Finite Group Databasebeta

← #144548

Subgroups — #144548

Order 512.

317 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 317 conjugacy classes of subgroups — too many to draw. Only its 84 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#28833C211yesmaximal, characteristic
2#13253C211yesmaximal, characteristic
3#13207C211yesmaximal, characteristic
4#9742C211yesmaximal, characteristic
5#7275C211yesmaximal, characteristic
6#7178C211yesmaximal, characteristic
7#7170C211yesmaximal, characteristic
8C2×#494C2211yescharacteristic
9#2570—21no—
10C2×C4⋊C16C2211yescharacteristic
11C2×#358—21no—
12C2×#358—21no—
13C2×#358—21no—
14C2×#358—21no—
15C2×#346C2211yescharacteristic
16#2085—21no—
17#2083—21no—
18#1988—21no—
19#1949—21no—
20#1944—21no—
21#1847—21no—
22#1846C2211yescharacteristic
23C4×#107C2211yescharacteristic
24#1770C2211yescharacteristic
25C2×#334C2211yescharacteristic
26C2×#332—21no—
27C22×Q16—21no—
28C22×Q16—21no—
29C2×C4⋊Q8—21no—
30C22×C16—21no—
31C22×C16—21no—
32#494—21no—
33#494—21no—
34#494—21no—
35#494Q812yes—
36C2×#107—21no—
37C2×#107D411yescharacteristic
38C2×#107D411yescharacteristic
39C2×#107D411yescharacteristic
40C2×#107D411yescharacteristic
41C2×#106—21no—
42C2×#106—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D411yescharacteristic
45C2×#97—21no—
46C2×C4×C8C2311yescharacteristic
47#400—41no—
48#398—41no—
49#389—21no—
50#389—21no—
51#387—41no—
52#387—41no—
53#384—21no—
54#382—21no—
55#382—21no—
56C4×C4⋊C4—21no—
57C4×C4⋊C4D411yescharacteristic
58C4⋊C16—21no—
59C4⋊C16—21no—
60#358—42no—
61#358—42no—
62#358—42no—
63#358—42no—
64#346—21no—
65#346—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#340—41no—
70#340—41no—
71#336—21no—
72#334—21no—
73#334—21no—
74#332—42no—
75C22×Q8—41no—
76C2×Q16—22no—
77C2×Q16—22no—
78C2×Q16—41no—
79C2×Q16—41no—
80C2×Q16—41no—
81C2×Q16—41no—
82C2×Q16—41no—
83C2×Q16—41no—
84C2×Q16—41no—
85C2×Q16—41no—
86C2×Q16—41no—
87C2×Q16—41no—
88C22×C8—21no—
89C22×C8—41no—
90C22×C8C2×D411yescharacteristic
91C22×C8C2×D411yescharacteristic
92C4⋊Q8—22no—
93C4⋊Q8—41no—
94C4⋊Q8—41no—
95C4⋊Q8—41no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4D811yescharacteristic
107C2×C4⋊C4D811yescharacteristic
108C2×C42—21no—
109C2×C42—41no—
110C2×C42C2×D411yescharacteristic
111C2×C16—22no—
112C2×C16—41no—
113C2×C16—41no—
114C2×C16—41no—
115C2×C16—41no—
116C2×C16—41no—
117#107—21no—
118#107—21no—
119#107—21no—
120#107—21no—
121#107—41no—
122#107—41no—
123#107—81no—
124#106—41no—
125#106—41no—
126#106—81no—
127C4⋊C8—21no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8SD1612yes—
131#97—41no—
132#97—41no—
133C4×C8C2×Q811yescharacteristic
134C4×C8#4111yescharacteristic
135C4×C8#4111yescharacteristic
136C4×C8#4111yescharacteristic
137#95—21no—
138#95—41no—
139#95—41no—
140#95—41no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—41no—
145C2×Q8—42no—
146C2×Q8—81no—
147C2×Q8—81no—
148C2×Q8—81no—
149C2×Q8—81no—
150C2×Q8—81no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—81no—
158C22×C4#12011yescharacteristic
159C22×C4C2×D811yescharacteristic
160C22×C4AGL(1,ℤ/8)11yescharacteristic
161Q16—42no—
162Q16—42no—
163Q16—42no—
164Q16—42no—
165Q16—81no—
166Q16—81no—
167Q16—81no—
168Q16—81no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8—22no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—81no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8C22⋊Q811yescharacteristic
178C2×C8C22⋊Q811yescharacteristic
179C2×C8#12411yescharacteristic
180C2×C8#12411yescharacteristic
181C2×C8#13511yescharacteristic
182C2×C8#13511yescharacteristic
183C2×C8AGL(1,ℤ/8)11yescharacteristic
184C2×C8AGL(1,ℤ/8)11yescharacteristic
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—42no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—161no—
202C4⋊C4—161no—
203C42—41no—
204C42—41no—
205C42—161no—
206C42C22⋊Q811yescharacteristic
207C42#12411yescharacteristic
208C42C2×SD1611yescharacteristic
209C42#13711yescharacteristic
210C16—42no—
211C16—81no—
212C23#44711yescharacteristic
213Q8—82no—
214Q8—82no—
215Q8—161no—
216Q8—161no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—81no—
228C2×C4—81no—
229C2×C4—81no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—81no—
236C2×C4—81no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—82no—
240C2×C4—161no—
241C2×C4—161no—
242C2×C4#39311yescharacteristic
243C2×C4#44811yescharacteristic
244C2×C4#44911yescharacteristic
245C2×C4#44911yescharacteristic
246C2×C4#45311yescharacteristic
247C2×C4#45411yescharacteristic
248C2×C4#47411yescharacteristic
249C2×C4#47611yescharacteristic
250C2×C4#48611yescharacteristic
251C2×C4#48911yescharacteristic
252C8—21no—
253C8—21no—
254C8—42no—
255C8—161no—
256C8#47811yescharacteristic
257C8#47811yescharacteristic
258C8#48811yescharacteristic
259C8#49011yescharacteristic
260C22#162111yescharacteristic
261C22#162511yescharacteristic
262C22#202311yescharacteristic
263C22#219111yescharacteristic
264C22#219111yescharacteristic
265C22#219411yescharacteristic
266C22#219511yescharacteristic
267C4—21no—
268C4—21no—
269C4—21no—
270C4—21no—
271C4—81no—
272C4—81no—
273C4—161no—
274C4—161no—
275C4—161no—
276C4—161no—
277C4—162no—
278C4#162211yescharacteristic
279C4#162611yescharacteristic
280C4#202511yescharacteristic
281C4#202711yescharacteristic
282C2#1035411yescharacteristic
283C2#1233811yescharacteristic
284C2#1233911yescharacteristic
285C2#1235011yescharacteristic
286C2#1235111yescharacteristic
287C2#1336811yescharacteristic
288C2#1337011yescharacteristic
subgroupG/H
center, socle, prime radicalC23#447
commutator, Frattini, cosocleC2×C4×C8C23
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1770 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#288332
#132532
#132072
#97422
#72752
#71782
#71702