Finite Group Databasebeta

← #415749

Subgroups — #415749

Order 512.

1040 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#1944C211yesmaximal, characteristic
2C2×#1943C211yesmaximal, characteristic
3C2×#1942C211yesmaximal, characteristic
4C2×#1941C211yesmaximal, characteristic
5#14277C211yesmaximal, characteristic
6#14276C211yesmaximal, characteristic
7#11325C211yesmaximal, characteristic
8#11325C211yesmaximal, characteristic
9#11325C211yesmaximal, characteristic
10#11325C211yesmaximal, characteristic
11#11324C211yesmaximal, characteristic
12#11324C211yesmaximal, characteristic
13#11323C211yesmaximal, characteristic
14#11323C211yesmaximal, characteristic
15#10694C211yesmaximal, characteristic
16C22×#107C2211yescharacteristic
17C22×#107C2211yescharacteristic
18C22×#107C2211yescharacteristic
19C22×#107C2211yescharacteristic
20C22×#106C2211yescharacteristic
21C22×#106C2211yescharacteristic
22C22×#106C2211yescharacteristic
23C22×#106C2211yescharacteristic
24C22×#97C2211yescharacteristic
25C22×C4×C8C2211yescharacteristic
26C2×#389C2211yescharacteristic
27C2×#389C2211yescharacteristic
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#384C2211yescharacteristic
31C2×#384C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×#382C2211yescharacteristic
34C2×#376C2211yescharacteristic
35#1944—24no—
36#1943—24no—
37#1942—24no—
38#1941—24no—
39C2×#340C2211yescharacteristic
40C2×#340C2211yescharacteristic
41C2×#340C2211yescharacteristic
42C2×#340C2211yescharacteristic
43C2×#340C2211yescharacteristic
44C2×#340C2211yescharacteristic
45C2×#340C2211yescharacteristic
46C2×#340C2211yescharacteristic
47C2×#336C2211yescharacteristic
48C2×#336C2211yescharacteristic
49C2×#336C2211yescharacteristic
50C2×#336C2211yescharacteristic
51#1444—22no—
52#1442—22no—
53#1441—22no—
54#1441—22no—
55C4⋊#95C2211yescharacteristic
56C4⋊#95C2211yescharacteristic
57C4⋊#95C2211yescharacteristic
58C4⋊#95C2211yescharacteristic
59C23×C8C2311yescharacteristic
60C23×C8C2311yescharacteristic
61C23×C8C2311yescharacteristic
62C23×C8C2311yescharacteristic
63C22×C4⋊C4—22no—
64C22×C4⋊C4—21no—
65C22×C4⋊C4—21no—
66C22×C4⋊C4—22no—
67C22×C4⋊C4—21no—
68C22×C4⋊C4—21no—
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2311yescharacteristic
72C22×C4⋊C4C2311yescharacteristic
73C22×C4⋊C4C2311yescharacteristic
74C22×C4⋊C4C2311yescharacteristic
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2311yescharacteristic
77C22×C42C2311yescharacteristic
78C22×C42C2311yescharacteristic
79C22×C42C2311yescharacteristic
80C2×#107—22no—
81C2×#107—22no—
82C2×#107—22no—
83C2×#107—22no—
84C2×#107—22no—
85C2×#107—22no—
86C2×#107—22no—
87C2×#107—22no—
88C2×#107—41no—
89C2×#107—41no—
90C2×#107—41no—
91C2×#107—41no—
92C2×#106—22no—
93C2×#106—22no—
94C2×#106—22no—
95C2×#106—22no—
96C2×#106—22no—
97C2×#106—22no—
98C2×#106—22no—
99C2×#106—22no—
100C2×#106—41no—
101C2×#106—41no—
102C2×#106—41no—
103C2×#106—41no—
104C2×#97—41no—
105C2×#97—41no—
106C2×#97D414yes—
107C2×C4×C8—41no—
108C2×C4×C8—41no—
109C2×C4×C8D414yes—
110#389—22no—
111#389—22no—
112#389—22no—
113#389—22no—
114#389—22no—
115#389—22no—
116#389—22no—
117#389—22no—
118#384—22no—
119#384—22no—
120#384—41no—
121#384—41no—
122#382—22no—
123#382—22no—
124#382—41no—
125#382—41no—
126#376—41no—
127#376—41no—
128C2×#95—22no—
129C2×#95—22no—
130C2×#95—21no—
131C2×#95—21no—
132C2×#95—21no—
133C2×#95—21no—
134C2×#95—22no—
135C2×#95—22no—
136C2×#95—22no—
137C2×#95—22no—
138C2×#95D412yes—
139C2×#95D412yes—
140#340—22no—
141#340—22no—
142#340—22no—
143#340—22no—
144#340—22no—
145#340—22no—
146#340—22no—
147#340—22no—
148#336Q814yes—
149#336Q814yes—
150#336Q814yes—
151#336Q814yes—
152C23×C4—21no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4—21no—
156C23×C4—21no—
157C23×C4—21no—
158C23×C4—21no—
159C23×C4—21no—
160C23×C4C2×D411yescharacteristic
161C23×C4C2×D411yescharacteristic
162C23×C4C2×D412yes—
163C23×C4C2×D412yes—
164C23×C4C2411yescharacteristic
165C22×C8—21no—
166C22×C8—21no—
167C22×C8—21no—
168C22×C8—21no—
169C22×C8—21no—
170C22×C8—21no—
171C22×C8—21no—
172C22×C8—21no—
173C22×C8—21no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—21no—
177C22×C8—21no—
178C22×C8—21no—
179C22×C8—21no—
180C22×C8—21no—
181C22×C8C2×D412yes—
182C22×C8C2×D412yes—
183C22×C8C2×D412yes—
184C22×C8C2×D412yes—
185C22×C8C2×Q812yes—
186C22×C8C2×Q812yes—
187C22×C8C2×Q812yes—
188C22×C8C2×Q812yes—
189C22×C8C2×Q812yes—
190C22×C8C2×Q812yes—
191C22×C8C2×Q812yes—
192C22×C8C2×Q812yes—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—28no—
238C2×C4⋊C4—44no—
239C2×C4⋊C4—42no—
240C2×C4⋊C4—42no—
241C2×C4⋊C4—42no—
242C2×C4⋊C4—42no—
243C2×C4⋊C4—82no—
244C2×C4⋊C4—82no—
245C2×C4⋊C4—82no—
246C2×C4⋊C4—82no—
247C2×C4⋊C4—82no—
248C2×C4⋊C4—82no—
249C2×C4⋊C4—82no—
250C2×C4⋊C4—82no—
251C2×C4⋊C4#4112yes—
252C2×C4⋊C4#4112yes—
253C2×C4⋊C4#4112yes—
254C2×C4⋊C4#4112yes—
255C2×C42—21no—
256C2×C42—21no—
257C2×C42—21no—
258C2×C42—21no—
259C2×C42—21no—
260C2×C42—21no—
261C2×C42—21no—
262C2×C42—21no—
263C2×C42—21no—
264C2×C42—21no—
265C2×C42—21no—
266C2×C42—21no—
267C2×C42C2×D412yes—
268C2×C42C2×D412yes—
269C2×C42C2×Q812yes—
270C2×C42C2×Q812yes—
271C2×C42C2×Q812yes—
272C2×C42C2×Q812yes—
273#107—28no—
274#107—28no—
275#107—44no—
276#107—44no—
277#106—28no—
278#106—28no—
279#106—44no—
280#106—44no—
281#97—44no—
282C4×C8—44no—
283#95—28no—
284#95—42no—
285#95—42no—
286#95—44no—
287#95—42no—
288#95—42no—
289#95—42no—
290#95—42no—
291#95—82no—
292#95—82no—
293#95—82no—
294#95—82no—
295C24C22×D411yescharacteristic
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—22no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—22no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—42no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4#12712yes—
357C22×C4#12712yes—
358C22×C4C4⋊Q814yes—
359C22×C4C4⋊Q814yes—
360C22×C4C22×D411yescharacteristic
361C22×C4C22×D411yescharacteristic
362C22×C4C22×Q811yescharacteristic
363C22×C4C22×Q811yescharacteristic
364C22×C4C22×Q811yescharacteristic
365C22×C4C22×Q811yescharacteristic
366C22×C4C2×#4111yescharacteristic
367C22×C4C2×#4111yescharacteristic
368C22×C4C2×#4111yescharacteristic
369C22×C4C2×#4111yescharacteristic
370C22×C4H(5,𝔽2)11yescharacteristic
371C22×C4H(5,𝔽2)11yescharacteristic
372C22×C4H(5,𝔽2)11yescharacteristic
373C22×C42−1+411yescharacteristic
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—22no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—22no—
390C2×C8—22no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—22no—
397C2×C8—22no—
398C2×C8C4⋊Q814yes—
399C2×C8C4⋊Q814yes—
400C2×C8C4⋊Q814yes—
401C2×C8C4⋊Q814yes—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—22no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—22no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—41no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—41no—
424C4⋊C4—41no—
425C4⋊C4—41no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4—41no—
429C4⋊C4—41no—
430C4⋊C4—41no—
431C4⋊C4—41no—
432C4⋊C4—41no—
433C4⋊C4—41no—
434C4⋊C4—84no—
435C4⋊C4—84no—
436C4⋊C4—84no—
437C4⋊C4—84no—
438C4⋊C4—88no—
439C4⋊C4—88no—
440C42—22no—
441C42—22no—
442C42—22no—
443C42—22no—
444C42—22no—
445C42—22no—
446C42—22no—
447C42—22no—
448C42—22no—
449C42—22no—
450C42—22no—
451C42—22no—
452C23#52511yescharacteristic
453C23#52511yescharacteristic
454C23C2×#12711yescharacteristic
455C23C2×C4⋊Q811yescharacteristic
456C23C2×C4⋊Q811yescharacteristic
457C23#53411yescharacteristic
458C23#53711yescharacteristic
459C23#57612yes—
460C23#57712yes—
461C23#57712yes—
462C23#57812yes—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—44no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—82no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—81no—
500C2×C4—81no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4—81no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4—82no—
524C2×C4—82no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4#52511yescharacteristic
528C2×C4#52511yescharacteristic
529C2×C4#52511yescharacteristic
530C2×C4#52511yescharacteristic
531C2×C4C2×C4⋊Q811yescharacteristic
532C2×C4C2×C4⋊Q811yescharacteristic
533C2×C4C2×C4⋊Q811yescharacteristic
534C2×C4C2×C4⋊Q811yescharacteristic
535C2×C4#53411yescharacteristic
536C2×C4#53411yescharacteristic
537C2×C4#53711yescharacteristic
538C2×C4#53711yescharacteristic
539C2×C4#55411yescharacteristic
540C2×C4#55411yescharacteristic
541C2×C4#55411yescharacteristic
542C2×C4#55411yescharacteristic
543C2×C4#55411yescharacteristic
544C2×C4#55411yescharacteristic
545C2×C4#55411yescharacteristic
546C2×C4#55411yescharacteristic
547C2×C4#55411yescharacteristic
548C2×C4#55411yescharacteristic
549C2×C4#55411yescharacteristic
550C2×C4#55411yescharacteristic
551C2×C4#55711yescharacteristic
552C2×C4#55711yescharacteristic
553C2×C4#55711yescharacteristic
554C2×C4#55711yescharacteristic
555C8—24no—
556C8—24no—
557C8—24no—
558C8—24no—
559C22#239711yescharacteristic
560C22#258311yescharacteristic
561C22#258311yescharacteristic
562C22#258411yescharacteristic
563C22#258411yescharacteristic
564C22#265611yescharacteristic
565C22#286811yescharacteristic
566C22#311812yes—
567C22#311912yes—
568C22#312012yes—
569C22#312112yes—
570C22#315411yescharacteristic
571C22#315411yescharacteristic
572C22#315511yescharacteristic
573C22#315611yescharacteristic
574C22#316312yes—
575C22#316312yes—
576C22#316412yes—
577C22#316412yes—
578C22#319812yes—
579C22#320112yes—
580C22#325712yes—
581C22#325812yes—
582C4—42no—
583C4—42no—
584C4—44no—
585C4—44no—
586C4—82no—
587C4—82no—
588C4—82no—
589C4—82no—
590C4—161no—
591C4—161no—
592C4—161no—
593C4—161no—
594C4#258311yescharacteristic
595C4#258311yescharacteristic
596C4#258311yescharacteristic
597C4#258311yescharacteristic
598C4#258411yescharacteristic
599C4#258411yescharacteristic
600C4#258411yescharacteristic
601C4#258411yescharacteristic
602C2#1521111yescharacteristic
603C2#2380811yescharacteristic
604C2#2380911yescharacteristic
605C2#2930812yes—
606C2#2930912yes—
607C2#2932412yes—
608C2#2932512yes—
609C2#3025111yescharacteristic
610C2#3025211yescharacteristic
611C2#3331811yescharacteristic
612C2#3331911yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ 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×#19442
C2×#19432
C2×#19422
C2×#19412
#142772
#142762
#113252
#113242
#113232
#106942