Finite Group Databasebeta

← #100470

Subgroups — #100470

Order 512.

433 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 433 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#33067C211yesmaximal, characteristic
2#20520C211yesmaximal, characteristic
3#9686C211yesmaximal, characteristic
4#8175C211yesmaximal, characteristic
5#7680C211yesmaximal, characteristic
6#7049C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8C2×#446—21no—
9#2859C2211yescharacteristic
10C42×Q8C2211yescharacteristic
11#1948C411yescharacteristic
12#1948C411yescharacteristic
13#1919—21no—
14#1919—21no—
15#1865—21no—
16#1865—21no—
17#1831C2211yescharacteristic
18#1803C411yescharacteristic
19#1803C411yescharacteristic
20#1771—22no—
21C8×C4⋊C4—21no—
22#1767—21no—
23#1767C2211yescharacteristic
24#1767C2211yescharacteristic
25#1744C2211yescharacteristic
26C4×#97—21no—
27C4×#97C2211yescharacteristic
28C2×#330—21no—
29C2×#330—21no—
30C2×Q8⋊C8—21no—
31#1279—21no—
32#1271—22no—
33C2×#125—21no—
34C2×C4×Q8C2×C411yescharacteristic
35C2×C4×Q8D411yescharacteristic
36C2×C4×Q8D411yescharacteristic
37#446—24no—
38#446—24no—
39C2×#106—21no—
40C2×#106—21no—
41C2×C4⋊C8—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8C2×C411yescharacteristic
45C2×C4⋊C8C2×C411yescharacteristic
46C2×#103—21no—
47C2×#103—21no—
48C2×#97—22no—
49C2×#97—21no—
50C2×#97—21no—
51C2×#97—21no—
52C2×#97D411yescharacteristic
53C2×#97D411yescharacteristic
54C2×C4×C8—21no—
55C2×C4×C8—21no—
56C2×C4×C8—22no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#384C2×C411yescharacteristic
62#384C2×C411yescharacteristic
63#382—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4C2×C411yescharacteristic
68C4×C4⋊C4D411yescharacteristic
69C4×C4⋊C4D411yescharacteristic
70C43—21no—
71C43C2311yescharacteristic
72#340—21no—
73#340—21no—
74#340—21no—
75#340—21no—
76#336—22no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336D412yes—
83#330—42no—
84#330—42no—
85Q8⋊C8—24no—
86C22×Q8C22⋊C411yescharacteristic
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—22no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—41no—
93C22×C8—41no—
94#125—41no—
95#125—41no—
96#125—41no—
97#125—41no—
98C4×Q8—22no—
99C4×Q8—22no—
100C4×Q8—22no—
101C4×Q8—22no—
102C4×Q8—41no—
103C4×Q8—41no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—21no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—21no—
124C2×C42C22×C411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130C2×C42#4111yescharacteristic
131#106—42no—
132#106—42no—
133C4⋊C8—28no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140#103—42no—
141#103—42no—
142#97—28no—
143#97—21no—
144#97—21no—
145#97—21no—
146#97—42no—
147#97—41no—
148#97—41no—
149#97—41no—
150#97—41no—
151#97SD1612yes—
152C4×C8—22no—
153C4×C8—22no—
154C4×C8—22no—
155C4×C8—41no—
156C4×C8—44no—
157#95—21no—
158#95—21no—
159#95—21no—
160#95—41no—
161#95—41no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8#10412yes—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4C2×C22⋊C411yescharacteristic
175C22×C4C4×D411yescharacteristic
176C22×C4C4×D411yescharacteristic
177C22×C4#12011yescharacteristic
178C22×C4#12111yescharacteristic
179C22×C4#12111yescharacteristic
180C22×C4#12311yescharacteristic
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—22no—
185C2×C8—24no—
186C2×C8—42no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—42no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—81no—
199C2×C8—81no—
200C2×C8—81no—
201C2×C8—81no—
202C4⋊C4—24no—
203C4⋊C4—21no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—81no—
218C4⋊C4—81no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4#10112yes—
223C4⋊C4#10412yes—
224C4⋊C4#10412yes—
225C42—24no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42—42no—
236C42—42no—
237C42—42no—
238C42—81no—
239C42—81no—
240C42C2×SD1611yescharacteristic
241C42#13511yescharacteristic
242C42AGL(1,ℤ/8)11yescharacteristic
243C42#13711yescharacteristic
244C23#38611yescharacteristic
245Q8—22no—
246Q8—22no—
247Q8—41no—
248Q8—41no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—22no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—81no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4C2×#10111yescharacteristic
283C2×C4#41311yescharacteristic
284C2×C4C2×#10411yescharacteristic
285C2×C4C2×#10411yescharacteristic
286C2×C4C2×#10411yescharacteristic
287C2×C4#42111yescharacteristic
288C2×C4C4×SD1611yescharacteristic
289C2×C4#44011yescharacteristic
290C2×C4#44811yescharacteristic
291C2×C4#44911yescharacteristic
292C2×C4#46011yescharacteristic
293C2×C4#46411yescharacteristic
294C8—24no—
295C8—42no—
296C8—44no—
297C8—82no—
298C8—82no—
299C8—81no—
300C8—81no—
301C22#187111yescharacteristic
302C22#188011yescharacteristic
303C22#188111yescharacteristic
304C22#189611yescharacteristic
305C22#190111yescharacteristic
306C22#190211yescharacteristic
307C22#190611yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—41no—
315C4—42no—
316C4—41no—
317C4—42no—
318C4—42no—
319C4—41no—
320C4—42no—
321C4—161no—
322C4—161no—
323C4#152411yescharacteristic
324C4#152611yescharacteristic
325C4#152811yescharacteristic
326C4#152911yescharacteristic
327C2#899211yescharacteristic
328C2#912211yescharacteristic
329C2#915911yescharacteristic
330C2#923411yescharacteristic
331C2#925211yescharacteristic
332C2#931211yescharacteristic
333C2#935111yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#330672
#205202
#96862
#81752
#76802
#70492
#70302