Finite Group Databasebeta

← #2737721

Subgroups — #2737721

Order 512.

1794 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2509C212yesmaximal
2#17202C212yesmaximal
3#17184C214yesmaximal
4#17120C212yesmaximal
5#17075C212yesmaximal
6#16517C214yesmaximal
7#15232C212yesmaximal
8#15221C212yesmaximal
9#15187C212yesmaximal
10#15151C211yesmaximal, characteristic
11#15137C212yesmaximal
12#15133C212yesmaximal
13#14634C212yesmaximal
14#13911C211yesmaximal, characteristic
15C4×#398C211yesmaximal, characteristic
16#2509—216no—
17C2×#400C2214yes—
18C2×#400C2214yes—
19C2×#398C2211yescharacteristic
20C2×#398C2212yes—
21C2×#398C2214yes—
22C2×#398C2214yes—
23C2×#398C2212yes—
24C2×#389C2212yes—
25C2×#389C2212yes—
26C2×#389C2212yes—
27C2×#389C2212yes—
28C2×#389C2214yes—
29C2×#389C2212yes—
30C2×#387C2214yes—
31C2×#384C2211yescharacteristic
32C2×#384C2211yescharacteristic
33C2×#382C2212yes—
34C2×#382C2212yes—
35C2×C4×C4⋊C4C2212yes—
36C2×C4×C4⋊C4C2211yescharacteristic
37C2×C4×C4⋊C4C2211yescharacteristic
38C2×C4×C4⋊C4C2211yescharacteristic
39#1445C2212yes—
40#1445C2214yes—
41#1445C2214yes—
42#1445C2211yescharacteristic
43#1445C2212yes—
44#1445C2214yes—
45#1444C2214yes—
46#1444C2211yescharacteristic
47#1444C2214yes—
48#1443C2214yes—
49#1443C2214yes—
50#1443C2214yes—
51#1442C2212yes—
52#1442C2212yes—
53#1442C2214yes—
54#1442C2214yes—
55#1442C2214yes—
56#1442C2214yes—
57#1442C2212yes—
58#1442C2214yes—
59#1441C2214yes—
60#1441C2214yes—
61#1441C2214yes—
62#1441C2214yes—
63#1441C2214yes—
64#1441C2211yescharacteristic
65#1441C2212yes—
66C4⋊#95C2212yes—
67C4⋊#95C2212yes—
68C4⋊#95C2212yes—
69C4⋊#95C2212yes—
70C4⋊#95C2212yes—
71C4⋊#95C2212yes—
72C4⋊#95C2211yescharacteristic
73C4⋊#95C2212yes—
74C4×#95C2212yes—
75C4×#95C2211yescharacteristic
76C22×C4⋊C4C2312yes—
77C22×C4⋊C4C2314yes—
78C22×C4⋊C4C2312yes—
79C22×C4⋊C4C2312yes—
80C22×C4⋊C4C2312yes—
81C22×C4⋊C4C2311yescharacteristic
82C22×C4⋊C4C2312yes—
83C22×C4⋊C4C2314yes—
84C22×C4⋊C4C2312yes—
85C22×C4⋊C4C2312yes—
86C22×C4⋊C4C2312yes—
87C22×C4⋊C4C2314yes—
88C22×C4⋊C4C2314yes—
89C22×C4⋊C4C2312yes—
90C22×C4⋊C4C2311yescharacteristic
91C22×C4⋊C4C2314yes—
92C22×C4⋊C4C2312yes—
93C22×C4⋊C4C2311yescharacteristic
94C22×C4⋊C4C2311yescharacteristic
95C22×C42C2311yescharacteristic
96C22×C42C2312yes—
97C22×C42C2311yescharacteristic
98C22×C42C2312yes—
99C22×C42C2311yescharacteristic
100C22×C42C2312yes—
101#400—216no—
102#400—216no—
103#398—24no—
104#398—28no—
105#398—48no—
106#398—44no—
107#398—48no—
108#389—28no—
109#389—28no—
110#389—28no—
111#389—216no—
112#389—28no—
113#389—44no—
114#387—216no—
115#384—42no—
116#384—42no—
117#382—28no—
118#382—44no—
119C4×C4⋊C4—28no—
120C4×C4⋊C4—42no—
121C4×C4⋊C4—42no—
122C4×C4⋊C4D418yes—
123C2×#95C2312yes—
124C2×#95C2312yes—
125C2×#95C2311yescharacteristic
126C2×#95C2314yes—
127C2×#95C2314yes—
128C2×#95C2312yes—
129C2×#95C2312yes—
130C2×#95C2314yes—
131C2×#95C2314yes—
132C2×#95C2314yes—
133C2×#95C2314yes—
134C2×#95C2314yes—
135C2×#95C2314yes—
136C2×#95C2312yes—
137C2×#95C2312yes—
138C2×#95C2312yes—
139C2×#95C2314yes—
140C2×#95C2314yes—
141C2×#95C2314yes—
142C2×#95C2314yes—
143C2×#95C2314yes—
144C2×#95C2312yes—
145C2×#95C2312yes—
146C2×#95C2311yescharacteristic
147C2×#95C2314yes—
148C2×#95C2314yes—
149C2×#95C2314yes—
150C2×#95C2314yes—
151C2×#95C2314yes—
152C2×#95C2314yes—
153C2×#95C2312yes—
154C2×#95C2311yescharacteristic
155C2×#95C2311yescharacteristic
156C2×#95C2312yes—
157C23×C4C2414yes—
158C23×C4C2412yes—
159C23×C4C2414yes—
160C23×C4C2414yes—
161C23×C4C2412yes—
162C23×C4C2412yes—
163C23×C4C2411yescharacteristic
164C23×C4C2414yes—
165C23×C4C2411yescharacteristic
166C23×C4C2411yescharacteristic
167C23×C4C2411yescharacteristic
168C23×C4C2411yescharacteristic
169C23×C4C2412yes—
170C23×C4C2411yescharacteristic
171C23×C4C2411yescharacteristic
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—28no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—24no—
182C2×C4⋊C4—28no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—24no—
185C2×C4⋊C4—24no—
186C2×C4⋊C4—22no—
187C2×C4⋊C4—24no—
188C2×C4⋊C4—28no—
189C2×C4⋊C4—24no—
190C2×C4⋊C4—28no—
191C2×C4⋊C4—24no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—28no—
197C2×C4⋊C4—28no—
198C2×C4⋊C4—24no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—24no—
201C2×C4⋊C4—41no—
202C2×C4⋊C4—44no—
203C2×C4⋊C4—42no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4—42no—
206C2×C4⋊C4—41no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4—41no—
210C2×C4⋊C4—44no—
211C2×C4⋊C4—44no—
212C2×C4⋊C4—42no—
213C2×C4⋊C4—44no—
214C2×C4⋊C4—42no—
215C2×C4⋊C4—42no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4—42no—
218C2×C4⋊C4—42no—
219C2×C4⋊C4—44no—
220C2×C4⋊C4—44no—
221C2×C4⋊C4—44no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—44no—
224C2×C4⋊C4—44no—
225C2×C4⋊C4C2×D418yes—
226C2×C4⋊C4#4114yes—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—24no—
230C2×C42—24no—
231C2×C42—22no—
232C2×C42—22no—
233C2×C42—24no—
234C2×C42—24no—
235C2×C42—24no—
236C2×C42—24no—
237C2×C42—24no—
238C2×C42—24no—
239C2×C42—42no—
240C2×C42—42no—
241C2×C42C2×D414yes—
242C2×C42C2×D418yes—
243#95—24no—
244#95—24no—
245#95—28no—
246#95—28no—
247#95—28no—
248#95—28no—
249#95—28no—
250#95—28no—
251#95—22no—
252#95—24no—
253#95—24no—
254#95—28no—
255#95—28no—
256#95—24no—
257#95—24no—
258#95—24no—
259#95—44no—
260#95—42no—
261#95—44no—
262#95—41no—
263#95—44no—
264#95—44no—
265#95—41no—
266#95—41no—
267#95—42no—
268#95—44no—
269#95—44no—
270#95—44no—
271#95—44no—
272#95—42no—
273#95—44no—
274#95—44no—
275#95—44no—
276#95C2×D418yes—
277C24C2511yescharacteristic
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4—21no—
306C22×C4—24no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—24no—
313C22×C4—22no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—22no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—24no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—21no—
326C22×C4—24no—
327C22×C4—24no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—24no—
332C22×C4—24no—
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—24no—
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—24no—
345C22×C4—22no—
346C22×C4—24no—
347C22×C4—24no—
348C22×C4—22no—
349C22×C4—24no—
350C22×C4—22no—
351C22×C4—24no—
352C22×C4—24no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—24no—
357C22×C4C22×D412yes—
358C22×C4C22×D418yes—
359C22×C4C22×D412yes—
360C22×C4C22×D412yes—
361C22×C4C2×#4112yes—
362C22×C4C2×#4112yes—
363C22×C4C2×#4112yes—
364C22×C4H(5,𝔽2)12yes—
365C22×C4H(5,𝔽2)12yes—
366C22×C4H(5,𝔽2)12yes—
367C22×C42−1+414yes—
368C22×C42−1+414yes—
369C22×C42−1+414yes—
370C22×C42−1+412yes—
371C4⋊C4—216no—
372C4⋊C4—44no—
373C4⋊C4—44no—
374C4⋊C4—48no—
375C4⋊C4—416no—
376C4⋊C4—44no—
377C4⋊C4—44no—
378C4⋊C4—48no—
379C4⋊C4—48no—
380C4⋊C4—48no—
381C4⋊C4—416no—
382C4⋊C4—48no—
383C4⋊C4—84no—
384C4⋊C4—88no—
385C4⋊C4—88no—
386C4⋊C4—84no—
387C4⋊C4—84no—
388C4⋊C4—84no—
389C4⋊C4—88no—
390C42—28no—
391C42—48no—
392C42—48no—
393C42—48no—
394C42—44no—
395C42—44no—
396C23C23×D411yescharacteristic
397C23C22×#4111yescharacteristic
398C23C2×H(5,𝔽2)11yescharacteristic
399C23C2×H(5,𝔽2)11yescharacteristic
400C23C2×H(5,𝔽2)11yescharacteristic
401C23C2×2−1+412yes—
402C23C2×2−1+412yes—
403C23C2×2−1+411yescharacteristic
404C23C2×2−1+412yes—
405C23#58512yes—
406C23#58511yescharacteristic
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—28no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—28no—
418C2×C4—28no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—22no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—44no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—44no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—44no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—44no—
452C2×C4—42no—
453C2×C4—44no—
454C2×C4—44no—
455C2×C4—42no—
456C2×C4—44no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—44no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—44no—
464C2×C4—42no—
465C2×C4—44no—
466C2×C4—44no—
467C2×C4—44no—
468C2×C4—41no—
469C2×C4—44no—
470C2×C4—41no—
471C2×C4—44no—
472C2×C4—42no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—41no—
480C2×C4—44no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—44no—
485C2×C4—44no—
486C2×C4—44no—
487C2×C4—44no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4#53618yes—
495C2×C4#53714yes—
496C2×C4#55014yes—
497C2×C4#56314yes—
498C2×C4#56314yes—
499C2×C4#56418yes—
500C22C2×#53612yes—
501C22C2×#53711yescharacteristic
502C22C2×#55011yescharacteristic
503C22#348912yes—
504C22#349611yescharacteristic
505C22#350511yescharacteristic
506C22#351111yescharacteristic
507C22#351512yes—
508C22#352312yes—
509C22C2×#56311yescharacteristic
510C22C2×#56311yescharacteristic
511C22C2×#56412yes—
512C22#353711yescharacteristic
513C22#354011yescharacteristic
514C22#354412yes—
515C22#355011yescharacteristic
516C22#355212yes—
517C22#355412yes—
518C22#355412yes—
519C22#355512yes—
520C22#355512yes—
521C22#355911yescharacteristic
522C22#356512yes—
523C4—24no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—48no—
528C4—44no—
529C4—42no—
530C4—82no—
531C4—84no—
532C4—82no—
533C4—82no—
534C4—84no—
535C4—81no—
536C4—84no—
537C4#282218yes—
538C2C2×#282211yescharacteristic
539C2#3913912yes—
540C2#3974211yescharacteristic
541C2#4244212yes—
542C2#4292911yescharacteristic
543C2#4569611yescharacteristic
544C2#4618112yes—
545C2#4634611yescharacteristic
546C2#5296811yescharacteristic
547C2#5298911yescharacteristic
548C2#5299612yes—
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×#25092
#172022
#171842
#171202
#170752
#165172
#152322
#152212
#151872
#151512
#151372
#151332
#146342
#139112
C4×#3982