Finite Group Databasebeta

← #6132611

Subgroups — #6132611

Order 512.

1806 conjugacy classes of subgroups.

The subgroup lattice has 449 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2863C211yesmaximal, characteristic
2C2×#2859C211yesmaximal, characteristic
3#17078C212yesmaximal
4#17074C212yesmaximal
5#17067C212yesmaximal
6#17063C212yesmaximal
7#17010C212yesmaximal
8#16965C214yesmaximal
9#16813C212yesmaximal
10#16700C214yesmaximal
11#16634C212yesmaximal
12#16608C212yesmaximal
13#16567C214yesmaximal
14#14689C211yesmaximal, characteristic
15C22×#125C2212yes—
16#2863—28no—
17#2859—28no—
18C2×#400C2214yes—
19C2×#400C2214yes—
20C2×#395C2214yes—
21C2×#391C2211yescharacteristic
22C2×#391C2211yescharacteristic
23C2×#391C2211yescharacteristic
24C2×#389C2212yes—
25C2×#389C2212yes—
26C2×#389C2212yes—
27C2×#389C2212yes—
28C2×#389C2211yescharacteristic
29C2×#389C2211yescharacteristic
30C2×#389C2211yescharacteristic
31C2×#387C2212yes—
32C2×#387C2212yes—
33C2×#387C2212yes—
34C2×#384C2211yescharacteristic
35C2×#384C2211yescharacteristic
36C2×#383C2212yes—
37C2×#382C2212yes—
38C2×#382C2212yes—
39C2×C43C2211yescharacteristic
40#1445C2218yes—
41#1445C2214yes—
42#1445C2214yes—
43#1445C2214yes—
44#1444C2214yes—
45#1444C2214yes—
46#1444C2214yes—
47#1443C2218yes—
48#1442C2214yes—
49#1442C2214yes—
50#1442C2218yes—
51#1441C2214yes—
52#1441C2214yes—
53#1441C2218yes—
54#1441C2218yes—
55#1441C2218yes—
56#1441C2214yes—
57#1441C2214yes—
58#1441C2214yes—
59C4⋊#95C2212yes—
60C4⋊#95C2212yes—
61#1434C2212yes—
62#1434C2212yes—
63#1434C2212yes—
64#1434C2212yes—
65C23×Q8C2311yescharacteristic
66C2×#125—28no—
67C2×#125—48no—
68C22×C4⋊C4C2314yes—
69C22×C4⋊C4C2311yescharacteristic
70C22×C4⋊C4C2312yes—
71C22×C4⋊C4C2312yes—
72C22×C4⋊C4C2312yes—
73C22×C4⋊C4C2312yes—
74C22×C4⋊C4C2312yes—
75C22×C4⋊C4C2312yes—
76C22×C4⋊C4C2314yes—
77C22×C4⋊C4C2312yes—
78C22×C4⋊C4C2314yes—
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2311yescharacteristic
81C22×C4⋊C4C2312yes—
82C22×C4⋊C4C2312yes—
83C22×C4⋊C4C2318yes—
84C22×C42C2311yescharacteristic
85C22×C42C2311yescharacteristic
86C22×C42C2311yescharacteristic
87C22×C42C2311yescharacteristic
88C22×C42C2311yescharacteristic
89C22×C42C2311yescharacteristic
90C22×C42C2311yescharacteristic
91#400—48no—
92#400—48no—
93#395—48no—
94#391—24no—
95#391—24no—
96#391—24no—
97#389—28no—
98#389—28no—
99#389—28no—
100#389—28no—
101#389—24no—
102#389—24no—
103#389—24no—
104#387—28no—
105#387—28no—
106#387—28no—
107#384—24no—
108#384—24no—
109#383—28no—
110#382—28no—
111#382—44no—
112C2×#95C2314yes—
113C2×#95C2314yes—
114C2×#95C2314yes—
115C2×#95C2314yes—
116C2×#95C2314yes—
117C2×#95C2312yes—
118C2×#95C2312yes—
119C2×#95C2312yes—
120C2×#95C2312yes—
121C2×#95C2312yes—
122C2×#95C2312yes—
123C2×#95C2314yes—
124C2×#95C2312yes—
125C2×#95C2312yes—
126C2×#95C2312yes—
127C2×#95C2318yes—
128C2×#95C2318yes—
129C2×#95C2318yes—
130C2×#95C2318yes—
131C2×#95C2318yes—
132C2×#95C2314yes—
133C2×#95C2314yes—
134C2×#95C2318yes—
135C2×#95C2318yes—
136C43D418yes—
137C22×Q8—22no—
138C22×Q8—24no—
139C22×Q8—42no—
140C22×Q8—42no—
141C23×C4C2414yes—
142C23×C4C2414yes—
143C23×C4C2412yes—
144C23×C4C2412yes—
145C23×C4C2412yes—
146C23×C4C2412yes—
147C23×C4C2418yes—
148C23×C4C2411yescharacteristic
149C23×C4C2411yescharacteristic
150C23×C4C2411yescharacteristic
151C23×C4C2411yescharacteristic
152C23×C4C2411yescharacteristic
153C23×C4C2411yescharacteristic
154C23×C4C2411yescharacteristic
155#125—432no—
156C2×C4⋊C4—24no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—28no—
159C2×C4⋊C4—28no—
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—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—28no—
171C2×C4⋊C4—28no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—28no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—28no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—24no—
181C2×C4⋊C4—28no—
182C2×C4⋊C4—44no—
183C2×C4⋊C4—44no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4—48no—
192C2×C4⋊C4—48no—
193C2×C4⋊C4—44no—
194C2×C4⋊C4—48no—
195C2×C42—24no—
196C2×C42—22no—
197C2×C42—24no—
198C2×C42—24no—
199C2×C42—24no—
200C2×C42—22no—
201C2×C42—42no—
202C2×C42—42no—
203C2×C42C2×D414yes—
204C2×C42C2×D414yes—
205C2×C42C2×D414yes—
206C2×C42C2×D414yes—
207C2×C42C2×D414yes—
208C2×C42C2×D414yes—
209C2×C42C2×D414yes—
210#95—28no—
211#95—28no—
212#95—24no—
213#95—24no—
214#95—24no—
215#95—24no—
216#95—24no—
217#95—24no—
218#95—24no—
219#95—24no—
220#95—24no—
221#95—28no—
222#95—28no—
223#95—28no—
224#95—28no—
225#95—44no—
226#95—48no—
227#95—48no—
228#95—44no—
229#95—48no—
230#95—48no—
231#95—48no—
232#95—48no—
233#95—48no—
234C24C2511yescharacteristic
235C2×Q8—44no—
236C2×Q8—44no—
237C2×Q8—44no—
238C2×Q8—88no—
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—21no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—28no—
264C22×C4—28no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—28no—
275C22×C4—28no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—28no—
286C22×C4—24no—
287C22×C4—24no—
288C22×C4—28no—
289C22×C4—28no—
290C22×C4—28no—
291C22×C4—28no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4C22×D412yes—
295C22×C4C22×D412yes—
296C22×C4C22×D412yes—
297C22×C4C22×D412yes—
298C22×C4C22×D412yes—
299C22×C4C22×D412yes—
300C22×C4C22×D412yes—
301C22×C4H(5,𝔽2)14yes—
302C22×C4H(5,𝔽2)12yes—
303C22×C42−1+414yes—
304C22×C42−1+414yes—
305C22×C42−1+414yes—
306C22×C42−1+412yes—
307C4⋊C4—48no—
308C4⋊C4—48no—
309C4⋊C4—44no—
310C4⋊C4—44no—
311C4⋊C4—48no—
312C4⋊C4—48no—
313C4⋊C4—416no—
314C4⋊C4—44no—
315C4⋊C4—416no—
316C4⋊C4—48no—
317C4⋊C4—48no—
318C4⋊C4—48no—
319C4⋊C4—48no—
320C4⋊C4—48no—
321C4⋊C4—88no—
322C4⋊C4—816no—
323C42—28no—
324C42—28no—
325C42—28no—
326C42—28no—
327C42—28no—
328C42—44no—
329C42—44no—
330C23C23×D411yescharacteristic
331C23C2×H(5,𝔽2)12yes—
332C23C2×H(5,𝔽2)11yescharacteristic
333C23C2×2−1+412yes—
334C23C2×2−1+412yes—
335C23C2×2−1+412yes—
336C23C2×2−1+411yescharacteristic
337C23#58512yes—
338C23#58512yes—
339Q8—88no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—28no—
351C2×C4—24no—
352C2×C4—28no—
353C2×C4—24no—
354C2×C4—28no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—22no—
362C2×C4—22no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—44no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—48no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—48no—
390C2×C4—48no—
391C2×C4—48no—
392C2×C4—48no—
393C2×C4—44no—
394C2×C4—48no—
395C2×C4—48no—
396C2×C4—48no—
397C2×C4—48no—
398C2×C4—48no—
399C2×C4—44no—
400C2×C4—48no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4#53514yes—
404C2×C4#53614yes—
405C2×C4#53614yes—
406C2×C4#53614yes—
407C2×C4#53714yes—
408C22C2×#53511yescharacteristic
409C22C2×#53611yescharacteristic
410C22C2×#53611yescharacteristic
411C22C2×#53611yescharacteristic
412C22C2×#53711yescharacteristic
413C22#344911yescharacteristic
414C22#344911yescharacteristic
415C22#354812yes—
416C22#355012yes—
417C22#355214yes—
418C22#355514yes—
419C22#355912yes—
420C22#356014yes—
421C22#356112yes—
422C22#356312yes—
423C22#356312yes—
424C22#356314yes—
425C4—24no—
426C4—24no—
427C4—24no—
428C4—24no—
429C4—24no—
430C4—42no—
431C4—42no—
432C4—84no—
433C4—88no—
434C4—84no—
435C4—82no—
436C4—82no—
437C4—82no—
438C4—82no—
439C2#3754011yescharacteristic
440C2#3754711yescharacteristic
441C2#3754911yescharacteristic
442C2#3755511yescharacteristic
443C2#3761711yescharacteristic
444C2#3763511yescharacteristic
445C2#3764011yescharacteristic
446C2#5334914yes—
447C2#5337414yes—
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×#28632
C2×#28592
#170782
#170742
#170672
#170632
#170102
#169652
#168132
#167002
#166342
#166082
#165672
#146892