Finite Group Databasebeta

← #387155

Subgroups — #387155

Order 512.

1040 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
1C2×#2506C211yesmaximal, characteristic
2#21146C211yesmaximal, characteristic
3#21023C211yesmaximal, characteristic
4#11354C211yesmaximal, characteristic
5#11204C211yesmaximal, characteristic
6#11204C211yesmaximal, characteristic
7#11204C211yesmaximal, characteristic
8#11204C211yesmaximal, characteristic
9#11204C211yesmaximal, characteristic
10#10913C211yesmaximal, characteristic
11#10913C211yesmaximal, characteristic
12#10913C211yesmaximal, characteristic
13#10857C211yesmaximal, characteristic
14#10847C211yesmaximal, characteristic
15#10802C211yesmaximal, characteristic
16C22×#125C412yes—
17C2×#423C2211yescharacteristic
18C2×#423C2211yescharacteristic
19C2×#423C2211yescharacteristic
20C2×#423C2211yescharacteristic
21C2×C4×M16C2211yescharacteristic
22C2×C4×M16C2211yescharacteristic
23#2506—21no—
24#2506—21no—
25#2506—21no—
26#2506—21no—
27#2506—21no—
28#2506—21no—
29#2506—21no—
30#2506—21no—
31C2×#400C412yes—
32C2×#398C412yes—
33C2×#389C2211yescharacteristic
34C2×#389C2211yescharacteristic
35C2×#389C2211yescharacteristic
36C2×#389C2211yescharacteristic
37C2×#387C412yes—
38C2×#384C2211yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41#1940—21no—
42#1940—21no—
43#1939—21no—
44#1939—21no—
45#1917—21no—
46#1917—21no—
47#1916—21no—
48#1916—21no—
49C2×#343C2211yescharacteristic
50C2×#343C2211yescharacteristic
51C2×#343C2211yescharacteristic
52C2×#343C2211yescharacteristic
53C2×#343C2211yescharacteristic
54C2×#343C2211yescharacteristic
55C2×#343C2211yescharacteristic
56C2×#343C2211yescharacteristic
57C2×#343C2211yescharacteristic
58C2×#343C2211yescharacteristic
59C2×#343C2211yescharacteristic
60C2×#343C2211yescharacteristic
61C2×#343C2211yescharacteristic
62C2×#343C2211yescharacteristic
63C2×#343C2211yescharacteristic
64C2×#343C2211yescharacteristic
65#1728C2211yescharacteristic
66#1728C2211yescharacteristic
67#1728C2211yescharacteristic
68#1728C2211yescharacteristic
69#1728C2211yescharacteristic
70#1728C2211yescharacteristic
71C22×M16C2311yescharacteristic
72C22×M16C2311yescharacteristic
73C22×M16C2311yescharacteristic
74C22×M16C2311yescharacteristic
75C22×M16C2311yescharacteristic
76C22×M16C2311yescharacteristic
77C22×M16C2311yescharacteristic
78C22×M16C2311yescharacteristic
79C2×#125—22no—
80C2×#125—22no—
81C2×#125—22no—
82C2×#125—22no—
83C2×#125—48no—
84C22×C4⋊C4C2×C411yescharacteristic
85C22×C4⋊C4C2×C412yes—
86C22×C4⋊C4C2×C412yes—
87C22×C4⋊C4C2×C412yes—
88C22×C4⋊C4C2×C412yes—
89C22×C4⋊C4C2×C412yes—
90C22×C4⋊C4C2×C412yes—
91C22×C4⋊C4C2×C411yescharacteristic
92C22×C4⋊C4C2311yescharacteristic
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2311yescharacteristic
96C22×C42C2×C412yes—
97C22×C42C2311yescharacteristic
98C22×C42C2311yescharacteristic
99C22×C42C2311yescharacteristic
100#423—22no—
101#423—22no—
102#423—22no—
103#423—41no—
104#423—41no—
105#423—41no—
106#423—41no—
107#423—41no—
108C2×C4⋊C8—21no—
109C2×C4⋊C8—21no—
110C2×C4⋊C8—21no—
111C2×C4⋊C8—21no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8—21no—
114C2×C4⋊C8—21no—
115C2×C4⋊C8—21no—
116C4×M16—22no—
117C4×M16—41no—
118C4×M16—41no—
119C4×M16—41no—
120C2×#97—21no—
121C2×#97—21no—
122C2×C4×C8—21no—
123C2×C4×C8—21no—
124#400—22no—
125#400—22no—
126#400—22no—
127#400—22no—
128#398—22no—
129#398—22no—
130#398—22no—
131#398—22no—
132#389—21no—
133#389—21no—
134#389—21no—
135#389—21no—
136#389—21no—
137#389—21no—
138#389—21no—
139#389—21no—
140#389—21no—
141#389—21no—
142#389—21no—
143#389—21no—
144#389—21no—
145#389—21no—
146#389—21no—
147#389—21no—
148#387—22no—
149#387—22no—
150#387—22no—
151#387—22no—
152#384—21no—
153#384—21no—
154#384—21no—
155#384—21no—
156C4×C4⋊C4—21no—
157C4×C4⋊C4—21no—
158C4×C4⋊C4—21no—
159C4×C4⋊C4—21no—
160C4×C4⋊C4D411yescharacteristic
161C4×C4⋊C4D411yescharacteristic
162C4×C4⋊C4D411yescharacteristic
163C4×C4⋊C4D411yescharacteristic
164C4×C4⋊C4D411yescharacteristic
165C4×C4⋊C4D411yescharacteristic
166C4×C4⋊C4D411yescharacteristic
167C4×C4⋊C4D411yescharacteristic
168C2×#95C2×C412yes—
169C2×#95C2×C412yes—
170C2×#95C2×C412yes—
171C2×#95C2×C412yes—
172C2×#95C2×C412yes—
173C2×#95C2×C411yescharacteristic
174C2×#95C2×C411yescharacteristic
175#343—22no—
176#343—22no—
177#343—22no—
178#343—22no—
179#343—22no—
180#343—41no—
181#343—41no—
182#343—41no—
183#343—41no—
184#343—41no—
185#343—41no—
186#343—41no—
187#343—41no—
188#343—41no—
189#343—41no—
190#343Q814yes—
191#336—21no—
192#336—21no—
193#336—21no—
194#336—21no—
195#336—21no—
196#336—21no—
197#336—21no—
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203C23×C4C22×C411yescharacteristic
204C23×C4C22×C411yescharacteristic
205C23×C4C22×C411yescharacteristic
206C23×C4C22×C411yescharacteristic
207C23×C4C22×C412yes—
208C23×C4C22×C412yes—
209C23×C4C22×C412yes—
210C23×C4C22×C411yescharacteristic
211C23×C4C22×C411yescharacteristic
212C23×C4C22×C412yes—
213C23×C4C2411yescharacteristic
214C2×M16—21no—
215C2×M16—21no—
216C2×M16—21no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C2×M16—21no—
231C2×M16—21no—
232C2×M16—21no—
233C2×M16—21no—
234C2×M16—21no—
235C2×M16—21no—
236C2×M16—21no—
237C2×M16—21no—
238C2×M16—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16—21no—
250C2×M16—21no—
251C2×M16—21no—
252C2×M16—21no—
253C2×M16—21no—
254C2×M16—21no—
255C2×M16—21no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16C2×Q812yes—
259C2×M16C2×Q812yes—
260C2×M16#4112yes—
261C2×M16#4112yes—
262C22×C8—21no—
263C22×C8—21no—
264C22×C8—21no—
265C22×C8—21no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—21no—
269C22×C8—21no—
270#125—48no—
271#125—48no—
272#125—48no—
273#125—48no—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—24no—
279C2×C4⋊C4—22no—
280C2×C4⋊C4—22no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4—22no—
283C2×C4⋊C4—22no—
284C2×C4⋊C4—22no—
285C2×C4⋊C4—22no—
286C2×C4⋊C4—22no—
287C2×C4⋊C4—22no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—44no—
311C2×C4⋊C4—44no—
312C2×C4⋊C4—44no—
313C2×C4⋊C4—44no—
314C2×C4⋊C4—44no—
315C2×C4⋊C4—44no—
316C2×C4⋊C4C22⋊C411yescharacteristic
317C2×C4⋊C4C22⋊C411yescharacteristic
318C2×C4⋊C4C22⋊C411yescharacteristic
319C2×C4⋊C4C22⋊C411yescharacteristic
320C2×C4⋊C4C22⋊C411yescharacteristic
321C2×C4⋊C4C22⋊C411yescharacteristic
322C2×C4⋊C4C22⋊C411yescharacteristic
323C2×C4⋊C4C22⋊C411yescharacteristic
324C2×C4⋊C4C2×Q812yes—
325C2×C4⋊C4#4112yes—
326C2×C42—21no—
327C2×C42—21no—
328C2×C42—21no—
329C2×C42—21no—
330C2×C42—21no—
331C2×C42—21no—
332C2×C42—21no—
333C2×C42—21no—
334C2×C42—21no—
335C2×C42—21no—
336C2×C42—21no—
337C2×C42—21no—
338C2×C42—22no—
339C2×C42—22no—
340C2×C42—44no—
341C2×C42C2×D411yescharacteristic
342C2×C42C2×D411yescharacteristic
343C2×C42C2×D411yescharacteristic
344C2×C42C2×D411yescharacteristic
345C2×C42C2×D411yescharacteristic
346C2×C42C2×D411yescharacteristic
347C2×C42C2×D411yescharacteristic
348C2×C42C2×D411yescharacteristic
349C2×C42C2×D411yescharacteristic
350C2×C42C2×D411yescharacteristic
351C2×C42C2×D411yescharacteristic
352C2×C42C2×D411yescharacteristic
353C4⋊C8—42no—
354C4⋊C8—42no—
355C4⋊C8—42no—
356C4⋊C8—42no—
357C4⋊C8—42no—
358C4⋊C8—42no—
359C4⋊C8—42no—
360C4⋊C8—42no—
361#97—42no—
362#97—42no—
363C4×C8—42no—
364C4×C8—42no—
365#95—22no—
366#95—22no—
367#95—22no—
368#95—22no—
369#95—22no—
370#95—22no—
371#95—22no—
372#95—22no—
373#95—22no—
374#95—22no—
375#95C22⋊C411yescharacteristic
376#95C22⋊C411yescharacteristic
377#95C22⋊C411yescharacteristic
378#95C22⋊C411yescharacteristic
379#95C22⋊C411yescharacteristic
380#95C22⋊C411yescharacteristic
381#95C22⋊C411yescharacteristic
382#95C22⋊C411yescharacteristic
383C24C23×C411yescharacteristic
384C22×C4—22no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—22no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—41no—
417C22×C4—41no—
418C22×C4—41no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—42no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—42no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4C2×C22⋊C411yescharacteristic
428C22×C4C2×C22⋊C411yescharacteristic
429C22×C4C2×C22⋊C411yescharacteristic
430C22×C4C2×C22⋊C411yescharacteristic
431C22×C4C2×C22⋊C411yescharacteristic
432C22×C4C2×C22⋊C411yescharacteristic
433C22×C4C2×C22⋊C411yescharacteristic
434C22×C4C2×C22⋊C411yescharacteristic
435C22×C4C2×C22⋊C411yescharacteristic
436C22×C4C2×C22⋊C411yescharacteristic
437C22×C4C2×C22⋊C411yescharacteristic
438C22×C4C2×C22⋊C411yescharacteristic
439C22×C4C4×Q814yes—
440C22×C4C22×D411yescharacteristic
441C22×C4C22×D411yescharacteristic
442C22×C4C22×Q811yescharacteristic
443C22×C4C2×#4111yescharacteristic
444C22×C4C2×#4111yescharacteristic
445C22×C4C2×#4111yescharacteristic
446C22×C4H(5,𝔽2)11yescharacteristic
447C22×C4H(5,𝔽2)11yescharacteristic
448C22×C4H(5,𝔽2)11yescharacteristic
449C22×C42−1+411yescharacteristic
450C22×C42−1+411yescharacteristic
451C22×C42−1+411yescharacteristic
452C22×C42−1+411yescharacteristic
453C22×C42−1+411yescharacteristic
454M16—22no—
455M16—22no—
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471M16—41no—
472M16—41no—
473M16—41no—
474M16—41no—
475M16—41no—
476M16—41no—
477M16—41no—
478M16—41no—
479M16—41no—
480M16—41no—
481M16—41no—
482M16—41no—
483M16—41no—
484M16—41no—
485M16—41no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C2×C8—41no—
499C2×C8—41no—
500C2×C8—41no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—41no—
506C2×C8—41no—
507C2×C8—41no—
508C2×C8—41no—
509C2×C8—41no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—22no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—22no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—44no—
522C4⋊C4—44no—
523C4⋊C4—44no—
524C4⋊C4—44no—
525C4⋊C4—44no—
526C4⋊C4—44no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—41no—
532C4⋊C4—41no—
533C4⋊C4—41no—
534C4⋊C4—41no—
535C4⋊C4—41no—
536C4⋊C4—41no—
537C4⋊C4—41no—
538C4⋊C4—41no—
539C4⋊C4—44no—
540C4⋊C4—44no—
541C4⋊C4—44no—
542C4⋊C4—44no—
543C4⋊C4—44no—
544C4⋊C4—44no—
545C4⋊C4#10014yes—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—44no—
571C42—44no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C22×C22⋊C411yescharacteristic
577C23C2×C4×Q811yescharacteristic
578C23C4×#4111yescharacteristic
579C23#51911yescharacteristic
580C23#52011yescharacteristic
581C23#52011yescharacteristic
582C23#52011yescharacteristic
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—24no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—44no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—44no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—82no—
642C2×C4—82no—
643C2×C4—82no—
644C2×C4—82no—
645C2×C4—82no—
646C2×C4—82no—
647C2×C4C2×#10012yes—
648C2×C4C2×#10012yes—
649C2×C4C2×#10012yes—
650C2×C4#41312yes—
651C2×C4#53511yescharacteristic
652C2×C4#53611yescharacteristic
653C2×C4#53711yescharacteristic
654C2×C4#53711yescharacteristic
655C2×C4#53911yescharacteristic
656C2×C4#53911yescharacteristic
657C2×C4#54011yescharacteristic
658C2×C4#54111yescharacteristic
659C2×C4#54111yescharacteristic
660C2×C4#54111yescharacteristic
661C2×C4#54411yescharacteristic
662C2×C4#54411yescharacteristic
663C2×C4#54611yescharacteristic
664C2×C4#54611yescharacteristic
665C2×C4#54711yescharacteristic
666C2×C4#54711yescharacteristic
667C2×C4#54811yescharacteristic
668C2×C4#54811yescharacteristic
669C2×C4D4×Q811yescharacteristic
670C2×C4D4×Q811yescharacteristic
671C2×C4#55211yescharacteristic
672C2×C4#55311yescharacteristic
673C2×C4#55411yescharacteristic
674C2×C4#55711yescharacteristic
675C2×C4#56211yescharacteristic
676C2×C4#56311yescharacteristic
677C2×C4#56311yescharacteristic
678C2×C4#56411yescharacteristic
679C8—42no—
680C8—42no—
681C8—42no—
682C8—42no—
683C8—81no—
684C8—81no—
685C8—81no—
686C8—81no—
687C22—21no—
688C22—21no—
689C22—21no—
690C22—21no—
691C22—21no—
692C22—21no—
693C22—21no—
694C22—21no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—21no—
699C22#231111yescharacteristic
700C22#233011yescharacteristic
701C22#233611yescharacteristic
702C22#233911yescharacteristic
703C22Q8×C22⋊C411yescharacteristic
704C22#237011yescharacteristic
705C22#238211yescharacteristic
706C22C22×#10011yescharacteristic
707C22C2×#41311yescharacteristic
708C22#288911yescharacteristic
709C22#288911yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—41no—
715C4—41no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—41no—
722C4—44no—
723C4—82no—
724C4—82no—
725C4—82no—
726C4#270411yescharacteristic
727C4#270711yescharacteristic
728C4#271111yescharacteristic
729C4#271311yescharacteristic
730C4#271911yescharacteristic
731C4#272011yescharacteristic
732C4#272511yescharacteristic
733C4#272611yescharacteristic
734C2—21no—
735C2—21no—
736C2—21no—
737C2—21no—
738C2#1445111yescharacteristic
739C2#2187811yescharacteristic
740C2#2188311yescharacteristic
741C2#2247911yescharacteristic
742C2#2248011yescharacteristic
743C2Q8×#10011yescharacteristic
744C2#2251711yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25062
#211462
#210232
#113542
#112042
#109132
#108572
#108472
#108022