Finite Group Databasebeta

← #6627461

Subgroups — #6627461

Order 512.

1400 conjugacy classes of subgroups.

The subgroup lattice has 757 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36584C211yesmaximal, characteristic
2C4×#557C211yesmaximal, characteristic
3#33200C212yesmaximal
4#33200C211yesmaximal, characteristic
5#29291C212yesmaximal
6#29288C211yesmaximal, characteristic
7#29227C212yesmaximal
8#29220C211yesmaximal, characteristic
9#26525C212yesmaximal
10#26523C212yesmaximal
11#26513C211yesmaximal, characteristic
12#26509C211yesmaximal, characteristic
13#26123C212yesmaximal
14#26123C212yesmaximal
15#26113C211yesmaximal, characteristic
16#26109C211yesmaximal, characteristic
17#22743C211yesmaximal, characteristic
18#22742C211yesmaximal, characteristic
19#22722C211yesmaximal, characteristic
20#22524C211yesmaximal, characteristic
21#22524C211yesmaximal, characteristic
22#21618C212yesmaximal
23C4×#479C211yesmaximal, characteristic
24C2×#557C2211yescharacteristic
25C2×#479C2211yescharacteristic
26C2×#479C2212yes—
27C2×#446C2211yescharacteristic
28C2×#446C2211yescharacteristic
29#2859C2211yescharacteristic
30#2859C2212yes—
31#2571C2211yescharacteristic
32#2571C2212yes—
33#2571C2212yes—
34#2571C2211yescharacteristic
35#2509—22no—
36#2509—21no—
37#2509—22no—
38#2509—21no—
39#2370—22no—
40#2370C2212yes—
41#2365—21no—
42#2365C2211yescharacteristic
43#2355—21no—
44#2355C2211yescharacteristic
45#2351—21no—
46#2351—21no—
47#2351C2212yes—
48Q8×C4⋊C4C2211yescharacteristic
49Q8×C4⋊C4C2211yescharacteristic
50Q8×C4⋊C4C2211yescharacteristic
51C4×C4⋊Q8—21no—
52C4×C4⋊Q8C2211yescharacteristic
53C4×#125—22no—
54C4×#125C2212yes—
55C4×#125C2211yescharacteristic
56C4×#125C2212yes—
57C42×Q8—21no—
58C42×Q8C2211yescharacteristic
59C42×Q8C2212yes—
60C42×Q8C2211yescharacteristic
61#2101C2212yes—
62#2101C2212yes—
63#2101C2212yes—
64#2101C2212yes—
65#2101C2212yes—
66#2101C2212yes—
67#2088C2212yes—
68#2088C2212yes—
69#2088C2212yes—
70#2087C2212yes—
71#2087C2212yes—
72#2086C2212yes—
73#1992C2212yes—
74#1992C2212yes—
75#1990C2211yescharacteristic
76#1990C2211yescharacteristic
77#1989C2212yes—
78#1989C2212yes—
79#1989C2211yescharacteristic
80#1989C2212yes—
81#1989C2212yes—
82#1989C2212yes—
83#1989C2212yes—
84#1988C2211yescharacteristic
85#1988C2211yescharacteristic
86#1949C2212yes—
87#1949C2212yes—
88#1949C2212yes—
89#1949C2211yescharacteristic
90#1949C2212yes—
91#1949C2212yes—
92#1949C2212yes—
93#1948C2211yescharacteristic
94#1948C2211yescharacteristic
95#1948C2212yes—
96#1947C2211yescharacteristic
97#1947C2211yescharacteristic
98#1947C2212yes—
99#1940C2212yes—
100#1940C2212yes—
101#1939C2211yescharacteristic
102#1939C2211yescharacteristic
103#1921C2212yes—
104#1920C2211yescharacteristic
105#1919C2212yes—
106#1918C2211yescharacteristic
107#1865C2212yes—
108#1865C2211yescharacteristic
109#1863C2211yescharacteristic
110#1863C2212yes—
111#1842C2211yescharacteristic
112#1842C2212yes—
113#1836C2212yes—
114#1836C2212yes—
115#1834C2211yescharacteristic
116#1834C2211yescharacteristic
117#1805C2212yes—
118#1805C2212yes—
119#1805C2212yes—
120#1805C2211yescharacteristic
121#1803C2211yescharacteristic
122#1803C2212yes—
123#1803C2212yes—
124#1803C2211yescharacteristic
125#1776C2212yes—
126#1776C2212yes—
127C4×#107C2211yescharacteristic
128C4×#106C2211yescharacteristic
129#1767C2212yes—
130C4×C4⋊C8C2211yescharacteristic
131#1763C2212yes—
132#1763C2212yes—
133C4×#103C2211yescharacteristic
134C4×#103C2211yescharacteristic
135#557—24no—
136#557Q818yes—
137C2×C4⋊Q8—21no—
138C2×C4⋊Q8C2311yescharacteristic
139C2×#125—22no—
140C2×#125C2311yescharacteristic
141C2×#125C2312yes—
142C2×#125C2312yes—
143C2×C4×Q8—21no—
144C2×C4×Q8—21no—
145C2×C4×Q8—21no—
146C2×C4×Q8—21no—
147C2×C4×Q8—21no—
148C2×C4×Q8D411yescharacteristic
149C2×C4×Q8D411yescharacteristic
150C2×C4×Q8C2312yes—
151C2×C4×Q8C2311yescharacteristic
152C2×C4×Q8C2311yescharacteristic
153C2×C4×Q8C2312yes—
154C2×C4×Q8C2311yescharacteristic
155C2×C4×Q8C2311yescharacteristic
156#479—24no—
157#479—28no—
158#446—24no—
159#446—24no—
160C2×#107C2311yescharacteristic
161C2×#107C2312yes—
162C2×#107C2312yes—
163C2×#107C2311yescharacteristic
164C2×#106C2312yes—
165C2×#106C2311yescharacteristic
166C2×#106C2312yes—
167C2×#106C2311yescharacteristic
168C2×C4⋊C8C2311yescharacteristic
169C2×C4⋊C8C2312yes—
170C2×C4⋊C8C2311yescharacteristic
171C2×C4⋊C8C2311yescharacteristic
172C2×C4⋊C8C2312yes—
173C2×C4⋊C8C2312yes—
174C2×C4⋊C8C2311yescharacteristic
175C2×C4⋊C8C2312yes—
176C2×C4⋊C8C2312yes—
177C2×C4⋊C8C2312yes—
178C2×#103C2311yescharacteristic
179C2×#103C2312yes—
180C2×#103C2311yescharacteristic
181C2×#103C2312yes—
182C2×#103C2311yescharacteristic
183C2×#103C2311yescharacteristic
184C2×#97C2312yes—
185C2×#97C2312yes—
186C2×C4×C8C2311yescharacteristic
187C2×C4×C8C2311yescharacteristic
188#400—22no—
189#400—22no—
190#400—22no—
191#400—22no—
192#400—22no—
193#400—22no—
194#391—21no—
195#391—21no—
196#391—21no—
197#389—22no—
198#389—22no—
199#389—22no—
200#389—21no—
201#389—21no—
202#389—22no—
203#389—22no—
204#389—21no—
205#389—21no—
206#389—22no—
207#389—22no—
208#389—21no—
209#389—21no—
210#389—21no—
211#389—22no—
212#389—22no—
213#389—22no—
214#389—21no—
215#389—22no—
216#389—21no—
217#389—22no—
218#389C2312yes—
219#389C2311yescharacteristic
220#389C2312yes—
221#389C2311yescharacteristic
222#389C2312yes—
223#389C2312yes—
224#389C2312yes—
225#387—22no—
226#387—22no—
227#387—22no—
228#387—22no—
229#387—22no—
230#387—21no—
231#387—22no—
232#387—21no—
233#387—22no—
234#387—22no—
235#384—21no—
236#384C2311yescharacteristic
237#384C2311yescharacteristic
238#384C2311yescharacteristic
239#384C2312yes—
240#384C2312yes—
241#382—21no—
242#382—21no—
243#382—22no—
244#382—22no—
245#382—22no—
246#382C2311yescharacteristic
247#382C2312yes—
248#382C2312yes—
249#382C2312yes—
250#382C2312yes—
251C4×C4⋊C4—21no—
252C4×C4⋊C4—21no—
253C4×C4⋊C4—21no—
254C4×C4⋊C4—21no—
255C4×C4⋊C4—22no—
256C4×C4⋊C4—22no—
257C4×C4⋊C4—22no—
258C4×C4⋊C4—21no—
259C4×C4⋊C4—21no—
260C4×C4⋊C4—22no—
261C4×C4⋊C4—22no—
262C4×C4⋊C4—21no—
263C4×C4⋊C4—22no—
264C4×C4⋊C4—22no—
265C4×C4⋊C4—21no—
266C4×C4⋊C4—22no—
267C4×C4⋊C4—22no—
268C4×C4⋊C4D412yes—
269C4×C4⋊C4D411yescharacteristic
270C4×C4⋊C4D412yes—
271C4×C4⋊C4D411yescharacteristic
272C4×C4⋊C4C2311yescharacteristic
273C4×C4⋊C4C2312yes—
274C4×C4⋊C4C2311yescharacteristic
275C4×C4⋊C4C2311yescharacteristic
276C4×C4⋊C4C2312yes—
277C4×C4⋊C4C2312yes—
278C4×C4⋊C4C2311yescharacteristic
279C4×C4⋊C4C2312yes—
280C4×C4⋊C4C2312yes—
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2312yes—
284C43—22no—
285C43—21no—
286C43C2312yes—
287C43C2311yescharacteristic
288#340C2312yes—
289#340C2312yes—
290#340C2312yes—
291#340C2312yes—
292#340C2312yes—
293#340C2312yes—
294#340C2312yes—
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2311yescharacteristic
301#340C2311yescharacteristic
302#340C2311yescharacteristic
303#340C2312yes—
304#340C2312yes—
305#340C2311yescharacteristic
306#340C2312yes—
307#340C2312yes—
308#340C2311yescharacteristic
309#340C2311yescharacteristic
310#340C2311yescharacteristic
311#340C2312yes—
312#340C2311yescharacteristic
313#340C2312yes—
314#336C2311yescharacteristic
315#336C2312yes—
316#336C2311yescharacteristic
317#336C2312yes—
318C22×Q8—21no—
319C22×Q8C2×D411yescharacteristic
320C22×Q8C2411yescharacteristic
321C22×C8C2411yescharacteristic
322C22×C8C2411yescharacteristic
323C22×C8C2411yescharacteristic
324C22×C8C2411yescharacteristic
325C22×C8C2412yes—
326C22×C8C2412yes—
327C4⋊Q8—28no—
328C4⋊Q8—22no—
329C4⋊Q8C2×Q814yes—
330#125—216no—
331#125—24no—
332#125—22no—
333#125—24no—
334#125—22no—
335#125—24no—
336#125C2×Q818yes—
337C4×Q8—28no—
338C4×Q8—24no—
339C4×Q8—22no—
340C4×Q8—22no—
341C4×Q8—24no—
342C4×Q8—22no—
343C4×Q8—42no—
344C4×Q8—42no—
345C4×Q8—42no—
346C4×Q8—41no—
347C4×Q8—44no—
348C4×Q8—44no—
349C4×Q8—44no—
350C4×Q8—44no—
351C4×Q8C2×Q818yes—
352C4×Q8C2×Q814yes—
353C4×Q8C2×Q814yes—
354C4×Q8#4114yes—
355C4×Q8#4114yes—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—22no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—22no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—22no—
375C2×C4⋊C4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4C2×D411yescharacteristic
386C2×C4⋊C4C2×D411yescharacteristic
387C2×C4⋊C4C2×D412yes—
388C2×C4⋊C4C2×D412yes—
389C2×C4⋊C4C2×D411yescharacteristic
390C2×C4⋊C4C2×D412yes—
391C2×C4⋊C4C2411yescharacteristic
392C2×C4⋊C4C2412yes—
393C2×C4⋊C4C2412yes—
394C2×C4⋊C4C2411yescharacteristic
395C2×C4⋊C4C2412yes—
396C2×C4⋊C4C2411yescharacteristic
397C2×C4⋊C4C2411yescharacteristic
398C2×C4⋊C4C2411yescharacteristic
399C2×C4⋊C4C2411yescharacteristic
400C2×C4⋊C4C2412yes—
401C2×C4⋊C4C2411yescharacteristic
402C2×C42—22no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42—22no—
406C2×C42—22no—
407C2×C42—21no—
408C2×C42—22no—
409C2×C42—22no—
410C2×C42—21no—
411C2×C42—21no—
412C2×C42—21no—
413C2×C42—22no—
414C2×C42—21no—
415C2×C42—22no—
416C2×C42—21no—
417C2×C42C2×D411yescharacteristic
418C2×C42C2×D411yescharacteristic
419C2×C42C2×D412yes—
420C2×C42C2×D412yes—
421C2×C42C2×D412yes—
422C2×C42C2×D411yescharacteristic
423C2×C42C2×D412yes—
424C2×C42C2×D411yescharacteristic
425C2×C42C2411yescharacteristic
426C2×C42C2412yes—
427C2×C42C2412yes—
428C2×C42C2411yescharacteristic
429C2×C42C2411yescharacteristic
430#107—22no—
431#107—24no—
432#107—41no—
433#107—42no—
434#106—24no—
435#106—22no—
436#106—42no—
437#106—41no—
438C4⋊C8—22no—
439C4⋊C8—22no—
440C4⋊C8—24no—
441C4⋊C8—24no—
442C4⋊C8—22no—
443C4⋊C8—24no—
444C4⋊C8—22no—
445C4⋊C8—42no—
446C4⋊C8—42no—
447C4⋊C8—42no—
448#103—22no—
449#103—24no—
450#103—24no—
451#103—22no—
452#103—22no—
453#103—22no—
454#97—24no—
455#97—24no—
456C4×C8—22no—
457C4×C8—22no—
458#95—22no—
459#95—21no—
460#95—21no—
461#95—22no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—22no—
466#95—22no—
467#95—22no—
468#95—21no—
469#95—22no—
470#95—22no—
471#95—21no—
472#95—22no—
473#95—22no—
474#95—22no—
475#95—22no—
476#95—22no—
477#95—21no—
478#95—21no—
479#95—22no—
480#95—22no—
481#95—22no—
482#95—22no—
483#95—22no—
484#95—22no—
485#95C2×D412yes—
486#95C2×D412yes—
487#95C2×D412yes—
488C2×Q8—24no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8C22⋊Q814yes—
497C2×Q8C22×Q812yes—
498C2×Q8C2×#4112yes—
499C2×Q82−1+412yes—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—21no—
512C22×C4C22×D411yescharacteristic
513C22×C4C22×D412yes—
514C22×C4C22×D412yes—
515C22×C4C22×D411yescharacteristic
516C22×C4C22×D412yes—
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D412yes—
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D411yescharacteristic
521C22×C4C22×D411yescharacteristic
522C22×C4C2511yescharacteristic
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—22no—
528C2×C8—22no—
529C2×C8—21no—
530C2×C8—22no—
531C2×C8—21no—
532C2×C8—22no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—22no—
539C2×C8—21no—
540C2×C8—22no—
541C4⋊C4—28no—
542C4⋊C4—24no—
543C4⋊C4—28no—
544C4⋊C4—24no—
545C4⋊C4—28no—
546C4⋊C4—24no—
547C4⋊C4—22no—
548C4⋊C4—22no—
549C4⋊C4—21no—
550C4⋊C4—22no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—21no—
562C4⋊C4—22no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—22no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—42no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—44no—
574C4⋊C4—44no—
575C4⋊C4—44no—
576C4⋊C4—42no—
577C4⋊C4—44no—
578C4⋊C4—42no—
579C4⋊C4—44no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—82no—
584C4⋊C4—81no—
585C4⋊C4—81no—
586C4⋊C4—82no—
587C4⋊C4—81no—
588C4⋊C4—81no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4—81no—
592C4⋊C4—82no—
593C4⋊C4C22⋊Q814yes—
594C4⋊C4C22⋊Q818yes—
595C4⋊C4C22×Q812yes—
596C4⋊C4C22×Q814yes—
597C4⋊C4C2×#4112yes—
598C42—28no—
599C42—24no—
600C42—24no—
601C42—22no—
602C42—22no—
603C42—22no—
604C42—21no—
605C42—22no—
606C42—21no—
607C42—42no—
608C42—41no—
609C42—42no—
610C42—41no—
611C42—42no—
612C42—42no—
613C42—44no—
614C42—42no—
615C42—42no—
616C42—44no—
617C42—44no—
618C42—44no—
619C42—44no—
620C42—42no—
621C42—42no—
622C42—42no—
623C42—82no—
624C42—81no—
625C42C22×Q814yes—
626C42C22×Q812yes—
627C42C2×#4112yes—
628C42C2×#4114yes—
629C42C2×#4112yes—
630C422−1+412yes—
631C23C23×D411yescharacteristic
632Q8—28no—
633Q8—22no—
634Q8—22no—
635Q8—22no—
636Q8—48no—
637Q8#55714yes—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—41no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—42no—
681C2×C4—41no—
682C2×C4—42no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4C2×C22⋊Q814yes—
697C2×C4C2×C22⋊Q812yes—
698C2×C4C2×C22⋊Q814yes—
699C2×C4C2×C22⋊Q812yes—
700C2×C4#54812yes—
701C2×C4#54812yes—
702C2×C4#57512yes—
703C2×C4#57512yes—
704C2×C4C23×Q811yescharacteristic
705C2×C4C22×#4111yescharacteristic
706C2×C4C22×#4111yescharacteristic
707C2×C4C2×2−1+411yescharacteristic
708C2×C4C2×2−1+411yescharacteristic
709C2×C4#58511yescharacteristic
710C8—41no—
711C8—41no—
712C8—42no—
713C8—42no—
714C8—41no—
715C8—41no—
716C22C22×C22⋊Q811yescharacteristic
717C22C2×#54811yescharacteristic
718C22#348911yescharacteristic
719C22C2×#57511yescharacteristic
720C22C2×#57511yescharacteristic
721C22#358411yescharacteristic
722C22#358611yescharacteristic
723C4—24no—
724C4—24no—
725C4—22no—
726C4—22no—
727C4—22no—
728C4—24no—
729C4—44no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—82no—
737C4—81no—
738C4—82no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4—82no—
743C4—81no—
744C4#308014yes—
745C4C2×#55711yescharacteristic
746C4#348011yescharacteristic
747C4#350211yescharacteristic
748C4#352311yescharacteristic
749C2#3657711yescharacteristic
750C2C2×#308011yescharacteristic
751C2#6049911yescharacteristic
752C2#6131611yescharacteristic
753C2#6132011yescharacteristic
754C2#6212411yescharacteristic
755C2#6214211yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C42×Q8 ◁ 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
#365842
C4×#5572
#332002
#292912
#292882
#292272
#292202
#265252
#265232
#265132
#265092
#261232
#261132
#261092
#227432
#227422
#227222
#225242
#216182
C4×#4792