Finite Group Databasebeta

← #145287

Subgroups — #145287

Order 512.

265 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 265 conjugacy classes of subgroups — too many to draw. Only its 72 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#19262C211yesmaximal, characteristic
2#12022C211yesmaximal, characteristic
3#11983C211yesmaximal, characteristic
4#11672C211yesmaximal, characteristic
5C2×Q8⋊C16C211yesmaximal, characteristic
6#8617C211yesmaximal, characteristic
7#7241C211yesmaximal, characteristic
8#3170C2211yescharacteristic
9#3078—21no—
10C2×C8×Q8C2211yescharacteristic
11C2×C4⋊C16C2211yescharacteristic
12C2×C4×C16C2211yescharacteristic
13#1801—21no—
14#1684—22no—
15#1676—21no—
16#1670—21no—
17#1567C2211yescharacteristic
18#1567C2211yescharacteristic
19#1567C2211yescharacteristic
20#1550—21no—
21#1371—22no—
22#1365—21no—
23#1362—21no—
24Q8⋊C16—21no—
25Q8⋊C16—21no—
26#1332—21no—
27#1332—21no—
28#1292—21no—
29#533—21no—
30C2×C4×Q8D411yescharacteristic
31C22×C16—21no—
32C22×C16—21no—
33#500D411yescharacteristic
34#494D411yescharacteristic
35#487—21no—
36#479—42no—
37#477—22no—
38#475—22no—
39#467—21no—
40#467—21no—
41C8×Q8—21no—
42C8×Q8—21no—
43C8×Q8—21no—
44C8×Q8—21no—
45C4×Q16—21no—
46C4×Q16—21no—
47#428—41no—
48#423—21no—
49#423—21no—
50#423—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8D411yescharacteristic
53#419—41no—
54C2×#101—41no—
55C2×C4×C8—21no—
56C2×C4×C8C2311yescharacteristic
57C4⋊C16—21no—
58C4⋊C16—21no—
59C4×C16—21no—
60C4×C16D411yescharacteristic
61C4×C16D411yescharacteristic
62#343—41no—
63#335—21no—
64#335—21no—
65#335—21no—
66#335—21no—
67#335—21no—
68#335D412yes—
69#333—22no—
70#332—22no—
71C22×Q8D811yescharacteristic
72C2×Q16—21no—
73C2×Q16—21no—
74C2×M16—41no—
75C2×M16—41no—
76C2×M16—41no—
77C22×C8—21no—
78C22×C8#4111yescharacteristic
79C22×C8#4111yescharacteristic
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82#125—41no—
83C22⋊Q8—41no—
84C22⋊Q8—41no—
85C4×Q8—21no—
86C4×Q8—21no—
87C4×Q8—21no—
88C4×Q8—21no—
89C4×Q8—41no—
90C4×Q8—41no—
91#117—41no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4D811yescharacteristic
94C2×C42—21no—
95C2×C42C2×D411yescharacteristic
96C2×C16—21no—
97C2×C16—21no—
98C2×C16—42no—
99C2×C16—41no—
100C2×C16—81no—
101#107—21no—
102#107—21no—
103#107—42no—
104#106—42no—
105C4⋊C8—21no—
106C4⋊C8—22no—
107C4⋊C8—21no—
108C4⋊C8—41no—
109C4⋊C8—41no—
110C4⋊C8—41no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115#103—42no—
116#103—42no—
117#103—41no—
118#103—41no—
119#101—82no—
120C4×C8—41no—
121C4×C8—41no—
122C4×C8C2×D411yescharacteristic
123C4×C8C2×D411yescharacteristic
124C4×C8C2×D411yescharacteristic
125C4×C8#4111yescharacteristic
126C2×Q8—21no—
127C2×Q8—21no—
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—41no—
132C2×Q8—41no—
133C2×Q8Q3212yes—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4#12311yescharacteristic
137C22×C4C2×D811yescharacteristic
138C22×C4#13711yescharacteristic
139Q16—41no—
140Q16—41no—
141Q16—81no—
142M16—81no—
143M16—81no—
144M16—81no—
145M16—81no—
146M16—81no—
147M16—81no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8—42no—
153C2×C8—81no—
154C2×C8—81no—
155C2×C8—81no—
156C2×C8#12111yescharacteristic
157C2×C8#12111yescharacteristic
158C2×C8#12311yescharacteristic
159C2×C8#12411yescharacteristic
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—81no—
169C4⋊C4—81no—
170C22⋊C4—81no—
171C42—41no—
172C42—41no—
173C42—81no—
174C42#12011yescharacteristic
175C42#12111yescharacteristic
176C42#13511yescharacteristic
177C42AGL(1,ℤ/8)11yescharacteristic
178C16—22no—
179C16—41no—
180C16—81no—
181C23#48011yescharacteristic
182Q8—22no—
183Q8—22no—
184Q8—41no—
185Q8—41no—
186Q8—81no—
187Q8—81no—
188Q8—161no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4#39411yescharacteristic
200C2×C4#44711yescharacteristic
201C2×C4#45211yescharacteristic
202C2×C4#46611yescharacteristic
203C2×C4#46811yescharacteristic
204C2×C4#48211yescharacteristic
205C2×C4C2×Q3211yescharacteristic
206C2×C4#50811yescharacteristic
207C2×C4#50911yescharacteristic
208C2×C4#51011yescharacteristic
209C8—21no—
210C8—21no—
211C8—21no—
212C8—81no—
213C8—82no—
214C8—161no—
215C8—161no—
216C8#47111yescharacteristic
217C8#47311yescharacteristic
218C22—21no—
219C22—21no—
220C22#203311yescharacteristic
221C22#223611yescharacteristic
222C22#223711yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—42no—
227C4—81no—
228C4—161no—
229C4—161no—
230C4#205011yescharacteristic
231C4#205211yescharacteristic
232C4#218611yescharacteristic
233C4#218811yescharacteristic
234C4#221611yescharacteristic
235C4#222011yescharacteristic
236C2—21no—
237C2—21no—
238C2#1045811yescharacteristic
239C2#1338311yescharacteristic
240C2#1339211yescharacteristic
subgroupG/H
center, socleC22#2033
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#480
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C8×Q8 ◁ 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
#192622
#120222
#119832
#116722
C2×Q8⋊C162
#86172
#72412