Finite Group Databasebeta

← #641205

Subgroups — #641205

Order 512.

2038 conjugacy classes of subgroups.

The subgroup lattice has 435 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2570C212yesmaximal
2#17076C214yesmaximal
3#17073C214yesmaximal
4#15231C212yesmaximal
5#15145C212yesmaximal
6#14809C218yesmaximal
7#14687C211yesmaximal, characteristic
8#14354C212yesmaximal
9#14277C212yesmaximal
10#13909C212yesmaximal
11C4×#384C211yesmaximal, characteristic
12#13755C211yesmaximal, characteristic
13#2570—216no—
14C2×#400C2214yes—
15C2×#398C2214yes—
16C2×#398C2218yes—
17C2×#389C2212yes—
18C2×#389C2212yes—
19C2×#387C2214yes—
20C2×#387C2214yes—
21C2×#384C2211yescharacteristic
22C2×#384C2212yes—
23C2×#384C2211yescharacteristic
24C2×#384C2212yes—
25C2×#384C2211yescharacteristic
26C2×#384C2211yescharacteristic
27C2×#382C2212yes—
28C2×#382C2212yes—
29C2×#382C2212yes—
30C2×#382C2212yes—
31C2×C4×C4⋊C4C2212yes—
32C2×C4×C4⋊C4C2214yes—
33C2×C4×C4⋊C4C2211yescharacteristic
34C2×C4×C4⋊C4C2211yescharacteristic
35C2×#376C2212yes—
36C2×C43C2211yescharacteristic
37#1444C2218yes—
38#1444C2218yes—
39#1444C2218yes—
40#1444C2218yes—
41#1442C2218yes—
42#1442C2218yes—
43#1441C2218yes—
44#1441C2218yes—
45#1436C2218yes—
46C4⋊#95C2212yes—
47C4⋊#95C2212yes—
48C4⋊#95C2212yes—
49C4⋊#95C2214yes—
50C4⋊#95C2214yes—
51C4⋊#95C2212yes—
52C4⋊#95C2214yes—
53C4⋊#95C2212yes—
54#1434C2214yes—
55C4×#95C2212yes—
56C22×C4⋊C4C2312yes—
57C22×C4⋊C4C2312yes—
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2312yes—
60C22×C4⋊C4C2314yes—
61C22×C4⋊C4C2314yes—
62C22×C4⋊C4C2314yes—
63C22×C4⋊C4C2314yes—
64C22×C4⋊C4C2314yes—
65C22×C4⋊C4C2314yes—
66C22×C4⋊C4C2314yes—
67C22×C4⋊C4C2314yes—
68C22×C4⋊C4C2318yes—
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2311yescharacteristic
71C22×C4⋊C4C2312yes—
72C22×C42C2312yes—
73C22×C42C2311yescharacteristic
74C22×C42C2312yes—
75C22×C42C2312yes—
76C22×C42C2314yes—
77C22×C42C2312yes—
78C22×C42C2311yescharacteristic
79C22×C42C2311yescharacteristic
80#400—216no—
81#398—216no—
82#398—416no—
83#389—28no—
84#389—28no—
85#387—216no—
86#387—216no—
87#384—28no—
88#384—24no—
89#384—24no—
90#384—44no—
91#384—42no—
92#384—42no—
93#382—28no—
94#382—28no—
95#382—28no—
96#382—44no—
97C4×C4⋊C4—28no—
98C4×C4⋊C4—48no—
99C4×C4⋊C4D418yes—
100C4×C4⋊C4Q818yes—
101#376—28no—
102C2×#95C2314yes—
103C2×#95C2314yes—
104C2×#95C2314yes—
105C2×#95C2318yes—
106C2×#95C2314yes—
107C2×#95C2314yes—
108C2×#95C2314yes—
109C2×#95C2314yes—
110C2×#95C2314yes—
111C2×#95C2314yes—
112C2×#95C2314yes—
113C2×#95C2314yes—
114C2×#95C2318yes—
115C2×#95C2318yes—
116C2×#95C2318yes—
117C2×#95C2318yes—
118C2×#95C2312yes—
119C2×#95C2312yes—
120C43Q818yes—
121C23×C4C2414yes—
122C23×C4C2414yes—
123C23×C4C2414yes—
124C23×C4C2414yes—
125C23×C4C2412yes—
126C23×C4C2412yes—
127C23×C4C2414yes—
128C23×C4C2411yescharacteristic
129C23×C4C2411yescharacteristic
130C23×C4C2412yes—
131C23×C4C2412yes—
132C23×C4C2411yescharacteristic
133C2×C4⋊C4—24no—
134C2×C4⋊C4—24no—
135C2×C4⋊C4—24no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—28no—
138C2×C4⋊C4—28no—
139C2×C4⋊C4—24no—
140C2×C4⋊C4—24no—
141C2×C4⋊C4—28no—
142C2×C4⋊C4—28no—
143C2×C4⋊C4—24no—
144C2×C4⋊C4—24no—
145C2×C4⋊C4—24no—
146C2×C4⋊C4—24no—
147C2×C4⋊C4—24no—
148C2×C4⋊C4—24no—
149C2×C4⋊C4—28no—
150C2×C4⋊C4—28no—
151C2×C4⋊C4—28no—
152C2×C4⋊C4—28no—
153C2×C4⋊C4—42no—
154C2×C4⋊C4—42no—
155C2×C4⋊C4—42no—
156C2×C4⋊C4—42no—
157C2×C4⋊C4—44no—
158C2×C4⋊C4—44no—
159C2×C4⋊C4—48no—
160C2×C4⋊C4—48no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4—44no—
163C2×C4⋊C4—44no—
164C2×C4⋊C4—44no—
165C2×C4⋊C4—48no—
166C2×C4⋊C4—44no—
167C2×C4⋊C4—44no—
168C2×C4⋊C4—48no—
169C2×C4⋊C4—48no—
170C2×C4⋊C4—48no—
171C2×C4⋊C4—48no—
172C2×C4⋊C4C2×D414yes—
173C2×C4⋊C4C2×D414yes—
174C2×C4⋊C4C2×Q818yes—
175C2×C42—24no—
176C2×C42—24no—
177C2×C42—24no—
178C2×C42—24no—
179C2×C42—22no—
180C2×C42—24no—
181C2×C42—22no—
182C2×C42—24no—
183C2×C42—28no—
184C2×C42—42no—
185C2×C42—42no—
186C2×C42—48no—
187C2×C42C2×D418yes—
188C2×C42C2×D414yes—
189C2×C42C2×Q818yes—
190C2×C42C2×Q814yes—
191C2×C42C2×Q818yes—
192C2×C42C2×Q818yes—
193C2×C42C2×Q814yes—
194C2×C42C2×Q814yes—
195C2×C42C2×Q814yes—
196C2×C42#4114yes—
197C2×C42#4114yes—
198#95—28no—
199#95—28no—
200#95—28no—
201#95—28no—
202#95—28no—
203#95—28no—
204#95—28no—
205#95—28no—
206#95—28no—
207#95—216no—
208#95—216no—
209#95—28no—
210#95—28no—
211#95—48no—
212#95—48no—
213#95—48no—
214#95C2×D418yes—
215#95C2×Q818yes—
216C24C2511yescharacteristic
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—24no—
232C22×C4—24no—
233C22×C4—24no—
234C22×C4—24no—
235C22×C4—24no—
236C22×C4—24no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—24no—
240C22×C4—24no—
241C22×C4—24no—
242C22×C4—24no—
243C22×C4—24no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—24no—
248C22×C4—24no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—28no—
252C22×C4—28no—
253C22×C4—24no—
254C22×C4—24no—
255C22×C4—28no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—28no—
259C22×C4—28no—
260C22×C4—28no—
261C22×C4—28no—
262C22×C4—28no—
263C22×C4C22×D414yes—
264C22×C4C22×D414yes—
265C22×C4C22×D412yes—
266C22×C4C22×D412yes—
267C22×C4C22×D412yes—
268C22×C4C22×Q818yes—
269C22×C4C22×Q814yes—
270C22×C4C22×Q812yes—
271C22×C4C22×Q812yes—
272C22×C4C22×Q812yes—
273C22×C4C22×Q812yes—
274C22×C4C22×Q814yes—
275C22×C4C22×Q812yes—
276C22×C4C22×Q812yes—
277C22×C4C2×#4114yes—
278C22×C4C2×#4114yes—
279C22×C4C2×#4112yes—
280C22×C4C2×#4112yes—
281C22×C4H(5,𝔽2)14yes—
282C22×C4H(5,𝔽2)12yes—
283C22×C42−1+414yes—
284C22×C42−1+412yes—
285C4⋊C4—44no—
286C4⋊C4—44no—
287C4⋊C4—48no—
288C4⋊C4—416no—
289C4⋊C4—416no—
290C4⋊C4—416no—
291C4⋊C4—416no—
292C4⋊C4—48no—
293C4⋊C4—48no—
294C4⋊C4—48no—
295C4⋊C4—48no—
296C4⋊C4—88no—
297C4⋊C4—88no—
298C4⋊C4—88no—
299C4⋊C4—88no—
300C4⋊C4—816no—
301C42—216no—
302C42—28no—
303C42—216no—
304C42—216no—
305C42—48no—
306C42—88no—
307C42#125116yes—
308C42C4⋊Q8116yes—
309C23C23×D411yescharacteristic
310C23C23×Q811yescharacteristic
311C23C23×Q811yescharacteristic
312C23C22×#4111yescharacteristic
313C23C22×#4111yescharacteristic
314C23C2×H(5,𝔽2)11yescharacteristic
315C23C2×H(5,𝔽2)12yes—
316C23C2×2−1+411yescharacteristic
317C23C2×2−1+412yes—
318C23#58512yes—
319C23#58512yes—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—24no—
334C2×C4—24no—
335C2×C4—24no—
336C2×C4—24no—
337C2×C4—24no—
338C2×C4—24no—
339C2×C4—24no—
340C2×C4—24no—
341C2×C4—24no—
342C2×C4—28no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—28no—
346C2×C4—24no—
347C2×C4—24no—
348C2×C4—28no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—44no—
356C2×C4—44no—
357C2×C4—44no—
358C2×C4—44no—
359C2×C4—44no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—44no—
363C2×C4—44no—
364C2×C4—44no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—48no—
370C2×C4—48no—
371C2×C4—48no—
372C2×C4—48no—
373C2×C4—48no—
374C2×C4—48no—
375C2×C4—48no—
376C2×C4—48no—
377C2×C4C2×#12518yes—
378C2×C4C2×#12514yes—
379C2×C4C2×C4⋊Q814yes—
380C2×C4C2×C4⋊Q814yes—
381C2×C4C2×C4⋊Q814yes—
382C2×C4#54418yes—
383C2×C4#54414yes—
384C2×C4#54714yes—
385C2×C4#55014yes—
386C2×C4#55414yes—
387C2×C4#55714yes—
388C22C22×#12511yescharacteristic
389C22C22×C4⋊Q811yescharacteristic
390C22#344911yescharacteristic
391C22#344911yescharacteristic
392C22C2×#54412yes—
393C22C2×#54411yescharacteristic
394C22#345812yes—
395C22#345812yes—
396C22C2×#54711yescharacteristic
397C22C2×#55011yescharacteristic
398C22C2×#55411yescharacteristic
399C22C2×#55711yescharacteristic
400C22#349811yescharacteristic
401C22#349911yescharacteristic
402C22#350312yes—
403C22#350612yes—
404C22#350612yes—
405C22#350712yes—
406C22#350712yes—
407C22#355812yes—
408C22#355912yes—
409C22#356112yes—
410C22#356312yes—
411C4—24no—
412C4—28no—
413C4—28no—
414C4—24no—
415C4—44no—
416C4—44no—
417C4—48no—
418C4—84no—
419C4—84no—
420C4—84no—
421C4—84no—
422C4#255218yes—
423C2#3464211yescharacteristic
424C2C2×#255211yescharacteristic
425C2#3518112yes—
426C2#3527511yescharacteristic
427C2#3756112yes—
428C2#3948311yescharacteristic
429C2#3948411yescharacteristic
430C2#3949312yes—
431C2#3973911yescharacteristic
432C2#3974011yescharacteristic
433C2#3974912yes—
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×#25702
#170762
#170732
#152312
#151452
#148092
#146872
#143542
#142772
#139092
C4×#3842
#137552