Finite Group Databasebeta

← #5035105

Subgroups — #5035105

Order 512.

1778 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2642C211yesmaximal, characteristic
2C2×#2381C211yesmaximal, characteristic
3#16109C214yesmaximal
4#16108C214yesmaximal
5#15715C214yesmaximal
6#15714C214yesmaximal
7#15712C214yesmaximal
8#15711C214yesmaximal
9#14289C211yesmaximal, characteristic
10#14289C211yesmaximal, characteristic
11#14161C211yesmaximal, characteristic
12#13964C211yesmaximal, characteristic
13#13964C211yesmaximal, characteristic
14C22×C4⋊Q8C2211yescharacteristic
15C22×#125C2211yescharacteristic
16#2642—28no—
17C2×#400C2214yes—
18C2×#400C2214yes—
19#2381—28no—
20C2×#391C2214yes—
21C2×#391C2212yes—
22C2×#391C2212yes—
23C2×#387C2214yes—
24C2×#387C2214yes—
25C2×#383C2211yescharacteristic
26C2×#383C2211yescharacteristic
27C2×C4×C4⋊C4C2211yescharacteristic
28C2×C4×C4⋊C4C2211yescharacteristic
29C2×#376C2211yescharacteristic
30#1446C2214yes—
31#1445C2214yes—
32#1445C2214yes—
33#1445C2214yes—
34#1445C2214yes—
35#1445C2212yes—
36#1445C2212yes—
37#1445C2212yes—
38#1445C2212yes—
39#1444C2214yes—
40#1443C2214yes—
41#1443C2214yes—
42#1443C2214yes—
43#1443C2214yes—
44#1442C2214yes—
45#1442C2214yes—
46#1442C2214yes—
47#1441C2214yes—
48#1441C2214yes—
49#1441C2214yes—
50#1441C2214yes—
51#1436C2212yes—
52#1436C2214yes—
53#1436C2212yes—
54#1436C2212yes—
55#1436C2214yes—
56#1436C2212yes—
57#1436C2214yes—
58#1436C2214yes—
59C4⋊#95C2212yes—
60C4⋊#95C2212yes—
61C4⋊#95C2212yes—
62C4⋊#95C2212yes—
63C4⋊#95C2212yes—
64C4⋊#95C2212yes—
65#1434C2212yes—
66#1434C2214yes—
67#1434C2214yes—
68#1434C2212yes—
69C23×Q8C2312yes—
70C2×C4⋊Q8—24no—
71C2×C4⋊Q8—24no—
72C2×C4⋊Q8D418yes—
73C2×#125—24no—
74C2×#125—24no—
75C2×#125—24no—
76C22×C4⋊C4C2312yes—
77C22×C4⋊C4C2312yes—
78C22×C4⋊C4C2311yescharacteristic
79C22×C4⋊C4C2311yescharacteristic
80C22×C4⋊C4C2312yes—
81C22×C4⋊C4C2312yes—
82C22×C4⋊C4C2312yes—
83C22×C4⋊C4C2312yes—
84C22×C4⋊C4C2314yes—
85C22×C4⋊C4C2314yes—
86C22×C4⋊C4C2314yes—
87C22×C42C2311yescharacteristic
88C22×C42C2311yescharacteristic
89C22×C42C2314yes—
90C22×C42C2311yescharacteristic
91C22×C42C2311yescharacteristic
92C22×C42C2312yes—
93C22×C42C2311yescharacteristic
94#400—216no—
95#400—216no—
96#391—216no—
97#391—28no—
98#391—28no—
99#387—216no—
100#387—216no—
101#383—24no—
102#383—24no—
103C4×C4⋊C4—24no—
104C4×C4⋊C4—24no—
105#376—24no—
106C2×#95C2312yes—
107C2×#95C2312yes—
108C2×#95C2314yes—
109C2×#95C2314yes—
110C2×#95C2314yes—
111C2×#95C2314yes—
112C2×#95C2314yes—
113C2×#95C2312yes—
114C2×#95C2312yes—
115C2×#95C2314yes—
116C2×#95C2312yes—
117C2×#95C2312yes—
118C2×#95C2314yes—
119C2×#95C2312yes—
120C2×#95C2312yes—
121C2×#95C2312yes—
122C2×#95C2312yes—
123C2×#95C2314yes—
124C2×#95C2314yes—
125C2×#95C2314yes—
126C2×#95C2314yes—
127C2×#95C2314yes—
128C2×#95C2314yes—
129C2×#95C2314yes—
130C2×#95C2314yes—
131C2×#95C2314yes—
132C2×#95C2314yes—
133C2×#95C2314yes—
134C2×#95C2314yes—
135C2×#95C2314yes—
136C2×#95C2314yes—
137C2×#95C2314yes—
138C2×#95C2314yes—
139C2×#95C2314yes—
140C22×Q8—24no—
141C22×Q8—24no—
142C22×Q8—44no—
143C22×Q8—44no—
144C22×Q8C2×D418yes—
145C23×C4C2412yes—
146C23×C4C2412yes—
147C23×C4C2414yes—
148C23×C4C2414yes—
149C23×C4C2414yes—
150C23×C4C2412yes—
151C23×C4C2412yes—
152C23×C4C2414yes—
153C23×C4C2412yes—
154C23×C4C2412yes—
155C23×C4C2411yescharacteristic
156C23×C4C2411yescharacteristic
157C23×C4C2411yescharacteristic
158C4⋊Q8—232no—
159#125—416no—
160C2×C4⋊C4—24no—
161C2×C4⋊C4—24no—
162C2×C4⋊C4—24no—
163C2×C4⋊C4—24no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—24no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—24no—
176C2×C4⋊C4—24no—
177C2×C4⋊C4—24no—
178C2×C4⋊C4—24no—
179C2×C4⋊C4—24no—
180C2×C4⋊C4—28no—
181C2×C4⋊C4—28no—
182C2×C4⋊C4—42no—
183C2×C4⋊C4—42no—
184C2×C4⋊C4—44no—
185C2×C4⋊C4—44no—
186C2×C4⋊C4—44no—
187C2×C4⋊C4—44no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4—44no—
190C2×C4⋊C4—44no—
191C2×C4⋊C4C2×D418yes—
192C2×C4⋊C4C2×D418yes—
193C2×C42—24no—
194C2×C42—28no—
195C2×C42—22no—
196C2×C42—22no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—44no—
200C2×C42—42no—
201C2×C42—42no—
202C2×C42—42no—
203C2×C42—42no—
204C2×C42—44no—
205C2×C42—44no—
206C2×C42C2×D414yes—
207C2×C42#4114yes—
208C2×C42#4114yes—
209#95—24no—
210#95—24no—
211#95—24no—
212#95—24no—
213#95—24no—
214#95—24no—
215#95—24no—
216#95—24no—
217#95—28no—
218#95—28no—
219#95—28no—
220#95—28no—
221#95—28no—
222#95—28no—
223#95—24no—
224#95—24no—
225#95—28no—
226#95—28no—
227#95—28no—
228#95—44no—
229#95—44no—
230#95—44no—
231#95—44no—
232#95—44no—
233#95—44no—
234#95—44no—
235#95—44no—
236#95—44no—
237#95—44no—
238#95—44no—
239#95—44no—
240#95—44no—
241#95—44no—
242#95—44no—
243C24C2511yescharacteristic
244C2×Q8—216no—
245C2×Q8—48no—
246C2×Q8—48no—
247C2×Q8—88no—
248C2×Q8—88no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4—22no—
256C22×C4—24no—
257C22×C4—24no—
258C22×C4—22no—
259C22×C4—24no—
260C22×C4—24no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—24no—
267C22×C4—22no—
268C22×C4—24no—
269C22×C4—24no—
270C22×C4—24no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—24no—
281C22×C4—24no—
282C22×C4—24no—
283C22×C4—24no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—22no—
287C22×C4—24no—
288C22×C4—24no—
289C22×C4—24no—
290C22×C4—24no—
291C22×C4—24no—
292C22×C4—24no—
293C22×C4—24no—
294C22×C4—24no—
295C22×C4—24no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—24no—
299C22×C4—24no—
300C22×C4—24no—
301C22×C4—24no—
302C22×C4—24no—
303C22×C4—24no—
304C22×C4—24no—
305C22×C4—24no—
306C22×C4—24no—
307C22×C4—24no—
308C22×C4—24no—
309C22×C4C22×D418yes—
310C22×C4C22×D412yes—
311C22×C4C22×D412yes—
312C22×C4C22×D412yes—
313C22×C4C2×#4112yes—
314C22×C4C2×#4112yes—
315C22×C4C2×#4112yes—
316C22×C4C2×#4112yes—
317C22×C4C2×#4112yes—
318C22×C4C2×#4112yes—
319C22×C42−1+414yes—
320C22×C42−1+414yes—
321C4⋊C4—216no—
322C4⋊C4—216no—
323C4⋊C4—48no—
324C4⋊C4—48no—
325C4⋊C4—48no—
326C4⋊C4—48no—
327C4⋊C4—44no—
328C4⋊C4—44no—
329C4⋊C4—88no—
330C4⋊C4—88no—
331C4⋊C4—88no—
332C42—48no—
333C42—82no—
334C42—82no—
335C42—82no—
336C42—82no—
337C42—88no—
338C42#123116yes—
339C23C23×D411yescharacteristic
340C23C22×#4111yescharacteristic
341C23C22×#4111yescharacteristic
342C23C2×2−1+412yes—
343C23C2×2−1+412yes—
344C23#58514yes—
345C23#58512yes—
346C23#58512yes—
347Q8—816no—
348C2×C4—24no—
349C2×C4—24no—
350C2×C4—24no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—28no—
360C2×C4—28no—
361C2×C4—28no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—28no—
365C2×C4—28no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—44no—
371C2×C4—44no—
372C2×C4—44no—
373C2×C4—44no—
374C2×C4—44no—
375C2×C4—44no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—44no—
379C2×C4—44no—
380C2×C4—44no—
381C2×C4—42no—
382C2×C4—42no—
383C2×C4—44no—
384C2×C4—44no—
385C2×C4—44no—
386C2×C4—44no—
387C2×C4—44no—
388C2×C4—44no—
389C2×C4—44no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—44no—
402C2×C4—44no—
403C2×C4—44no—
404C2×C4—44no—
405C2×C4—44no—
406C2×C4—44no—
407C2×C4—44no—
408C2×C4—44no—
409C2×C4—44no—
410C2×C4—44no—
411C2×C4—44no—
412C2×C4—44no—
413C2×C4—44no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4C2×#12314yes—
418C2×C4C2×#12314yes—
419C2×C4C2×#12314yes—
420C22C22×#12311yescharacteristic
421C22#348512yes—
422C22#349512yes—
423C22#349512yes—
424C22#349712yes—
425C22#349712yes—
426C22#350911yescharacteristic
427C22#350911yescharacteristic
428C22#351012yes—
429C22#351011yescharacteristic
430C22#351012yes—
431C22#351011yescharacteristic
432C22#355314yes—
433C22#355514yes—
434C22#356414yes—
435C22#356614yes—
436C4—24no—
437C4—24no—
438C4—24no—
439C4—44no—
440C4—48no—
441C4—44no—
442C4—82no—
443C4—82no—
444C4—82no—
445C4—84no—
446C4—84no—
447C4—84no—
448C4—82no—
449C2#3562611yescharacteristic
450C2#3567311yescharacteristic
451C2#3567311yescharacteristic
452C2#5091512yes—
453C2#5092012yes—
454C2#5122712yes—
455C2#5122812yes—
456C2#5207714yes—
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×#26422
C2×#23812
#161092
#161082
#157152
#157142
#157122
#157112
#142892
#141612
#139642