Finite Group Databasebeta

← #6856450

Subgroups — #6856450

Order 512.

1593 conjugacy classes of subgroups.

The subgroup lattice has 937 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36577C211yesmaximal, characteristic
2C2×#2581C211yesmaximal, characteristic
3#32906C211yesmaximal, characteristic
4#32619C212yesmaximal, complemented
5#32608C212yesmaximal, complemented
6#32557C212yesmaximal, complemented
7#32553C212yesmaximal, complemented
8#29715C211yesmaximal, characteristic
9#29715C211yesmaximal, characteristic
10#29335C211yesmaximal, characteristic
11#29329C211yesmaximal, characteristic
12#29243C211yesmaximal, characteristic
13#29240C211yesmaximal, characteristic
14#28198C212yesmaximal, complemented
15#27983C211yesmaximal, characteristic
16#27686C211yesmaximal, characteristic
17#25306C212yesmaximal, complemented
18#25004C212yesmaximal, complemented
19#24203C212yesmaximal, complemented
20#22510C211yesmaximal, characteristic
21#22050C211yesmaximal, characteristic
22#22044C211yesmaximal, characteristic
23#21455C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C22×C4×Q8C2211yescharacteristic
26C22×C4×Q8C2211yescharacteristic
27C2×#462C2212yes—
28C2×#451C2211yescharacteristic
29C2×#451C2211yescharacteristic
30C2×#451C2211yescharacteristic
31C2×#446C2212yes—
32C2×#441C2212yes—
33#2857C2211yescharacteristic
34#2857C2211yescharacteristic
35#2857C2211yescharacteristic
36#2582C2211yescharacteristic
37#2582C2211yescharacteristic
38#2582C2211yescharacteristic
39#2581—21no—
40#2581—21no—
41#2581—21no—
42#2581—21no—
43#2581C2212yes—
44#2581C2212yes—
45#2581C2212yes—
46#2581C2212yes—
47#2568C2211yescharacteristic
48#2568C2211yescharacteristic
49#2568C2211yescharacteristic
50#2453—21no—
51#2453—21no—
52#2453—21no—
53#2442—21no—
54#2442—21no—
55#2442—21no—
56C2×#400—21no—
57C2×#395—21no—
58#2351—21no—
59Q8×C4⋊C4C2211yescharacteristic
60Q8×C22⋊C4—21no—
61C4×C22⋊Q8C2211yescharacteristic
62C4×C22⋊Q8C2211yescharacteristic
63C4×C22⋊Q8C2211yescharacteristic
64C2×#391C2211yescharacteristic
65C2×#391C2211yescharacteristic
66C2×#389C2211yescharacteristic
67C2×#389C2211yescharacteristic
68C2×#387—21no—
69C2×#387—21no—
70C2×#382C2211yescharacteristic
71#2101C2212yes—
72#2100C2212yes—
73#2099C2212yes—
74#2097C2212yes—
75#2088C2212yes—
76#2088C2212yes—
77#2074C2212yes—
78#2074C2212yes—
79#2072C2212yes—
80#2072C2212yes—
81#2068C2212yes—
82#2066C2212yes—
83#2056C2212yes—
84#2056C2212yes—
85#2056C2212yes—
86#2056C2212yes—
87#2043C2212yes—
88#2043C2212yes—
89#2016C2212yes—
90#2016C2212yes—
91#1985C2212yes—
92#1985C2212yes—
93#1984C2212yes—
94#1971C2212yes—
95#1969C2212yes—
96#1960C2212yes—
97#1949C2212yes—
98#1935C2212yes—
99#1935C2212yes—
100#1935C2212yes—
101#1933C2212yes—
102#1933C2212yes—
103#1933C2212yes—
104#1928C2212yes—
105#1927C2212yes—
106#1919C2212yes—
107#1918C2212yes—
108#1878C2212yes—
109#1878C2212yes—
110#1878C2212yes—
111#1878C2212yes—
112#1878C2212yes—
113#1872C2211yescharacteristic
114#1872C2211yescharacteristic
115#1872C2211yescharacteristic
116#1872C2211yescharacteristic
117#1872C2211yescharacteristic
118#1872C2211yescharacteristic
119#1872C2211yescharacteristic
120#1872C2211yescharacteristic
121#1872C2211yescharacteristic
122#1865C2212yes—
123#1865C2212yes—
124#1865C2212yes—
125#1853C2211yescharacteristic
126#1853C2211yescharacteristic
127#1852C2211yescharacteristic
128#1836C2212yes—
129#1805C2212yes—
130#1803C2212yes—
131#1797C2211yescharacteristic
132#1797C2211yescharacteristic
133#1797C2211yescharacteristic
134#1787C2211yescharacteristic
135#1763C2212yes—
136#1749C2211yescharacteristic
137#1749C2211yescharacteristic
138C4×C22⋊C8C2211yescharacteristic
139C23×Q8D411yescharacteristic
140C23×Q8C2311yescharacteristic
141C22×Q16C2312yes—
142C22×Q16C2312yes—
143C22×Q16C2312yes—
144#557—44no—
145C2×C4⋊Q8C2311yescharacteristic
146C2×C4⋊Q8C2311yescharacteristic
147C2×C4⋊Q8C2311yescharacteristic
148C2×#125—21no—
149C2×#125—21no—
150C2×#125—21no—
151C2×C22⋊Q8C2311yescharacteristic
152C2×C22⋊Q8C2311yescharacteristic
153C2×C22⋊Q8C2311yescharacteristic
154C2×C4×Q8—21no—
155C2×C4×Q8—21no—
156C2×C4×Q8—21no—
157C2×C4×Q8—21no—
158C2×C4×Q8—44no—
159C2×C4×Q8—44no—
160C2×C4×Q8D411yescharacteristic
161C2×C4×Q8D411yescharacteristic
162C2×C4×Q8D411yescharacteristic
163C2×C4×Q8D411yescharacteristic
164C2×C4×Q8C2312yes—
165C2×C4×Q8C2311yescharacteristic
166C2×C4×Q8C2312yes—
167C2×C4×Q8C2311yescharacteristic
168C2×C4×Q8C2311yescharacteristic
169C2×C4×Q8C2311yescharacteristic
170C2×C4×Q8C2311yescharacteristic
171C2×C4×Q8C2311yescharacteristic
172C2×C4×Q8C2311yescharacteristic
173C22×C4⋊C4—21no—
174C22×C4⋊C4—21no—
175C22×C4⋊C4—21no—
176C22×C4⋊C4D411yescharacteristic
177C22×C4⋊C4D411yescharacteristic
178C22×C4⋊C4D411yescharacteristic
179C22×C4⋊C4C2311yescharacteristic
180C22×C4⋊C4C2311yescharacteristic
181C22×C4⋊C4C2311yescharacteristic
182C22×C42—21no—
183C22×C42C2311yescharacteristic
184C22×C42C2311yescharacteristic
185C22×C42C2311yescharacteristic
186#462—44no—
187#451—24no—
188#451—24no—
189#451—24no—
190#446—44no—
191#441—44no—
192C2×#107C2312yes—
193C2×#106C2312yes—
194C2×#106C2312yes—
195C2×C4⋊C8C2312yes—
196C2×C4⋊C8C2312yes—
197C2×C4⋊C8C2312yes—
198C2×#103C2312yes—
199C2×#103C2312yes—
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#103C2312yes—
208C2×#103C2312yes—
209C2×#103C2312yes—
210C2×#103C2312yes—
211C2×#103C2312yes—
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2311yescharacteristic
214C2×C22⋊C8C2311yescharacteristic
215C2×C22⋊C8C2311yescharacteristic
216C2×#97C2312yes—
217C2×#97C2312yes—
218C2×C4×C8C2312yes—
219#400—21no—
220#400—21no—
221#400—21no—
222#400—21no—
223#400—21no—
224#400—21no—
225#400—22no—
226#400—22no—
227#400—22no—
228#400—22no—
229#398—21no—
230#398—21no—
231#398—21no—
232#398—21no—
233#398—21no—
234#398—21no—
235#395—22no—
236#395—22no—
237#395—22no—
238#395—22no—
239#391—21no—
240#391—21no—
241#391—21no—
242#391—21no—
243#391—21no—
244#391—21no—
245#391—21no—
246#391—21no—
247#391—21no—
248#391—21no—
249#391C2311yescharacteristic
250#391C2311yescharacteristic
251#391C2311yescharacteristic
252#391C2311yescharacteristic
253#391C2312yes—
254#391C2312yes—
255#391C2311yescharacteristic
256#391C2311yescharacteristic
257#391C2311yescharacteristic
258#391C2311yescharacteristic
259#391C2311yescharacteristic
260#391C2312yes—
261#391C2312yes—
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#389—21no—
272#389—21no—
273#389—21no—
274#389—21no—
275#389—21no—
276#389—21no—
277#389—21no—
278#389C2312yes—
279#389C2312yes—
280#389C2312yes—
281#389C2312yes—
282#389C2311yescharacteristic
283#389C2311yescharacteristic
284#389C2311yescharacteristic
285#387—22no—
286#387—22no—
287#387—22no—
288#387—22no—
289#387—22no—
290#387—22no—
291#387—22no—
292#387—22no—
293#387—21no—
294#387—21no—
295#387—21no—
296#385—21no—
297#385—21no—
298#385—21no—
299#384C2311yescharacteristic
300#384C2311yescharacteristic
301#384C2311yescharacteristic
302#382—21no—
303#382—21no—
304#382—21no—
305#382—21no—
306#382—21no—
307#382C2312yes—
308#382C2312yes—
309#380—21no—
310#380—21no—
311#380—21no—
312#380—21no—
313#380—21no—
314#380—21no—
315#380C2311yescharacteristic
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—
331C2×#95—21no—
332C2×#95—21no—
333#340C2312yes—
334#340C2312yes—
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#336C2312yes—
346#336C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8—24no—
352C22×Q8—21no—
353C22×Q8—22no—
354C22×Q8—42no—
355C22×Q8—42no—
356C22×Q8—42no—
357C22×Q8—42no—
358C22×Q8C2×D411yescharacteristic
359C22×Q8C2×D411yescharacteristic
360C22×Q8C2×D411yescharacteristic
361C22×Q8C2×D411yescharacteristic
362C22×Q8#4114yes—
363C22×Q8C2411yescharacteristic
364C22×Q8C2411yescharacteristic
365C22×Q8C2411yescharacteristic
366C22×Q8C2412yes—
367C23×C4—21no—
368C23×C4—21no—
369C23×C4—21no—
370C23×C4—21no—
371C23×C4C2×D411yescharacteristic
372C23×C4C2×D411yescharacteristic
373C23×C4C2×D411yescharacteristic
374C23×C4C2×D411yescharacteristic
375C23×C4C2×D411yescharacteristic
376C23×C4C2×D411yescharacteristic
377C23×C4C2411yescharacteristic
378C2×Q16—24no—
379C2×Q16—24no—
380C2×Q16—24no—
381C2×Q16—42no—
382C2×Q16—42no—
383C2×Q16—42no—
384C2×Q16—42no—
385C2×Q16—42no—
386C2×Q16—42no—
387C22×C8C2412yes—
388C22×C8C2412yes—
389C22×C8C2412yes—
390C22×C8C2412yes—
391C4⋊Q8—24no—
392C4⋊Q8—42no—
393C4⋊Q8—42no—
394#125—44no—
395#125—44no—
396#125—44no—
397C22⋊Q8—22no—
398C22⋊Q8—22no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403C4×Q8—24no—
404C4×Q8—24no—
405C4×Q8—24no—
406C4×Q8—24no—
407C4×Q8—24no—
408C4×Q8—42no—
409C4×Q8—42no—
410C4×Q8—42no—
411C4×Q8—42no—
412C4×Q8—42no—
413C4×Q8—42no—
414C4×Q8—42no—
415C4×Q8—42no—
416C4×Q8—42no—
417C4×Q8—42no—
418C4×Q8—44no—
419C4×Q8—44no—
420C4×Q8—44no—
421C4×Q8—44no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
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—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—42no—
453C2×C4⋊C4—42no—
454C2×C4⋊C4—42no—
455C2×C4⋊C4—42no—
456C2×C4⋊C4—42no—
457C2×C4⋊C4—42no—
458C2×C4⋊C4—44no—
459C2×C4⋊C4—44no—
460C2×C4⋊C4—44no—
461C2×C4⋊C4C2×D411yescharacteristic
462C2×C4⋊C4C2×D411yescharacteristic
463C2×C4⋊C4C2×D411yescharacteristic
464C2×C4⋊C4C2×D411yescharacteristic
465C2×C4⋊C4C2×D411yescharacteristic
466C2×C4⋊C4C2×D411yescharacteristic
467C2×C4⋊C4C2×D411yescharacteristic
468C2×C4⋊C4C2×D411yescharacteristic
469C2×C4⋊C4C2×D411yescharacteristic
470C2×C4⋊C4C2×D411yescharacteristic
471C2×C4⋊C4C2×D411yescharacteristic
472C2×C4⋊C4C2×D411yescharacteristic
473C2×C4⋊C4C2412yes—
474C2×C4⋊C4C2412yes—
475C2×C4⋊C4C2412yes—
476C2×C4⋊C4C2411yescharacteristic
477C2×C4⋊C4C2411yescharacteristic
478C2×C4⋊C4C2411yescharacteristic
479C2×C4⋊C4C2411yescharacteristic
480C2×C4⋊C4C2411yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C42—24no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—22no—
490C2×C42—22no—
491C2×C42—21no—
492C2×C42—21no—
493C2×C42—21no—
494C2×C42—42no—
495C2×C42—42no—
496C2×C42—44no—
497C2×C42C2×D411yescharacteristic
498C2×C42C2×D411yescharacteristic
499C2×C42C2×D411yescharacteristic
500C2×C42C2×D411yescharacteristic
501C2×C42C2×D411yescharacteristic
502C2×C42C2×D411yescharacteristic
503C2×C42C2411yescharacteristic
504C2×C42C2411yescharacteristic
505C2×C42C2411yescharacteristic
506C2×C42C2411yescharacteristic
507C2×C42C2411yescharacteristic
508C2×C42C2411yescharacteristic
509#107—42no—
510#106—42no—
511#106—42no—
512C4⋊C8—24no—
513C4⋊C8—42no—
514C4⋊C8—42no—
515#103—24no—
516#103—24no—
517#103—24no—
518#103—42no—
519#103—42no—
520#103—42no—
521#103—42no—
522#103—42no—
523#103—42no—
524#103—42no—
525#103—42no—
526#103—42no—
527#103—42no—
528#103—42no—
529C22⋊C8—22no—
530C22⋊C8—22no—
531C22⋊C8—22no—
532C22⋊C8—22no—
533#97—24no—
534#97—42no—
535C4×C8—42no—
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—22no—
546#95—22no—
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
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—
570#95—21no—
571#95—21no—
572#95—21no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577C24C22×D411yescharacteristic
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—24no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—22no—
595C2×Q8—22no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—22no—
600C2×Q8—22no—
601C2×Q8—22no—
602C2×Q8—22no—
603C2×Q8—22no—
604C2×Q8—41no—
605C2×Q8—41no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8—48no—
609C2×Q8—42no—
610C2×Q8—42no—
611C2×Q8—48no—
612C2×Q8—416no—
613C2×Q8C2×#4114yes—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—22no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—42no—
647C22×C4—42no—
648C22×C4—42no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—42no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4#13714yes—
658C22×C4C22×D411yescharacteristic
659C22×C4C22×D411yescharacteristic
660C22×C4C22×D411yescharacteristic
661C22×C4C22×D411yescharacteristic
662C22×C4C22×D411yescharacteristic
663C22×C4C22×D411yescharacteristic
664C22×C4C22×D411yescharacteristic
665C22×C4C22×D411yescharacteristic
666C22×C4C22×D411yescharacteristic
667C22×C4C22×D411yescharacteristic
668C22×C4C22×D411yescharacteristic
669C22×C4C22×D411yescharacteristic
670C22×C4C22×D411yescharacteristic
671C22×C4C2×#4112yes—
672C22×C42−1+412yes—
673C22×C4C2511yescharacteristic
674Q16—48no—
675Q16—84no—
676Q16—84no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—22no—
682C2×C8—22no—
683C2×C8—22no—
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—22no—
688C2×C8—22no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—22no—
705C4⋊C4—22no—
706C4⋊C4—22no—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—41no—
710C4⋊C4—41no—
711C4⋊C4—41no—
712C4⋊C4—41no—
713C4⋊C4—41no—
714C4⋊C4—41no—
715C4⋊C4—42no—
716C4⋊C4—42no—
717C4⋊C4—44no—
718C4⋊C4—42no—
719C4⋊C4—44no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—42no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—44no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C4⋊C4—42no—
732C4⋊C4—42no—
733C4⋊C4—42no—
734C4⋊C4—42no—
735C4⋊C4—44no—
736C4⋊C4—44no—
737C4⋊C4—44no—
738C4⋊C4—42no—
739C4⋊C4—81no—
740C4⋊C4—81no—
741C4⋊C4—81no—
742C4⋊C4—81no—
743C4⋊C4—81no—
744C4⋊C4—81no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C42—22no—
750C42—22no—
751C42—22no—
752C42—22no—
753C42—22no—
754C42—22no—
755C42—22no—
756C42—41no—
757C42—41no—
758C42—41no—
759C42—41no—
760C42—44no—
761C42—42no—
762C42—42no—
763C42—42no—
764C42—42no—
765C42—44no—
766C42—42no—
767C42—42no—
768C42H(5,𝔽2)14yes—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23#54812yes—
774C23C2×#13712yes—
775C23#57812yes—
776C23C23×D411yescharacteristic
777Q8—28no—
778Q8—24no—
779Q8—24no—
780Q8—44no—
781Q8—44no—
782Q8—48no—
783Q8—44no—
784Q8—42no—
785Q8—42no—
786Q8—42no—
787Q8—42no—
788Q8—42no—
789Q8—42no—
790Q8—42no—
791Q8—42no—
792C2×C4—21no—
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—24no—
805C2×C4—24no—
806C2×C4—21no—
807C2×C4—21no—
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—21no—
818C2×C4—24no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—44no—
831C2×C4—44no—
832C2×C4—48no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—41no—
841C2×C4—42no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—42no—
864C2×C4—42no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—82no—
869C2×C4—82no—
870C2×C4—84no—
871C2×C4—84no—
872C2×C4—84no—
873C2×C4#53412yes—
874C2×C4#53412yes—
875C2×C4#54812yes—
876C2×C4C2×#13712yes—
877C2×C4C2×#13712yes—
878C2×C4#57512yes—
879C2×C4C22×#4111yescharacteristic
880C2×C4C2×H(5,𝔽2)12yes—
881C2×C4C2×2−1+411yescharacteristic
882C2×C4#58512yes—
883C8—42no—
884C8—42no—
885C8—42no—
886C8—42no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22#337414yes—
894C22C2×#53411yescharacteristic
895C22C2×#54811yescharacteristic
896C22#348711yescharacteristic
897C22C22×#13711yescharacteristic
898C22C2×#57511yescharacteristic
899C22C2×#57811yescharacteristic
900C22#358611yescharacteristic
901C4—22no—
902C4—22no—
903C4—22no—
904C4—22no—
905C4—22no—
906C4—22no—
907C4—44no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—81no—
916C4—81no—
917C4—81no—
918C4—82no—
919C4—81no—
920C4—81no—
921C4—81no—
922C4—81no—
923C4—82no—
924C4—81no—
925C4—82no—
926C4#350512yes—
927C4#354112yes—
928C2—24no—
929C2#3972311yescharacteristic
930C2#6075111yescharacteristic
931C2#6075911yescharacteristic
932C2C2×#337411yescharacteristic
933C2#6132011yescharacteristic
934C2#6188911yescharacteristic
935C2#6190511yescharacteristic
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. #32619C2semidirect
5. #32608C2semidirect
6. #32557C2semidirect
7. #32553C2semidirect
14. #28198C2semidirect
17. #25306C2semidirect
18. #25004C2semidirect
19. #24203C2semidirect

Maximal subgroups

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

subgroupindex
#365772
C2×#25812
#329062
#326192
#326082
#325572
#325532
#297152
#293352
#293292
#292432
#292402
#281982
#279832
#276862
#253062
#250042
#242032
#225102
#220502
#220442
#214552