Finite Group Databasebeta

← #6852525

Subgroups — #6852525

Order 512.

1587 conjugacy classes of subgroups.

The subgroup lattice has 923 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36545C211yesmaximal, characteristic
2C2×#2582C211yesmaximal, characteristic
3#32960C211yesmaximal, characteristic
4#32660C212yesmaximal, complemented
5#32650C212yesmaximal, complemented
6#32587C212yesmaximal, complemented
7#32566C212yesmaximal, complemented
8#29957C211yesmaximal, characteristic
9#29953C211yesmaximal, characteristic
10#29301C211yesmaximal, characteristic
11#29298C211yesmaximal, characteristic
12#29244C211yesmaximal, characteristic
13#29243C211yesmaximal, characteristic
14#28278C212yesmaximal, complemented
15#27953C211yesmaximal, characteristic
16#27681C211yesmaximal, characteristic
17#25484C212yesmaximal, complemented
18#25075C212yesmaximal, complemented
19#24348C212yesmaximal, complemented
20#22510C211yesmaximal, characteristic
21#22050C211yesmaximal, characteristic
22#22044C211yesmaximal, characteristic
23#21455C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C2×#479C2212yes—
28C2×#451C2211yescharacteristic
29C2×#446C2212yes—
30C2×#441C2212yes—
31#2857C2211yescharacteristic
32#2851C2211yescharacteristic
33#2851C2211yescharacteristic
34#2584C2211yescharacteristic
35#2584C2211yescharacteristic
36#2582—21no—
37#2582—21no—
38#2582—21no—
39#2582—21no—
40#2582C2212yes—
41#2582C2212yes—
42#2582C2212yes—
43#2582C2212yes—
44#2582C2211yescharacteristic
45#2581C2211yescharacteristic
46#2581C2211yescharacteristic
47#2546C2211yescharacteristic
48#2473—21no—
49#2473—21no—
50#2462—21no—
51#2462—21no—
52#2446—21no—
53#2434—21no—
54C2×#398—21no—
55C2×#398—21no—
56#2365—21no—
57#2360—21no—
58#2355C2211yescharacteristic
59C4×C22⋊Q8C2211yescharacteristic
60C4×C22⋊Q8C2211yescharacteristic
61C4×C22⋊Q8C2211yescharacteristic
62C2×#391—21no—
63C2×#391C2211yescharacteristic
64C2×#391C2211yescharacteristic
65C2×#389—21no—
66C2×#389C2211yescharacteristic
67C2×#389C2211yescharacteristic
68C2×#384C2211yescharacteristic
69#2100C2212yes—
70#2097C2212yes—
71#2095C2212yes—
72#2095C2212yes—
73#2088C2212yes—
74#2086C2212yes—
75#2085C2212yes—
76#2084C2212yes—
77#2083C2212yes—
78#2083C2212yes—
79#2068C2212yes—
80#2068C2212yes—
81#2068C2212yes—
82#2068C2212yes—
83#2066C2212yes—
84#2066C2212yes—
85#2059C2212yes—
86#2058C2212yes—
87#2026C2212yes—
88#2024C2212yes—
89#1992C2212yes—
90#1985C2212yes—
91#1985C2212yes—
92#1984C2212yes—
93#1971C2212yes—
94#1969C2212yes—
95#1947C2212yes—
96#1943C2212yes—
97#1943C2212yes—
98#1942C2212yes—
99#1941C2212yes—
100#1935C2212yes—
101#1933C2212yes—
102#1928C2212yes—
103#1927C2212yes—
104#1920C2212yes—
105#1918C2212yes—
106#1878C2212yes—
107#1878C2212yes—
108#1878C2212yes—
109#1872C2211yescharacteristic
110#1872C2211yescharacteristic
111#1872C2211yescharacteristic
112#1865C2212yes—
113#1865C2212yes—
114#1865C2212yes—
115#1863C2212yes—
116#1863C2212yes—
117#1853C2211yescharacteristic
118#1853C2211yescharacteristic
119#1853C2211yescharacteristic
120#1853C2211yescharacteristic
121#1852C2211yescharacteristic
122#1852C2211yescharacteristic
123#1852C2211yescharacteristic
124#1852C2211yescharacteristic
125#1852C2211yescharacteristic
126#1847C2212yes—
127#1805C2212yes—
128#1803C2212yes—
129#1797C2211yescharacteristic
130#1797C2211yescharacteristic
131#1797C2211yescharacteristic
132#1787C2211yescharacteristic
133#1787C2211yescharacteristic
134#1787C2211yescharacteristic
135#1763C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8D411yescharacteristic
140C23×Q8C2311yescharacteristic
141C22×Q16C2312yes—
142#557—44no—
143C2×C4⋊Q8—21no—
144C2×C4⋊Q8—21no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×#125—21no—
147C2×#125—21no—
148C2×#125C2311yescharacteristic
149C2×#125C2311yescharacteristic
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8C2311yescharacteristic
152C2×C4×Q8—21no—
153C2×C4×Q8—21no—
154C2×C4×Q8—21no—
155C2×C4×Q8—44no—
156C2×C4×Q8—44no—
157C2×C4×Q8D411yescharacteristic
158C2×C4×Q8D411yescharacteristic
159C2×C4×Q8D411yescharacteristic
160C2×C4×Q8D411yescharacteristic
161C2×C4×Q8C2312yes—
162C2×C4×Q8C2311yescharacteristic
163C2×C4×Q8C2311yescharacteristic
164C2×C4×Q8C2312yes—
165C2×C4×Q8C2311yescharacteristic
166C2×C4×Q8C2311yescharacteristic
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2311yescharacteristic
169C2×C4×Q8C2311yescharacteristic
170C22×C4⋊C4—21no—
171C22×C4⋊C4—21no—
172C22×C4⋊C4—21no—
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4D411yescharacteristic
176C22×C4⋊C4D411yescharacteristic
177C22×C4⋊C4D411yescharacteristic
178C22×C4⋊C4C2311yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C42—21no—
182C22×C42C2311yescharacteristic
183C22×C42C2311yescharacteristic
184C22×C42C2311yescharacteristic
185#479—44no—
186#451Q818yescomplemented
187#446—44no—
188#441—44no—
189C2×#107C2312yes—
190C2×#107C2312yes—
191C2×#107C2312yes—
192C2×#107C2312yes—
193C2×#107C2312yes—
194C2×#106C2312yes—
195C2×#106C2312yes—
196C2×#106C2312yes—
197C2×#106C2312yes—
198C2×C4⋊C8C2312yes—
199C2×C4⋊C8C2312yes—
200C2×C4⋊C8C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×C22⋊C8C2311yescharacteristic
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2311yescharacteristic
214C2×C22⋊C8C2311yescharacteristic
215C2×#97C2312yes—
216C2×#97C2312yes—
217C2×C4×C8C2312yes—
218#400—21no—
219#400—21no—
220#398—22no—
221#398—22no—
222#398—22no—
223#398—22no—
224#398—22no—
225#398—22no—
226#398—22no—
227#398—22no—
228#398—21no—
229#398—21no—
230#398—21no—
231#398—21no—
232#398—21no—
233#398—21no—
234#395—21no—
235#395—21no—
236#395—21no—
237#395—21no—
238#391—22no—
239#391—22no—
240#391—22no—
241#391—22no—
242#391—21no—
243#391—21no—
244#391—21no—
245#391—21no—
246#391—21no—
247#391—21no—
248#391—21no—
249#391—21no—
250#391C2311yescharacteristic
251#391C2312yes—
252#391C2311yescharacteristic
253#391C2312yes—
254#391C2311yescharacteristic
255#391C2312yes—
256#391C2312yes—
257#389—22no—
258#389—22no—
259#389—22no—
260#389—22no—
261#389—21no—
262#389—21no—
263#389—21no—
264#389—21no—
265#389—21no—
266#389—21no—
267#389—21no—
268#389—21no—
269#389—21no—
270#389—21no—
271#389C2312yes—
272#389C2312yes—
273#389C2311yescharacteristic
274#389C2312yes—
275#389C2311yescharacteristic
276#389C2311yescharacteristic
277#389C2311yescharacteristic
278#389C2312yes—
279#389C2311yescharacteristic
280#389C2311yescharacteristic
281#389C2311yescharacteristic
282#389C2311yescharacteristic
283#389C2311yescharacteristic
284#387—21no—
285#387—21no—
286#387—21no—
287#387—21no—
288#387—21no—
289#387—21no—
290#387—21no—
291#387—21no—
292#387—21no—
293#387—21no—
294#387—21no—
295#387—21no—
296#387—21no—
297#385—21no—
298#385—21no—
299#385—21no—
300#385—21no—
301#385—21no—
302#385—21no—
303#385—21no—
304#384—21no—
305#384—21no—
306#384C2312yes—
307#384C2312yes—
308#384C2311yescharacteristic
309#382C2311yescharacteristic
310#382C2311yescharacteristic
311#380—21no—
312#380C2311yescharacteristic
313#380C2311yescharacteristic
314#380C2311yescharacteristic
315C4×C4⋊C4—21no—
316C4×C4⋊C4—21no—
317C4×C4⋊C4—21no—
318C4×C4⋊C4—21no—
319C4×C4⋊C4C2311yescharacteristic
320C4×C4⋊C4C2311yescharacteristic
321C4×C4⋊C4C2311yescharacteristic
322C4×C22⋊C4—21no—
323C4×C22⋊C4—21no—
324C4×C22⋊C4—21no—
325C2×#95—21no—
326C2×#95—21no—
327C2×#95—21no—
328C2×#95—21no—
329C2×#95—21no—
330C2×#95—21no—
331#340C2312yes—
332#340C2312yes—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#336C2312yes—
344#336C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349C22×Q8—24no—
350C22×Q8—21no—
351C22×Q8—21no—
352C22×Q8—22no—
353C22×Q8—42no—
354C22×Q8—42no—
355C22×Q8—42no—
356C22×Q8—42no—
357C22×Q8C2×D411yescharacteristic
358C22×Q8C2×D411yescharacteristic
359C22×Q8C2×D411yescharacteristic
360C22×Q8C2×D411yescharacteristic
361C22×Q8C2×Q814yes—
362C22×Q8C2411yescharacteristic
363C22×Q8C2412yes—
364C23×C4—21no—
365C23×C4—21no—
366C23×C4—21no—
367C23×C4—21no—
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2×D411yescharacteristic
372C23×C4C2×D411yescharacteristic
373C23×C4C2×D411yescharacteristic
374C23×C4C2411yescharacteristic
375C2×Q16—42no—
376C2×Q16—42no—
377C2×Q16C2×Q818yescomplemented
378C22×C8C2412yes—
379C22×C8C2412yes—
380C22×C8C2412yes—
381C22×C8C2412yes—
382C4⋊Q8—42no—
383C4⋊Q8—44no—
384C4⋊Q8—44no—
385#125—24no—
386#125—42no—
387#125—44no—
388#125—44no—
389C22⋊Q8—22no—
390C22⋊Q8—44no—
391C22⋊Q8C2×Q814yes—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×Q8—24no—
397C4×Q8—42no—
398C4×Q8—42no—
399C4×Q8—42no—
400C4×Q8—42no—
401C4×Q8—42no—
402C4×Q8—42no—
403C4×Q8—42no—
404C4×Q8—42no—
405C4×Q8—42no—
406C4×Q8—42no—
407C4×Q8—44no—
408C4×Q8—44no—
409C4×Q8—44no—
410C2×C4⋊C4—21no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—22no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—22no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—42no—
444C2×C4⋊C4—42no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—42no—
449C2×C4⋊C4—44no—
450C2×C4⋊C4—44no—
451C2×C4⋊C4—82no—
452C2×C4⋊C4—82no—
453C2×C4⋊C4—82no—
454C2×C4⋊C4C2×D411yescharacteristic
455C2×C4⋊C4C2×D411yescharacteristic
456C2×C4⋊C4C2×D411yescharacteristic
457C2×C4⋊C4C2×D411yescharacteristic
458C2×C4⋊C4C2×D411yescharacteristic
459C2×C4⋊C4C2×D411yescharacteristic
460C2×C4⋊C4C2×D411yescharacteristic
461C2×C4⋊C4C2×D411yescharacteristic
462C2×C4⋊C4C2×D411yescharacteristic
463C2×C4⋊C4C2×D411yescharacteristic
464C2×C4⋊C4C2×D411yescharacteristic
465C2×C4⋊C4C2×D411yescharacteristic
466C2×C4⋊C4C2412yes—
467C2×C4⋊C4C2412yes—
468C2×C4⋊C4C2412yes—
469C2×C4⋊C4C2411yescharacteristic
470C2×C4⋊C4C2411yescharacteristic
471C2×C4⋊C4C2411yescharacteristic
472C2×C4⋊C4C2411yescharacteristic
473C2×C4⋊C4C2411yescharacteristic
474C2×C4⋊C4C2411yescharacteristic
475C2×C4⋊C4C2411yescharacteristic
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C42—24no—
481C2×C42—21no—
482C2×C42—21no—
483C2×C42—21no—
484C2×C42—22no—
485C2×C42—22no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—42no—
490C2×C42—42no—
491C2×C42—44no—
492C2×C42C2×D411yescharacteristic
493C2×C42C2×D411yescharacteristic
494C2×C42C2×D411yescharacteristic
495C2×C42C2×D411yescharacteristic
496C2×C42C2×D411yescharacteristic
497C2×C42C2×D411yescharacteristic
498C2×C42C2411yescharacteristic
499C2×C42C2411yescharacteristic
500C2×C42C2411yescharacteristic
501C2×C42C2411yescharacteristic
502C2×C42C2411yescharacteristic
503C2×C42C2411yescharacteristic
504#107—42no—
505#107—42no—
506#107—42no—
507#107—42no—
508#107—42no—
509#106—42no—
510#106—42no—
511#106—42no—
512#106—42no—
513C4⋊C8—24no—
514C4⋊C8—42no—
515C4⋊C8—42no—
516#103—42no—
517#103—42no—
518#103—42no—
519#103—42no—
520#103—42no—
521#103—42no—
522#103—42no—
523#103—42no—
524#103—42no—
525#103C2×Q818yescomplemented
526C22⋊C8—22no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8C2×Q814yes—
530#97—24no—
531#97—42no—
532C4×C8—42no—
533#95—22no—
534#95—22no—
535#95—22no—
536#95—22no—
537#95—22no—
538#95—22no—
539#95—22no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544#95—22no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95—21no—
551#95—21no—
552#95—21no—
553#95—21no—
554#95—21no—
555#95—21no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566#95—21no—
567#95—21no—
568#95—21no—
569#95—21no—
570C24C22×D411yescharacteristic
571C2×Q8—22no—
572C2×Q8—22no—
573C2×Q8—24no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—41no—
586C2×Q8—41no—
587C2×Q8—41no—
588C2×Q8—41no—
589C2×Q8—41no—
590C2×Q8—41no—
591C2×Q8—48no—
592C2×Q8—42no—
593C2×Q8—416no—
594C2×Q8—42no—
595C2×Q8—48no—
596C2×Q8—42no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8#13714yes—
600C2×Q8C22×Q814yes—
601C2×Q8C22×Q812yes—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—24no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—41no—
632C22×C4—41no—
633C22×C4—41no—
634C22×C4—41no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—42no—
645C22×C4—42no—
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C22×D411yescharacteristic
649C22×C4C22×D411yescharacteristic
650C22×C4C22×D411yescharacteristic
651C22×C4C22×D411yescharacteristic
652C22×C4C22×D411yescharacteristic
653C22×C4C22×D411yescharacteristic
654C22×C4C22×D411yescharacteristic
655C22×C4C22×D411yescharacteristic
656C22×C4C22×D411yescharacteristic
657C22×C4C22×D411yescharacteristic
658C22×C4C22×D411yescharacteristic
659C22×C4C22×Q812yes—
660C22×C42−1+412yes—
661C22×C4C2511yescharacteristic
662Q16—48no—
663C2×C8—22no—
664C2×C8—22no—
665C2×C8—22no—
666C2×C8—22no—
667C2×C8—22no—
668C2×C8—22no—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8C22×Q814yes—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—41no—
696C4⋊C4—41no—
697C4⋊C4—41no—
698C4⋊C4—41no—
699C4⋊C4—41no—
700C4⋊C4—41no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—42no—
706C4⋊C4—44no—
707C4⋊C4—42no—
708C4⋊C4—42no—
709C4⋊C4—42no—
710C4⋊C4—42no—
711C4⋊C4—42no—
712C4⋊C4—42no—
713C4⋊C4—42no—
714C4⋊C4—42no—
715C4⋊C4—44no—
716C4⋊C4—42no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—81no—
724C4⋊C4—81no—
725C4⋊C4—81no—
726C4⋊C4—81no—
727C4⋊C4—82no—
728C4⋊C4—82no—
729C4⋊C4—82no—
730C4⋊C4—82no—
731C4⋊C4—82no—
732C4⋊C4—82no—
733C4⋊C4C22×Q812yes—
734C22⋊C4—24no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C42—22no—
739C42—22no—
740C42—22no—
741C42—22no—
742C42—22no—
743C42—22no—
744C42—22no—
745C42—41no—
746C42—41no—
747C42—41no—
748C42—41no—
749C42—44no—
750C42—42no—
751C42—42no—
752C42—44no—
753C42—42no—
754C42—42no—
755C42—81no—
756C42—81no—
757C42H(5,𝔽2)14yes—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23D4×Q812yes—
763C23#57512yes—
764C23#57812yes—
765C23C23×D411yescharacteristic
766Q8—24no—
767Q8—24no—
768Q8—24no—
769Q8—44no—
770Q8—44no—
771Q8—44no—
772Q8—44no—
773Q8—48no—
774Q8—42no—
775Q8—42no—
776Q8—42no—
777Q8—84no—
778C2×C4—28no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—24no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—44no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—42no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—42no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—82no—
855C2×C4—82no—
856C2×C4—84no—
857C2×C4—84no—
858C2×C4—84no—
859C2×C4#53412yes—
860C2×C4#53412yes—
861C2×C4D4×Q812yes—
862C2×C4C2×#13712yes—
863C2×C4C2×#13712yes—
864C2×C4C2×#13712yes—
865C2×C4C23×Q811yescharacteristic
866C2×C4C2×H(5,𝔽2)12yes—
867C2×C4C2×2−1+411yescharacteristic
868C2×C4#58512yes—
869C8—24no—
870C8—42no—
871C8—42no—
872C8—42no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22#339014yes—
880C22C2×#53411yescharacteristic
881C22C2×D4×Q811yescharacteristic
882C22#348711yescharacteristic
883C22C22×#13711yescharacteristic
884C22C2×#57511yescharacteristic
885C22C2×#57811yescharacteristic
886C22#358511yescharacteristic
887C4—22no—
888C4—22no—
889C4—22no—
890C4—22no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4—41no—
898C4—41no—
899C4—41no—
900C4—44no—
901C4—42no—
902C4—42no—
903C4—81no—
904C4—81no—
905C4—81no—
906C4—82no—
907C4—81no—
908C4—81no—
909C4—82no—
910C4—82no—
911C4—81no—
912C4#350112yes—
913C4#354112yes—
914C2—24no—
915C2#3959511yescharacteristic
916C2#6075111yescharacteristic
917C2#6076411yescharacteristic
918C2C2×#339011yescharacteristic
919C2Q8×#13711yescharacteristic
920C2#6189511yescharacteristic
921C2#6190011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
4. #32660C2semidirect
5. #32650C2semidirect
6. #32587C2semidirect
7. #32566C2semidirect
14. #28278C2semidirect
17. #25484C2semidirect
18. #25075C2semidirect
19. #24348C2semidirect
186. #451Q8semidirect
377. C2×Q16C2×Q8semidirect
525. #103C2×Q8semidirect

Maximal subgroups

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

subgroupindex
#365452
C2×#25822
#329602
#326602
#326502
#325872
#325662
#299572
#299532
#293012
#292982
#292442
#292432
#282782
#279532
#276812
#254842
#250752
#243482
#225102
#220502
#220442
#214552