Finite Group Databasebeta

← #145177

Subgroups — #145177

Order 512.

289 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 289 conjugacy classes of subgroups — too many to draw. Only its 78 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#28297C211yesmaximal, characteristic
2#12891C211yesmaximal, characteristic
3#12819C211yesmaximal, characteristic
4#11608C211yesmaximal, characteristic
5C2×#1332C211yesmaximal, characteristic
6#8685C211yesmaximal, characteristic
7#7281C211yesmaximal, characteristic
8#3078—21no—
9#2960C2211yescharacteristic
10C2×C4×Q16C2211yescharacteristic
11#2150C2211yescharacteristic
12C2×#362—21no—
13C2×C4×C16C2211yescharacteristic
14#2064—22no—
15#1979—21no—
16#1952—21no—
17#1848C2211yescharacteristic
18#1848C2211yescharacteristic
19#1801—21no—
20C2×#335C2211yescharacteristic
21#1550—21no—
22#1387—21no—
23#1381—22no—
24Q8⋊C16—22no—
25#1332—22no—
26#1292—21no—
27C22×Q16D411yescharacteristic
28#533D411yescharacteristic
29C2×C4×Q8—21no—
30C2×M32—21no—
31C22×C16—21no—
32#479—42no—
33#477—41no—
34#475—41no—
35#446—21no—
36#446—21no—
37C8×Q8—21no—
38C8×Q8—21no—
39C4×Q16—21no—
40C4×Q16—21no—
41C4×Q16—21no—
42C4×Q16—21no—
43C2×#108—21no—
44C2×#108—21no—
45C2×#108—21no—
46C2×#108D412yes—
47#428—22no—
48C2×#107D411yescharacteristic
49#424—21no—
50#423—21no—
51#423—21no—
52#423D411yescharacteristic
53C2×C4⋊C8—21no—
54#419—22no—
55C2×#103—21no—
56C2×#101—22no—
57#405—21no—
58C2×C4×C8C2311yescharacteristic
59C4⋊C16—21no—
60C4⋊C16—21no—
61#362—42no—
62C4×C16—21no—
63C4×C16D412yes—
64#343—22no—
65#335—21no—
66#335—21no—
67#333—41no—
68#332—41no—
69C22×Q8—21no—
70C2×Q16—21no—
71C2×Q16—21no—
72C2×Q16—21no—
73C2×Q16—21no—
74C2×Q16—21no—
75C2×Q16SD1612yes—
76C2×M16—21no—
77C2×M16—22no—
78C2×M16—41no—
79C22×C8—41no—
80C22×C8C2×D411yescharacteristic
81C22×C8C2×D411yescharacteristic
82C4⋊Q8D811yescharacteristic
83C4⋊Q8D811yescharacteristic
84#125—21no—
85C22⋊Q8—21no—
86C22⋊Q8—21no—
87C4×Q8—21no—
88C4×Q8—21no—
89C4×Q8—41no—
90C4×Q8—41no—
91C4×Q8—41no—
92C4×Q8—41no—
93#117—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—41no—
96C2×C42—41no—
97C2×C42C2×D411yescharacteristic
98M32—41no—
99M32—41no—
100C2×C16—22no—
101C2×C16—41no—
102C2×C16—41no—
103C2×C16—41no—
104#108—42no—
105#108—42no—
106#108—41no—
107#108—41no—
108#108—41no—
109#108—41no—
110#107—21no—
111#107—21no—
112#107—42no—
113#106—42no—
114C4⋊C8—21no—
115C4⋊C8—21no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124#103—42no—
125#103—42no—
126#103—41no—
127#103—41no—
128#101—82no—
129#97—41no—
130C4×C8—41no—
131C4×C8C2×D411yescharacteristic
132C4×C8#4111yescharacteristic
133C4×C8#4111yescharacteristic
134C4×C8#4111yescharacteristic
135C2×Q8—22no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—41no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4#12011yescharacteristic
146C22×C4#13511yescharacteristic
147C22×C4#13711yescharacteristic
148Q16—22no—
149Q16—22no—
150Q16—41no—
151Q16—41no—
152M16—42no—
153M16—41no—
154M16—41no—
155M16—42no—
156M16—81no—
157M16—81no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—42no—
162C2×C8—81no—
163C2×C8—81no—
164C2×C8—161no—
165C2×C8#12111yescharacteristic
166C2×C8#12111yescharacteristic
167C2×C8#12311yescharacteristic
168C2×C8#12411yescharacteristic
169C2×C8C2×SD1611yescharacteristic
170C2×C8#13511yescharacteristic
171C2×C8#13711yescharacteristic
172C2×C8#13711yescharacteristic
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—81no—
182C4⋊C4—81no—
183C22⋊C4—41no—
184C42—41no—
185C42—81no—
186C42—81no—
187C42#12111yescharacteristic
188C42#12311yescharacteristic
189C42C2×D811yescharacteristic
190C42AGL(1,ℤ/8)11yescharacteristic
191C16—42no—
192C16—81no—
193C23#45211yescharacteristic
194Q8—42no—
195Q8—41no—
196Q8—41no—
197Q8—42no—
198Q8—81no—
199Q8—81no—
200Q8—81no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—81no—
208C2×C4—81no—
209C2×C4—81no—
210C2×C4—161no—
211C2×C4#39411yescharacteristic
212C2×C4#44711yescharacteristic
213C2×C4#44811yescharacteristic
214C2×C4#45211yescharacteristic
215C2×C4#45411yescharacteristic
216C2×C4#45511yescharacteristic
217C2×C4#46611yescharacteristic
218C2×C4#46811yescharacteristic
219C2×C4#48011yescharacteristic
220C2×C4#48211yescharacteristic
221C8—21no—
222C8—21no—
223C8—82no—
224C8—81no—
225C8—161no—
226C8—161no—
227C8#46511yescharacteristic
228C8#47011yescharacteristic
229C8#48311yescharacteristic
230C8#48511yescharacteristic
231C22—21no—
232C22—21no—
233C22#163811yescharacteristic
234C22#164311yescharacteristic
235C22#203311yescharacteristic
236C4—21no—
237C4—21no—
238C4—21no—
239C4—81no—
240C4—81no—
241C4—82no—
242C4—161no—
243C4#162711yescharacteristic
244C4#164111yescharacteristic
245C4#203511yescharacteristic
246C4#204011yescharacteristic
247C4#222211yescharacteristic
248C4#222311yescharacteristic
249C2—21no—
250C2—21no—
251C2#1043311yescharacteristic
252C2#1339211yescharacteristic
253C2#1339411yescharacteristic
subgroupG/H
center, socleC22#2033
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#452
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
#282972
#128912
#128192
#116082
C2×#13322
#86852
#72812