Finite Group Databasebeta

← #406639

Subgroups — #406639

Order 512.

1340 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2862C211yesmaximal, characteristic
2C2×#1935C212yesmaximal
3#14699C211yesmaximal, characteristic
4#11384C211yesmaximal, characteristic
5#11384C211yesmaximal, characteristic
6#11190C212yesmaximal
7#11067C212yesmaximal
8#11010C211yesmaximal, characteristic
9#11010C211yesmaximal, characteristic
10#10928C212yesmaximal
11#10693C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×C4⋊Q8C2211yescharacteristic
14C22×#103C2212yes—
15C22×#103C2212yes—
16C22×#103C2212yes—
17C22×#103C2212yes—
18C22×#97C2212yes—
19#2862—28no—
20C2×#391—21no—
21C2×#391—21no—
22C2×#391C2212yes—
23C2×#391C2212yes—
24C2×#389C2211yescharacteristic
25C2×#389C2211yescharacteristic
26C2×#387—21no—
27C2×#382—21no—
28C2×#382—21no—
29C2×C43C2211yescharacteristic
30#1935—28no—
31C2×#340C2212yes—
32C2×#340C2212yes—
33C2×#340C2212yes—
34C2×#340C2212yes—
35C2×#336C2211yescharacteristic
36C2×#336C2211yescharacteristic
37C2×#336C2212yes—
38#1436—21no—
39#1436—21no—
40C4⋊#95C2211yescharacteristic
41C4⋊#95C2211yescharacteristic
42C4⋊#95C2211yescharacteristic
43C4⋊#95C2211yescharacteristic
44#1434—21no—
45C23×Q8—21no—
46C23×Q8C2312yes—
47C23×C8C2312yes—
48C23×C8C2312yes—
49C2×C4⋊Q8—24no—
50C2×C4⋊Q8—24no—
51C2×C4⋊Q8—22no—
52C2×C4⋊Q8—22no—
53C2×C4⋊Q8—22no—
54C2×C4⋊Q8—22no—
55C2×C4⋊Q8—42no—
56C2×C4⋊Q8—42no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4—21no—
59C22×C4⋊C4—21no—
60C22×C4⋊C4—21no—
61C22×C4⋊C4—21no—
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2311yescharacteristic
64C22×C4⋊C4C2312yes—
65C22×C4⋊C4C2311yescharacteristic
66C22×C4⋊C4C2311yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42D411yescharacteristic
69C22×C42D411yescharacteristic
70C22×C42D411yescharacteristic
71C22×C42C2311yescharacteristic
72C22×C42C2311yescharacteristic
73C22×C42C2311yescharacteristic
74C2×#103—24no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—24no—
79C2×#103—24no—
80C2×#103—24no—
81C2×#103—24no—
82C2×#103—42no—
83C2×#103—42no—
84C2×#103—42no—
85C2×#103—42no—
86C2×#97—24no—
87C2×#97—24no—
88C2×#97—42no—
89#391—28no—
90#391—28no—
91#391—24no—
92#391—24no—
93#391—24no—
94#391D418yes—
95#389—22no—
96#389—22no—
97#389—24no—
98#387—44no—
99#382—28no—
100#382—28no—
101C2×#95—21no—
102C2×#95—22no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—21no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95—21no—
113C2×#95—21no—
114C2×#95—21no—
115C43—24no—
116#340—24no—
117#340—24no—
118#340—42no—
119#340—42no—
120#336—24no—
121#336—22no—
122#336—22no—
123C22×Q8—24no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—22no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8—22no—
133C22×Q8—22no—
134C22×Q8—22no—
135C22×Q8—22no—
136C22×Q8—22no—
137C22×Q8—42no—
138C22×Q8—42no—
139C22×Q8—42no—
140C22×Q8—42no—
141C22×Q8—42no—
142C22×Q8—42no—
143C22×Q8C2×D414yes—
144C23×C4—21no—
145C23×C4—22no—
146C23×C4—22no—
147C23×C4—21no—
148C23×C4—21no—
149C23×C4—21no—
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D411yescharacteristic
153C23×C4C2×D411yescharacteristic
154C23×C4C2×D411yescharacteristic
155C23×C4C2×D411yescharacteristic
156C23×C4C2411yescharacteristic
157C22×C8—22no—
158C22×C8—22no—
159C22×C8—22no—
160C22×C8—22no—
161C22×C8—22no—
162C22×C8—22no—
163C22×C8—22no—
164C22×C8—22no—
165C22×C8—22no—
166C22×C8—22no—
167C22×C8—22no—
168C22×C8—22no—
169C22×C8#4114yes—
170C22×C8#4114yes—
171C4⋊Q8—48no—
172C4⋊Q8—48no—
173C4⋊Q8—48no—
174C4⋊Q8—48no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—24no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—22no—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—42no—
199C2×C4⋊C4—42no—
200C2×C4⋊C4—42no—
201C2×C4⋊C4—42no—
202C2×C4⋊C4—42no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—42no—
205C2×C4⋊C4—42no—
206C2×C4⋊C4—42no—
207C2×C4⋊C4—42no—
208C2×C4⋊C4—42no—
209C2×C4⋊C4C2×D414yes—
210C2×C4⋊C4#4112yes—
211C2×C4⋊C4#4112yes—
212C2×C42—22no—
213C2×C42—22no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—22no—
217C2×C42—22no—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42—22no—
221C2×C42—21no—
222C2×C42—21no—
223C2×C42—22no—
224C2×C42—22no—
225C2×C42—22no—
226C2×C42—22no—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—21no—
230C2×C42—21no—
231C2×C42—41no—
232C2×C42—41no—
233C2×C42C2×D414yes—
234C2×C42#4112yes—
235C2×C42#4112yes—
236#103—216no—
237#103—48no—
238#103—48no—
239#103—48no—
240#97—48no—
241#95—28no—
242#95—28no—
243#95—24no—
244#95—28no—
245#95—28no—
246#95—42no—
247#95—42no—
248#95—42no—
249#95—42no—
250#95—42no—
251#95—42no—
252#95—42no—
253#95—42no—
254#95—42no—
255C24C22×D411yescharacteristic
256C2×Q8—24no—
257C2×Q8—24no—
258C2×Q8—24no—
259C2×Q8—24no—
260C2×Q8—24no—
261C2×Q8—24no—
262C2×Q8—48no—
263C2×Q8—48no—
264C2×Q8—48no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×Q8—42no—
279C2×Q8—42no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—42no—
283C2×Q8—42no—
284C2×Q8—42no—
285C2×Q8—42no—
286C2×Q8—42no—
287C2×Q8—84no—
288C2×Q8—84no—
289C2×Q8—84no—
290C2×Q8—84no—
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—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—24no—
324C22×C4—24no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—41no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—42no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—42no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—41no—
337C22×C4—42no—
338C22×C4—42no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—42no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4—41no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4#12012yes—
366C22×C4#12012yes—
367C22×C4#12412yes—
368C22×C4#12412yes—
369C22×C4AGL(1,ℤ/8)12yes—
370C22×C4#13712yes—
371C22×C4#13712yes—
372C22×C4#13712yes—
373C22×C4#13712yes—
374C22×C4#13712yes—
375C22×C4C22×D412yes—
376C22×C4C2×#4111yescharacteristic
377C22×C4C2×#4112yes—
378C22×C4C2×#4111yescharacteristic
379C22×C4C2×#4111yescharacteristic
380C22×C4C2×#4112yes—
381C22×C4C2×#4111yescharacteristic
382C22×C4H(5,𝔽2)11yescharacteristic
383C22×C4H(5,𝔽2)12yes—
384C22×C42−1+411yescharacteristic
385C2×C8—24no—
386C2×C8—24no—
387C2×C8—24no—
388C2×C8—24no—
389C2×C8—24no—
390C2×C8—24no—
391C2×C8—42no—
392C2×C8—42no—
393C2×C8—42no—
394C2×C8—42no—
395C2×C8—42no—
396C2×C8—42no—
397C2×C8—42no—
398C2×C8—42no—
399C4⋊C4—24no—
400C4⋊C4—24no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C4⋊C4—48no—
404C4⋊C4—48no—
405C4⋊C4—48no—
406C4⋊C4—48no—
407C4⋊C4—42no—
408C4⋊C4—42no—
409C4⋊C4—42no—
410C4⋊C4—42no—
411C4⋊C4—42no—
412C4⋊C4—42no—
413C4⋊C4—42no—
414C4⋊C4—42no—
415C4⋊C4—84no—
416C42—28no—
417C42—28no—
418C42—24no—
419C42—24no—
420C42—24no—
421C42—24no—
422C42—44no—
423C42—44no—
424C42—42no—
425C42—42no—
426C23C2×#12011yescharacteristic
427C23#52511yescharacteristic
428C23C2×#12411yescharacteristic
429C23#53211yescharacteristic
430C23#53211yescharacteristic
431C23#53511yescharacteristic
432C23#53711yescharacteristic
433C23C2×AGL(1,ℤ/8)11yescharacteristic
434C23C2×#13711yescharacteristic
435C23C2×#13711yescharacteristic
436C23C2×#13711yescharacteristic
437C23C2×#13711yescharacteristic
438C23C2×#13711yescharacteristic
439C23#57511yescharacteristic
440C23#57511yescharacteristic
441Q8—44no—
442Q8—44no—
443Q8—44no—
444Q8—44no—
445Q8—816no—
446Q8—82no—
447Q8—82no—
448Q8—82no—
449Q8—82no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—44no—
497C2×C4—44no—
498C2×C4—44no—
499C2×C4—44no—
500C2×C4—44no—
501C2×C4—44no—
502C2×C4—82no—
503C2×C4—82no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—81no—
508C2×C4—82no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—81no—
513C2×C4—82no—
514C2×C4—82no—
515C2×C4—81no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—81no—
519C2×C4—81no—
520C2×C4—81no—
521C2×C4—81no—
522C2×C4—81no—
523C2×C4—81no—
524C2×C4—81no—
525C2×C4—81no—
526C2×C4—81no—
527C2×C4—81no—
528C2×C4—81no—
529C2×C4—81no—
530C2×C4—81no—
531C2×C4—81no—
532C2×C4#48914yes—
533C2×C4#49114yes—
534C2×C4#52512yes—
535C2×C4#52912yes—
536C2×C4#52912yes—
537C2×C4#53212yes—
538C2×C4#53812yes—
539C2×C4#54212yes—
540C2×C4#54612yes—
541C2×C4#54612yes—
542C2×C4#54612yes—
543C2×C4#54712yes—
544C2×C4#55112yes—
545C2×C4#55512yes—
546C2×C4#55611yescharacteristic
547C2×C4#55611yescharacteristic
548C2×C4#55911yescharacteristic
549C2×C4#55911yescharacteristic
550C8—44no—
551C8—44no—
552C22#238811yescharacteristic
553C22#243011yescharacteristic
554C22#243511yescharacteristic
555C22#259211yescharacteristic
556C22#261011yescharacteristic
557C22#266211yescharacteristic
558C22#286111yescharacteristic
559C22#300411yescharacteristic
560C22#300411yescharacteristic
561C22#300611yescharacteristic
562C22#300711yescharacteristic
563C22#311011yescharacteristic
564C22#311311yescharacteristic
565C22#311611yescharacteristic
566C22#311611yescharacteristic
567C22C2×#48911yescharacteristic
568C22C2×#49111yescharacteristic
569C22#313911yescharacteristic
570C22#314011yescharacteristic
571C22#317211yescharacteristic
572C22#317211yescharacteristic
573C22#318111yescharacteristic
574C22#318111yescharacteristic
575C22#318211yescharacteristic
576C22#318211yescharacteristic
577C22#318511yescharacteristic
578C22#318511yescharacteristic
579C22#321311yescharacteristic
580C22#321511yescharacteristic
581C22#321811yescharacteristic
582C22#321811yescharacteristic
583C22#325211yescharacteristic
584C22#325211yescharacteristic
585C22#325411yescharacteristic
586C22#325511yescharacteristic
587C4—24no—
588C4—24no—
589C4—42no—
590C4—42no—
591C4—42no—
592C4—42no—
593C4—84no—
594C4—82no—
595C4—84no—
596C4—82no—
597C4—161no—
598C4—161no—
599C4#245912yes—
600C4#247412yes—
601C4#252112yes—
602C4#255712yes—
603C2#1493211yescharacteristic
604C2#2357411yescharacteristic
605C2#2357711yescharacteristic
606C2#2550311yescharacteristic
607C2#2550411yescharacteristic
608C2#2586111yescharacteristic
609C2#2586411yescharacteristic
610C2#2935511yescharacteristic
611C2#2935711yescharacteristic
612C2#2955911yescharacteristic
613C2#2956011yescharacteristic
614C2#3034411yescharacteristic
615C2#3034511yescharacteristic
616C2#3328111yescharacteristic
617C2#3328711yescharacteristic
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
C2×#28622
C2×#19352
#146992
#113842
#111902
#110672
#110102
#109282
#106932