Finite Group Databasebeta

← #145193

Subgroups — #145193

Order 512.

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

normal subgroups only

This group has 297 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#28297C211yesmaximal, characteristic
2#12904C211yesmaximal, characteristic
3#12814C211yesmaximal, characteristic
4#11606C211yesmaximal, characteristic
5#11594C211yesmaximal, characteristic
6#8677C211yesmaximal, characteristic
7#7276C211yesmaximal, characteristic
8#3078—21no—
9#2960C2211yescharacteristic
10C2×C4×Q16C2211yescharacteristic
11C2×#365—22no—
12C2×C4⋊C16C2211yescharacteristic
13C2×#358—21no—
14C4×M32C2211yescharacteristic
15#2064—22no—
16#1979—21no—
17#1952—21no—
18#1848C2211yescharacteristic
19#1846C2211yescharacteristic
20#1801—21no—
21#1564C2211yescharacteristic
22#1518—21no—
23#1380—21no—
24Q8⋊C16—22no—
25#1332—22no—
26#1286—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—
43#431—21no—
44C2×#108—21no—
45C2×#108D412yes—
46#428—22no—
47C2×#107—21no—
48C2×#107D411yescharacteristic
49C2×#106—21no—
50#424—21no—
51#423—21no—
52#423D411yescharacteristic
53#419—22no—
54C2×#103—21no—
55C2×#101—22no—
56#405—21no—
57C2×C4×C8C2311yescharacteristic
58#382—21no—
59#365—44no—
60C4⋊C16—21no—
61C4⋊C16—21no—
62#358—42no—
63#346—21no—
64C4×C16D412yes—
65#343—22no—
66#335—21no—
67#334—21no—
68#328—42no—
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—
78C22×C8C2×D411yescharacteristic
79C22×C8C2×D411yescharacteristic
80C4⋊Q8SD1611yescharacteristic
81C4⋊Q8SD1611yescharacteristic
82#125—21no—
83C22⋊Q8—21no—
84C22⋊Q8—21no—
85C4×Q8—21no—
86C4×Q8—21no—
87C4×Q8—41no—
88C4×Q8—41no—
89C4×Q8—41no—
90C4×Q8—41no—
91#117—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C42—41no—
96C2×C42C2×D411yescharacteristic
97M32—22no—
98M32—22no—
99C2×C16—22no—
100C2×C16—41no—
101C2×C16—41no—
102C2×C16—41no—
103#108—42no—
104#108—41no—
105#108—41no—
106#107—21no—
107#107—21no—
108#107—42no—
109#107—41no—
110#107—41no—
111#106—42no—
112#106—42no—
113C4⋊C8—21no—
114C4⋊C8—21no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120#103—42no—
121#103—42no—
122#103—41no—
123#103—41no—
124#101—82no—
125C22⋊C8—41no—
126#97—41no—
127C4×C8—41no—
128C4×C8—41no—
129C4×C8C2×D411yescharacteristic
130C4×C8#4111yescharacteristic
131C4×C8#4111yescharacteristic
132C4×C8#4111yescharacteristic
133#95—41no—
134#95—41no—
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—81no—
146C22×C4#12011yescharacteristic
147C22×C4#13511yescharacteristic
148C22×C4AGL(1,ℤ/8)11yescharacteristic
149Q16—22no—
150Q16—22no—
151Q16—41no—
152Q16—41no—
153M16—42no—
154M16—41no—
155M16—42no—
156M16—41no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—41no—
160C2×C8—42no—
161C2×C8—81no—
162C2×C8#12111yescharacteristic
163C2×C8#12111yescharacteristic
164C2×C8#12311yescharacteristic
165C2×C8#12411yescharacteristic
166C2×C8C2×SD1611yescharacteristic
167C2×C8#13511yescharacteristic
168C2×C8#13711yescharacteristic
169C2×C8#13711yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—81no—
179C4⋊C4—81no—
180C4⋊C4—81no—
181C4⋊C4—81no—
182C22⋊C4—41no—
183C42—41no—
184C42—81no—
185C42—81no—
186C42#12111yescharacteristic
187C42#12311yescharacteristic
188C42C2×SD1611yescharacteristic
189C42AGL(1,ℤ/8)11yescharacteristic
190C16—24no—
191C16—81no—
192C23#44911yescharacteristic
193Q8—42no—
194Q8—42no—
195Q8—42no—
196Q8—81no—
197Q8—81no—
198Q8—81no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—42no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4—81no—
207C2×C4—161no—
208C2×C4—161no—
209C2×C4—161no—
210C2×C4—161no—
211C2×C4#39411yescharacteristic
212C2×C4#44811yescharacteristic
213C2×C4#45011yescharacteristic
214C2×C4#45211yescharacteristic
215C2×C4#45311yescharacteristic
216C2×C4#45611yescharacteristic
217C2×C4#46511yescharacteristic
218C2×C4#46911yescharacteristic
219C2×C4#48111yescharacteristic
220C2×C4#48211yescharacteristic
221C8—21no—
222C8—21no—
223C8—82no—
224C8—81no—
225C8—161no—
226C8#46511yescharacteristic
227C8#47011yescharacteristic
228C8#48311yescharacteristic
229C8#48511yescharacteristic
230C22—21no—
231C22—21no—
232C22#162211yescharacteristic
233C22#165211yescharacteristic
234C22#203411yescharacteristic
235C4—21no—
236C4—21no—
237C4—21no—
238C4—21no—
239C4—81no—
240C4—81no—
241C4—82no—
242C4—161no—
243C4—321no—
244C4#163111yescharacteristic
245C4#165111yescharacteristic
246C4#203511yescharacteristic
247C4#203911yescharacteristic
248C2—21no—
249C2—21no—
250C2#1043511yescharacteristic
251C2#1340511yescharacteristic
252C2#1340611yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#449
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
#129042
#128142
#116062
#115942
#86772
#72762