Finite Group Databasebeta

← #6833892

Subgroups — #6833892

Order 512.

1236 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39769C211yesmaximal, characteristic
2#39753C211yesmaximal, characteristic
3#33289C211yesmaximal, characteristic
4#32429C212yesmaximal
5#32313C212yesmaximal
6#32229C212yesmaximal
7#31457C212yesmaximal
8#29983C211yesmaximal, characteristic
9#29866C211yesmaximal, characteristic
10#29073C212yesmaximal
11#28794C212yesmaximal
12#28030C212yesmaximal
13#27816C211yesmaximal, characteristic
14#27732C212yesmaximal
15#27730C211yesmaximal, characteristic
16#26513C211yesmaximal, characteristic
17#26447C211yesmaximal, characteristic
18#24818C211yesmaximal, characteristic
19#24683C211yesmaximal, characteristic
20#23062C211yesmaximal, characteristic
21#22964C211yesmaximal, characteristic
22C8×#125C211yesmaximal, characteristic
23#21276C211yesmaximal, characteristic
24C2×#475C2211yescharacteristic
25C2×#475C2211yescharacteristic
26C2×C4×Q16C2211yescharacteristic
27#2868C2211yescharacteristic
28#2868C2211yescharacteristic
29#2794—22no—
30#2794—22no—
31#2791—22no—
32#2713—22no—
33#2660—21no—
34#2642—21no—
35#2571C2211yescharacteristic
36#2570—21no—
37#2570C2212yes—
38#2570C2212yes—
39#2568C2211yescharacteristic
40#2568C2211yescharacteristic
41#2565C2212yes—
42#2552—21no—
43#2552C2211yescharacteristic
44#2550C2212yes—
45#2511C2212yes—
46#2511C2212yes—
47#2506C2212yes—
48#2451C2212yes—
49#2446—21no—
50#2446—21no—
51#2365C2211yescharacteristic
52#2365C2211yescharacteristic
53#2355C2211yescharacteristic
54Q8×C4⋊C4C2211yescharacteristic
55#2331—21no—
56#2327—21no—
57C4×#125C2211yescharacteristic
58#2295C2211yescharacteristic
59#2295C2211yescharacteristic
60#2101C2212yes—
61#2101C2212yes—
62#2101C2212yes—
63#2099C2212yes—
64#2096C2212yes—
65#2088C2212yes—
66#2087C2212yes—
67#2085C2212yes—
68#2084C2212yes—
69#2084C2212yes—
70#2074C2212yes—
71#2074C2212yes—
72#2072C2212yes—
73#2072C2212yes—
74#2066C2212yes—
75#2059C2212yes—
76#2058C2212yes—
77#2056C2212yes—
78#2026C2212yes—
79#2024C2212yes—
80#1991C2212yes—
81#1990C2211yescharacteristic
82#1990C2211yescharacteristic
83#1990C2211yescharacteristic
84#1990C2212yes—
85#1990C2211yescharacteristic
86#1990C2212yes—
87#1989C2212yes—
88#1988C2211yescharacteristic
89#1988C2211yescharacteristic
90#1969C2211yescharacteristic
91#1969C2211yescharacteristic
92#1949C2212yes—
93#1949C2212yes—
94#1948C2211yescharacteristic
95#1948C2211yescharacteristic
96#1942C2211yescharacteristic
97#1942C2211yescharacteristic
98#1941C2212yes—
99#1939C2211yescharacteristic
100#1939C2211yescharacteristic
101#1933C2212yes—
102#1933C2211yescharacteristic
103#1933C2211yescharacteristic
104#1933C2211yescharacteristic
105#1933C2211yescharacteristic
106#1933C2212yes—
107#1933C2212yes—
108#1927C2212yes—
109#1927C2212yes—
110#1921C2212yes—
111#1920C2212yes—
112#1919C2212yes—
113#1919C2212yes—
114#1916C2212yes—
115#1916C2212yes—
116#1878C2212yes—
117#1865C2212yes—
118#1835C2212yes—
119#1834C2212yes—
120#1834C2212yes—
121#1831C2211yescharacteristic
122#1805C2212yes—
123#1803C2211yescharacteristic
124#1803C2211yescharacteristic
125C4×#107C2211yescharacteristic
126C4×#106C2212yes—
127C8×C4⋊C4C2211yescharacteristic
128C8×C4⋊C4C2212yes—
129C8×C4⋊C4C2212yes—
130C8×C4⋊C4C2211yescharacteristic
131C4×#103C2211yescharacteristic
132C4×#103C2211yescharacteristic
133C4×#103C2212yes—
134C42×C8C2211yescharacteristic
135C22×Q16C2311yescharacteristic
136C2×C4⋊Q8—21no—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8—21no—
139C2×C4⋊Q8—21no—
140C2×C4⋊Q8C2311yescharacteristic
141C2×C4⋊Q8C2311yescharacteristic
142C2×C4⋊Q8C2312yes—
143C2×#125—22no—
144C2×#125D411yescharacteristic
145C2×#125C2312yes—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8C2311yescharacteristic
149C2×C4×Q8C2311yescharacteristic
150C2×C4×Q8C2312yes—
151#475—24no—
152#475—24no—
153C4×Q16—24no—
154C2×#107C2311yescharacteristic
155C2×#107C2311yescharacteristic
156C2×#107C2311yescharacteristic
157C2×#106C2312yes—
158C2×#106C2312yes—
159C2×#106C2312yes—
160C2×#106C2312yes—
161C2×C4⋊C8C2311yescharacteristic
162C2×C4⋊C8C2311yescharacteristic
163C2×C4⋊C8C2312yes—
164C2×C4⋊C8C2312yes—
165C2×#103C2312yes—
166C2×#103C2312yes—
167C2×#103C2311yescharacteristic
168C2×#103C2311yescharacteristic
169C2×#103C2311yescharacteristic
170C2×#103C2311yescharacteristic
171C2×#103C2312yes—
172C2×#103C2312yes—
173C2×#103C2311yescharacteristic
174C2×#103C2311yescharacteristic
175C2×C4×C8C2311yescharacteristic
176C2×C4×C8C2311yescharacteristic
177C2×C4×C8C2312yes—
178C2×C4×C8C2311yescharacteristic
179C2×C4×C8C2311yescharacteristic
180C2×C4×C8C2311yescharacteristic
181C2×C4×C8C2312yes—
182C2×C4×C8C2311yescharacteristic
183#400—22no—
184#400—22no—
185#400—22no—
186#400—22no—
187#400—22no—
188#400—22no—
189#400—22no—
190#400—22no—
191#400—22no—
192#400—22no—
193#398—22no—
194#398—22no—
195#398—22no—
196#398—22no—
197#398—22no—
198#398—22no—
199#398—22no—
200#398—22no—
201#395—22no—
202#395—22no—
203#391—21no—
204#391—21no—
205#391—21no—
206#391—21no—
207#391—21no—
208#391—21no—
209#391—22no—
210#391—22no—
211#391C2311yescharacteristic
212#391C2312yes—
213#391C2312yes—
214#391C2312yes—
215#391C2311yescharacteristic
216#391C2311yescharacteristic
217#391C2311yescharacteristic
218#389—21no—
219#389—21no—
220#389—22no—
221#389—22no—
222#389D411yescharacteristic
223#389D411yescharacteristic
224#389C2311yescharacteristic
225#389C2311yescharacteristic
226#389C2312yes—
227#389C2312yes—
228#389C2312yes—
229#389C2312yes—
230#389C2311yescharacteristic
231#389C2311yescharacteristic
232#389C2312yes—
233#387—22no—
234#387—22no—
235#387—22no—
236#387—21no—
237#387—21no—
238#387—21no—
239#387—21no—
240#387—22no—
241#387—22no—
242#387—22no—
243#387—22no—
244#387—22no—
245#387—22no—
246#387—22no—
247#387—22no—
248#387—22no—
249#387—22no—
250#387—22no—
251#387—22no—
252#387D412yes—
253#387D412yes—
254#384—21no—
255#384—21no—
256#384—21no—
257#384—21no—
258#384—21no—
259#384—21no—
260#384C2312yes—
261#384C2312yes—
262#384C2312yes—
263#384C2311yescharacteristic
264#384C2311yescharacteristic
265#382—21no—
266#382—21no—
267#382D411yescharacteristic
268#382C2312yes—
269#382C2312yes—
270#382C2312yes—
271C4×C4⋊C4—21no—
272C4×C4⋊C4—21no—
273C4×C4⋊C4—21no—
274C4×C4⋊C4—21no—
275C4×C4⋊C4C2312yes—
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2311yescharacteristic
278C4×C4⋊C4C2312yes—
279C4×C4⋊C4C2311yescharacteristic
280C4×C4⋊C4C2312yes—
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2312yes—
284#376—21no—
285#376—21no—
286C43C2311yescharacteristic
287#340C2312yes—
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2311yescharacteristic
300#340C2312yes—
301#340C2312yes—
302#340C2312yes—
303#340C2311yescharacteristic
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2311yescharacteristic
307#340C2311yescharacteristic
308#340C2311yescharacteristic
309#336C2312yes—
310#336C2312yes—
311#336C2312yes—
312#336C2312yes—
313#336C2312yes—
314#336C2312yes—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8—22no—
318C22×Q8C2411yescharacteristic
319C22×Q8C2411yescharacteristic
320C2×Q16—22no—
321C2×Q16—22no—
322C2×Q16—41no—
323C22×C8C2411yescharacteristic
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2411yescharacteristic
327C22×C8C2411yescharacteristic
328C22×C8C2411yescharacteristic
329C4⋊Q8—22no—
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—42no—
334C4⋊Q8—42no—
335C4⋊Q8—44no—
336C4⋊Q8—44no—
337C4⋊Q8—82no—
338C4⋊Q8—82no—
339#125—24no—
340#125—42no—
341#125—42no—
342#125—84no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—22no—
346C4×Q8—42no—
347C4×Q8—42no—
348C4×Q8—82no—
349C4×Q8—82no—
350C4×Q8#4114yes—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—22no—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4C2×D411yescharacteristic
379C2×C4⋊C4C2×D411yescharacteristic
380C2×C4⋊C4C2×D412yes—
381C2×C4⋊C4C2×D411yescharacteristic
382C2×C4⋊C4C2×D411yescharacteristic
383C2×C4⋊C4C2×D412yes—
384C2×C4⋊C4C2×D412yes—
385C2×C4⋊C4C2×D412yes—
386C2×C4⋊C4C2412yes—
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2411yescharacteristic
389C2×C4⋊C4C2412yes—
390C2×C4⋊C4C2412yes—
391C2×C4⋊C4C2412yes—
392C2×C4⋊C4C2411yescharacteristic
393C2×C4⋊C4C2411yescharacteristic
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2411yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42—22no—
401C2×C42—22no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42C2×D411yescharacteristic
405C2×C42C2×D411yescharacteristic
406C2×C42C2×D411yescharacteristic
407C2×C42C2×D411yescharacteristic
408C2×C42C2412yes—
409C2×C42C2411yescharacteristic
410C2×C42C2411yescharacteristic
411C2×C42C2412yes—
412C2×C42C2411yescharacteristic
413#107—22no—
414#107—22no—
415#107—41no—
416#106—24no—
417#106—24no—
418#106—42no—
419#106—42no—
420C4⋊C8—24no—
421C4⋊C8—22no—
422C4⋊C8—22no—
423C4⋊C8—42no—
424#103—22no—
425#103—24no—
426#103—24no—
427#103—22no—
428#103—22no—
429#103—22no—
430#103—41no—
431#103—42no—
432#103—41no—
433#103—42no—
434C4×C8—22no—
435C4×C8—24no—
436C4×C8—22no—
437C4×C8—22no—
438C4×C8—22no—
439C4×C8—42no—
440C4×C8—41no—
441C4×C8—41no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—21no—
458#95—21no—
459#95—22no—
460#95—22no—
461#95—22no—
462#95—22no—
463#95—22no—
464#95—22no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—22no—
469#95—22no—
470#95—22no—
471#95—22no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95C2×D412yes—
477#95C2×D412yes—
478#95C2×D412yes—
479#95C2×D412yes—
480#95C2×D412yes—
481#95C2×D412yes—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—44no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—82no—
501C2×Q8—82no—
502C2×Q8C2×#4112yes—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D412yes—
518C22×C4C22×D412yes—
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C22×D411yescharacteristic
525C22×C4C2511yescharacteristic
526Q16—44no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—22no—
539C2×C8—21no—
540C2×C8—22no—
541C2×C8—21no—
542C2×C8—22no—
543C2×C82−1+412yes—
544C2×C82−1+412yes—
545C4⋊C4—24no—
546C4⋊C4—24no—
547C4⋊C4—24no—
548C4⋊C4—22no—
549C4⋊C4—22no—
550C4⋊C4—22no—
551C4⋊C4—22no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—21no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—22no—
569C4⋊C4—21no—
570C4⋊C4—22no—
571C4⋊C4—22no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—44no—
577C4⋊C4—44no—
578C4⋊C4—44no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—44no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—82no—
587C4⋊C4—82no—
588C4⋊C4—82no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4—82no—
592C4⋊C4—82no—
593C4⋊C4—82no—
594C4⋊C4—82no—
595C4⋊C4—81no—
596C4⋊C4—82no—
597C4⋊C4—82no—
598C4⋊C4—81no—
599C4⋊C4C2×#4112yes—
600C42—24no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—21no—
605C42—21no—
606C42—22no—
607C42—22no—
608C42—22no—
609C42—21no—
610C42—21no—
611C42—22no—
612C42—42no—
613C42—42no—
614C42—42no—
615C42—82no—
616C42—82no—
617C42—82no—
618C42—82no—
619C42#13514yes—
620C42C2×#4112yes—
621C422−1+412yes—
622C23C23×D411yescharacteristic
623Q8—22no—
624Q8—22no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629Q8—41no—
630Q8—41no—
631Q8—84no—
632Q8—84no—
633Q8—164no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—42no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—41no—
671C2×C4—42no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4#54812yes—
693C2×C4#54812yes—
694C2×C4C2×#13512yes—
695C2×C4C2×#13512yes—
696C2×C4C2×#13512yes—
697C2×C4#57712yes—
698C2×C4#57712yes—
699C2×C4#57812yes—
700C2×C4C22×#4111yescharacteristic
701C2×C4C2×2−1+411yescharacteristic
702C2×C4C2×2−1+411yescharacteristic
703C2×C4C2×2−1+411yescharacteristic
704C2×C4#58511yescharacteristic
705C2×C4#58511yescharacteristic
706C8—22no—
707C8—22no—
708C8—41no—
709C8—42no—
710C8—42no—
711C8—41no—
712C22C2×#54811yescharacteristic
713C22#349911yescharacteristic
714C22#350011yescharacteristic
715C22C22×#13511yescharacteristic
716C22C2×#57711yescharacteristic
717C22C2×#57711yescharacteristic
718C22C2×#57811yescharacteristic
719C4—22no—
720C4—22no—
721C4—22no—
722C4—22no—
723C4—22no—
724C4—42no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—81no—
731C4—81no—
732C4—81no—
733C4—82no—
734C4—82no—
735C4—81no—
736C4—81no—
737C4—82no—
738C4—82no—
739C4—81no—
740C4#336514yes—
741C4#346111yescharacteristic
742C4#349511yescharacteristic
743C4#355511yescharacteristic
744C4#356311yescharacteristic
745C2#3942711yescharacteristic
746C2C2×#336511yescharacteristic
747C2#6133011yescharacteristic
748C2#6247311yescharacteristic
749C2#6248611yescharacteristic
750C2#6253111yescharacteristic
751C2#6255311yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#397692
#397532
#332892
#324292
#323132
#322292
#314572
#299832
#298662
#290732
#287942
#280302
#278162
#277322
#277302
#265132
#264472
#248182
#246832
#230622
#229642
C8×#1252
#212762