Finite Group Databasebeta

← #6462365

Subgroups — #6462365

Order 512.

1677 conjugacy classes of subgroups.

The subgroup lattice has 927 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36638C211yesmaximal, characteristic
2C2×#2295C211yesmaximal, characteristic, complemented
3#29577C212yesmaximal, complemented
4#29557C212yesmaximal, complemented
5#29450C212yesmaximal, complemented
6#29446C212yesmaximal, complemented
7#29336C211yesmaximal, characteristic
8#29303C211yesmaximal, characteristic, complemented
9#29112C211yesmaximal, characteristic, complemented
10#28315C211yesmaximal, characteristic
11#24603C211yesmaximal, characteristic
12#24602C211yesmaximal, characteristic, complemented
13#24503C211yesmaximal, characteristic
14#24502C211yesmaximal, characteristic, complemented
15#23785C212yesmaximal, complemented
16#23687C212yesmaximal, complemented
17#21581C211yesmaximal, characteristic, complemented
18#21580C211yesmaximal, characteristic
19#21455C211yesmaximal, characteristic, complemented
20#21454C211yesmaximal, characteristic
21#21288C212yesmaximal, complemented
22#21287C212yesmaximal, complemented
23#20463C211yesmaximal, characteristic, complemented
24C22×C4×Q8C2211yescharacteristic
25C2×#484C2211yescharacteristic
26C2×#481C2211yescharacteristic
27C2×#451C2211yescharacteristic
28C2×#448C2211yescharacteristic
29C2×#441C2212yes—
30C2×#440C2212yes—
31C2×#431C2211yescharacteristic
32C2×#431C2211yescharacteristic
33#2866—21no—
34#2865—21no—
35#2864C2211yescharacteristic
36#2863C2211yescharacteristic
37#2861C2211yescharacteristic
38#2860C2211yescharacteristic
39#2855C2211yescharacteristic
40#2854C2211yescharacteristic
41#2853—21no—
42#2852—21no—
43#2851C2211yescharacteristic
44#2850C2211yescharacteristic
45C4×#125C2211yescharacteristic
46C4×#126—21no—
47C4×#124C2211yescharacteristic
48C4×C22⋊Q8C2211yescharacteristic
49C4×#123—21no—
50C4×#121C2211yescharacteristic
51#2298—21no—
52#2295—21no—
53#2295—21no—
54#2295—21no—
55#2295—21no—
56#2295C2212yes—
57#2295C2211yescharacteristic
58#2295C2212yes—
59#2295C2212yes—
60#2295C2212yes—
61C2×#391C2211yescharacteristic
62C2×#391C2211yescharacteristic
63#2293C2211yescharacteristic
64C2×#389C2211yescharacteristic
65C2×#389C2211yescharacteristic
66#2290—21no—
67C2×#387—21no—
68C2×#387—21no—
69C2×C4×C4⋊C4—21no—
70C2×C4×C4⋊C4C2211yescharacteristic
71C2×#376—21no—
72C2×C43C2211yescharacteristic
73#2101C2212yes—
74#2097C2212yes—
75#2088C2212yes—
76#2087C2212yes—
77#2085C2212yes—
78#2074C2212yes—
79#2068C2212yes—
80#2068C2212yes—
81#2066C2212yes—
82#2065C2212yes—
83#2059C2212yes—
84#2056C2212yes—
85#2055C2212yes—
86#2042C2212yes—
87#2026C2212yes—
88#2015C2212yes—
89#1973C2212yes—
90#1971C2212yes—
91#1969C2212yes—
92#1968C2212yes—
93#1944C2212yes—
94#1943C2212yes—
95#1942C2212yes—
96#1941C2212yes—
97#1936C2212yes—
98#1935C2212yes—
99#1935C2212yes—
100#1935C2212yes—
101#1934C2212yes—
102#1933C2212yes—
103#1933C2212yes—
104#1933C2212yes—
105#1927C2212yes—
106#1925C2212yes—
107#1920C2212yes—
108#1918C2212yes—
109#1880C2212yes—
110#1878C2212yes—
111#1874C2211yescharacteristic
112#1874C2211yescharacteristic
113#1872C2211yescharacteristic
114#1872C2211yescharacteristic
115#1865C2212yes—
116#1863C2212yes—
117#1853C2211yescharacteristic
118#1853C2211yescharacteristic
119#1852C2211yescharacteristic
120#1852C2211yescharacteristic
121#1824C2211yescharacteristic
122#1824C2211yescharacteristic
123#1787C2211yescharacteristic
124#1787C2211yescharacteristic
125#1776C2212yes—
126#1776C2212yes—
127#1767C2212yes—
128#1767C2212yes—
129#1763C2212yes—
130#1763C2212yes—
131#1763C2212yes—
132#1762C2212yes—
133#1749C2211yescharacteristic
134#1749C2211yescharacteristic
135#1749C2211yescharacteristic
136#1749C2211yescharacteristic
137#1744C2212yes—
138C4×#97C2212yes—
139C23×Q8C2311yescharacteristic
140C22×Q16C2312yes—
141C22×SD16C2312yes—
142C2×#126—21no—
143C2×#125C2311yescharacteristic
144C2×#124C2311yescharacteristic
145C2×#123—21no—
146C2×C22⋊Q8C2311yescharacteristic
147C2×#121C2311yescharacteristic
148C2×C4×Q8—28no—
149C2×C4×Q8—21no—
150C2×C4×Q8—21no—
151C2×C4×Q8C2312yes—
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2312yes—
154C2×C4×D4—21no—
155C2×C4×D4C2311yescharacteristic
156C2×#117—21no—
157C22×C4⋊C4—21no—
158C22×C4⋊C4—21no—
159C22×C4⋊C4—21no—
160C22×C4⋊C4C2311yescharacteristic
161C22×C4⋊C4C2311yescharacteristic
162C22×C4⋊C4C2311yescharacteristic
163C22×C42—21no—
164C22×C42—21no—
165C22×C42D411yescharacteristic
166C22×C42D411yescharacteristic
167C22×C42D411yescharacteristic
168C22×C42D411yescharacteristic
169C22×C42C2311yescharacteristic
170C22×C42C2311yescharacteristic
171C22×C42C2311yescharacteristic
172#484—24no—
173#481—24no—
174#451—24no—
175#448—24no—
176#441—28no—
177#440—28no—
178#431—24no—
179#431—24no—
180C2×#107C2312yes—
181C2×#107C2312yes—
182C2×#107C2312yes—
183C2×#106C2312yes—
184C2×#106C2312yes—
185C2×#106C2312yes—
186C2×C4⋊C8C2312yes—
187C2×C4⋊C8C2312yes—
188C2×#103C2312yes—
189C2×#103C2312yes—
190C2×#103C2312yes—
191C2×#103C2312yes—
192C2×#103C2312yes—
193C2×#103C2312yes—
194C2×#103C2312yes—
195C2×#103C2312yes—
196C2×#103C2312yes—
197C2×#102C2312yes—
198C2×#102C2312yes—
199C2×#102C2312yes—
200C2×C22⋊C8C2311yescharacteristic
201C2×C22⋊C8C2311yescharacteristic
202C2×C22⋊C8C2311yescharacteristic
203C2×C22⋊C8C2311yescharacteristic
204C2×#97C2312yes—
205C2×#97C2312yes—
206C2×#97C2312yes—
207C2×#97C2312yes—
208C2×C4×C8C2312yes—
209C2×C4×C8C2312yes—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391C2312yes—
215#391C2311yescharacteristic
216#391C2312yes—
217#391C2311yescharacteristic
218#391C2311yescharacteristic
219#391C2311yescharacteristic
220#391C2312yes—
221#391C2312yes—
222#390C2311yescharacteristic
223#390C2311yescharacteristic
224#390C2311yescharacteristic
225#390C2311yescharacteristic
226#389—21no—
227#389—21no—
228#389—21no—
229#389—21no—
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2312yes—
233#389C2312yes—
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2311yescharacteristic
239#389C2311yescharacteristic
240#389C2312yes—
241#389C2312yes—
242#388—21no—
243#388—21no—
244#388—21no—
245#388—21no—
246#388—21no—
247#388—21no—
248#388—21no—
249#388—21no—
250#388—21no—
251#388—21no—
252#388—21no—
253#388—21no—
254#388—21no—
255#388—21no—
256#388—21no—
257#388—21no—
258#387—21no—
259#387—21no—
260#387—21no—
261#387—21no—
262#387—21no—
263#387—21no—
264#387—21no—
265#387—21no—
266#387—21no—
267#387—21no—
268#387—21no—
269#387—21no—
270#387—21no—
271#387—21no—
272#387—21no—
273#387—21no—
274#387—22no—
275#387—22no—
276#387—22no—
277#387—22no—
278#387—22no—
279#387—22no—
280#387—22no—
281#387—22no—
282#386—21no—
283#386—21no—
284#386—21no—
285#386—21no—
286#385—21no—
287#385—21no—
288#385—21no—
289#385—21no—
290#383—21no—
291#382C2311yescharacteristic
292#382C2311yescharacteristic
293#381—21no—
294#380C2311yescharacteristic
295#380C2311yescharacteristic
296C4×C4⋊C4—21no—
297C4×C4⋊C4—21no—
298C4×C4⋊C4—21no—
299C4×C4⋊C4—21no—
300C4×C4⋊C4—22no—
301C4×C4⋊C4—22no—
302C4×C4⋊C4—22no—
303C4×C4⋊C4—22no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4C2311yescharacteristic
307C4×C4⋊C4C2311yescharacteristic
308C4×C4⋊C4C2312yes—
309C4×C4⋊C4C2312yes—
310C4×C22⋊C4—21no—
311C4×C22⋊C4—21no—
312C4×C22⋊C4—21no—
313C4×C22⋊C4—21no—
314C4×C22⋊C4—21no—
315#376—22no—
316#376—22no—
317#376—22no—
318#376—22no—
319#376—21no—
320C2×#95—21no—
321C2×#95—21no—
322C2×#95—21no—
323C2×#95—21no—
324C2×#95—21no—
325C2×#95—21no—
326C2×#95—21no—
327C43D411yescharacteristic
328C43D411yescharacteristic
329C43D411yescharacteristic
330C43D411yescharacteristic
331C43C2311yescharacteristic
332C43C2311yescharacteristic
333C43C2311yescharacteristic
334C43C2311yescharacteristic
335#340C2312yes—
336#340C2312yes—
337#340C2312yes—
338#340C2312yes—
339#340C2312yes—
340#340C2312yes—
341#340C2312yes—
342#340C2312yes—
343#340C2312yes—
344#340C2312yes—
345#340C2312yes—
346#340C2312yes—
347#336C2312yes—
348#336C2312yes—
349#336C2312yes—
350#336C2312yes—
351C22×Q8—24no—
352C22×Q8—21no—
353C22×Q8—22no—
354C22×Q8—22no—
355C22×Q8—42no—
356C22×Q8C2411yescharacteristic
357C22×Q8C2412yes—
358C22×D4—21no—
359C22×D4C2411yescharacteristic
360C23×C4—21no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—21no—
364C23×C4—21no—
365C23×C4C2×D411yescharacteristic
366C23×C4C2×D411yescharacteristic
367C23×C4C2×D411yescharacteristic
368C23×C4C2×D411yescharacteristic
369C23×C4C2×D411yescharacteristic
370C23×C4C2×D411yescharacteristic
371C23×C4C2411yescharacteristic
372C2×Q16—24no—
373C2×Q16—24no—
374C2×Q16—42no—
375C2×SD16—24no—
376C2×SD16—24no—
377C2×SD16—42no—
378C22×C8C2412yes—
379C22×C8C2412yes—
380C22×C8C2412yes—
381C22×C8C2412yes—
382#126—44no—
383#125—42no—
384#124—42no—
385#123—44no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388#121—22no—
389#121—22no—
390C4×Q8—28no—
391C4×Q8—28no—
392C4×Q8—24no—
393C4×Q8—24no—
394C4×Q8—24no—
395C4×Q8—24no—
396C4×Q8#4118yes—
397C4×D4—24no—
398C4×D4—44no—
399#117—44no—
400C2×C4⋊C4—28no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—22no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—21no—
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—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—42no—
426C2×C4⋊C4—44no—
427C2×C4⋊C4—44no—
428C2×C4⋊C4C2412yes—
429C2×C4⋊C4C2412yes—
430C2×C4⋊C4C2411yescharacteristic
431C2×C4⋊C4C2411yescharacteristic
432C2×C4⋊C4C2411yescharacteristic
433C2×C4⋊C4C2411yescharacteristic
434C2×C4⋊C4C2411yescharacteristic
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2412yes—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C42—28no—
453C2×C42—24no—
454C2×C42—22no—
455C2×C42—22no—
456C2×C42—22no—
457C2×C42—22no—
458C2×C42—24no—
459C2×C42—21no—
460C2×C42—21no—
461C2×C42—21no—
462C2×C42—22no—
463C2×C42—22no—
464C2×C42—42no—
465C2×C42—42no—
466C2×C42—42no—
467C2×C42—42no—
468C2×C42—44no—
469C2×C42C2×D411yescharacteristic
470C2×C42C2×D411yescharacteristic
471C2×C42C2×D411yescharacteristic
472C2×C42C2×D411yescharacteristic
473C2×C42C2×D411yescharacteristic
474C2×C42C2×D411yescharacteristic
475C2×C42C2×D411yescharacteristic
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D411yescharacteristic
479C2×C42C2×D411yescharacteristic
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×C42C2×D411yescharacteristic
489C2×C42C2×D411yescharacteristic
490C2×C42C2×D411yescharacteristic
491C2×C42C2411yescharacteristic
492C2×C42C2411yescharacteristic
493C2×C42C2411yescharacteristic
494C2×C42C2411yescharacteristic
495C2×C42C2411yescharacteristic
496C2×C42C2411yescharacteristic
497#107—24no—
498#107—24no—
499#107—42no—
500#106—24no—
501#106—24no—
502#106—42no—
503C4⋊C8—24no—
504C4⋊C8—24no—
505#103—24no—
506#103—24no—
507#103—24no—
508#103—24no—
509#103—24no—
510#103—24no—
511#103—42no—
512#103—42no—
513#103—42no—
514#102—24no—
515#102—24no—
516#102—42no—
517C22⋊C8—22no—
518C22⋊C8—22no—
519C22⋊C8#4114yes—
520C22⋊C8#4114yes—
521#97—24no—
522#97—24no—
523#97—42no—
524#97—42no—
525C4×C8—24no—
526C4×C8—24no—
527#95—22no—
528#95—22no—
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#95—22no—
541#95—21no—
542#95—21no—
543#95—21no—
544#95—21no—
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—
565C24—21no—
566C24C22×D411yescharacteristic
567C2×Q8—24no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—21no—
572C2×Q8—22no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—48no—
578C2×Q8—48no—
579C2×Q8—42no—
580C2×Q8—42no—
581C2×Q8C2×#4114yes—
582C2×D4—21no—
583C2×D4—22no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—24no—
597C22×C4—24no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—41no—
616C22×C4—41no—
617C22×C4—41no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—42no—
626C22×C4—42no—
627C22×C4—42no—
628C22×C4—42no—
629C22×C4—42no—
630C22×C4—42no—
631C22×C4—42no—
632C22×C4—42no—
633C22×C4—42no—
634C22×C4#13714yes—
635C22×C4C22×D411yescharacteristic
636C22×C4C22×D411yescharacteristic
637C22×C4C22×D411yescharacteristic
638C22×C4C22×D411yescharacteristic
639C22×C4C22×D411yescharacteristic
640C22×C4C22×D411yescharacteristic
641C22×C4C22×D411yescharacteristic
642C22×C4C22×D411yescharacteristic
643C22×C4C22×D411yescharacteristic
644C22×C4C22×D411yescharacteristic
645C22×C4C22×D411yescharacteristic
646C22×C4C22×D411yescharacteristic
647C22×C4C22×D411yescharacteristic
648C22×C4C2×#4112yes—
649C22×C4C2×#4112yes—
650C22×C4C2511yescharacteristic
651Q16—48no—
652SD16—48no—
653C2×C8—22no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—22no—
657C2×C8—22no—
658C2×C8—22no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8C2×#4114yes—
664C2×C8C2×#4114yes—
665C4⋊C4—24no—
666C4⋊C4—28no—
667C4⋊C4—28no—
668C4⋊C4—22no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—42no—
682C4⋊C4—44no—
683C4⋊C4—44no—
684C4⋊C4—44no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—42no—
689C4⋊C4—42no—
690C4⋊C4—42no—
691C4⋊C4—42no—
692C4⋊C4—42no—
693C4⋊C4—42no—
694C4⋊C4—42no—
695C4⋊C4—42no—
696C4⋊C4—44no—
697C4⋊C4—42no—
698C4⋊C4—42no—
699C4⋊C4C2×#4114yes—
700C22⋊C4—42no—
701C22⋊C4—42no—
702C22⋊C4—42no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C42—28no—
716C42—28no—
717C42—22no—
718C42—22no—
719C42—22no—
720C42—22no—
721C42—22no—
722C42—22no—
723C42—22no—
724C42—22no—
725C42—22no—
726C42—22no—
727C42—22no—
728C42—22no—
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—22no—
734C42—22no—
735C42—22no—
736C42—41no—
737C42—41no—
738C42—41no—
739C42—41no—
740C42—41no—
741C42—41no—
742C42—41no—
743C42—41no—
744C42—41no—
745C42—41no—
746C42—44no—
747C42—42no—
748C42—42no—
749C42—42no—
750C42—44no—
751C42C2×#4114yes—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23#53212yes—
764C23C2×#13712yes—
765C23#57512yes—
766C23C23×D411yescharacteristic
767Q8—24no—
768Q8—24no—
769Q8—48no—
770Q8—42no—
771Q8—42no—
772Q8—42no—
773Q8—42no—
774D4—42no—
775D4—42no—
776D4—84no—
777C2×C4—28no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—28no—
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—21no—
792C2×C4—21no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—21no—
796C2×C4—24no—
797C2×C4—24no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
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—44no—
816C2×C4—44no—
817C2×C4—44no—
818C2×C4—44no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—42no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—42no—
840C2×C4—42no—
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—84no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4#52512yes—
856C2×C4#52512yes—
857C2×C4#53212yes—
858C2×C4C2×#13712yes—
859C2×C4C2×#13712yes—
860C2×C4#57512yes—
861C2×C4#57512yes—
862C2×C4C22×#4112yes—
863C2×C4C22×#4111yescharacteristic
864C2×C4C22×#4111yescharacteristic
865C2×C4#58512yes—
866C8—24no—
867C8—24no—
868C8—42no—
869C8—42no—
870C22—22no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22#318114yes—
884C22C2×#52511yescharacteristic
885C22C2×#53211yescharacteristic
886C22#344911yescharacteristic
887C22C22×#13711yescharacteristic
888C22C2×#57511yescharacteristic
889C22C2×#57511yescharacteristic
890C22C2×#57511yescharacteristic
891C4—22no—
892C4—22no—
893C4—22no—
894C4—22no—
895C4—22no—
896C4—22no—
897C4—22no—
898C4—41no—
899C4—41no—
900C4—41no—
901C4—41no—
902C4—41no—
903C4—44no—
904C4—41no—
905C4—44no—
906C4—81no—
907C4—81no—
908C4—82no—
909C4—81no—
910C4—81no—
911C4—82no—
912C4—81no—
913C4—81no—
914C4—81no—
915C4#347512yes—
916C4#347512yes—
917C2—24no—
918C2—161no—
919C2#3487711yescharacteristic
920C2#6056011yescharacteristic
921C2#6056311yescharacteristic
922C2C2×#318111yescharacteristic
923C2#6070211yescharacteristic
924C2#6096611yescharacteristic
925C2#6097011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C43 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#2295C2semidirect
3. #29577C2semidirect
4. #29557C2semidirect
5. #29450C2semidirect
6. #29446C2semidirect
8. #29303C2semidirect
9. #29112C2semidirect
12. #24602C2semidirect
14. #24502C2semidirect
15. #23785C2semidirect
16. #23687C2semidirect
17. #21581C2semidirect
19. #21455C2semidirect
21. #21288C2semidirect
22. #21287C2semidirect
23. #20463C2semidirect

Maximal subgroups

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

subgroupindex
#366382
C2×#22952
#295772
#295572
#294502
#294462
#293362
#293032
#291122
#283152
#246032
#246022
#245032
#245022
#237852
#236872
#215812
#215802
#214552
#214542
#212882
#212872
#204632