Finite Group Databasebeta

← #304511

Subgroups — #304511

Order 512.

796 conjugacy classes of subgroups.

The subgroup lattice has 395 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36598C211yesmaximal, characteristic
2#33225C211yesmaximal, characteristic
3#33198C211yesmaximal, characteristic
4#29218C211yesmaximal, characteristic
5#10352C214yesmaximal
6#9898C211yesmaximal, characteristic
7#9870C211yesmaximal, characteristic
8#8974C214yesmaximal
9C4×Q8⋊C8C211yesmaximal, characteristic
10C2×#487—22no—
11C2×#477C2212yes—
12#2868C2211yescharacteristic
13#2868C2211yescharacteristic
14#2862—21no—
15#2582—21no—
16#2571C2212yes—
17#2570—22no—
18#2568—21no—
19#2511—22no—
20#2446—22no—
21#2365—21no—
22#2355—21no—
23#2355C2212yes—
24C4×C4⋊Q8—21no—
25C4×C4⋊Q8C2211yescharacteristic
26C42×Q8C2211yescharacteristic
27#2100—22no—
28#1990—21no—
29#1987C2214yes—
30#1987C2212yes—
31#1956—22no—
32#1956C2214yes—
33#1947—21no—
34#1947—21no—
35#1842C2211yescharacteristic
36#1834—21no—
37#1803—21no—
38#1803—21no—
39C4×C4⋊C8C2211yescharacteristic
40C42×C8C2211yescharacteristic
41C2×Q8⋊C8C2212yes—
42#1296C2214yes—
43#1279C2214yes—
44#1279C2212yes—
45C2×C4⋊Q8—21no—
46C2×C4⋊Q8—21no—
47C2×C4⋊Q8—21no—
48C2×C4⋊Q8—21no—
49C2×C4⋊Q8D411yescharacteristic
50C2×C4⋊Q8D412yes—
51C2×C4⋊Q8C2312yes—
52C2×C4×Q8—22no—
53C2×C4×Q8—21no—
54C2×C4×Q8D411yescharacteristic
55C2×C4×Q8D411yescharacteristic
56C2×C4×Q8C2311yescharacteristic
57#487—48no—
58#477—28no—
59C2×#107—22no—
60C2×C4⋊C8—21no—
61C2×C4⋊C8—21no—
62C2×C4⋊C8C2312yes—
63C2×C4⋊C8C2312yes—
64C2×#103—22no—
65C2×#103—28no—
66C2×C4×C8—21no—
67C2×C4×C8—21no—
68C2×C4×C8—21no—
69C2×C4×C8C2312yes—
70#400—24no—
71#400—24no—
72#398—24no—
73#391—22no—
74#391—22no—
75#391—22no—
76#391—22no—
77#391—22no—
78#391—22no—
79#391—21no—
80#389—22no—
81#389—22no—
82#389—22no—
83#389—21no—
84#389D412yes—
85#387—24no—
86#387—24no—
87#387—24no—
88#384—21no—
89#384—21no—
90#384—21no—
91#384—21no—
92#384—21no—
93#384—21no—
94#384D411yescharacteristic
95#384D412yes—
96#384C2312yes—
97#382—22no—
98#382—22no—
99#382—22no—
100C4×C4⋊C4—22no—
101C4×C4⋊C4—22no—
102C4×C4⋊C4—22no—
103C4×C4⋊C4—21no—
104C4×C4⋊C4—21no—
105C4×C4⋊C4—21no—
106C4×C4⋊C4—21no—
107C4×C4⋊C4D411yescharacteristic
108C4×C4⋊C4D411yescharacteristic
109C4×C4⋊C4C2312yes—
110C4×C4⋊C4C2311yescharacteristic
111C43—21no—
112C43C2311yescharacteristic
113#340—22no—
114#340—22no—
115#340—24no—
116#340—24no—
117#336—21no—
118Q8⋊C8—24no—
119C22×Q8—22no—
120C22×Q8—21no—
121C22×Q8—22no—
122C22×Q8C2×D411yescharacteristic
123C22×C8—22no—
124C22×C8—22no—
125C22×C8—22no—
126C4⋊Q8—22no—
127C4⋊Q8—22no—
128C4⋊Q8—24no—
129C4⋊Q8—24no—
130C4⋊Q8—44no—
131C4⋊Q8—44no—
132C4⋊Q8—44no—
133C4⋊Q8—42no—
134C4⋊Q8—42no—
135C4⋊Q8—42no—
136C4⋊Q8—42no—
137C4×Q8—22no—
138C4×Q8—22no—
139C4×Q8—22no—
140C4×Q8—22no—
141C4×Q8—22no—
142C4×Q8—42no—
143C4×Q8—42no—
144C4×Q8—84no—
145C4×Q8#4114yes—
146C2×C4⋊C4—21no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—22no—
153C2×C4⋊C4—22no—
154C2×C4⋊C4—21no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—24no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—41no—
162C2×C4⋊C4—41no—
163C2×C4⋊C4—41no—
164C2×C4⋊C4—41no—
165C2×C4⋊C4C2×D411yescharacteristic
166C2×C4⋊C4C2×D411yescharacteristic
167C2×C4⋊C4C2×D412yes—
168C2×C4⋊C4C2×D412yes—
169C2×C4⋊C4C2×D411yescharacteristic
170C2×C4⋊C4C2×D414yes—
171C2×C42—21no—
172C2×C42—21no—
173C2×C42—21no—
174C2×C42—21no—
175C2×C42—21no—
176C2×C42—22no—
177C2×C42—21no—
178C2×C42—24no—
179C2×C42C2×D411yescharacteristic
180C2×C42C2×D411yescharacteristic
181C2×C42C2×D411yescharacteristic
182C2×C42C2×D411yescharacteristic
183C2×C42C2×D411yescharacteristic
184C2×C42C2×D411yescharacteristic
185C2×C42C2411yescharacteristic
186#107—44no—
187C4⋊C8—22no—
188C4⋊C8—24no—
189C4⋊C8—22no—
190C4⋊C8—42no—
191C4⋊C8—42no—
192#103—416no—
193#103—44no—
194C4×C8—24no—
195C4×C8—22no—
196C4×C8—22no—
197C4×C8—42no—
198C4×C8—42no—
199#95—24no—
200#95—24no—
201#95—24no—
202#95—24no—
203#95—24no—
204#95—24no—
205#95—21no—
206#95—21no—
207#95—22no—
208#95—21no—
209#95—22no—
210C2×Q8—21no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8—44no—
216C2×Q8—44no—
217C2×Q8—42no—
218C2×Q8—42no—
219C2×Q8—44no—
220C2×Q8—44no—
221C2×Q8—44no—
222C2×Q8—42no—
223C2×Q8—44no—
224C2×Q8#12412yes—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—21no—
230C22×C4—22no—
231C22×C4—24no—
232C22×C4—42no—
233C22×C4#12011yescharacteristic
234C22×C4#12011yescharacteristic
235C22×C4#12011yescharacteristic
236C22×C4#12011yescharacteristic
237C22×C4C22×D411yescharacteristic
238C22×C4C22×D411yescharacteristic
239C22×C4C22×D411yescharacteristic
240C2×C8—24no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C4⋊C4—21no—
250C4⋊C4—24no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—22no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—22no—
257C4⋊C4—24no—
258C4⋊C4—44no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—42no—
264C4⋊C4—42no—
265C4⋊C4—42no—
266C4⋊C4—44no—
267C4⋊C4—42no—
268C4⋊C4—44no—
269C4⋊C4—44no—
270C4⋊C4—42no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—44no—
274C4⋊C4—82no—
275C4⋊C4—82no—
276C4⋊C4—82no—
277C4⋊C4—84no—
278C4⋊C4—82no—
279C4⋊C4—82no—
280C4⋊C4#12412yes—
281C42—24no—
282C42—22no—
283C42—22no—
284C42—22no—
285C42—42no—
286C42—42no—
287C42—42no—
288C42—42no—
289C42—42no—
290C42—42no—
291C42—42no—
292C42—84no—
293C42#13512yes—
294C42#13512yes—
295C42#13512yes—
296C42#13712yes—
297C42#13712yes—
298C42#13712yes—
299C42C2×#4112yes—
300C422−1+412yes—
301C23C2×#12011yescharacteristic
302Q8—22no—
303Q8—22no—
304Q8—41no—
305Q8—41no—
306Q8—88no—
307Q8—88no—
308Q8—84no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—44no—
327C2×C4—44no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—44no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—82no—
339C2×C4#45212yes—
340C2×C4#45212yes—
341C2×C4#45212yes—
342C2×C4#45212yes—
343C2×C4#45212yes—
344C2×C4#45212yes—
345C2×C4#45312yes—
346C2×C4#45412yes—
347C2×C4C2×#12411yescharacteristic
348C2×C4#53611yescharacteristic
349C2×C4#54812yes—
350C2×C4#54812yes—
351C2×C4C2×#13511yescharacteristic
352C2×C4C2×#13511yescharacteristic
353C2×C4C2×#13511yescharacteristic
354C2×C4C2×#13711yescharacteristic
355C2×C4C2×#13711yescharacteristic
356C2×C4C2×#13711yescharacteristic
357C2×C4#57812yes—
358C8—44no—
359C8—82no—
360C8—82no—
361C22#243611yescharacteristic
362C22C2×#45211yescharacteristic
363C22C2×#45211yescharacteristic
364C22C2×#45211yescharacteristic
365C22#301111yescharacteristic
366C22C2×#45311yescharacteristic
367C22C2×#45411yescharacteristic
368C4—22no—
369C4—22no—
370C4—22no—
371C4—42no—
372C4—42no—
373C4—84no—
374C4—82no—
375C4—81no—
376C4—82no—
377C4—81no—
378C4—162no—
379C4#163014yes—
380C4#163814yes—
381C4#313111yescharacteristic
382C4#313911yescharacteristic
383C4#323111yescharacteristic
384C4#323111yescharacteristic
385C4#336412yes—
386C4#337412yes—
387C2C2×#163011yescharacteristic
388C2C2×#163811yescharacteristic
389C2#1862711yescharacteristic
390C2#1864511yescharacteristic
391C2#2590411yescharacteristic
392C2#2592411yescharacteristic
393C2#2593111yescharacteristic
subgroupG/H
center, socle, prime radicalC23C2×#120
commutator, Frattini, cosocleC2×C42C24
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#365982
#332252
#331982
#292182
#103522
#98982
#98702
#89742
C4×Q8⋊C82