Finite Group Databasebeta

← #145406

Subgroups — #145406

Order 512.

285 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 285 conjugacy classes of subgroups — too many to draw. Only its 76 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#19204C211yesmaximal, characteristic
2#13267C211yesmaximal, characteristic
3#13207C211yesmaximal, characteristic
4#11999C211yesmaximal, characteristic
5#11932C211yesmaximal, characteristic
6#8677C211yesmaximal, characteristic
7#7279C211yesmaximal, characteristic
8#3229—21no—
9C2×#494C2211yescharacteristic
10#2960C2211yescharacteristic
11#2150C2211yescharacteristic
12C2×#358—21no—
13C2×#358—21no—
14C2×#346C2211yescharacteristic
15#1846C2211yescharacteristic
16#1690—22no—
17#1670—22no—
18#1564C2211yescharacteristic
19#1564C2211yescharacteristic
20#1546—21no—
21#1518—21no—
22#1379—21no—
23#1379—21no—
24#1368—22no—
25#1362—22no—
26#1286—21no—
27C22×Q16—21no—
28C22×Q16—21no—
29#533D411yescharacteristic
30C2×C4⋊Q8—21no—
31C2×M32—21no—
32C22×C16D411yescharacteristic
33C22×C16D411yescharacteristic
34#498—41no—
35#494—21no—
36#494—21no—
37#494—21no—
38#494D412yes—
39#487—41no—
40#483—42no—
41#475—24no—
42#446—21no—
43#446—21no—
44C8×Q8—21no—
45C8×Q8—21no—
46#431—21no—
47#431—21no—
48C2×#107—21no—
49C2×#106—21no—
50#424—21no—
51#423D411yescharacteristic
52#405—21no—
53C2×C4×C8C2311yescharacteristic
54#382—21no—
55C4⋊C16—21no—
56C4⋊C16—21no—
57#358—42no—
58#358—42no—
59#346—21no—
60#346—21no—
61#335—21no—
62#335—21no—
63#334—21no—
64#334D412yes—
65#332—24no—
66#328—42no—
67C22×Q8—41no—
68C2×Q16—22no—
69C2×Q16—22no—
70C2×Q16—41no—
71C2×Q16—41no—
72C2×Q16—41no—
73C2×Q16—41no—
74C2×Q16—41no—
75C2×Q16—41no—
76C2×Q16—81no—
77C2×Q16—81no—
78C2×M16—21no—
79C22×C8C2×D411yescharacteristic
80C22×C8#4111yescharacteristic
81C4⋊Q8—22no—
82C4⋊Q8—41no—
83C4⋊Q8—41no—
84C4⋊Q8—41no—
85C4⋊Q8SD1611yescharacteristic
86C4⋊Q8SD1611yescharacteristic
87#125—21no—
88C22⋊Q8—21no—
89C22⋊Q8—21no—
90C4×Q8—21no—
91C4×Q8—21no—
92#117—21no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C42C2×D411yescharacteristic
97M32—41no—
98M32—41no—
99C2×C16—21no—
100C2×C16—21no—
101C2×C16—21no—
102C2×C16—21no—
103C2×C16—21no—
104C2×C16—41no—
105C2×C16SD1612yes—
106#107—41no—
107#107—41no—
108#106—44no—
109#106—81no—
110C4⋊C8—21no—
111C4⋊C8—22no—
112C4⋊C8—21no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116#103—44no—
117C22⋊C8—41no—
118C22⋊C8—41no—
119#97—41no—
120C4×C8—41no—
121C4×C8—41no—
122C4×C8—41no—
123C4×C8C2×D411yescharacteristic
124C4×C8C2×D411yescharacteristic
125C4×C8#4111yescharacteristic
126C4×C8#4111yescharacteristic
127#95—41no—
128#95—41no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—42no—
132C2×Q8—81no—
133C2×Q8—81no—
134C2×Q8—81no—
135C2×Q8—81no—
136C2×Q8—81no—
137C22×C4—81no—
138C22×C4—81no—
139C22×C4#12111yescharacteristic
140C22×C4AGL(1,ℤ/8)11yescharacteristic
141C22×C4AGL(1,ℤ/8)11yescharacteristic
142Q16—42no—
143Q16—42no—
144Q16—82no—
145Q16—82no—
146Q16—81no—
147Q16—81no—
148M16—41no—
149M16—41no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—41no—
153C2×C8—42no—
154C2×C8—81no—
155C2×C8#12111yescharacteristic
156C2×C8#12111yescharacteristic
157C2×C8#12311yescharacteristic
158C2×C8#12411yescharacteristic
159C2×C8C2×SD1611yescharacteristic
160C2×C8#13511yescharacteristic
161C2×C8AGL(1,ℤ/8)11yescharacteristic
162C2×C8#13711yescharacteristic
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—81no—
172C4⋊C4—81no—
173C4⋊C4—81no—
174C4⋊C4—81no—
175C22⋊C4—41no—
176C42—41no—
177C42#12011yescharacteristic
178C42#12311yescharacteristic
179C42C2×SD1611yescharacteristic
180C42#13511yescharacteristic
181C16—22no—
182C16—41no—
183C16—81no—
184C23#46911yescharacteristic
185Q8—42no—
186Q8—81no—
187Q8—82no—
188Q8—82no—
189Q8—161no—
190Q8—161no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—82no—
196C2×C4—161no—
197C2×C4—161no—
198C2×C4—161no—
199C2×C4—161no—
200C2×C4—161no—
201C2×C4#39411yescharacteristic
202C2×C4#44911yescharacteristic
203C2×C4#45011yescharacteristic
204C2×C4#46011yescharacteristic
205C2×C4#46411yescharacteristic
206C2×C4#46511yescharacteristic
207C2×C4#47111yescharacteristic
208C2×C4#47211yescharacteristic
209C2×C4#48111yescharacteristic
210C2×C4#48211yescharacteristic
211C8—21no—
212C8—21no—
213C8—82no—
214C8—81no—
215C8—161no—
216C8#46111yescharacteristic
217C8#46311yescharacteristic
218C8#46511yescharacteristic
219C8#46811yescharacteristic
220C22—21no—
221C22—21no—
222C22#168811yescharacteristic
223C22#170211yescharacteristic
224C22#203411yescharacteristic
225C4—21no—
226C4—21no—
227C4—21no—
228C4—21no—
229C4—81no—
230C4—81no—
231C4—162no—
232C4—321no—
233C4#166611yescharacteristic
234C4#167811yescharacteristic
235C4#205111yescharacteristic
236C4#205511yescharacteristic
237C2—21no—
238C2—21no—
239C2#1047511yescharacteristic
240C2#1339711yescharacteristic
241C2#1340511yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#469
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2960 ◁ 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
#192042
#132672
#132072
#119992
#119322
#86772
#72792