Finite Group Databasebeta

← #217151

Subgroups — #217151

Order 512.

794 conjugacy classes of subgroups.

The subgroup lattice has 726 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2533C211yesmaximal, characteristic
2#20814C211yesmaximal, characteristic
3#20779C211yesmaximal, characteristic
4#9881C211yesmaximal, characteristic
5#9880C211yesmaximal, characteristic
6#9654C211yesmaximal, characteristic
7#9650C211yesmaximal, characteristic
8#9086C211yesmaximal, characteristic
9#9086C211yesmaximal, characteristic
10#9082C211yesmaximal, characteristic
11#9082C211yesmaximal, characteristic
12#8562C211yesmaximal, characteristic
13#8562C211yesmaximal, characteristic
14#8560C211yesmaximal, characteristic
15#8558C211yesmaximal, characteristic
16C2×#432C2211yescharacteristic
17C2×#431C2211yescharacteristic
18#2533—21no—
19#2533—21no—
20#2533—21no—
21#2533—21no—
22#2533—21no—
23#2533—21no—
24#2533—21no—
25#2533—21no—
26C2×#400C411yescharacteristic
27C2×#400C411yescharacteristic
28C2×#400C411yescharacteristic
29C2×#400C411yescharacteristic
30C2×#389C411yescharacteristic
31C2×#389C2211yescharacteristic
32C2×#387C411yescharacteristic
33C2×#387C411yescharacteristic
34C2×#387C2211yescharacteristic
35C2×#387C2211yescharacteristic
36C2×#387C2211yescharacteristic
37C2×#387C2211yescharacteristic
38C2×#383C411yescharacteristic
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×#376C2211yescharacteristic
41#1843—21no—
42#1840—21no—
43#1832—21no—
44#1832—21no—
45#1817C2211yescharacteristic
46#1817C2211yescharacteristic
47#1797C2211yescharacteristic
48#1797C2211yescharacteristic
49#1797C2211yescharacteristic
50#1797C2211yescharacteristic
51#1797C2211yescharacteristic
52#1797C2211yescharacteristic
53#1768—21no—
54#1768—21no—
55#1768—21no—
56#1749C2211yescharacteristic
57C4×C22⋊C8C2211yescharacteristic
58#1746—21no—
59C2×#324C2211yescharacteristic
60C2×#324C2211yescharacteristic
61C2×#324C2211yescharacteristic
62C2×#324C2211yescharacteristic
63C2×#324C2211yescharacteristic
64C2×#324C2211yescharacteristic
65C2×#324C2211yescharacteristic
66C2×#324C2211yescharacteristic
67#1280C2211yescharacteristic
68#1280C2211yescharacteristic
69#1280C2211yescharacteristic
70#1280C2211yescharacteristic
71#1280C2211yescharacteristic
72#1280C2211yescharacteristic
73#1280C2211yescharacteristic
74#1280C2211yescharacteristic
75C22×C4⋊C4C2×C411yescharacteristic
76C22×C4⋊C4C2×C411yescharacteristic
77C22×C4⋊C4C2×C411yescharacteristic
78C22×C4⋊C4C2×C411yescharacteristic
79C22×C4⋊C4C2×C411yescharacteristic
80C22×C4⋊C4C2×C411yescharacteristic
81C22×C4⋊C4C2×C411yescharacteristic
82C22×C4⋊C4C2×C411yescharacteristic
83C22×C4⋊C4C2311yescharacteristic
84C22×C4⋊C4C2311yescharacteristic
85C22×C42C2×C411yescharacteristic
86C22×C42C2×C411yescharacteristic
87C22×C42C2311yescharacteristic
88C22×C42C2311yescharacteristic
89C22×C42C2311yescharacteristic
90#432—41no—
91#432—41no—
92#431—41no—
93#431—41no—
94C2×C4⋊C8—21no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C22⋊C8C2311yescharacteristic
103C2×C22⋊C8C2311yescharacteristic
104C2×C22⋊C8C2311yescharacteristic
105C2×C22⋊C8C2311yescharacteristic
106C2×C22⋊C8C2311yescharacteristic
107C2×C22⋊C8C2311yescharacteristic
108C2×C22⋊C8C2311yescharacteristic
109C2×C22⋊C8C2311yescharacteristic
110C2×#97—21no—
111C2×#97—21no—
112C2×C4×C8—21no—
113C2×C4×C8—21no—
114#400—21no—
115#400—21no—
116#400—21no—
117#400—21no—
118#400—21no—
119#400—21no—
120#400—21no—
121#400—21no—
122#400—21no—
123#400—21no—
124#400—21no—
125#400—21no—
126#400—21no—
127#400—21no—
128#400—21no—
129#400—21no—
130#389—21no—
131#389—21no—
132#389—21no—
133#389—21no—
134#389—21no—
135#389—21no—
136#389—21no—
137#389—21no—
138#387—21no—
139#387—21no—
140#387—21no—
141#387—21no—
142#387—21no—
143#387—21no—
144#387—21no—
145#387—21no—
146#387—21no—
147#387—21no—
148#387—21no—
149#387—21no—
150#387—21no—
151#387—21no—
152#387—21no—
153#387—21no—
154#387—21no—
155#387—21no—
156#387—21no—
157#387—21no—
158#387—21no—
159#387—21no—
160#387—21no—
161#387—21no—
162#383—21no—
163#383—21no—
164#383—21no—
165#383—21no—
166C4×C4⋊C4—21no—
167C4×C4⋊C4—21no—
168C4×C4⋊C4—21no—
169C4×C4⋊C4—21no—
170#376D411yescharacteristic
171#376D411yescharacteristic
172#376D411yescharacteristic
173#376D411yescharacteristic
174#376D411yescharacteristic
175#376D411yescharacteristic
176#376D411yescharacteristic
177#376D411yescharacteristic
178C2×#95C2×C411yescharacteristic
179C2×#95C2×C411yescharacteristic
180C2×#95C2×C411yescharacteristic
181C2×#95C2×C411yescharacteristic
182C2×#95C2×C411yescharacteristic
183C2×#95C2×C411yescharacteristic
184C2×#95C2×C411yescharacteristic
185C2×#95C2×C411yescharacteristic
186C2×#95C2×C411yescharacteristic
187C2×#95C2×C411yescharacteristic
188C2×#95C2×C411yescharacteristic
189C2×#95C2×C411yescharacteristic
190C2×#95C2×C411yescharacteristic
191C2×#95C2×C411yescharacteristic
192C2×#95C2×C411yescharacteristic
193C2×#95C2×C411yescharacteristic
194C2×#95C2×C411yescharacteristic
195C2×#95C2×C411yescharacteristic
196C2×#95C2311yescharacteristic
197C2×#95C2311yescharacteristic
198#336—21no—
199#336—21no—
200#336—21no—
201#336—21no—
202#336—21no—
203#336—21no—
204#336—21no—
205#336—21no—
206#336—21no—
207#336—21no—
208#336—21no—
209#336—21no—
210#324—41no—
211#324—41no—
212#324—41no—
213#324—41no—
214#324—41no—
215#324—41no—
216#324—41no—
217#324—41no—
218C23×C4C22×C411yescharacteristic
219C23×C4C22×C411yescharacteristic
220C23×C4C22×C411yescharacteristic
221C23×C4C22×C411yescharacteristic
222C23×C4C22×C411yescharacteristic
223C23×C4C22×C411yescharacteristic
224C23×C4C22×C411yescharacteristic
225C23×C4C22×C411yescharacteristic
226C23×C4C22×C411yescharacteristic
227C23×C4C22×C411yescharacteristic
228C23×C4C22×C411yescharacteristic
229C23×C4C22×C411yescharacteristic
230C23×C4C22×C411yescharacteristic
231C23×C4C22×C411yescharacteristic
232C23×C4C2411yescharacteristic
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8—21no—
239C22×C8—21no—
240C22×C8—21no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—22no—
261C2×C4⋊C4—22no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—21no—
270C2×C4⋊C4—21no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—21no—
273C2×C4⋊C4—21no—
274C2×C4⋊C4—41no—
275C2×C4⋊C4—41no—
276C2×C4⋊C4—41no—
277C2×C4⋊C4—41no—
278C2×C4⋊C4—41no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4—42no—
282C2×C42—21no—
283C2×C42—21no—
284C2×C42—21no—
285C2×C42—21no—
286C2×C42—21no—
287C2×C42—21no—
288C2×C42—21no—
289C2×C42—21no—
290C2×C42—22no—
291C2×C42—42no—
292C2×C42—42no—
293C2×C42—41no—
294C2×C42—42no—
295C2×C42C2×D411yescharacteristic
296C2×C42C2×D411yescharacteristic
297C2×C42C2×D411yescharacteristic
298C2×C42C2×D411yescharacteristic
299C2×C42C2×D411yescharacteristic
300C2×C42C2×D411yescharacteristic
301C2×C42C2×D411yescharacteristic
302C2×C42C2×D411yescharacteristic
303C2×C42C2×D411yescharacteristic
304C2×C42C2×D411yescharacteristic
305C2×C42C2×D411yescharacteristic
306C2×C42C2×D411yescharacteristic
307C4⋊C8—42no—
308C4⋊C8—42no—
309C4⋊C8—42no—
310C4⋊C8—42no—
311C4⋊C8—42no—
312C4⋊C8—42no—
313C4⋊C8—42no—
314C4⋊C8—42no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8—21no—
320C22⋊C8—21no—
321C22⋊C8—21no—
322C22⋊C8—21no—
323C22⋊C8—21no—
324C22⋊C8—21no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—21no—
329C22⋊C8—21no—
330C22⋊C8—21no—
331#97—42no—
332#97—42no—
333C4×C8—42no—
334C4×C8—42no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—21no—
341#95—21no—
342#95—21no—
343#95—21no—
344#95—21no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—21no—
355#95—21no—
356#95—21no—
357#95—21no—
358#95—21no—
359#95—21no—
360#95—21no—
361#95—21no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—21no—
366#95—21no—
367#95C22⋊C411yescharacteristic
368#95C22⋊C411yescharacteristic
369#95C22⋊C411yescharacteristic
370#95C22⋊C411yescharacteristic
371#95C22⋊C411yescharacteristic
372#95C22⋊C411yescharacteristic
373#95C22⋊C411yescharacteristic
374#95C22⋊C411yescharacteristic
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—21no—
385C22×C4—21no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
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—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4C2×C22⋊C411yescharacteristic
455C22×C4C2×C22⋊C411yescharacteristic
456C22×C4C2×C22⋊C411yescharacteristic
457C22×C4C2×C22⋊C411yescharacteristic
458C22×C4C2×C22⋊C411yescharacteristic
459C22×C4C2×C22⋊C411yescharacteristic
460C22×C4C2×C22⋊C411yescharacteristic
461C22×C4C2×C22⋊C411yescharacteristic
462C22×C4C2×C22⋊C411yescharacteristic
463C22×C4C2×C22⋊C411yescharacteristic
464C22×C4C2×C22⋊C411yescharacteristic
465C22×C4C2×C22⋊C411yescharacteristic
466C22×C4#13112yes—
467C22×C4#13112yes—
468C22×C4C22×D411yescharacteristic
469C22×C4C22×D411yescharacteristic
470C22×C4H(5,𝔽2)11yescharacteristic
471C22×C4H(5,𝔽2)11yescharacteristic
472C22×C42−1+411yescharacteristic
473C22×C42−1+411yescharacteristic
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—41no—
487C2×C8—41no—
488C2×C8—41no—
489C2×C8—41no—
490C2×C8—41no—
491C2×C8—41no—
492C2×C8—41no—
493C2×C8—41no—
494C2×C8—41no—
495C2×C8—41no—
496C2×C8—41no—
497C2×C8—41no—
498C4⋊C4—42no—
499C4⋊C4—42no—
500C4⋊C4—42no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—42no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4—41no—
518C4⋊C4—41no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—22no—
531C42—22no—
532C42—22no—
533C42—22no—
534C42—41no—
535C42—41no—
536C42—41no—
537C42—41no—
538C42—42no—
539C42—42no—
540C42—42no—
541C42—42no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23C22×C22⋊C411yescharacteristic
547C23#52011yescharacteristic
548C23#52011yescharacteristic
549C23C2×#13111yescharacteristic
550C23C2×#13111yescharacteristic
551C23#56811yescharacteristic
552C23#56811yescharacteristic
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
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—22no—
594C2×C4—22no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—42no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—81no—
638C2×C4—81no—
639C2×C4—81no—
640C2×C4—81no—
641C2×C4—81no—
642C2×C4—81no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4—81no—
646C2×C4—81no—
647C2×C4—81no—
648C2×C4—81no—
649C2×C4—81no—
650C2×C4—81no—
651C2×C4—81no—
652C2×C4—81no—
653C2×C4#41012yes—
654C2×C4#41012yes—
655C2×C4#53511yescharacteristic
656C2×C4#53611yescharacteristic
657C2×C4#53711yescharacteristic
658C2×C4#53711yescharacteristic
659C8—81no—
660C8—81no—
661C8—81no—
662C8—81no—
663C8—81no—
664C8—81no—
665C8—81no—
666C8—81no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—21no—
672C22—21no—
673C22—21no—
674C22—21no—
675C22—21no—
676C22—21no—
677C22—21no—
678C22—21no—
679C22#231111yescharacteristic
680C22#288011yescharacteristic
681C22#288011yescharacteristic
682C22C2×#41011yescharacteristic
683C22C2×#41011yescharacteristic
684C22#288911yescharacteristic
685C22#288911yescharacteristic
686C22#299211yescharacteristic
687C22#299311yescharacteristic
688C22#299411yescharacteristic
689C22#299511yescharacteristic
690C4—22no—
691C4—22no—
692C4—21no—
693C4—21no—
694C4—21no—
695C4—21no—
696C4—41no—
697C4—41no—
698C4—42no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—42no—
706C4—41no—
707C4—41no—
708C4—81no—
709C4—81no—
710C4—81no—
711C4—81no—
712C4—81no—
713C4—81no—
714C2—21no—
715C2—21no—
716C2—21no—
717C2—21no—
718C2#1741311yescharacteristic
719C2#1741711yescharacteristic
720C2#1741711yescharacteristic
721C2#1742011yescharacteristic
722C2#2185511yescharacteristic
723C2#2187511yescharacteristic
724C2#2188311yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#376 ◁ G
LECSG ▷ C23×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25332
#208142
#207792
#98812
#98802
#96542
#96502
#90862
#90822
#85622
#85602
#85582