q8—44no—
384C22⋊Q8—44no—
385C22⋊Q8—44no—
386C4×Q8—44no—
387C4×D4—24no—
388C4×D4—24no—
389C4×D4—48no—
390C4×D4C2×Q818yes—
391#117—22no—
392#117—41no—
393#117—42no—
394C2×C4⋊C4—22no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—41no—
434C2×C4⋊C4—42no—
435C2×C4⋊C4—42no—
436C2×C4⋊C4—42no—
437C2×C4⋊C4—42no—
438C2×C4⋊C4—42no—
439C2×C4⋊C4—44no—
440C2×C4⋊C4—44no—
441C2×C4⋊C4—44no—
442C2×C4⋊C4—82no—
443C2×C4⋊C4—82no—
444C2×C4⋊C4C2×D411yescharacteristic
445C2×C4⋊C4C2×D411yescharacteristic
446C2×C4⋊C4C2×D411yescharacteristic
447C2×C4⋊C4C2412yes—
448C2×C4⋊C4C2411yescharacteristic
449C2×C4⋊C4C2411yescharacteristic
450C2×C4⋊C4C2412yes—
451C2×C4⋊C4C2412yes—
452C2×C4⋊C4C2411yescharacteristic
453C2×C4⋊C4C2411yescharacteristic
454C2×C4⋊C4C2411yescharacteristic
455C2×C4⋊C4C2411yescharacteristic
456C2×C4⋊C4C2411yescharacteristic
457C2×C4⋊C4C2412yes—
458C2×C4⋊C4C2411yescharacteristic
459C2×C22⋊C4—21no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4C2×D411yescharacteristic
468C2×C22⋊C4C2×D411yescharacteristic
469C2×C22⋊C4C2×D411yescharacteristic
470C2×C22⋊C4C2×D411yescharacteristic
471C2×C22⋊C4C2×D411yescharacteristic
472C2×C22⋊C4C2×D411yescharacteristic
473C2×C42—21no—
474C2×C42—22no—
475C2×C42—21no—
476C2×C42—21no—
477C2×C42—21no—
478C2×C42—42no—
479C2×C42—42no—
480C2×C42C2×D411yescharacteristic
481C2×C42C2×D411yescharacteristic
482C2×C42C2×D411yescharacteristic
483C2×C42C2×D411yescharacteristic
484C2×C42C2×D411yescharacteristic
485C2×C42C2×D411yescharacteristic
486C2×C42C2×D411yescharacteristic
487C2×C42C2×D411yescharacteristic
488C2×C42C2411yescharacteristic
489C2×C42C2411yescharacteristic
490C2×C42C2411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493#107—24no—
494#107—24no—
495#107—24no—
496#107—42no—
497#107—42no—
498#107—42no—
499#107—42no—
500#107—42no—
501#106—42no—
502#106—42no—
503#106—42no—
504#106—42no—
505#106—42no—
506#106—42no—
507#106—42no—
508#106—42no—
509C4⋊C8C2×Q818yes—
510C22⋊C8C2×Q818yes—
511C22⋊C8C2×Q818yes—
512#97—42no—
513#97—42no—
514#97C2×Q818yes—
515C4×C8—42no—
516#95—21no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95—21no—
527#95—21no—
528#95—21no—
529#95—22no—
530#95—21no—
531#95—22no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—22no—
536#95—22no—
537#95—21no—
538#95—22no—
539#95—22no—
540#95—21no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95C2×D411yescharacteristic
547#95C2×D411yescharacteristic
548#95C2×D411yescharacteristic
549#95C2×D411yescharacteristic
550#95C2×D411yescharacteristic
551#95C2×D411yescharacteristic
552C24C22×D411yescharacteristic
553C24C22×D411yescharacteristic
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8—44no—
557C2×Q8—42no—
558C2×Q8—42no—
559C2×Q8—81no—
560C2×Q8—82no—
561C2×Q8—82no—
562C2×Q8—81no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4C4⋊Q814yes—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—41no—
591C22×C4—41no—
592C22×C4—41no—
593C22×C4—41no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—42no—
599C22×C4—81no—
600C22×C4—81no—
601C22×C4—82no—
602C22×C4—82no—
603C22×C4—82no—
604C22×C4—82no—
605C22×C4—81no—
606C22×C4AGL(1,ℤ/8)14yes—
607C22×C4#13714yes—
608C22×C4C22×D411yescharacteristic
609C22×C4C22×D411yescharacteristic
610C22×C4C22×D411yescharacteristic
611C22×C4C22×D411yescharacteristic
612C22×C4C22×D411yescharacteristic
613C22×C4C22×D411yescharacteristic
614C22×C4C22×D411yescharacteristic
615C22×C4C22×D411yescharacteristic
616C22×C4C22×D411yescharacteristic
617C22×C4C22×D411yescharacteristic
618C22×C4C22×D411yescharacteristic
619C22×C4C22×D411yescharacteristic
620C22×C4C22×Q814yes—
621C22×C4C22×Q814yes—
622C22×C4C2511yescharacteristic
623M16—48no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—22no—
627C2×C8—22no—
628C2×C8—22no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—22no—
632C2×C8—48no—
633C2×C8C22×Q814yes—
634C2×C8C22×Q814yes—
635C2×C8C22×Q814yes—
636C2×C8C22×Q814yes—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—22no—
643C4⋊C4—22no—
644C4⋊C4—22no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—22no—
653C4⋊C4—22no—
654C4⋊C4—21no—
655C4⋊C4—22no—
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—42no—
659C4⋊C4—42no—
660C4⋊C4—42no—
661C4⋊C4—44no—
662C4⋊C4—42no—
663C4⋊C4—42no—
664C4⋊C4—42no—
665C4⋊C4—44no—
666C4⋊C4—44no—
667C4⋊C4—44no—
668C4⋊C4—42no—
669C4⋊C4—42no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—44no—
675C4⋊C4—42no—
676C4⋊C4—42no—
677C4⋊C4—44no—
678C4⋊C4—42no—
679C4⋊C4—42no—
680C4⋊C4—42no—
681C4⋊C4—81no—
682C4⋊C4—81no—
683C4⋊C4—81no—
684C4⋊C4—81no—
685C4⋊C4—81no—
686C4⋊C4—81no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—82no—
690C4⋊C4—82no—
691C4⋊C4—81no—
692C4⋊C4—81no—
693C4⋊C4—81no—
694C4⋊C4—82no—
695C4⋊C4—82no—
696C4⋊C4C4⋊Q814yes—
697C4⋊C4H(5,𝔽2)12yes—
698C22⋊C4—22no—
699C22⋊C4—22no—
700C22⋊C4—22no—
701C22⋊C4—22no—
702C22⋊C4—42no—
703C22⋊C4—44no—
704C22⋊C4—44no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4C4⋊Q814yes—
711C22⋊C4C4⋊Q814yes—
712C42—22no—
713C42—22no—
714C42—21no—
715C42—22no—
716C42—22no—
717C42—22no—
718C42—21no—
719C42—41no—
720C42—41no—
721C42—41no—
722C42—41no—
723C42—41no—
724C42—41no—
725C42—42no—
726C42—44no—
727C42—81no—
728C42—81no—
729C42—81no—
730C42C22×Q814yes—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23C2×C4⋊Q812yes—
742C23C2×C4⋊Q812yes—
743C23C2×AGL(1,ℤ/8)12yes—
744C23C2×#13712yes—
745C23C23×D411yescharacteristic
746Q8—84no—
747Q8—162no—
748Q8—164no—
749D4—28no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—24no—
767C2×C4—24no—
768C2×C4—24no—
769C2×C4—24no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—44no—
786C2×C4—44no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—42no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—42no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—84no—
823C2×C4—164no—
824C2×C4—162no—
825C2×C4—164no—
826C2×C4C2×C4⋊Q812yes—
827C2×C4C2×C4⋊Q812yes—
828C2×C4C2×C4⋊Q812yes—
829C2×C4C2×C4⋊Q812yes—
830C2×C4C2×AGL(1,ℤ/8)12yes—
831C2×C4C2×AGL(1,ℤ/8)12yes—
832C2×C4C2×#13712yes—
833C2×C4C2×#13712yes—
834C2×C4C23×Q812yes—
835C2×C4C2×H(5,𝔽2)11yescharacteristic
836C2×C4#58512yes—
837C2×C4#58511yescharacteristic
838C8—24no—
839C8—24no—
840C8—24no—
841C8—24no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22#316514yes—
856C22C22×C4⋊Q811yescharacteristic
857C22#348511yescharacteristic
858C22#348811yescharacteristic
859C22C22×AGL(1,ℤ/8)11yescharacteristic
860C22C22×#13711yescharacteristic
861C22#358511yescharacteristic
862C22#358611yescharacteristic
863C4—22no—
864C4—22no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—41no—
872C4—42no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—81no—
877C4—82no—
878C4—82no—
879C4—82no—
880C4—81no—
881C4—81no—
882C4—82no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4—81no—
887C4#350112yes—
888C4#350412yes—
889C2—24no—
890C2—42no—
891C2#3595011yescharacteristic
892C2C2×#316511yescharacteristic
893C2#6066811yescharacteristic
894C2#6170611yescharacteristic
895C2#6170911yescharacteristic
896C2#6195911yescharacteristic
897C2#6196411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
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
3. #30309C2semidirect
4. #30295C2semidirect
5. #30293C2semidirect
6. #29317C2semidirect
7. #29304C2semidirect
8. #29296C2semidirect
9. #28837C2semidirect
10. #28804C2semidirect
11. #28784C2semidirect
12. #28776C2semidirect
13. #28694C2semidirect
14. #27953C2semidirect
15. #27948C2semidirect
16. #26078C2semidirect
17. #26071C2semidirect
18. #23841C2semidirect
19. #23658C2semidirect
20. C2×#2083C2semidirect
174. #435Q8semidirect

Maximal subgroups

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

subgroupindex
#363872
#361802
#303092
#302952
#302932
#293172
#293042
#292962
#288372
#288042
#287842
#287762
#286942
#279532
#279482
#260782
#260712
#238412
#236582
C2×#20832
#227112
#226612
#205562