Finite Group Databasebeta

← #719573

Subgroups — #719573

Order 512.

2478 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2546C211yesmaximal, characteristic
2C2×#2446C212yesmaximal
3C2×#2365C211yesmaximal, characteristic
4#16529C214yesmaximal
5#15454C214yesmaximal
6#15414C214yesmaximal
7#15192C212yesmaximal
8#15180C212yesmaximal
9#14794C214yesmaximal
10#14274C211yesmaximal, characteristic
11#14150C211yesmaximal, characteristic
12#14017C212yesmaximal
13#13942C211yesmaximal, characteristic
14#13856C211yesmaximal, characteristic
15#13786C211yesmaximal, characteristic
16C22×C4⋊Q8C2212yes—
17C22×C4⋊Q8C2211yescharacteristic
18C22×C4×Q8C2211yescharacteristic
19C22×C4×Q8C2212yes—
20#2546—28no—
21#2446—216no—
22C2×#400C2214yes—
23C2×#398C2214yes—
24C2×#398C2214yes—
25#2365—28no—
26C2×#391C2211yescharacteristic
27C2×#391C2212yes—
28C2×#391C2212yes—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#391C2212yes—
32C2×#391C2211yescharacteristic
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#389C2212yes—
37C2×#387C2214yes—
38C2×#387C2214yes—
39C2×#387C2214yes—
40C2×#382C2211yescharacteristic
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2212yes—
43C2×C4×C4⋊C4C2211yescharacteristic
44C2×C4×C4⋊C4C2211yescharacteristic
45C2×C4×C4⋊C4C2212yes—
46C2×C4×C4⋊C4C2212yes—
47C2×#376C2211yescharacteristic
48#1445C2214yes—
49#1445C2214yes—
50#1445C2214yes—
51#1444C2212yes—
52#1444C2212yes—
53#1444C2212yes—
54#1444C2212yes—
55#1444C2212yes—
56#1444C2214yes—
57#1443C2214yes—
58#1443C2214yes—
59#1442C2214yes—
60#1442C2212yes—
61#1442C2214yes—
62#1442C2214yes—
63#1442C2214yes—
64#1441C2214yes—
65#1441C2214yes—
66#1441C2212yes—
67#1441C2212yes—
68#1436C2214yes—
69#1436C2214yes—
70#1436C2214yes—
71#1436C2214yes—
72C4⋊#95C2212yes—
73C4⋊#95C2211yescharacteristic
74C4⋊#95C2212yes—
75C4⋊#95C2211yescharacteristic
76#1434C2214yes—
77#1434C2214yes—
78C23×Q8C2311yescharacteristic
79C23×Q8C2312yes—
80C2×C4⋊Q8—28no—
81C2×C4⋊Q8—28no—
82C2×C4⋊Q8—24no—
83C2×C4⋊Q8—24no—
84C2×C4⋊Q8—44no—
85C2×C4⋊Q8D418yes—
86C2×C4×Q8—28no—
87C2×C4×Q8—28no—
88C2×C4×Q8—24no—
89C2×C4×Q8—24no—
90C2×C4×Q8—24no—
91C2×C4×Q8—44no—
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2311yescharacteristic
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2314yes—
101C22×C4⋊C4C2312yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2314yes—
104C22×C4⋊C4C2314yes—
105C22×C4⋊C4C2312yes—
106C22×C4⋊C4C2312yes—
107C22×C4⋊C4C2311yescharacteristic
108C22×C4⋊C4C2312yes—
109C22×C4⋊C4C2312yes—
110C22×C4⋊C4C2311yescharacteristic
111C22×C42C2312yes—
112C22×C42C2312yes—
113C22×C42C2312yes—
114C22×C42C2314yes—
115C22×C42C2311yescharacteristic
116C22×C42C2311yescharacteristic
117C22×C42C2312yes—
118C22×C42C2311yescharacteristic
119#400—216no—
120#398—216no—
121#398—216no—
122#391—28no—
123#391—28no—
124#391—28no—
125#391—28no—
126#391—24no—
127#391—28no—
128#391D418yes—
129#389—28no—
130#389—28no—
131#389—28no—
132#389—28no—
133#387—216no—
134#387—216no—
135#387—216no—
136#382—24no—
137C4×C4⋊C4—28no—
138C4×C4⋊C4—24no—
139C4×C4⋊C4—24no—
140C4×C4⋊C4—28no—
141C4×C4⋊C4—24no—
142C4×C4⋊C4—44no—
143#376—24no—
144C2×#95C2312yes—
145C2×#95C2314yes—
146C2×#95C2314yes—
147C2×#95C2314yes—
148C2×#95C2314yes—
149C2×#95C2312yes—
150C2×#95C2314yes—
151C2×#95C2314yes—
152C2×#95C2312yes—
153C2×#95C2312yes—
154C2×#95C2312yes—
155C2×#95C2312yes—
156C2×#95C2314yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2312yes—
161C2×#95C2312yes—
162C2×#95C2314yes—
163C2×#95C2314yes—
164C2×#95C2314yes—
165C2×#95C2314yes—
166C2×#95C2312yes—
167C2×#95C2314yes—
168C2×#95C2314yes—
169C2×#95C2314yes—
170C2×#95C2314yes—
171C2×#95C2312yes—
172C2×#95C2312yes—
173C2×#95C2314yes—
174C22×Q8—22no—
175C22×Q8—24no—
176C22×Q8—22no—
177C22×Q8—22no—
178C22×Q8—24no—
179C22×Q8—24no—
180C22×Q8—22no—
181C22×Q8—24no—
182C22×Q8—24no—
183C22×Q8—22no—
184C22×Q8—22no—
185C22×Q8—24no—
186C22×Q8C2×D418yes—
187C22×Q8C2×D414yes—
188C23×C4C2412yes—
189C23×C4C2414yes—
190C23×C4C2412yes—
191C23×C4C2412yes—
192C23×C4C2414yes—
193C23×C4C2412yes—
194C23×C4C2412yes—
195C23×C4C2412yes—
196C23×C4C2412yes—
197C23×C4C2412yes—
198C23×C4C2412yes—
199C23×C4C2412yes—
200C23×C4C2411yescharacteristic
201C23×C4C2411yescharacteristic
202C23×C4C2411yescharacteristic
203C4⋊Q8—232no—
204C4⋊Q8—432no—
205C4×Q8—432no—
206C4×Q8—416no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—24no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—24no—
222C2×C4⋊C4—28no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—28no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—28no—
228C2×C4⋊C4—28no—
229C2×C4⋊C4—28no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—24no—
233C2×C4⋊C4—28no—
234C2×C4⋊C4—24no—
235C2×C4⋊C4—24no—
236C2×C4⋊C4—24no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—24no—
240C2×C4⋊C4—24no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4—24no—
243C2×C4⋊C4—24no—
244C2×C4⋊C4—24no—
245C2×C4⋊C4—28no—
246C2×C4⋊C4—24no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—42no—
249C2×C4⋊C4—44no—
250C2×C4⋊C4—42no—
251C2×C4⋊C4—42no—
252C2×C4⋊C4—44no—
253C2×C4⋊C4—44no—
254C2×C4⋊C4—44no—
255C2×C4⋊C4—42no—
256C2×C4⋊C4—42no—
257C2×C4⋊C4C2×D414yes—
258C2×C4⋊C4C2×D418yes—
259C2×C4⋊C4C2×D418yes—
260C2×C42—22no—
261C2×C42—22no—
262C2×C42—22no—
263C2×C42—22no—
264C2×C42—28no—
265C2×C42—24no—
266C2×C42—24no—
267C2×C42—28no—
268C2×C42—24no—
269C2×C42—24no—
270C2×C42—24no—
271C2×C42—24no—
272C2×C42—24no—
273C2×C42—24no—
274C2×C42—24no—
275C2×C42—24no—
276C2×C42—44no—
277C2×C42—44no—
278C2×C42C2×D414yes—
279C2×C42C2×D414yes—
280C2×C42#4114yes—
281C2×C42#4114yes—
282C2×C42#4114yes—
283#95—24no—
284#95—24no—
285#95—24no—
286#95—28no—
287#95—24no—
288#95—24no—
289#95—28no—
290#95—28no—
291#95—28no—
292#95—28no—
293#95—28no—
294#95—28no—
295#95—28no—
296#95—28no—
297#95—24no—
298#95—24no—
299#95—24no—
300#95—24no—
301#95—28no—
302#95—28no—
303#95—28no—
304#95—28no—
305#95—28no—
306#95—44no—
307#95—44no—
308#95—44no—
309#95—44no—
310#95—42no—
311#95—42no—
312#95C2×D4116yes—
313C24C2511yescharacteristic
314C2×Q8—216no—
315C2×Q8—28no—
316C2×Q8—216no—
317C2×Q8—28no—
318C2×Q8—28no—
319C2×Q8—216no—
320C2×Q8—44no—
321C2×Q8—48no—
322C2×Q8—44no—
323C2×Q8—48no—
324C2×Q8—48no—
325C2×Q8—44no—
326C2×Q8—44no—
327C2×Q8—48no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—24no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—24no—
348C22×C4—24no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—24no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—22no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—22no—
376C22×C4—24no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—24no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—24no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—22no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—24no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—24no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—22no—
402C22×C4C22×D414yes—
403C22×C4C22×D414yes—
404C22×C4C22×D418yes—
405C22×C4C22×D414yes—
406C22×C4C22×D412yes—
407C22×C4C22×D412yes—
408C22×C4C22×D412yes—
409C22×C4C22×D412yes—
410C22×C4C2×#4114yes—
411C22×C4C2×#4112yes—
412C22×C4C2×#4112yes—
413C22×C4C2×#4112yes—
414C22×C4C2×#4112yes—
415C22×C4C2×#4112yes—
416C22×C4C2×#4112yes—
417C22×C4C2×#4112yes—
418C22×C4H(5,𝔽2)12yes—
419C22×C42−1+414yes—
420C22×C42−1+414yes—
421C22×C42−1+414yes—
422C22×C42−1+412yes—
423C4⋊C4—28no—
424C4⋊C4—28no—
425C4⋊C4—28no—
426C4⋊C4—216no—
427C4⋊C4—216no—
428C4⋊C4—216no—
429C4⋊C4—28no—
430C4⋊C4—48no—
431C4⋊C4—416no—
432C4⋊C4—48no—
433C4⋊C4—416no—
434C4⋊C4—416no—
435C4⋊C4—416no—
436C4⋊C4—44no—
437C4⋊C4—48no—
438C4⋊C4—48no—
439C4⋊C4—44no—
440C4⋊C4—48no—
441C4⋊C4—44no—
442C42—28no—
443C42—28no—
444C42—416no—
445C42—48no—
446C42—48no—
447C42—48no—
448C42—48no—
449C42#123116yes—
450C23C23×D411yescharacteristic
451C23C23×D411yescharacteristic
452C23C22×#4111yescharacteristic
453C23C22×#4111yescharacteristic
454C23C22×#4111yescharacteristic
455C23C2×H(5,𝔽2)11yescharacteristic
456C23C2×2−1+411yescharacteristic
457C23C2×2−1+412yes—
458C23C2×2−1+412yes—
459C23C2×2−1+412yes—
460C23#58512yes—
461Q8—432no—
462Q8—416no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—28no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—28no—
475C2×C4—24no—
476C2×C4—24no—
477C2×C4—28no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—28no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—44no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—42no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—44no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—44no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—44no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—44no—
542C2×C4—44no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—44no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—44no—
549C2×C4C2×#12314yes—
550C2×C4C2×#12314yes—
551C2×C4C2×#12314yes—
552C2×C4#53214yes—
553C2×C4#54214yes—
554C2×C4D4214yes—
555C2×C4#54714yes—
556C2×C4#54714yes—
557C2×C4#55314yes—
558C22C22×#12311yescharacteristic
559C22C2×#53211yescharacteristic
560C22C2×#54211yescharacteristic
561C22#346112yes—
562C22C2×D4211yescharacteristic
563C22C2×#54711yescharacteristic
564C22C2×#54711yescharacteristic
565C22C2×#55311yescharacteristic
566C22#348611yescharacteristic
567C22#348611yescharacteristic
568C22#348611yescharacteristic
569C22#348612yes—
570C22#348711yescharacteristic
571C22#348912yes—
572C22#350712yes—
573C22#350712yes—
574C22#350912yes—
575C22#350912yes—
576C22#350912yes—
577C22#353812yes—
578C22#354112yes—
579C22#355512yes—
580C22#355612yes—
581C4—24no—
582C4—24no—
583C4—44no—
584C4—44no—
585C4—48no—
586C4—44no—
587C4—44no—
588C4—44no—
589C4—44no—
590C4—44no—
591C4—82no—
592C4—84no—
593C4—82no—
594C4—82no—
595C4#242218yes—
596C2C2×#242211yescharacteristic
597C2#3518211yescharacteristic
598C2#3567411yescharacteristic
599C2#3593812yes—
600C2#3779312yes—
601C2#3981912yes—
602C2#4270112yes—
603C2#4526711yescharacteristic
604C2#4533411yescharacteristic
605C2#4539411yescharacteristic
606C2#4541811yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, prime radical, cosocleC24C25
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#25462
C2×#24462
C2×#23652
#165292
#154542
#154142
#151922
#151802
#147942
#142742
#141502
#140172
#139422
#138562
#137862