Finite Group Databasebeta

← #145597

Subgroups — #145597

Order 512.

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

normal subgroups only

This group has 294 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#19632C211yesmaximal, characteristic
2#11983C211yesmaximal, characteristic
3#11962C211yesmaximal, characteristic
4C2×#1362C211yesmaximal, characteristic
5#11646C211yesmaximal, characteristic
6#9624C211yesmaximal, characteristic
7#7209C211yesmaximal, characteristic
8#3230—21no—
9#3170C2211yescharacteristic
10#3165—21no—
11C2×#494C2211yescharacteristic
12#2162C2211yescharacteristic
13C2×C4⋊C16C2211yescharacteristic
14#1950—21no—
15#1723—22no—
16#1713—21no—
17#1707—21no—
18#1567C2211yescharacteristic
19C2×#335C2211yescharacteristic
20C8×M16C2211yescharacteristic
21#1365—21no—
22#1362—22no—
23#1362—21no—
24#1362—22no—
25#1332—22no—
26#1301—21no—
27C22×Q16—21no—
28C22×Q16—21no—
29#533—21no—
30C2×C4⋊Q8—21no—
31C22×C16—21no—
32#501—42no—
33#500—22no—
34#500—22no—
35#500D411yescharacteristic
36#498—22no—
37#494—21no—
38#494—21no—
39#494—21no—
40#494D412yes—
41#494D411yescharacteristic
42#487—22no—
43#487—21no—
44#484—42no—
45#477—42no—
46#467—21no—
47#467—21no—
48C4×Q16—21no—
49C4×Q16—21no—
50#431D411yescharacteristic
51C2×#108—41no—
52#428—41no—
53#428—41no—
54#423—21no—
55C2×C4⋊C8—21no—
56C4×M16D411yescharacteristic
57C2×C4×C8C2311yescharacteristic
58C4⋊C16—21no—
59C4⋊C16—21no—
60C4⋊C16—21no—
61C22⋊C16—21no—
62C4×C16—21no—
63#341—41no—
64#335—21no—
65#335—21no—
66#335—21no—
67#335D412yes—
68#322—21no—
69C82—21no—
70C22×Q8—41no—
71C2×Q16—21no—
72C2×Q16—22no—
73C2×Q16—22no—
74C2×Q16—21no—
75C2×Q16—41no—
76C2×Q16—41no—
77C2×Q16—81no—
78C2×Q16—81no—
79C2×Q16—82no—
80C2×M16—41no—
81C2×M16D811yescharacteristic
82C2×M16D811yescharacteristic
83C22×C8—41no—
84C22×C8#4111yescharacteristic
85C22×C8#4111yescharacteristic
86C4⋊Q8—22no—
87C4⋊Q8—21no—
88C4⋊Q8—21no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92#125—41no—
93C22⋊Q8—41no—
94C22⋊Q8—41no—
95C4×Q8—41no—
96C4×Q8—41no—
97#117—41no—
98C2×C4⋊C4—41no—
99C2×C4⋊C4—41no—
100C2×C42C2×D411yescharacteristic
101C2×C16—41no—
102C2×C16—41no—
103C2×C16—81no—
104#108—82no—
105#107—21no—
106#107—21no—
107#107—42no—
108#107—42no—
109#107—44no—
110#106—42no—
111#106—42no—
112C4⋊C8—22no—
113C4⋊C8—21no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117#103—44no—
118#103—41no—
119#103—41no—
120C22⋊C8SD1612yes—
121#97—21no—
122C4×C8—21no—
123C4×C8—21no—
124C4×C8C2×D411yescharacteristic
125C4×C8C2×D411yescharacteristic
126C4×C8C2×D411yescharacteristic
127C4×C8#4111yescharacteristic
128C2×Q8—41no—
129C2×Q8—42no—
130C2×Q8—41no—
131C2×Q8—82no—
132C2×Q8—82no—
133C2×Q8—81no—
134C22×C4—81no—
135C22×C4#12411yescharacteristic
136C22×C4C2×D811yescharacteristic
137C22×C4C2×SD1611yescharacteristic
138Q16—41no—
139Q16—41no—
140Q16—81no—
141Q16—82no—
142Q16—82no—
143Q16—82no—
144Q16—81no—
145Q16—81no—
146M16—21no—
147M16—21no—
148M16—81no—
149M16—81no—
150M16SD3212yes—
151M16Q3212yes—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—22no—
157C2×C8—41no—
158C2×C8—42no—
159C2×C8—81no—
160C2×C8—81no—
161C2×C8—81no—
162C2×C8#12111yescharacteristic
163C2×C8#12111yescharacteristic
164C2×C8#12311yescharacteristic
165C2×C8#12311yescharacteristic
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—42no—
169C4⋊C4—41no—
170C4⋊C4—42no—
171C4⋊C4—41no—
172C4⋊C4—81no—
173C4⋊C4—81no—
174C4⋊C4—81no—
175C4⋊C4—81no—
176C22⋊C4—81no—
177C42—81no—
178C42#12011yescharacteristic
179C42#12111yescharacteristic
180C42AGL(1,ℤ/8)11yescharacteristic
181C42AGL(1,ℤ/8)11yescharacteristic
182C16—81no—
183C16—81no—
184C23#48611yescharacteristic
185Q8—82no—
186Q8—82no—
187Q8—81no—
188Q8—81no—
189Q8—82no—
190Q8—162no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—81no—
196C2×C4—82no—
197C2×C4—162no—
198C2×C4#39411yescharacteristic
199C2×C4#44711yescharacteristic
200C2×C4#45011yescharacteristic
201C2×C4#45911yescharacteristic
202C2×C4#46011yescharacteristic
203C2×C4#49011yescharacteristic
204C2×C4C2×SD3211yescharacteristic
205C2×C4C2×Q3211yescharacteristic
206C2×C4#51011yescharacteristic
207C2×C4#51011yescharacteristic
208C8—21no—
209C8—21no—
210C8—21no—
211C8—22no—
212C8—22no—
213C8—42no—
214C8—82no—
215C8—161no—
216C8#47111yescharacteristic
217C8#47211yescharacteristic
218C22—21no—
219C22—21no—
220C22#204111yescharacteristic
221C22#224111yescharacteristic
222C22#224511yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—162no—
227C4—161no—
228C4—161no—
229C4#204811yescharacteristic
230C4#205111yescharacteristic
231C4#218511yescharacteristic
232C4#218811yescharacteristic
233C4#220811yescharacteristic
234C4#220911yescharacteristic
235C2—21no—
236C2—21no—
237C2#1054911yescharacteristic
238C2#1340911yescharacteristic
239C2#1341811yescharacteristic
subgroupG/H
center, socleC22#2041
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#486
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C8×M16 ◁ 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
#196322
#119832
#119622
C2×#13622
#116462
#96242
#72092