Finite Group Databasebeta

← #473881

Subgroups — #473881

Order 512.

1080 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14714C211yesmaximal, characteristic
2#14699C211yesmaximal, characteristic
3#11371C211yesmaximal, characteristic
4#11371C211yesmaximal, characteristic
5#11190C212yesmaximal
6#11190C212yesmaximal
7#11067C212yesmaximal
8#11067C212yesmaximal
9#11010C211yesmaximal, characteristic
10#11010C211yesmaximal, characteristic
11#10795C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×#103C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16C22×#103C2212yes—
17C2×#391C2212yes—
18C2×#391C2212yes—
19C2×#389C2211yescharacteristic
20C2×#389C2211yescharacteristic
21C2×#387—21no—
22C2×#384C2211yescharacteristic
23C2×C43C2211yescharacteristic
24C2×#340C2212yes—
25C2×#340C2212yes—
26C2×#340C2212yes—
27C2×#340C2212yes—
28C2×#336C2211yescharacteristic
29C2×#336C2211yescharacteristic
30C2×#336C2212yes—
31C2×#336C2212yes—
32#1436—21no—
33#1436—21no—
34C4⋊#95—21no—
35C4⋊#95—21no—
36C4⋊#95—21no—
37C4⋊#95—21no—
38C4⋊#95C2211yescharacteristic
39C4⋊#95C2211yescharacteristic
40C4⋊#95C2211yescharacteristic
41C4⋊#95C2211yescharacteristic
42#1434—21no—
43C23×Q8C2312yes—
44C23×C8C2312yes—
45C23×C8C2312yes—
46C2×C4⋊Q8—24no—
47C2×C4⋊Q8—22no—
48C2×C4⋊Q8—22no—
49C2×C4⋊Q8—42no—
50C22×C4⋊C4—21no—
51C22×C4⋊C4—21no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4C2311yescharacteristic
57C22×C4⋊C4C2311yescharacteristic
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C42D411yescharacteristic
62C22×C42D411yescharacteristic
63C22×C42D411yescharacteristic
64C22×C42D411yescharacteristic
65C22×C42C2311yescharacteristic
66C22×C42C2311yescharacteristic
67C22×C42C2311yescharacteristic
68C2×#103—24no—
69C2×#103—24no—
70C2×#103—24no—
71C2×#103—24no—
72C2×#103—42no—
73C2×#103—42no—
74C2×#103—42no—
75C2×#103—42no—
76C2×#103—42no—
77C2×#103—42no—
78C2×#103—42no—
79C2×#103—42no—
80#391—42no—
81#391—42no—
82#391—42no—
83#391—42no—
84#389—22no—
85#389—22no—
86#389—42no—
87#387—44no—
88#384—22no—
89#384—22no—
90C2×#95—21no—
91C2×#95—21no—
92C2×#95—21no—
93C2×#95—21no—
94C2×#95—21no—
95C2×#95—21no—
96C2×#95—22no—
97C2×#95—22no—
98C2×#95—22no—
99C2×#95—22no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—21no—
104C43—42no—
105#340—42no—
106#340—42no—
107#340—42no—
108#340—42no—
109#336—22no—
110#336—22no—
111#336—42no—
112#336—42no—
113C22×Q8—22no—
114C22×Q8—22no—
115C22×Q8—22no—
116C22×Q8—22no—
117C22×Q8—22no—
118C22×Q8—22no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8#4114yes—
127C23×C4—21no—
128C23×C4—22no—
129C23×C4—21no—
130C23×C4—22no—
131C23×C4—21no—
132C23×C4—21no—
133C23×C4C2×D411yescharacteristic
134C23×C4C2×D411yescharacteristic
135C23×C4C2×D411yescharacteristic
136C23×C4C2×D411yescharacteristic
137C23×C4C2×D411yescharacteristic
138C23×C4C2×D411yescharacteristic
139C23×C4C2411yescharacteristic
140C22×C8—22no—
141C22×C8—22no—
142C22×C8—22no—
143C22×C8—22no—
144C22×C8—22no—
145C22×C8—22no—
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C4⋊Q8—48no—
155C4⋊Q8—48no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—22no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—42no—
180C2×C4⋊C4—42no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4#4112yes—
195C2×C4⋊C4#4112yes—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—21no—
201C2×C42—21no—
202C2×C42—21no—
203C2×C42—22no—
204C2×C42—22no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42—21no—
208C2×C42—41no—
209C2×C42—41no—
210C2×C42—41no—
211C2×C42—41no—
212C2×C42—41no—
213C2×C42—41no—
214C2×C42—41no—
215C2×C42—41no—
216C2×C42SD1614yes—
217C2×C42Q1614yes—
218C2×C42#4112yes—
219C2×C42#4112yes—
220#103—48no—
221#103—48no—
222#103—48no—
223#103—48no—
224#95—24no—
225#95—42no—
226#95—42no—
227#95—42no—
228#95—44no—
229#95—44no—
230#95—44no—
231#95—44no—
232#95—42no—
233#95—42no—
234#95—42no—
235#95—42no—
236#95—42no—
237#95—42no—
238C24C22×D411yescharacteristic
239C2×Q8—24no—
240C2×Q8—24no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—24no—
244C2×Q8—24no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—42no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8—42no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×Q8—42no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—42no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—22no—
300C22×C4—22no—
301C22×C4—24no—
302C22×C4—41no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4—42no—
309C22×C4—41no—
310C22×C4—41no—
311C22×C4—42no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—41no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—41no—
321C22×C4—42no—
322C22×C4—41no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—42no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—42no—
340C22×C4—41no—
341C22×C4#12412yes—
342C22×C4#12412yes—
343C22×C4C2×SD1612yes—
344C22×C4C2×SD1612yes—
345C22×C4C2×SD1612yes—
346C22×C4C2×Q1612yes—
347C22×C4C2×Q1612yes—
348C22×C4C2×Q1612yes—
349C22×C4#13712yes—
350C22×C4#13712yes—
351C22×C4C2×#4111yescharacteristic
352C22×C4C2×#4112yes—
353C22×C4C2×#4111yescharacteristic
354C22×C4C2×#4111yescharacteristic
355C22×C4C2×#4111yescharacteristic
356C22×C4H(5,𝔽2)12yes—
357C22×C4H(5,𝔽2)11yescharacteristic
358C22×C4H(5,𝔽2)12yes—
359C22×C4H(5,𝔽2)12yes—
360C22×C42−1+411yescharacteristic
361C2×C8—42no—
362C2×C8—42no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—42no—
366C2×C8—42no—
367C2×C8—42no—
368C2×C8—42no—
369C2×C8—42no—
370C2×C8—42no—
371C2×C8—42no—
372C2×C8—42no—
373C2×C8—42no—
374C2×C8—42no—
375C4⋊C4—24no—
376C4⋊C4—24no—
377C4⋊C4—48no—
378C4⋊C4—48no—
379C4⋊C4—48no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—84no—
391C4⋊C4—84no—
392C4⋊C4—84no—
393C42—24no—
394C42—24no—
395C42—44no—
396C42—44no—
397C42—44no—
398C42—44no—
399C42—42no—
400C42—42no—
401C42—42no—
402C42—42no—
403C23#52511yescharacteristic
404C23#52511yescharacteristic
405C23C2×#12411yescharacteristic
406C23#53411yescharacteristic
407C23#53511yescharacteristic
408C23#53511yescharacteristic
409C23#53711yescharacteristic
410C23C22×SD1611yescharacteristic
411C23C22×Q1611yescharacteristic
412C23C2×#13711yescharacteristic
413C23C2×#13711yescharacteristic
414C23#57511yescharacteristic
415C23#57511yescharacteristic
416C23#57511yescharacteristic
417C23#57511yescharacteristic
418Q8—44no—
419Q8—44no—
420Q8—44no—
421Q8—44no—
422Q8—82no—
423Q8—82no—
424Q8—82no—
425Q8—82no—
426C2×C4—22no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—81no—
476C2×C4—82no—
477C2×C4—81no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4—81no—
483C2×C4—81no—
484C2×C4—81no—
485C2×C4—81no—
486C2×C4—82no—
487C2×C4—81no—
488C2×C4—81no—
489C2×C4—82no—
490C2×C4—82no—
491C2×C4—81no—
492C2×C4—82no—
493C2×C4—81no—
494C2×C4—81no—
495C2×C4—81no—
496C2×C4—81no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4#48714yes—
509C2×C4#49114yes—
510C2×C4#53812yes—
511C2×C4#53812yes—
512C2×C4#53912yes—
513C2×C4#54012yes—
514C2×C4#54012yes—
515C2×C4#54012yes—
516C2×C4#55112yes—
517C2×C4#55112yes—
518C2×C4#55112yes—
519C2×C4#55312yes—
520C2×C4#55611yescharacteristic
521C2×C4#55611yescharacteristic
522C2×C4#55911yescharacteristic
523C2×C4#55911yescharacteristic
524C2×C4#56012yes—
525C2×C4#56212yes—
526C8—82no—
527C8—82no—
528C22#256111yescharacteristic
529C22#259211yescharacteristic
530C22#259811yescharacteristic
531C22#263511yescharacteristic
532C22#263611yescharacteristic
533C22#264111yescharacteristic
534C22#281311yescharacteristic
535C22#310111yescharacteristic
536C22#310311yescharacteristic
537C22#310411yescharacteristic
538C22#310411yescharacteristic
539C22#311611yescharacteristic
540C22#311611yescharacteristic
541C22#311711yescharacteristic
542C22#311711yescharacteristic
543C22C2×#48711yescharacteristic
544C22C2×#49111yescharacteristic
545C22#314011yescharacteristic
546C22#314011yescharacteristic
547C22#318711yescharacteristic
548C22#318911yescharacteristic
549C22#319611yescharacteristic
550C22#319611yescharacteristic
551C22#320611yescharacteristic
552C22#320611yescharacteristic
553C22#320911yescharacteristic
554C22#320911yescharacteristic
555C22#321911yescharacteristic
556C22#321911yescharacteristic
557C22#321911yescharacteristic
558C22#321911yescharacteristic
559C22#324611yescharacteristic
560C22#324911yescharacteristic
561C22#325211yescharacteristic
562C22#325211yescharacteristic
563C4—24no—
564C4—24no—
565C4—42no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—82no—
570C4—82no—
571C4—84no—
572C4—162no—
573C4—161no—
574C4—161no—
575C4#274012yes—
576C4#275212yes—
577C4#278612yes—
578C4#279712yes—
579C2#1688611yescharacteristic
580C2#2910511yescharacteristic
581C2#2911211yescharacteristic
582C2#2934711yescharacteristic
583C2#2935711yescharacteristic
584C2#2936811yescharacteristic
585C2#2937011yescharacteristic
586C2#3010611yescharacteristic
587C2#3010911yescharacteristic
588C2#3012911yescharacteristic
589C2#3013111yescharacteristic
590C2#3022011yescharacteristic
591C2#3022511yescharacteristic
592C2#3272211yescharacteristic
593C2#3272411yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ 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
#147142
#146992
#113712
#111902
#110672
#110102
#107952