Finite Group Databasebeta

← #535463

Subgroups — #535463

Order 512.

2490 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2370C212yesmaximal
2C2×#2330C211yesmaximal, characteristic
3#14465C214yesmaximal
4#14406C214yesmaximal
5#14151C212yesmaximal
6#14115C214yesmaximal
7#14046C212yesmaximal
8#14045C212yesmaximal
9#14005C214yesmaximal
10#13910C212yesmaximal
11#13856C211yesmaximal, characteristic
12#13804C212yesmaximal
13#13779C211yesmaximal, characteristic
14C22×#125C2211yescharacteristic
15#2370—216no—
16#2330C4116yescomplemented
17C2×#389C2214yes—
18C2×#389C2212yes—
19C2×#389C2212yes—
20C2×#389C2214yes—
21C2×#389C2212yes—
22C2×#389C2212yes—
23C2×#389C2214yes—
24C2×#389C2214yes—
25C2×#389C2212yes—
26C2×#387C2214yes—
27C2×#387C2214yes—
28C2×#387C2214yes—
29C2×#384C2211yescharacteristic
30C2×#384C2214yes—
31C2×#384C2211yescharacteristic
32C2×#382C2211yescharacteristic
33C2×C4×C4⋊C4C2212yes—
34C2×C4×C4⋊C4C2212yes—
35C2×C4×C4⋊C4C2214yes—
36C2×C4×C4⋊C4C2212yes—
37C2×C4×C4⋊C4C2212yes—
38C2×C4×C4⋊C4C2212yes—
39C2×C4×C4⋊C4C2211yescharacteristic
40C2×C4×C4⋊C4C2211yescharacteristic
41C2×C4×C4⋊C4C2212yes—
42C2×#376C2211yescharacteristic
43#1444C2212yes—
44#1444C2212yes—
45#1444C2212yes—
46#1444C2212yes—
47#1444C2214yes—
48#1444C2214yes—
49#1444C2214yes—
50#1442C2214yes—
51#1441C2214yes—
52#1441C2214yes—
53#1441C2214yes—
54#1441C2214yes—
55#1436C2214yes—
56#1436C2214yes—
57#1436C2214yes—
58#1436C2214yes—
59#1436C2214yes—
60#1436C2214yes—
61C4⋊#95C2214yes—
62C4⋊#95C2214yes—
63C4⋊#95C2212yes—
64C4⋊#95C2212yes—
65C4⋊#95C2214yes—
66C4⋊#95C2212yes—
67#1434C2214yes—
68C4×#95C2214yes—
69C2×#125C2×C418yes—
70C2×#125D418yes—
71C2×#125Q818yes—
72C22×C4⋊C4C2312yes—
73C22×C4⋊C4C2312yes—
74C22×C4⋊C4C2312yes—
75C22×C4⋊C4C2311yescharacteristic
76C22×C4⋊C4C2312yes—
77C22×C4⋊C4C2314yes—
78C22×C4⋊C4C2312yes—
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2312yes—
81C22×C4⋊C4C2312yes—
82C22×C4⋊C4C2314yes—
83C22×C4⋊C4C2314yes—
84C22×C4⋊C4C2314yes—
85C22×C4⋊C4C2311yescharacteristic
86C22×C4⋊C4C2314yes—
87C22×C4⋊C4C2311yescharacteristic
88C22×C4⋊C4C2314yes—
89C22×C4⋊C4C2314yes—
90C22×C4⋊C4C2312yes—
91C22×C4⋊C4C2314yes—
92C22×C42C2312yes—
93C22×C42C2312yes—
94C22×C42C2314yes—
95C22×C42C2311yescharacteristic
96C22×C42C2314yes—
97C22×C42C2314yes—
98C22×C42C2314yes—
99C22×C42C2311yescharacteristic
100C22×C42C2311yescharacteristic
101#389—28no—
102#389—216no—
103#389—28no—
104#389—48no—
105#389—48no—
106#389—44no—
107#389—44no—
108#389C2×C4132yes—
109#389C2×C4116yes—
110#387—216no—
111#387—216no—
112#387C2×C4132yes—
113#384—24no—
114#384—48no—
115#384C2×C418yes—
116#382Q818yes—
117C4×C4⋊C4—216no—
118C4×C4⋊C4—28no—
119C4×C4⋊C4—28no—
120C4×C4⋊C4—28no—
121C4×C4⋊C4—28no—
122C4×C4⋊C4—28no—
123C4×C4⋊C4—42no—
124C4×C4⋊C4—42no—
125C4×C4⋊C4C2×C4116yes—
126#376C2×C418yes—
127C2×#95C2312yes—
128C2×#95C2314yes—
129C2×#95C2312yes—
130C2×#95C2314yes—
131C2×#95C2314yes—
132C2×#95C2314yes—
133C2×#95C2314yes—
134C2×#95C2314yes—
135C2×#95C2312yes—
136C2×#95C2312yes—
137C2×#95C2314yes—
138C2×#95C2314yes—
139C2×#95C2314yes—
140C2×#95C2314yes—
141C2×#95C2314yes—
142C2×#95C2314yes—
143C2×#95C2312yes—
144C2×#95C2314yes—
145C2×#95C2312yes—
146C2×#95C2314yes—
147C2×#95C2312yes—
148C2×#95C2312yes—
149C2×#95C2314yes—
150C2×#95C2314yes—
151C23×C4C2412yes—
152C23×C4C2414yes—
153C23×C4C2412yes—
154C23×C4C2414yes—
155C23×C4C2411yescharacteristic
156C23×C4C2411yescharacteristic
157C23×C4C2414yes—
158C23×C4C2412yes—
159C23×C4C2412yes—
160C23×C4C2414yes—
161C23×C4C2412yes—
162C23×C4C2412yes—
163C23×C4C2411yescharacteristic
164#125C4⋊C4164yescomplemented
165C2×C4⋊C4—24no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—24no—
169C2×C4⋊C4—24no—
170C2×C4⋊C4—24no—
171C2×C4⋊C4—28no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—28no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—24no—
183C2×C4⋊C4—24no—
184C2×C4⋊C4—28no—
185C2×C4⋊C4—28no—
186C2×C4⋊C4—28no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—44no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4—41no—
198C2×C4⋊C4—41no—
199C2×C4⋊C4—41no—
200C2×C4⋊C4—44no—
201C2×C4⋊C4—44no—
202C2×C4⋊C4—44no—
203C2×C4⋊C4—44no—
204C2×C4⋊C4—44no—
205C2×C4⋊C4—44no—
206C2×C4⋊C4—44no—
207C2×C4⋊C4—44no—
208C2×C4⋊C4—44no—
209C2×C4⋊C4—44no—
210C2×C4⋊C4—44no—
211C2×C4⋊C4C22×C418yes—
212C2×C4⋊C4C22×C4116yes—
213C2×C4⋊C4C22×C4116yes—
214C2×C4⋊C4C22×C418yes—
215C2×C4⋊C4C22×C4116yes—
216C2×C4⋊C4C2×D418yes—
217C2×C4⋊C4C2×D4116yes—
218C2×C4⋊C4C2×Q818yes—
219C2×C4⋊C4C2×Q8116yes—
220C2×C4⋊C4C2×Q818yes—
221C2×C42—22no—
222C2×C42—22no—
223C2×C42—28no—
224C2×C42—24no—
225C2×C42—24no—
226C2×C42—24no—
227C2×C42—24no—
228C2×C42—24no—
229C2×C42—24no—
230C2×C42—28no—
231C2×C42—28no—
232C2×C42—28no—
233C2×C42—44no—
234C2×C42—44no—
235C2×C42—44no—
236C2×C42—44no—
237C2×C42—44no—
238C2×C42—44no—
239C2×C42—44no—
240C2×C42C22×C414yes—
241C2×C42C22×C4116yes—
242C2×C42C22×C414yes—
243C2×C42C22×C414yes—
244C2×C42C2×D414yes—
245C2×C42C2×Q814yes—
246C2×C42C2×Q814yes—
247C2×C42#4114yes—
248#95—24no—
249#95—28no—
250#95—24no—
251#95—28no—
252#95—28no—
253#95—28no—
254#95—28no—
255#95—24no—
256#95—24no—
257#95—28no—
258#95—44no—
259#95—44no—
260#95—44no—
261#95—42no—
262#95—42no—
263#95—44no—
264#95—44no—
265#95—44no—
266#95—44no—
267#95C22×C418yes—
268#95C22×C418yes—
269#95C22×C4116yes—
270#95C22×C4116yes—
271#95C2×Q8116yes—
272C24C2511yescharacteristic
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—24no—
281C22×C4—22no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—24no—
286C22×C4—22no—
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—24no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—22no—
307C22×C4—24no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—24no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—24no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—24no—
323C22×C4—22no—
324C22×C4—24no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—24no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—24no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4C23×C412yes—
339C22×C4C23×C412yes—
340C22×C4C23×C418yes—
341C22×C4C23×C418yes—
342C22×C4C23×C414yes—
343C22×C4C23×C414yes—
344C22×C4C23×C412yes—
345C22×C4C22×D414yes—
346C22×C4C22×D418yes—
347C22×C4C22×D412yes—
348C22×C4C22×Q818yes—
349C22×C4C22×Q814yes—
350C22×C4C22×Q818yes—
351C22×C4C22×Q814yes—
352C22×C4C22×Q812yes—
353C22×C4C22×Q812yes—
354C22×C4C2×#4114yes—
355C22×C4C2×#4112yes—
356C22×C4H(5,𝔽2)14yes—
357C22×C4H(5,𝔽2)12yes—
358C22×C42−1+414yes—
359C22×C42−1+412yes—
360C4⋊C4—216no—
361C4⋊C4—216no—
362C4⋊C4—416no—
363C4⋊C4—416no—
364C4⋊C4—48no—
365C4⋊C4—416no—
366C4⋊C4—48no—
367C4⋊C4—48no—
368C4⋊C4—48no—
369C4⋊C4—44no—
370C4⋊C4—44no—
371C4⋊C4—44no—
372C4⋊C4—44no—
373C4⋊C4—48no—
374C4⋊C4—88no—
375C4⋊C4—88no—
376C4⋊C4—88no—
377C4⋊C4—88no—
378C4⋊C4C2×C4⋊C4164yes—
379C4⋊C4C2×C4⋊C4132yes—
380C42—28no—
381C42—416no—
382C42—416no—
383C42—48no—
384C42—48no—
385C42—88no—
386C42—88no—
387C42C2×C4⋊C4116yes—
388C42C4×Q8116yes—
389C23C24×C411yescharacteristic
390C23C23×D411yescharacteristic
391C23C23×Q811yescharacteristic
392C23C23×Q811yescharacteristic
393C23C22×#4111yescharacteristic
394C23C2×H(5,𝔽2)11yescharacteristic
395C23C2×H(5,𝔽2)12yes—
396C23C2×2−1+411yescharacteristic
397C23C2×2−1+412yes—
398C23#58512yes—
399C23#58512yes—
400C2×C4—24no—
401C2×C4—28no—
402C2×C4—24no—
403C2×C4—28no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—28no—
408C2×C4—28no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—28no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—28no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—28no—
421C2×C4—28no—
422C2×C4—28no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—28no—
426C2×C4—24no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—28no—
431C2×C4—28no—
432C2×C4—24no—
433C2×C4—24no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—44no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—44no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—44no—
459C2×C4—44no—
460C2×C4—42no—
461C2×C4—44no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—44no—
477C2×C4C22×C4⋊C418yes—
478C2×C4C22×C4⋊C4116yes—
479C2×C4C22×C4⋊C414yes—
480C2×C4C2×C4×Q818yes—
481C2×C4C2×C4×Q814yes—
482C2×C4#52014yes—
483C2×C4D4×Q814yes—
484C2×C4#55014yes—
485C2×C4#55714yes—
486C2×C4Q8214yes—
487C22C23×C4⋊C411yescharacteristic
488C22C22×C4×Q811yescharacteristic
489C22C2×#52011yescharacteristic
490C22C4×H(5,𝔽2)12yes—
491C22C4×2−1+412yes—
492C22C2×D4×Q811yescharacteristic
493C22C2×#55011yescharacteristic
494C22C2×#55711yescharacteristic
495C22C2×Q8211yescharacteristic
496C22#348812yes—
497C22#348912yes—
498C22#349412yes—
499C22#349512yes—
500C22#350312yes—
501C22#350312yes—
502C22#350412yes—
503C22#350412yes—
504C22#353711yescharacteristic
505C22#353811yescharacteristic
506C22#353911yescharacteristic
507C22#353911yescharacteristic
508C22#355412yes—
509C22#355512yes—
510C4—216no—
511C4—28no—
512C4—28no—
513C4—44no—
514C4—48no—
515C4—42no—
516C4—48no—
517C4—42no—
518C4—44no—
519C4—82no—
520C4—84no—
521C4—82no—
522C4Q8×C4⋊C418yes—
523C2C2×Q8×C4⋊C411yescharacteristic
524C2#3425012yes—
525C2#3427212yes—
526C2#3441811yescharacteristic
527C2#3442011yescharacteristic
528C2#4542311yescharacteristic
529C2#4542412yes—
530C2#4542612yes—
531C2#4542711yescharacteristic
532C2#4543211yescharacteristic
533C2#4543511yescharacteristic
subgroupG/H
center, Frattini, socle, prime radical, cosocleC24C25
commutatorC23C24×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C24 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
16. #2330C4semidirect
164. #125C4⋊C4semidirect

Maximal subgroups

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

subgroupindex
C2×#23702
C2×#23302
#144652
#144062
#141512
#141152
#140462
#140452
#140052
#139102
#138562
#138042
#137792