Finite Group Databasebeta

← #923693

Subgroups — #923693

Order 512.

2318 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2451C212yesmaximal
2C2×#2446C212yesmaximal
3#17114C212yesmaximal
4#17112C212yesmaximal
5#16354C214yesmaximal
6#16293C214yesmaximal
7#15981C212yesmaximal
8#15965C212yesmaximal
9#15192C212yesmaximal
10#15180C211yesmaximal, characteristic
11#15149C212yesmaximal
12#15128C211yesmaximal, characteristic
13#14261C212yesmaximal
14#14017C212yesmaximal
15#13856C211yesmaximal, characteristic
16C22×C4⋊Q8C2211yescharacteristic
17C22×C4⋊Q8C2211yescharacteristic
18C22×C4×Q8C2212yes—
19#2451—216no—
20#2446—216no—
21C2×#400C2214yes—
22C2×#398C2214yes—
23C2×#398C2214yes—
24C2×#398C2214yes—
25C2×#395C2214yes—
26C2×#395C2212yes—
27C2×#391C2212yes—
28C2×#391C2212yes—
29C2×#391C2212yes—
30C2×#391C2212yes—
31C2×#391C2214yes—
32C2×#391C2212yes—
33C2×#389C2212yes—
34C2×#389C2212yes—
35C2×#389C2212yes—
36C2×#387C2214yes—
37C2×#387C2214yes—
38C2×#387C2214yes—
39C2×C4×C4⋊C4C2212yes—
40C2×C4×C4⋊C4C2212yes—
41C2×C4×C4⋊C4C2211yescharacteristic
42C2×C4×C4⋊C4C2211yescharacteristic
43C2×#376C2211yescharacteristic
44#1446C2212yes—
45#1445C2214yes—
46#1444C2212yes—
47#1444C2211yescharacteristic
48#1444C2211yescharacteristic
49#1444C2212yes—
50#1444C2211yescharacteristic
51#1444C2211yescharacteristic
52#1444C2212yes—
53#1444C2214yes—
54#1443C2214yes—
55#1443C2214yes—
56#1443C2214yes—
57#1443C2214yes—
58#1442C2214yes—
59#1442C2214yes—
60#1442C2212yes—
61#1442C2212yes—
62#1442C2214yes—
63#1442C2214yes—
64#1442C2214yes—
65#1442C2214yes—
66#1441C2212yes—
67#1441C2214yes—
68#1441C2212yes—
69#1441C2212yes—
70#1436C2214yes—
71#1436C2214yes—
72C4⋊#95C2211yescharacteristic
73C4⋊#95C2212yes—
74C4⋊#95C2211yescharacteristic
75C4⋊#95C2212yes—
76C4⋊#95C2212yes—
77C23×Q8C2312yes—
78C23×Q8C2312yes—
79C2×C4⋊Q8—28no—
80C2×C4⋊Q8—28no—
81C2×C4⋊Q8—42no—
82C2×C4⋊Q8—42no—
83C2×C4×Q8—28no—
84C2×C4×Q8—28no—
85C2×C4×Q8—44no—
86C22×C4⋊C4C2312yes—
87C22×C4⋊C4C2312yes—
88C22×C4⋊C4C2312yes—
89C22×C4⋊C4C2312yes—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2312yes—
92C22×C4⋊C4C2314yes—
93C22×C4⋊C4C2314yes—
94C22×C4⋊C4C2312yes—
95C22×C4⋊C4C2312yes—
96C22×C4⋊C4C2312yes—
97C22×C4⋊C4C2312yes—
98C22×C4⋊C4C2311yescharacteristic
99C22×C4⋊C4C2311yescharacteristic
100C22×C4⋊C4C2312yes—
101C22×C4⋊C4C2314yes—
102C22×C4⋊C4C2314yes—
103C22×C4⋊C4C2311yescharacteristic
104C22×C42C2312yes—
105C22×C42C2311yescharacteristic
106C22×C42C2311yescharacteristic
107C22×C42C2314yes—
108C22×C42C2312yes—
109C22×C42C2311yescharacteristic
110#400—216no—
111#398—216no—
112#398—216no—
113#398—48no—
114#395—216no—
115#395—44no—
116#391—28no—
117#391—28no—
118#391—28no—
119#391—28no—
120#391—216no—
121#391D4116yes—
122#389—28no—
123#389—28no—
124#389—28no—
125#387—216no—
126#387—216no—
127#387—216no—
128C4×C4⋊C4—28no—
129C4×C4⋊C4—28no—
130C4×C4⋊C4—42no—
131C4×C4⋊C4—42no—
132#376—24no—
133C2×#95C2314yes—
134C2×#95C2314yes—
135C2×#95C2312yes—
136C2×#95C2312yes—
137C2×#95C2314yes—
138C2×#95C2314yes—
139C2×#95C2314yes—
140C2×#95C2312yes—
141C2×#95C2314yes—
142C2×#95C2314yes—
143C2×#95C2314yes—
144C2×#95C2312yes—
145C2×#95C2312yes—
146C2×#95C2314yes—
147C2×#95C2314yes—
148C2×#95C2314yes—
149C2×#95C2314yes—
150C2×#95C2311yescharacteristic
151C2×#95C2312yes—
152C2×#95C2312yes—
153C2×#95C2311yescharacteristic
154C2×#95C2312yes—
155C2×#95C2314yes—
156C2×#95C2312yes—
157C2×#95C2314yes—
158C2×#95C2314yes—
159C2×#95C2314yes—
160C2×#95C2314yes—
161C2×#95C2312yes—
162C2×#95C2311yescharacteristic
163C2×#95C2311yescharacteristic
164C2×#95C2314yes—
165C2×#95C2314yes—
166C22×Q8—24no—
167C22×Q8—28no—
168C22×Q8—24no—
169C22×Q8—24no—
170C22×Q8—24no—
171C22×Q8—24no—
172C22×Q8—24no—
173C22×Q8—24no—
174C22×Q8—42no—
175C22×Q8—44no—
176C22×Q8—42no—
177C22×Q8C2×D418yes—
178C23×C4C2412yes—
179C23×C4C2414yes—
180C23×C4C2414yes—
181C23×C4C2414yes—
182C23×C4C2412yes—
183C23×C4C2414yes—
184C23×C4C2412yes—
185C23×C4C2411yescharacteristic
186C23×C4C2411yescharacteristic
187C23×C4C2411yescharacteristic
188C23×C4C2411yescharacteristic
189C23×C4C2411yescharacteristic
190C23×C4C2411yescharacteristic
191C23×C4C2412yes—
192C23×C4C2411yescharacteristic
193C4⋊Q8—416no—
194C4⋊Q8—416no—
195C4×Q8—432no—
196C2×C4⋊C4—24no—
197C2×C4⋊C4—24no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—24no—
203C2×C4⋊C4—24no—
204C2×C4⋊C4—28no—
205C2×C4⋊C4—28no—
206C2×C4⋊C4—28no—
207C2×C4⋊C4—28no—
208C2×C4⋊C4—28no—
209C2×C4⋊C4—24no—
210C2×C4⋊C4—24no—
211C2×C4⋊C4—28no—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—24no—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—28no—
217C2×C4⋊C4—24no—
218C2×C4⋊C4—24no—
219C2×C4⋊C4—22no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—24no—
223C2×C4⋊C4—24no—
224C2×C4⋊C4—24no—
225C2×C4⋊C4—24no—
226C2×C4⋊C4—28no—
227C2×C4⋊C4—28no—
228C2×C4⋊C4—42no—
229C2×C4⋊C4—42no—
230C2×C4⋊C4—44no—
231C2×C4⋊C4—42no—
232C2×C4⋊C4—44no—
233C2×C4⋊C4—42no—
234C2×C4⋊C4—42no—
235C2×C4⋊C4—42no—
236C2×C4⋊C4—41no—
237C2×C4⋊C4—41no—
238C2×C4⋊C4—41no—
239C2×C4⋊C4—41no—
240C2×C4⋊C4—44no—
241C2×C4⋊C4—44no—
242C2×C4⋊C4—44no—
243C2×C4⋊C4—44no—
244C2×C4⋊C4C2×D418yes—
245C2×C42—24no—
246C2×C42—22no—
247C2×C42—22no—
248C2×C42—24no—
249C2×C42—24no—
250C2×C42—24no—
251C2×C42—28no—
252C2×C42—28no—
253C2×C42—24no—
254C2×C42—24no—
255C2×C42—24no—
256C2×C42—22no—
257C2×C42—22no—
258C2×C42—44no—
259C2×C42C2×D418yes—
260C2×C42#4114yes—
261#95—24no—
262#95—24no—
263#95—24no—
264#95—24no—
265#95—28no—
266#95—28no—
267#95—28no—
268#95—28no—
269#95—28no—
270#95—28no—
271#95—28no—
272#95—28no—
273#95—28no—
274#95—22no—
275#95—24no—
276#95—22no—
277#95—28no—
278#95—28no—
279#95—24no—
280#95—28no—
281#95—24no—
282#95—24no—
283#95—44no—
284#95—44no—
285#95—42no—
286#95—41no—
287#95—41no—
288#95—44no—
289#95—42no—
290#95—44no—
291#95—44no—
292#95C2×D4116yes—
293#95C2×D4116yes—
294C24C2511yescharacteristic
295C2×Q8—216no—
296C2×Q8—216no—
297C2×Q8—216no—
298C2×Q8—48no—
299C2×Q8—416no—
300C2×Q8—48no—
301C2×Q8—48no—
302C2×Q8—48no—
303C2×Q8—48no—
304C2×Q8—88no—
305C2×Q8—84no—
306C2×Q8—84no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—22no—
314C22×C4—24no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—24no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—24no—
353C22×C4—24no—
354C22×C4—24no—
355C22×C4—24no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—24no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—24no—
362C22×C4—22no—
363C22×C4—24no—
364C22×C4—24no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—24no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4C22×D414yes—
385C22×C4C22×D418yes—
386C22×C4C22×D414yes—
387C22×C4C22×D418yes—
388C22×C4C22×D414yes—
389C22×C4C2×#4112yes—
390C22×C4C2×#4112yes—
391C22×C4C2×#4112yes—
392C22×C4H(5,𝔽2)12yes—
393C22×C4H(5,𝔽2)12yes—
394C22×C42−1+414yes—
395C22×C42−1+412yes—
396C22×C42−1+412yes—
397C22×C42−1+412yes—
398C22×C42−1+412yes—
399C22×C42−1+414yes—
400C4⋊C4—216no—
401C4⋊C4—216no—
402C4⋊C4—216no—
403C4⋊C4—48no—
404C4⋊C4—416no—
405C4⋊C4—48no—
406C4⋊C4—44no—
407C4⋊C4—44no—
408C4⋊C4—44no—
409C4⋊C4—416no—
410C4⋊C4—48no—
411C4⋊C4—48no—
412C4⋊C4—48no—
413C4⋊C4—44no—
414C4⋊C4—48no—
415C4⋊C4—48no—
416C4⋊C4—88no—
417C4⋊C4—88no—
418C42—28no—
419C42—216no—
420C42—416no—
421C42—48no—
422C42—44no—
423C42—44no—
424C23C23×D412yes—
425C23C22×#4111yescharacteristic
426C23C2×H(5,𝔽2)11yescharacteristic
427C23C2×H(5,𝔽2)11yescharacteristic
428C23C2×2−1+411yescharacteristic
429C23C2×2−1+412yes—
430C23C2×2−1+412yes—
431C23C2×2−1+411yescharacteristic
432C23C2×2−1+411yescharacteristic
433C23C2×2−1+411yescharacteristic
434C23#58512yes—
435Q8—432no—
436Q8—816no—
437C2×C4—28no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—28no—
442C2×C4—28no—
443C2×C4—24no—
444C2×C4—24no—
445C2×C4—28no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—28no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—28no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—44no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—44no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—44no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—44no—
486C2×C4—41no—
487C2×C4—44no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—42no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—44no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—44no—
523C2×C4—44no—
524C2×C4—44no—
525C2×C4#53618yes—
526C2×C4#53914yes—
527C2×C4D4214yes—
528C2×C4#54718yes—
529C2×C4#56314yes—
530C22C2×#53612yes—
531C22C2×#53911yescharacteristic
532C22#346112yes—
533C22C2×D4211yescharacteristic
534C22C2×#54712yes—
535C22#348612yes—
536C22#348612yes—
537C22#348812yes—
538C22#348912yes—
539C22#350911yescharacteristic
540C22#351111yescharacteristic
541C22C2×#56311yescharacteristic
542C22#353611yescharacteristic
543C22#353811yescharacteristic
544C22#353811yescharacteristic
545C22#354011yescharacteristic
546C22#355011yescharacteristic
547C22#355012yes—
548C22#355512yes—
549C22#355512yes—
550C22#355512yes—
551C22#355611yescharacteristic
552C22#355612yes—
553C4—44no—
554C4—42no—
555C4—42no—
556C4—42no—
557C4—48no—
558C4—42no—
559C4—48no—
560C4—42no—
561C4—44no—
562C4—44no—
563C4—42no—
564C4—84no—
565C4—82no—
566C4—84no—
567C4#268018yes—
568C2#3732311yescharacteristic
569C2#3752611yescharacteristic
570C2#3779312yes—
571C2#3779512yes—
572C2#4280912yes—
573C2#4281112yes—
574C2#4541811yescharacteristic
575C2#4542211yescharacteristic
576C2C2×#268011yescharacteristic
577C2#5303311yescharacteristic
578C2#5310011yescharacteristic
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×#24512
C2×#24462
#171142
#171122
#163542
#162932
#159812
#159652
#151922
#151802
#151492
#151282
#142612
#140172
#138562