Finite Group Databasebeta

← #6866186

Subgroups — #6866186

Order 512.

1651 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36492C211yesmaximal, characteristic
2#34947C211yesmaximal, characteristic, complemented
3#33148C211yesmaximal, characteristic, complemented
4#31394C212yesmaximal, complemented
5#31330C212yesmaximal, complemented
6#31326C212yesmaximal, complemented
7#30565C212yesmaximal, complemented
8#30174C212yesmaximal, complemented
9#29414C212yesmaximal, complemented
10#29158C212yesmaximal, complemented
11#28705C211yesmaximal, characteristic, complemented
12#28598C211yesmaximal, characteristic, complemented
13#26317C211yesmaximal, characteristic, complemented
14#26277C211yesmaximal, characteristic, complemented
15#25934C211yesmaximal, characteristic, complemented
16#25839C211yesmaximal, characteristic, complemented
17#25674C211yesmaximal, characteristic, complemented
18#25385C211yesmaximal, characteristic, complemented
19#25339C211yesmaximal, characteristic, complemented
20#24151C211yesmaximal, characteristic, complemented
21#22469C211yesmaximal, characteristic, complemented
22#22185C212yesmaximal, complemented
23C4×#480C211yesmaximal, characteristic, complemented
24C2×#554C2211yescharacteristic
25C2×#533C2211yescharacteristic
26C2×C4×#41C2211yescharacteristic
27C2×#500C2211yescharacteristic
28C2×#487C2211yescharacteristic
29C2×#480C2211yescharacteristic
30C2×#476C2211yescharacteristic
31C2×#465C2212yes—
32C2×#461C2211yescharacteristic
33C2×C8×D4C2211yescharacteristic
34C2×C8×D4C2211yescharacteristic
35#2857C2211yescharacteristic
36#2851C2212yes—
37#2568C2211yescharacteristic
38#2567C2211yescharacteristic
39#2566—21no—
40#2565—21no—
41#2564—22no—
42#2563C2211yescharacteristic
43#2563C2211yescharacteristic
44#2562C2212yes—
45#2542C2211yescharacteristic
46#2537C2211yescharacteristic
47#2535C2212yes—
48#2477—22no—
49#2463—22no—
50#2421—21no—
51#2417C2212yes—
52#2417C2212yes—
53#2407—21no—
54#2396—22no—
55#2361—21no—
56#2355C2211yescharacteristic
57#2352—21no—
58C4×C22⋊Q8C2212yes—
59C4×C22⋊Q8C2212yes—
60C4×#121C2211yescharacteristic
61C4×#121C2212yes—
62#2297—21no—
63#2285—21no—
64C2×C4×C4⋊C4C2211yescharacteristic
65#2101C2212yes—
66#2097C2212yes—
67#2085C2212yes—
68#2077C2212yes—
69#2076C2212yes—
70#2076C2212yes—
71#2074C2212yes—
72#2059C2212yes—
73#2059C2212yes—
74#2036C2212yes—
75#2036C2212yes—
76#2036C2212yes—
77#2036C2212yes—
78#2035C2212yes—
79#2035C2212yes—
80#2034C2212yes—
81#2026C2212yes—
82#2026C2212yes—
83#2000C2212yes—
84#2000C2212yes—
85#1990C2211yescharacteristic
86#1987C2211yescharacteristic
87#1987C2211yescharacteristic
88#1987C2211yescharacteristic
89#1984C2211yescharacteristic
90#1984C2211yescharacteristic
91#1981C2211yescharacteristic
92#1956C2211yescharacteristic
93#1948C2211yescharacteristic
94#1948C2211yescharacteristic
95#1928C2212yes—
96#1927C2212yes—
97#1925C2211yescharacteristic
98#1925C2211yescharacteristic
99#1920C2212yes—
100#1920C2212yes—
101#1919C2212yes—
102#1918C2211yescharacteristic
103#1918C2211yescharacteristic
104#1918C2212yes—
105#1893C2212yes—
106#1892C2212yes—
107#1892C2212yes—
108#1892C2212yes—
109#1880C2212yes—
110#1877C2212yes—
111#1877C2212yes—
112#1874C2211yescharacteristic
113#1869C2212yes—
114#1869C2212yes—
115#1865C2212yes—
116#1863C2212yes—
117#1863C2212yes—
118#1862C2212yes—
119#1862C2212yes—
120#1853C2212yes—
121#1852C2211yescharacteristic
122#1823C2211yescharacteristic
123#1823C2212yes—
124#1817C2212yes—
125#1808C2212yes—
126#1808C2212yes—
127#1807C2212yes—
128#1797C2211yescharacteristic
129C4×#107C2211yescharacteristic
130C4×#107C2211yescharacteristic
131C4×#102C2211yescharacteristic
132C4×#102C2211yescharacteristic
133C4×C22⋊C8C2211yescharacteristic
134C2×#336C2212yes—
135C22×#41D411yescharacteristic
136C22×SD16C2312yes—
137C23×C8C2312yes—
138C23×C8C2312yes—
139#554—42no—
140#554—42no—
141#533—42no—
142#533—42no—
143C2×C4⋊Q8C2311yescharacteristic
144C2×C4⋊Q8C2311yescharacteristic
145C2×C4⋊Q8C2311yescharacteristic
146C2×#125—21no—
147C2×#125C2312yes—
148C2×C22⋊Q8—21no—
149C2×C22⋊Q8—21no—
150C2×C22⋊Q8—21no—
151C2×C22⋊Q8—22no—
152C2×C22⋊Q8C2312yes—
153C2×C22⋊Q8C2312yes—
154C2×C22⋊Q8C2312yes—
155C2×#121—21no—
156C2×#121C2311yescharacteristic
157C2×#121C2312yes—
158C4×#41—42no—
159C4×#41—42no—
160C2×C4×Q8—21no—
161C2×C4×Q8D411yescharacteristic
162C2×C4×Q8C2312yes—
163C2×C4×Q8C2311yescharacteristic
164C2×C4×D4—21no—
165C2×C4×D4—22no—
166C2×C4×D4D412yes—
167C2×C4×D4D411yescharacteristic
168C2×C4×D4C2311yescharacteristic
169C2×C4×D4C2312yes—
170C2×C4×D4C2311yescharacteristic
171C2×C4×D4C2312yes—
172C2×#117—21no—
173C2×#117D411yescharacteristic
174C2×#117D412yes—
175C22×C4⋊C4—21no—
176C22×C4⋊C4C2311yescharacteristic
177C22×C4⋊C4C2311yescharacteristic
178C22×C42—21no—
179C22×C42C2311yescharacteristic
180C22×C42C2312yes—
181#500—42no—
182#487—42no—
183#480—24no—
184#476—42no—
185#465—28no—
186#461—42no—
187C8×D4—42no—
188C8×D4—42no—
189C2×#107C2311yescharacteristic
190C2×#107C2311yescharacteristic
191C2×#107C2311yescharacteristic
192C2×#107C2312yes—
193C2×#107C2312yes—
194C2×#107C2311yescharacteristic
195C2×#106C2312yes—
196C2×#106C2312yes—
197C2×#106C2312yes—
198C2×C4⋊C8C2311yescharacteristic
199C2×C4⋊C8C2311yescharacteristic
200C2×#103C2312yes—
201C2×#103C2312yes—
202C2×#103C2312yes—
203C2×#103C2312yes—
204C2×#103C2312yes—
205C2×#103C2312yes—
206C2×#103C2312yes—
207C2×#102C2311yescharacteristic
208C2×#102C2311yescharacteristic
209C2×#102C2312yes—
210C2×#102C2311yescharacteristic
211C2×#102C2311yescharacteristic
212C2×C22⋊C8C2311yescharacteristic
213C2×C22⋊C8C2312yes—
214C2×C22⋊C8C2312yes—
215C2×C22⋊C8C2312yes—
216C2×C22⋊C8C2311yescharacteristic
217C2×C4×C8C2311yescharacteristic
218C2×C4×C8C2311yescharacteristic
219#400—22no—
220#400—22no—
221#399—22no—
222#398—22no—
223#398—22no—
224#397—22no—
225#396—22no—
226#396—22no—
227#395—22no—
228#394—22no—
229#394—22no—
230#393—22no—
231#393—22no—
232#392—22no—
233#391—21no—
234#391—21no—
235#391—21no—
236#391—21no—
237#391C2312yes—
238#391C2312yes—
239#390—21no—
240#390—21no—
241#390—21no—
242#390C2311yescharacteristic
243#389—21no—
244#389C2312yes—
245#389C2312yes—
246#389C2311yescharacteristic
247#389C2312yes—
248#388—22no—
249#388—22no—
250#388—22no—
251#388—21no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#386—22no—
258#386—22no—
259#386—22no—
260#386—21no—
261#386—22no—
262#386—22no—
263#385—22no—
264#385—22no—
265#385—22no—
266#385—22no—
267#384—21no—
268#384—21no—
269#384C2311yescharacteristic
270#382—21no—
271#382—21no—
272#382—21no—
273#382C2312yes—
274#380—21no—
275#380—21no—
276#380—22no—
277#380—22no—
278#380C2311yescharacteristic
279#380C2312yes—
280#380C2312yes—
281#380C2312yes—
282#380C2312yes—
283#380C2312yes—
284#380C2312yes—
285C4×C4⋊C4—21no—
286C4×C4⋊C4—21no—
287C4×C4⋊C4—21no—
288C4×C4⋊C4—22no—
289C4×C4⋊C4—22no—
290C4×C4⋊C4C2312yes—
291C4×C4⋊C4C2311yescharacteristic
292C4×C4⋊C4C2311yescharacteristic
293C4×C4⋊C4C2311yescharacteristic
294C4×C4⋊C4C2311yescharacteristic
295C4×C4⋊C4C2311yescharacteristic
296C4×C22⋊C4—22no—
297C4×C22⋊C4—22no—
298C4×C22⋊C4—22no—
299C4×C22⋊C4—21no—
300C2×#95—21no—
301#340C2311yescharacteristic
302#340C2311yescharacteristic
303#340C2312yes—
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#340C2311yescharacteristic
312#340C2312yes—
313#340C2311yescharacteristic
314#340C2311yescharacteristic
315#340C2312yes—
316#340C2312yes—
317#340C2311yescharacteristic
318#340C2311yescharacteristic
319#336C2312yes—
320#336C2312yes—
321#336C2312yes—
322#336C2311yescharacteristic
323#336C2312yes—
324#336C2312yes—
325#336C2311yescharacteristic
326C2×#41—24no—
327C2×#41—24no—
328C2×#41—42no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×Q8C2×D411yescharacteristic
332C22×Q8C2412yes—
333C22×D4—22no—
334C22×D4—21no—
335C22×D4C2×D412yes—
336C22×D4C2×D411yescharacteristic
337C22×D4C2411yescharacteristic
338C23×C4—21no—
339C23×C4—21no—
340C23×C4—21no—
341C23×C4—22no—
342C23×C4C2×D412yes—
343C23×C4C2×D411yescharacteristic
344C23×C4C2×D411yescharacteristic
345C23×C4C2×D412yes—
346C23×C4C2411yescharacteristic
347C23×C4C2412yes—
348C2×SD16—24no—
349C2×SD16—42no—
350C2×SD16—42no—
351C22×C8—24no—
352C22×C8—42no—
353C22×C8—42no—
354C22×C8—42no—
355C22×C8—42no—
356C22×C8—42no—
357C22×C8C2411yescharacteristic
358C22×C8C2412yes—
359C22×C8C2412yes—
360C22×C8C2411yescharacteristic
361C22×C8C2411yescharacteristic
362C22×C8C2411yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4⋊Q8—22no—
367C4⋊Q8—22no—
368C4⋊Q8—22no—
369#125—42no—
370#125—42no—
371#125—44no—
372C22⋊Q8—24no—
373C22⋊Q8—24no—
374C22⋊Q8—42no—
375C22⋊Q8—42no—
376C22⋊Q8—42no—
377C22⋊Q8—42no—
378C22⋊Q8—48no—
379C22⋊Q8—44no—
380C22⋊Q8—44no—
381C22⋊Q8—82no—
382#121—24no—
383#121—22no—
384#121—41no—
385#121—42no—
386#121—44no—
387C4×Q8—22no—
388C4×Q8—22no—
389C4×Q8—42no—
390C4×Q8—42no—
391C4×Q8—42no—
392C4×Q8—44no—
393C4×D4—22no—
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—22no—
397C4×D4—42no—
398C4×D4—42no—
399C4×D4—42no—
400C4×D4—42no—
401C4×D4—42no—
402C4×D4—44no—
403C4×D4—44no—
404C4×D4—84no—
405#117—44no—
406#117—42no—
407#117—44no—
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—22no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—41no—
429C2×C4⋊C4—41no—
430C2×C4⋊C4—44no—
431C2×C4⋊C4C2×D411yescharacteristic
432C2×C4⋊C4C2×D412yes—
433C2×C4⋊C4C2×D411yescharacteristic
434C2×C4⋊C4C2×D412yes—
435C2×C4⋊C4C2411yescharacteristic
436C2×C4⋊C4C2411yescharacteristic
437C2×C4⋊C4C2411yescharacteristic
438C2×C4⋊C4C2412yes—
439C2×C4⋊C4C2412yes—
440C2×C4⋊C4C2411yescharacteristic
441C2×C4⋊C4C2412yes—
442C2×C4⋊C4C2411yescharacteristic
443C2×C4⋊C4C2411yescharacteristic
444C2×C4⋊C4C2411yescharacteristic
445C2×C22⋊C4—22no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—22no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—22no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—22no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—22no—
457C2×C22⋊C4—22no—
458C2×C22⋊C4—22no—
459C2×C22⋊C4—22no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4C2×D412yes—
462C2×C22⋊C4C2×D412yes—
463C2×C22⋊C4C2×D412yes—
464C2×C42—22no—
465C2×C42—22no—
466C2×C42—22no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—21no—
471C2×C42—21no—
472C2×C42—22no—
473C2×C42—42no—
474C2×C42—42no—
475C2×C42—44no—
476C2×C42C2×D411yescharacteristic
477C2×C42C2×D411yescharacteristic
478C2×C42C2×D412yes—
479C2×C42C2×D412yes—
480C2×C42C2412yes—
481C2×C42C2411yescharacteristic
482C2×C42C2411yescharacteristic
483#107—22no—
484#107—22no—
485#107—22no—
486#107—41no—
487#107—42no—
488#107—42no—
489#106—24no—
490#106—42no—
491#106—42no—
492C4⋊C8—22no—
493C4⋊C8—22no—
494#103—24no—
495#103—42no—
496#103—42no—
497#103—42no—
498#103—42no—
499#103—42no—
500#103—42no—
501#102—22no—
502#102—22no—
503#102—41no—
504#102—42no—
505#102#4114yescomplemented
506C22⋊C8—22no—
507C22⋊C8—41no—
508C22⋊C8—42no—
509C22⋊C8—42no—
510C22⋊C8—42no—
511C4×C8—22no—
512C4×C8—22no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517#95—22no—
518#95—22no—
519#95—21no—
520#95—21no—
521#95—22no—
522#95—22no—
523#95—22no—
524#95—22no—
525#95—22no—
526#95—22no—
527#95—22no—
528#95—22no—
529#95—22no—
530#95—21no—
531#95—22no—
532#95—22no—
533#95—22no—
534#95—22no—
535#95—22no—
536C24—21no—
537C24C22×D411yescharacteristic
538C24C22×D412yes—
539#41—416no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—42no—
550C2×Q8—42no—
551C2×Q8—81no—
552C2×Q8—81no—
553C2×Q8—81no—
554C2×Q8—81no—
555C2×D4—24no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—42no—
565C2×D4—44no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—44no—
569C2×D4—82no—
570C2×D4—81no—
571C2×D4#13714yes—
572C2×D4C2×#4112yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—24no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—22no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—41no—
605C22×C4—41no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—44no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—42no—
615C22×C4—82no—
616C22×C4—82no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4#13514yes—
620C22×C4C22×D412yes—
621C22×C4C22×D412yes—
622C22×C4C22×D412yes—
623C22×C4C22×D411yescharacteristic
624C22×C4C22×D411yescharacteristic
625C22×C4C22×D411yescharacteristic
626C22×C4C22×D411yescharacteristic
627C22×C4C22×D411yescharacteristic
628C22×C4C2511yescharacteristic
629SD16—84no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—22no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—22no—
638C2×C8—22no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—22no—
643C2×C8—21no—
644C2×C8—22no—
645C2×C8—21no—
646C2×C8—22no—
647C2×C8—84no—
648C2×C8—84no—
649C2×C8C2×#4112yes—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—22no—
657C4⋊C4—21no—
658C4⋊C4—22no—
659C4⋊C4—21no—
660C4⋊C4—22no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—22no—
670C4⋊C4—21no—
671C4⋊C4—42no—
672C4⋊C4—42no—
673C4⋊C4—42no—
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—42no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—82no—
688C4⋊C4—82no—
689C4⋊C4—81no—
690C4⋊C4C2×#4112yes—
691C4⋊C42−1+412yes—
692C22⋊C4—24no—
693C22⋊C4—42no—
694C22⋊C4—42no—
695C22⋊C4—44no—
696C22⋊C4—42no—
697C22⋊C4—44no—
698C22⋊C4—44no—
699C22⋊C4—44no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C22⋊C4—42no—
703C22⋊C4—44no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—82no—
707C22⋊C4—82no—
708C22⋊C4—82no—
709C22⋊C4—82no—
710C22⋊C4—82no—
711C42—22no—
712C42—22no—
713C42—21no—
714C42—21no—
715C42—22no—
716C42—22no—
717C42—42no—
718C42—42no—
719C42—44no—
720C42—42no—
721C42—42no—
722C42—42no—
723C42—42no—
724C42—42no—
725C42—82no—
726C42H(5,𝔽2)12yes—
727C42H(5,𝔽2)12yes—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—22no—
732C23—22no—
733C23—21no—
734C23—22no—
735C23—21no—
736C23—22no—
737C23—21no—
738C23—22no—
739C23—21no—
740C23—22no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23C2×#13512yes—
748C23C2×#13714yes—
749C23C23×D411yescharacteristic
750Q8—44no—
751Q8—42no—
752Q8—42no—
753Q8—42no—
754Q8—42no—
755Q8—84no—
756Q8—162no—
757D4—28no—
758D4—22no—
759D4—22no—
760D4—48no—
761D4—41no—
762D4—41no—
763D4—88no—
764D4—84no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—28no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—21no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—48no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—42no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—42no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—41no—
805C2×C4—42no—
806C2×C4—42no—
807C2×C4—41no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—41no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—42no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—42no—
827C2×C4—82no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4—84no—
831C2×C4—84no—
832C2×C4—164no—
833C2×C4#53412yes—
834C2×C4#53412yes—
835C2×C4C2×#13512yes—
836C2×C4C2×#13512yes—
837C2×C4C2×#13712yes—
838C2×C4C22×#4111yescharacteristic
839C2×C4C2×H(5,𝔽2)11yescharacteristic
840C2×C4C2×H(5,𝔽2)11yescharacteristic
841C2×C4C2×2−1+411yescharacteristic
842C2×C4#58511yescharacteristic
843C2×C4#58511yescharacteristic
844C8—22no—
845C8—41no—
846C8—42no—
847C8—41no—
848C8—42no—
849C8—41no—
850C22—24no—
851C22—22no—
852C22—24no—
853C22—22no—
854C22—24no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—42no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22C2×#53411yescharacteristic
872C22D4×#4111yescharacteristic
873C22#348911yescharacteristic
874C22C22×#13511yescharacteristic
875C22C22×#13711yescharacteristic
876C22#358411yescharacteristic
877C22#358511yescharacteristic
878C4—22no—
879C4—22no—
880C4—42no—
881C4—41no—
882C4—42no—
883C4—42no—
884C4—41no—
885C4—42no—
886C4—42no—
887C4—82no—
888C4—81no—
889C4—82no—
890C4—82no—
891C4—81no—
892C4—81no—
893C4—82no—
894C4—81no—
895C4—81no—
896C4#319014yes—
897C4#351111yescharacteristic
898C4#351411yescharacteristic
899C4#355411yescharacteristic
900C4#356211yescharacteristic
901C2—44no—
902C2—42no—
903C2—82no—
904C2#3986411yescharacteristic
905C2C2×#319011yescharacteristic
906C2#6076011yescharacteristic
907C2#6142711yescharacteristic
908C2#6145311yescharacteristic
909C2#6209811yescharacteristic
910C2#6213911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#36492C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×#41 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34947C2semidirect
3. #33148C2semidirect
4. #31394C2semidirect
5. #31330C2semidirect
6. #31326C2semidirect
7. #30565C2semidirect
8. #30174C2semidirect
9. #29414C2semidirect
10. #29158C2semidirect
11. #28705C2semidirect
12. #28598C2semidirect
13. #26317C2semidirect
14. #26277C2semidirect
15. #25934C2semidirect
16. #25839C2semidirect
17. #25674C2semidirect
18. #25385C2semidirect
19. #25339C2semidirect
20. #24151C2semidirect
21. #22469C2semidirect
22. #22185C2semidirect
23. C4×#480C2semidirect
505. #102#41semidirect

Maximal subgroups

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

subgroupindex
#364922
#349472
#331482
#313942
#313302
#313262
#305652
#301742
#294142
#291582
#287052
#285982
#263172
#262772
#259342
#258392
#256742
#253852
#253392
#241512
#224692
#221852
C4×#4802