Finite Group Databasebeta

← #924203

Subgroups — #924203

Order 512.

1754 conjugacy classes of subgroups.

The subgroup lattice has 495 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17299C214yesmaximal
2#16981C214yesmaximal
3#16412C214yesmaximal
4#15864C214yesmaximal
5#15218C212yesmaximal
6#15218C211yesmaximal, characteristic
7#15196C211yesmaximal, characteristic
8#15133C212yesmaximal
9#14266C212yesmaximal
10#14046C212yesmaximal
11#14045C212yesmaximal
12#14042C212yesmaximal
13#13856C211yesmaximal, characteristic
14C22×#125C2211yescharacteristic
15C2×#398C2214yes—
16C2×#389C2212yes—
17C2×#389C2214yes—
18C2×#389C2212yes—
19C2×#389C2212yes—
20C2×#389C2212yes—
21C2×#389C2212yes—
22C2×#387C2214yes—
23C2×#384C2211yescharacteristic
24C2×C4×C4⋊C4C2212yes—
25C2×C4×C4⋊C4C2211yescharacteristic
26C2×C4×C4⋊C4C2212yes—
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2212yes—
29C2×#376C2211yescharacteristic
30#1445C2214yes—
31#1444C2212yes—
32#1444C2214yes—
33#1444C2214yes—
34#1444C2212yes—
35#1444C2212yes—
36#1444C2212yes—
37#1444C2214yes—
38#1444C2214yes—
39#1444C2214yes—
40#1443C2214yes—
41#1443C2214yes—
42#1442C2214yes—
43#1442C2214yes—
44#1441C2214yes—
45#1441C2214yes—
46#1441C2214yes—
47#1441C2214yes—
48#1441C2214yes—
49#1441C2214yes—
50#1441C2214yes—
51#1441C2214yes—
52#1441C2214yes—
53#1441C2214yes—
54#1441C2214yes—
55#1436C2214yes—
56#1436C2214yes—
57C4⋊#95C2212yes—
58C4⋊#95C2212yes—
59C4⋊#95C2212yes—
60C4⋊#95C2214yes—
61C4⋊#95C2212yes—
62C4⋊#95C2211yescharacteristic
63C4⋊#95C2212yes—
64C4⋊#95C2212yes—
65C4⋊#95C2211yescharacteristic
66#1434C2214yes—
67C2×#125—42no—
68C2×#125—44no—
69C22×C4⋊C4C2312yes—
70C22×C4⋊C4C2312yes—
71C22×C4⋊C4C2312yes—
72C22×C4⋊C4C2312yes—
73C22×C4⋊C4C2312yes—
74C22×C4⋊C4C2314yes—
75C22×C4⋊C4C2314yes—
76C22×C4⋊C4C2314yes—
77C22×C4⋊C4C2312yes—
78C22×C4⋊C4C2312yes—
79C22×C4⋊C4C2312yes—
80C22×C4⋊C4C2312yes—
81C22×C4⋊C4C2314yes—
82C22×C4⋊C4C2314yes—
83C22×C4⋊C4C2314yes—
84C22×C4⋊C4C2312yes—
85C22×C4⋊C4C2314yes—
86C22×C42C2311yescharacteristic
87C22×C42C2312yes—
88C22×C42C2311yescharacteristic
89C22×C42C2312yes—
90C22×C42C2311yescharacteristic
91C22×C42C2314yes—
92#398—48no—
93#389—28no—
94#389—44no—
95#389—44no—
96#389—44no—
97#389—48no—
98#389Q8116yes—
99#387—48no—
100#384—42no—
101C4×C4⋊C4—44no—
102C4×C4⋊C4—42no—
103C4×C4⋊C4—44no—
104C4×C4⋊C4—42no—
105C4×C4⋊C4—44no—
106#376—24no—
107C2×#95C2314yes—
108C2×#95C2314yes—
109C2×#95C2311yescharacteristic
110C2×#95C2311yescharacteristic
111C2×#95C2312yes—
112C2×#95C2314yes—
113C2×#95C2314yes—
114C2×#95C2312yes—
115C2×#95C2314yes—
116C2×#95C2314yes—
117C2×#95C2314yes—
118C2×#95C2314yes—
119C2×#95C2312yes—
120C2×#95C2314yes—
121C2×#95C2314yes—
122C2×#95C2314yes—
123C2×#95C2314yes—
124C2×#95C2314yes—
125C2×#95C2314yes—
126C2×#95C2314yes—
127C2×#95C2314yes—
128C2×#95C2311yescharacteristic
129C2×#95C2314yes—
130C2×#95C2314yes—
131C2×#95C2312yes—
132C2×#95C2314yes—
133C2×#95C2312yes—
134C2×#95C2312yes—
135C2×#95C2311yescharacteristic
136C2×#95C2314yes—
137C23×C4C2414yes—
138C23×C4C2414yes—
139C23×C4C2412yes—
140C23×C4C2412yes—
141C23×C4C2412yes—
142C23×C4C2414yes—
143C23×C4C2414yes—
144C23×C4C2412yes—
145C23×C4C2411yescharacteristic
146C23×C4C2411yescharacteristic
147C23×C4C2412yes—
148C23×C4C2412yes—
149C23×C4C2411yescharacteristic
150#125—416no—
151C2×C4⋊C4—24no—
152C2×C4⋊C4—24no—
153C2×C4⋊C4—24no—
154C2×C4⋊C4—24no—
155C2×C4⋊C4—28no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—24no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—24no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—28no—
169C2×C4⋊C4—28no—
170C2×C4⋊C4—44no—
171C2×C4⋊C4—42no—
172C2×C4⋊C4—42no—
173C2×C4⋊C4—44no—
174C2×C4⋊C4—42no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—42no—
177C2×C4⋊C4—42no—
178C2×C4⋊C4—44no—
179C2×C4⋊C4—44no—
180C2×C4⋊C4—44no—
181C2×C4⋊C4—42no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4—44no—
192C2×C4⋊C4—44no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—44no—
195C2×C4⋊C4—44no—
196C2×C4⋊C4—44no—
197C2×C4⋊C4—44no—
198C2×C4⋊C4—44no—
199C2×C4⋊C4C2×Q818yes—
200C2×C4⋊C4C2×Q818yes—
201C2×C4⋊C4C2×Q8116yes—
202C2×C42—24no—
203C2×C42—22no—
204C2×C42—24no—
205C2×C42—22no—
206C2×C42—22no—
207C2×C42—24no—
208C2×C42—24no—
209C2×C42—22no—
210C2×C42—24no—
211C2×C42—24no—
212C2×C42—24no—
213C2×C42—28no—
214C2×C42—44no—
215C2×C42—44no—
216C2×C42C2×Q818yes—
217C2×C42#4114yes—
218#95—24no—
219#95—22no—
220#95—22no—
221#95—28no—
222#95—28no—
223#95—44no—
224#95—44no—
225#95—44no—
226#95—44no—
227#95—44no—
228#95—44no—
229#95—42no—
230#95—42no—
231#95—41no—
232#95—42no—
233#95—42no—
234#95—41no—
235#95—42no—
236#95—44no—
237#95—44no—
238#95—44no—
239#95—44no—
240#95—44no—
241#95—44no—
242#95—44no—
243#95—44no—
244#95—44no—
245#95—44no—
246#95—44no—
247#95C2×Q8116yes—
248C24C2511yescharacteristic
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—24no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—22no—
289C22×C4—22no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—22no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—22no—
304C22×C4—22no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4—24no—
310C22×C4—24no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—24no—
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—24no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4C22×Q814yes—
322C22×C4C22×Q818yes—
323C22×C4C22×Q818yes—
324C22×C4C22×Q814yes—
325C22×C4C22×Q814yes—
326C22×C4C2×#4112yes—
327C22×C4C2×#4112yes—
328C22×C4C2×#4112yes—
329C22×C4H(5,𝔽2)14yes—
330C22×C4H(5,𝔽2)12yes—
331C22×C4H(5,𝔽2)14yes—
332C22×C42−1+414yes—
333C22×C42−1+412yes—
334C4⋊C4—216no—
335C4⋊C4—216no—
336C4⋊C4—416no—
337C4⋊C4—48no—
338C4⋊C4—416no—
339C4⋊C4—48no—
340C4⋊C4—48no—
341C4⋊C4—48no—
342C4⋊C4—48no—
343C4⋊C4—48no—
344C4⋊C4—416no—
345C4⋊C4—48no—
346C4⋊C4—48no—
347C4⋊C4—88no—
348C4⋊C4—88no—
349C4⋊C4—88no—
350C4⋊C4—88no—
351C42—28no—
352C42—216no—
353C42—44no—
354C42—48no—
355C42—44no—
356C42—88no—
357C23C23×Q812yes—
358C23C22×#4111yescharacteristic
359C23C2×H(5,𝔽2)11yescharacteristic
360C23C2×H(5,𝔽2)12yes—
361C23C2×H(5,𝔽2)12yes—
362C23C2×2−1+411yescharacteristic
363C23C2×2−1+412yes—
364C23#58512yes—
365C23#58512yes—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—28no—
369C2×C4—24no—
370C2×C4—24no—
371C2×C4—24no—
372C2×C4—28no—
373C2×C4—24no—
374C2×C4—28no—
375C2×C4—28no—
376C2×C4—24no—
377C2×C4—24no—
378C2×C4—28no—
379C2×C4—24no—
380C2×C4—28no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—24no—
385C2×C4—24no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—44no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—44no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—44no—
399C2×C4—42no—
400C2×C4—44no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—41no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—44no—
417C2×C4—41no—
418C2×C4—44no—
419C2×C4—44no—
420C2×C4—44no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—44no—
424C2×C4—44no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—44no—
434C2×C4—42no—
435C2×C4—44no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—44no—
440C2×C4—44no—
441C2×C4—44no—
442C2×C4—44no—
443C2×C4—42no—
444C2×C4—44no—
445C2×C4—44no—
446C2×C4#53914yes—
447C2×C4#54418yes—
448C2×C4#55418yes—
449C2×C4Q8214yes—
450C2×C4#56014yes—
451C22C2×#53911yescharacteristic
452C22C2×#54412yes—
453C22#346012yes—
454C22C2×#55412yes—
455C22C2×Q8211yescharacteristic
456C22#350112yes—
457C22#350212yes—
458C22#350312yes—
459C22#350412yes—
460C22#350911yescharacteristic
461C22#351211yescharacteristic
462C22C2×#56011yescharacteristic
463C22#353612yes—
464C22#353912yes—
465C22#354112yes—
466C22#354112yes—
467C22#354212yes—
468C22#354212yes—
469C22#354811yescharacteristic
470C22#355512yes—
471C22#355711yescharacteristic
472C4—44no—
473C4—44no—
474C4—48no—
475C4—42no—
476C4—44no—
477C4—44no—
478C4—42no—
479C4—48no—
480C4—82no—
481C4—82no—
482C4—84no—
483C4—84no—
484C4#279218yes—
485C2#3739411yescharacteristic
486C2#3752011yescharacteristic
487C2#3969112yes—
488C2#3969212yes—
489C2#4249412yes—
490C2#4281912yes—
491C2#4495012yes—
492C2C2×#279211yescharacteristic
493C2#5309812yes—
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
#172992
#169812
#164122
#158642
#152182
#151962
#151332
#142662
#140462
#140452
#140422
#138562