Finite Group Databasebeta

← #6559887

Subgroups — #6559887

Order 512.

1228 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39643C211yesmaximal, characteristic
2#38986C211yesmaximal, characteristic
3#30388C212yesmaximal
4#30281C211yesmaximal, characteristic
5#29591C212yesmaximal
6#29525C212yesmaximal
7#29347C211yesmaximal, characteristic
8#29222C211yesmaximal, characteristic
9#28969C212yesmaximal
10#28946C212yesmaximal
11#28682C211yesmaximal, characteristic
12#28677C211yesmaximal, characteristic
13#28646C211yesmaximal, characteristic
14#28638C211yesmaximal, characteristic
15#28047C212yesmaximal
16#28033C212yesmaximal
17#23838C211yesmaximal, characteristic
18#23788C212yesmaximal
19#23221C211yesmaximal, characteristic
20#23214C211yesmaximal, characteristic
21#23163C211yesmaximal, characteristic
22#23158C211yesmaximal, characteristic
23#20571C211yesmaximal, characteristic
24C2×#500C2211yescharacteristic
25C2×#498C2211yescharacteristic
26C2×#487C2211yescharacteristic
27C2×#487C2211yescharacteristic
28C2×#446C2211yescharacteristic
29C2×C8×Q8C2211yescharacteristic
30#2862C2211yescharacteristic
31#2862C2211yescharacteristic
32#2799—22no—
33#2789—22no—
34#2758—22no—
35#2755—22no—
36#2647C2212yes—
37#2645C2212yes—
38#2582—21no—
39#2571—21no—
40#2570—21no—
41#2568—21no—
42#2568C2211yescharacteristic
43#2567C2211yescharacteristic
44#2567C2211yescharacteristic
45#2546C2211yescharacteristic
46#2514—21no—
47#2514—21no—
48#2514C2212yes—
49#2511—21no—
50#2509C2212yes—
51#2508C2212yes—
52#2453C2212yes—
53#2446—21no—
54#2369C2211yescharacteristic
55#2369C2211yescharacteristic
56#2365C2211yescharacteristic
57#2365C2211yescharacteristic
58#2331C2212yes—
59#2320C2212yes—
60C4×C4⋊Q8C2211yescharacteristic
61C4×#125C2211yescharacteristic
62#2295C2211yescharacteristic
63#2101C2212yes—
64#2101C2212yes—
65#2097C2212yes—
66#2097C2212yes—
67#2097C2212yes—
68#2097C2212yes—
69#2088C2212yes—
70#2088C2212yes—
71#2086C2212yes—
72#2086C2212yes—
73#2085C2211yescharacteristic
74#2085C2211yescharacteristic
75#2084C2211yescharacteristic
76#2083C2211yescharacteristic
77#2072C2212yes—
78#2068C2212yes—
79#2068C2212yes—
80#2068C2212yes—
81#2068C2212yes—
82#2059C2211yescharacteristic
83#2059C2211yescharacteristic
84#2058C2211yescharacteristic
85#2057C2211yescharacteristic
86#2024C2212yes—
87#1991C2212yes—
88#1988C2211yescharacteristic
89#1988C2211yescharacteristic
90#1987C2211yescharacteristic
91#1987C2211yescharacteristic
92#1987C2211yescharacteristic
93#1987C2211yescharacteristic
94#1981C2211yescharacteristic
95#1981C2211yescharacteristic
96#1944C2212yes—
97#1944C2212yes—
98#1944C2212yes—
99#1942C2212yes—
100#1941C2212yes—
101#1941C2212yes—
102#1935C2212yes—
103#1935C2212yes—
104#1935C2212yes—
105#1933C2212yes—
106#1933C2212yes—
107#1933C2212yes—
108#1933C2212yes—
109#1933C2212yes—
110#1927C2212yes—
111#1927C2212yes—
112#1921C2212yes—
113#1921C2212yes—
114#1920C2212yes—
115#1919C2212yes—
116#1865C2212yes—
117#1865C2212yes—
118#1835C2212yes—
119#1776C2212yes—
120C4×#107C2211yescharacteristic
121C4×#107C2211yescharacteristic
122C4×#107C2212yes—
123C4×#106C2211yescharacteristic
124C4×#106C2211yescharacteristic
125#1771C2212yes—
126#1770C2211yescharacteristic
127C8×C4⋊C4C2212yes—
128C8×C4⋊C4C2211yescharacteristic
129#1768C2212yes—
130C4×C4⋊C8C2211yescharacteristic
131#1763C2212yes—
132C4×#103C2212yes—
133#1746C2212yes—
134#1744C2211yescharacteristic
135C2×C4⋊Q8—21no—
136C2×C4⋊Q8C2311yescharacteristic
137C2×C4⋊Q8C2311yescharacteristic
138C2×C4⋊Q8C2311yescharacteristic
139C2×C4⋊Q8C2311yescharacteristic
140C2×C4⋊Q8C2311yescharacteristic
141C2×#125C2311yescharacteristic
142C2×C4×Q8—21no—
143C2×C4×Q8—21no—
144C2×C4×Q8C2312yes—
145C2×C4×Q8C2311yescharacteristic
146#500—24no—
147#498—24no—
148#487—24no—
149#487—24no—
150#446—24no—
151C8×Q8—24no—
152C2×#107C2311yescharacteristic
153C2×#107C2311yescharacteristic
154C2×#107C2312yes—
155C2×#107C2312yes—
156C2×#107C2311yescharacteristic
157C2×#107C2311yescharacteristic
158C2×#106C2311yescharacteristic
159C2×#106C2311yescharacteristic
160C2×#106C2311yescharacteristic
161C2×#106C2311yescharacteristic
162C2×#106C2312yes—
163C2×#106C2312yes—
164C2×C4⋊C8C2312yes—
165C2×C4⋊C8C2312yes—
166C2×C4⋊C8C2311yescharacteristic
167C2×C4⋊C8C2311yescharacteristic
168C2×#103C2312yes—
169C2×#103C2312yes—
170C2×#103C2312yes—
171C2×#103C2312yes—
172C2×#103C2312yes—
173C2×#103C2312yes—
174C2×#103C2312yes—
175C2×#103C2312yes—
176C2×#97C2312yes—
177C2×#97C2312yes—
178C2×C4×C8C2312yes—
179C2×C4×C8C2312yes—
180C2×C4×C8C2312yes—
181C2×C4×C8C2311yescharacteristic
182C2×C4×C8C2311yescharacteristic
183#401—22no—
184#401—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#400—22no—
194#400—22no—
195#400—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—21no—
210#391—21no—
211#391—21no—
212#391—21no—
213#391—21no—
214#391—21no—
215#391—22no—
216#391—22no—
217#391—22no—
218#391—22no—
219#391D411yescharacteristic
220#391D411yescharacteristic
221#391C2312yes—
222#391C2312yes—
223#391C2312yes—
224#391C2312yes—
225#391C2312yes—
226#389—21no—
227#389—21no—
228#389—22no—
229#389—21no—
230#389—22no—
231#389—21no—
232#389D411yescharacteristic
233#389D411yescharacteristic
234#389C2311yescharacteristic
235#389C2311yescharacteristic
236#389C2311yescharacteristic
237#389C2311yescharacteristic
238#389C2312yes—
239#389C2312yes—
240#389C2312yes—
241#389C2312yes—
242#389C2312yes—
243#389C2312yes—
244#389C2312yes—
245#389C2312yes—
246#389C2312yes—
247#387—22no—
248#387—22no—
249#387—21no—
250#387—21no—
251#387—22no—
252#387—22no—
253#387—22no—
254#387—22no—
255#387—22no—
256#387—22no—
257#387—22no—
258#387—22no—
259#387D412yes—
260#387D412yes—
261#384—21no—
262#384—21no—
263#384C2311yescharacteristic
264#383—22no—
265#383—22no—
266#382—21no—
267#382—21no—
268#382—21no—
269#382—22no—
270#382—22no—
271#382C2311yescharacteristic
272#382C2312yes—
273#382C2312yes—
274C4×C4⋊C4—21no—
275C4×C4⋊C4—21no—
276C4×C4⋊C4—21no—
277C4×C4⋊C4—21no—
278C4×C4⋊C4—21no—
279C4×C4⋊C4—21no—
280C4×C4⋊C4C2311yescharacteristic
281C4×C4⋊C4C2311yescharacteristic
282C4×C4⋊C4C2311yescharacteristic
283C4×C4⋊C4C2311yescharacteristic
284C4×C4⋊C4C2312yes—
285C4×C4⋊C4C2312yes—
286C4×C4⋊C4C2312yes—
287C4×C4⋊C4C2311yescharacteristic
288C4×C4⋊C4C2312yes—
289#376C2312yes—
290C43C2311yescharacteristic
291#340C2311yescharacteristic
292#340C2311yescharacteristic
293#340C2311yescharacteristic
294#340C2311yescharacteristic
295#340C2312yes—
296#340C2312yes—
297#340C2312yes—
298#340C2312yes—
299#340C2312yes—
300#340C2312yes—
301#340C2311yescharacteristic
302#340C2311yescharacteristic
303#340C2311yescharacteristic
304#340C2311yescharacteristic
305#340C2312yes—
306#340C2312yes—
307#340C2312yes—
308#340C2312yes—
309#340C2312yes—
310#340C2312yes—
311#336C2311yescharacteristic
312#336C2311yescharacteristic
313#336C2311yescharacteristic
314#336C2311yescharacteristic
315#336C2312yes—
316#336C2312yes—
317#336C2312yes—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—21no—
321C22×Q8—21no—
322C22×Q8C2×D411yescharacteristic
323C22×Q8C2412yes—
324C22×C8C2412yes—
325C22×C8C2412yes—
326C22×C8C2411yescharacteristic
327C22×C8C2411yescharacteristic
328C22×C8C2411yescharacteristic
329C22×C8C2411yescharacteristic
330C4⋊Q8—22no—
331C4⋊Q8—22no—
332C4⋊Q8—22no—
333C4⋊Q8—22no—
334C4⋊Q8—22no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339C4⋊Q8—22no—
340C4⋊Q8—82no—
341#125—22no—
342#125—41no—
343C4×Q8—22no—
344C4×Q8—22no—
345C4×Q8—24no—
346C4×Q8—42no—
347C4×Q8—82no—
348C4×Q8—82no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
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⋊C4C2×D411yescharacteristic
374C2×C4⋊C4C2×D411yescharacteristic
375C2×C4⋊C4C2×D412yes—
376C2×C4⋊C4C2×D411yescharacteristic
377C2×C4⋊C4C2×D412yes—
378C2×C4⋊C4C2×D412yes—
379C2×C4⋊C4C2411yescharacteristic
380C2×C4⋊C4C2412yes—
381C2×C4⋊C4C2412yes—
382C2×C4⋊C4C2412yes—
383C2×C4⋊C4C2411yescharacteristic
384C2×C4⋊C4C2411yescharacteristic
385C2×C4⋊C4C2411yescharacteristic
386C2×C4⋊C4C2411yescharacteristic
387C2×C4⋊C4C2411yescharacteristic
388C2×C4⋊C4C2411yescharacteristic
389C2×C4⋊C4C2411yescharacteristic
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—22no—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—22no—
396C2×C42—22no—
397C2×C42—22no—
398C2×C42C2×D411yescharacteristic
399C2×C42C2×D411yescharacteristic
400C2×C42C2×D411yescharacteristic
401C2×C42C2×D411yescharacteristic
402C2×C42C2412yes—
403C2×C42C2412yes—
404C2×C42C2411yescharacteristic
405C2×C42C2411yescharacteristic
406C2×C42C2411yescharacteristic
407#107—24no—
408#107—24no—
409#107—22no—
410#107—22no—
411#107—41no—
412#107—41no—
413#106—24no—
414#106—24no—
415#106—22no—
416#106—22no—
417#106—22no—
418#106—22no—
419C4⋊C8—24no—
420C4⋊C8—24no—
421C4⋊C8—22no—
422C4⋊C8—22no—
423#103—24no—
424#103—24no—
425#103—24no—
426#103—24no—
427#103—24no—
428#103—24no—
429#103—42no—
430#103—42no—
431#97—24no—
432#97—42no—
433C4×C8—24no—
434C4×C8—42no—
435C4×C8—42no—
436C4×C8#4114yes—
437C4×C8#4114yes—
438#95—21no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—22no—
445#95—22no—
446#95—22no—
447#95—22no—
448#95—21no—
449#95—21no—
450#95—22no—
451#95—21no—
452#95—22no—
453#95—21no—
454#95—22no—
455#95—22no—
456#95—22no—
457#95—22no—
458#95—22no—
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#95C2×D412yes—
475#95C2×D412yes—
476#95C2×D412yes—
477#95C2×D412yes—
478#95C2×D412yes—
479#95C2×D412yes—
480#95C2×D412yes—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—81no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×Q8—81no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—22no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4C22×D411yescharacteristic
515C22×C4C22×D412yes—
516C22×C4C22×D412yes—
517C22×C4C22×D411yescharacteristic
518C22×C4C22×D411yescharacteristic
519C22×C4C22×D411yescharacteristic
520C22×C4C22×D412yes—
521C22×C4C22×D412yes—
522C22×C4C22×D411yescharacteristic
523C22×C4C22×D411yescharacteristic
524C22×C4C2511yescharacteristic
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—22no—
537C2×C8—22no—
538C2×C8—22no—
539C2×C8C2×#4112yes—
540C2×C8C2×#4112yes—
541C2×C8C2×#4112yes—
542C2×C8C2×#4112yes—
543C4⋊C4—24no—
544C4⋊C4—22no—
545C4⋊C4—24no—
546C4⋊C4—22no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
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—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—42no—
568C4⋊C4—42no—
569C4⋊C4—44no—
570C4⋊C4—42no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—42no—
576C4⋊C4—42no—
577C4⋊C4—81no—
578C4⋊C4—81no—
579C4⋊C4—81no—
580C4⋊C4—82no—
581C4⋊C4—82no—
582C4⋊C4—82no—
583C4⋊C4—82no—
584C4⋊C4—82no—
585C4⋊C4—82no—
586C4⋊C4—81no—
587C4⋊C4—81no—
588C4⋊C4—81no—
589C4⋊C4—82no—
590C4⋊C4—82no—
591C4⋊C4—82no—
592C4⋊C42−1+412yes—
593C4⋊C42−1+412yes—
594C4⋊C42−1+412yes—
595C42—22no—
596C42—22no—
597C42—22no—
598C42—22no—
599C42—22no—
600C42—21no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—22no—
605C42—41no—
606C42—41no—
607C42—44no—
608C42—42no—
609C42—42no—
610C42—42no—
611C42—42no—
612C42—82no—
613C42—82no—
614C42—82no—
615C42C2×#4112yes—
616C42C2×#4112yes—
617C23C23×D411yescharacteristic
618Q8—44no—
619Q8—42no—
620Q8—42no—
621Q8—42no—
622Q8—42no—
623Q8—84no—
624Q8—84no—
625Q8—162no—
626Q8—162no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—42no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4#53212yes—
690C2×C4#53212yes—
691C2×C4#57712yes—
692C2×C4#57812yes—
693C2×C4C22×#4111yescharacteristic
694C2×C4C22×#4111yescharacteristic
695C2×C4C2×2−1+411yescharacteristic
696C2×C4C2×2−1+411yescharacteristic
697C2×C4C2×2−1+411yescharacteristic
698C2×C4#58511yescharacteristic
699C8—22no—
700C8—22no—
701C8—22no—
702C8—22no—
703C8—42no—
704C8—42no—
705C22C2×#53211yescharacteristic
706C22#348611yescharacteristic
707C22#348911yescharacteristic
708C22C2×#57711yescharacteristic
709C22C2×#57811yescharacteristic
710C22#358411yescharacteristic
711C22#358411yescharacteristic
712C4—22no—
713C4—41no—
714C4—42no—
715C4—42no—
716C4—42no—
717C4—41no—
718C4—42no—
719C4—42no—
720C4—41no—
721C4—42no—
722C4—42no—
723C4—41no—
724C4—82no—
725C4—81no—
726C4—81no—
727C4—81no—
728C4—82no—
729C4—82no—
730C4—82no—
731C4—81no—
732C4—81no—
733C4#317814yes—
734C4#350711yescharacteristic
735C4#350711yescharacteristic
736C4#350911yescharacteristic
737C4#350911yescharacteristic
738C2#3593811yescharacteristic
739C2C2×#317811yescharacteristic
740C2#6071311yescharacteristic
741C2#6186411yescharacteristic
742C2#6186611yescharacteristic
743C2#6221711yescharacteristic
744C2#6221911yescharacteristic
subgroupG/H
center, socle, prime radicalC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ 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
#396432
#389862
#303882
#302812
#295912
#295252
#293472
#292222
#289692
#289462
#286822
#286772
#286462
#286382
#280472
#280332
#238382
#237882
#232212
#232142
#231632
#231582
#205712