Finite Group Databasebeta

← #480465

Subgroups — #480465

Order 512.

836 conjugacy classes of subgroups.

The subgroup lattice has 397 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35674C211yesmaximal, characteristic
2#17371C211yesmaximal, characteristic
3#17352C211yesmaximal, characteristic
4#11548C214yesmaximal
5#11544C214yesmaximal
6#11452C212yesmaximal
7#11428C212yesmaximal
8C22×C4⋊Q8C411yescharacteristic
9C2×#519C2211yescharacteristic
10#2983—21no—
11#2982—21no—
12#2484C412yes—
13#2484C412yes—
14#2484C2212yes—
15#2484C2212yes—
16#2446—22no—
17#2446—21no—
18#2446—21no—
19#2446—22no—
20#2446—21no—
21#2446—21no—
22#2310C411yescharacteristic
23#2310C411yescharacteristic
24#2310C2211yescharacteristic
25#2296C411yescharacteristic
26#2296C2211yescharacteristic
27#1467—22no—
28#1464C2214yes—
29#1461—22no—
30#1461—21no—
31#1461—21no—
32#1458C2214yes—
33#1458C2212yes—
34#1458C2212yes—
35#1326C2214yes—
36#1326C2214yes—
37#1317C2218yes—
38C23×Q8C2×C411yescharacteristic
39C23×Q8C2×C411yescharacteristic
40C2×C4⋊Q8—21no—
41C2×C4⋊Q8—22no—
42C2×C4⋊Q8—21no—
43C2×C4⋊Q8—44no—
44#519—44no—
45C2×C4×Q8D412yes—
46C2×C4×Q8D411yescharacteristic
47C2×C4×Q8D411yescharacteristic
48C2×C4×Q8D412yes—
49C2×C4×Q8D411yescharacteristic
50C2×C4×Q8D411yescharacteristic
51C2×#117C2×C411yescharacteristic
52C2×#117C2×C411yescharacteristic
53C2×#117C2×C411yescharacteristic
54C2×#117C2×C412yes—
55C2×#117C2311yescharacteristic
56C2×#117C2312yes—
57C22×C4⋊C4C2×C412yes—
58C22×C4⋊C4C2×C412yes—
59C22×C42C2×C411yescharacteristic
60#446—44no—
61C8×Q8—44no—
62#432—24no—
63#431—22no—
64#431—24no—
65#431—22no—
66#400—22no—
67#400—22no—
68#400—22no—
69#400—22no—
70#398—22no—
71#398—22no—
72#398—22no—
73#398—22no—
74#391—21no—
75#391—22no—
76#391—21no—
77#391—21no—
78#391—21no—
79#391—21no—
80#391—21no—
81#391—22no—
82#391—21no—
83#391—21no—
84#389—21no—
85#389—21no—
86#389—21no—
87#389—21no—
88#387—22no—
89#387—22no—
90#387—22no—
91#387—22no—
92#387—22no—
93#387—22no—
94#387—22no—
95#387—22no—
96#385C2×C411yescharacteristic
97#385C2×C411yescharacteristic
98#385C2×C412yes—
99#385C2×C412yes—
100#385C2311yescharacteristic
101#385C2311yescharacteristic
102#381C2×C412yes—
103#381C2×C412yes—
104#381C2×C412yes—
105#381C2×C412yes—
106#381C2×C412yes—
107#381C2312yes—
108C4×C4⋊C4—22no—
109C4×C4⋊C4—21no—
110C4×C4⋊C4—21no—
111#324—22no—
112#324—24no—
113#324—22no—
114#324—24no—
115#323C2314yes—
116#323C2314yes—
117C22×Q8—24no—
118C22×Q8—21no—
119C22×Q8—21no—
120C22×Q8—24no—
121C22×Q8—24no—
122C22×Q8—42no—
123C22×Q8—42no—
124C22×Q8—42no—
125C22×Q8C22⋊C411yescharacteristic
126C22×Q8C22⋊C412yes—
127C22×Q8C22⋊C411yescharacteristic
128C23×C4C22×C412yes—
129C23×C4C22×C411yescharacteristic
130C23×C4C22×C412yes—
131C23×C4C22×C411yescharacteristic
132C23×C4C22×C411yescharacteristic
133C4⋊Q8—48no—
134C4⋊Q8—44no—
135C4⋊Q8—44no—
136C4×Q8—24no—
137C4×Q8—24no—
138C4×Q8—44no—
139C4×Q8—42no—
140C4×Q8—42no—
141C4×Q8—44no—
142#117—24no—
143#117—42no—
144#117—44no—
145#117—42no—
146#117—44no—
147#117—42no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4—21no—
154C2×C4⋊C4—22no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—44no—
161C2×C4⋊C4—44no—
162C2×C4⋊C4C22⋊C411yescharacteristic
163C2×C4⋊C4C22⋊C411yescharacteristic
164C2×C4⋊C4C22⋊C412yes—
165C2×C4⋊C4C22⋊C412yes—
166C2×C4⋊C4C2×D411yescharacteristic
167C2×C4⋊C4C2×D411yescharacteristic
168C2×C4⋊C4C2×D412yes—
169C2×C4⋊C4C2×D412yes—
170C2×C22⋊C4C22×C411yescharacteristic
171C2×C22⋊C4C22×C411yescharacteristic
172C2×C22⋊C4C22×C412yes—
173C2×C22⋊C4C22×C412yes—
174C2×C22⋊C4C22×C411yescharacteristic
175C2×C22⋊C4C2411yescharacteristic
176C2×C42—21no—
177C2×C42—21no—
178C2×C42—21no—
179C2×C42—21no—
180C2×C42—42no—
181C2×C42C22⋊C412yes—
182C2×C42C22⋊C412yes—
183C2×C42C22⋊C412yes—
184C2×C42C2×D411yescharacteristic
185C2×C42C2×D411yescharacteristic
186C2×C42C2×D412yes—
187C2×C42C2×D412yes—
188C4⋊C8—44no—
189C4⋊C8—42no—
190C4⋊C8—42no—
191C4⋊C8—44no—
192C22⋊C8—24no—
193C22⋊C8—24no—
194#97—44no—
195C4×C8—44no—
196C4×C8—42no—
197C4×C8—42no—
198#95—22no—
199#95—22no—
200#95—21no—
201#95—21no—
202#95—22no—
203#95—22no—
204#95—22no—
205#95—22no—
206#95—22no—
207#95—22no—
208#95—22no—
209#95—22no—
210#95—22no—
211#95—22no—
212#95—21no—
213#95—21no—
214#95—22no—
215#95—22no—
216C24C23×C411yescharacteristic
217C2×Q8—22no—
218C2×Q8—24no—
219C2×Q8—22no—
220C2×Q8—24no—
221C2×Q8—22no—
222C2×Q8—22no—
223C2×Q8—22no—
224C2×Q8—42no—
225C2×Q8—416no—
226C2×Q8—42no—
227C2×Q8—42no—
228C2×Q8—42no—
229C2×Q8—42no—
230C2×Q8—42no—
231C2×Q8—42no—
232C2×Q8—88no—
233C2×Q8#9914yes—
234C22×C4—22no—
235C22×C4—22no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—24no—
239C22×C4—24no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—24no—
245C22×C4—42no—
246C22×C4—42no—
247C22×C4—42no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—42no—
252C22×C4C2×C22⋊C412yes—
253C22×C4C2×C22⋊C411yescharacteristic
254C22×C4C2×C22⋊C412yes—
255C22×C4C2×C22⋊C412yes—
256C22×C4C2×C22⋊C412yes—
257C22×C4C2×C22⋊C411yescharacteristic
258C22×C4C2×C22⋊C411yescharacteristic
259C22×C4C2×C22⋊C411yescharacteristic
260C22×C4#13114yes—
261C22×C4C22×D411yescharacteristic
262C22×C4C22×D411yescharacteristic
263C2×C8—44no—
264C2×C8—44no—
265C4⋊C4—24no—
266C4⋊C4—24no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—42no—
273C4⋊C4—44no—
274C4⋊C4—44no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—44no—
280C4⋊C4—44no—
281C4⋊C4—42no—
282C4⋊C4—44no—
283C4⋊C4—44no—
284C4⋊C4—42no—
285C22⋊C4—22no—
286C22⋊C4—22no—
287C22⋊C4—41no—
288C22⋊C4—42no—
289C22⋊C4—41no—
290C22⋊C4—42no—
291C42—24no—
292C42—22no—
293C42—22no—
294C42—24no—
295C42—42no—
296C42—42no—
297C42—42no—
298C42—42no—
299C42—42no—
300C42—42no—
301C42—42no—
302C23—21no—
303C23—21no—
304C23—41no—
305C23—41no—
306C23C22×C22⋊C411yescharacteristic
307C23C2×#13112yes—
308Q8—28no—
309Q8—48no—
310Q8—44no—
311Q8—84no—
312Q8—84no—
313C2×C4—22no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—22no—
317C2×C4—28no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—48no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—42no—
349C2×C4—42no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—84no—
357C2×C4#40812yes—
358C2×C4#40812yes—
359C2×C4C2×#9914yes—
360C2×C4C2×#9912yes—
361C2×C4#41312yes—
362C8—84no—
363C8—84no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—42no—
368C22—42no—
369C22—41no—
370C22—41no—
371C22C2×#40811yescharacteristic
372C22C22×#9911yescharacteristic
373C22C2×#41311yescharacteristic
374C4—22no—
375C4—24no—
376C4—41no—
377C4—41no—
378C4—42no—
379C4—41no—
380C4—41no—
381C4—42no—
382C4—42no—
383C4—42no—
384C4—42no—
385C4—81no—
386C4—81no—
387C4—82no—
388C4—82no—
389C4#146814yes—
390C2—21no—
391C2—21no—
392C2—42no—
393C2C2×#146811yescharacteristic
394C2#3334911yescharacteristic
395C2#3334911yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutator, prime radicalC24C23×C4
Frattini, cosocleC2×C22⋊C4C24
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×Q8 ◁ C2×#519 ◁ G
LECSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#356742
#173712
#173522
#115482
#115442
#114522
#114282