Finite Group Databasebeta

← #145201

Subgroups — #145201

Order 512.

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

normal subgroups only

This group has 289 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#12887C211yesmaximal, 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×C4⋊C16C2211yescharacteristic
12C2×#358—21no—
13C4×M32C2211yescharacteristic
14#2064—22no—
15#1979—21no—
16#1952—21no—
17#1848C2211yescharacteristic
18#1846C2211yescharacteristic
19#1801—21no—
20#1564C2211yescharacteristic
21#1518—21no—
22#1383—22no—
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—
59C4⋊C16—21no—
60C4⋊C16—21no—
61#358—42no—
62#346—21no—
63C4×C16D412yes—
64#343—22no—
65#335—21no—
66#334—21no—
67#328—42no—
68C22×Q8—21no—
69C2×Q16—21no—
70C2×Q16—21no—
71C2×Q16—21no—
72C2×Q16—21no—
73C2×Q16—21no—
74C2×Q16Q1612yes—
75C2×M16—21no—
76C2×M16—22no—
77C22×C8C2×D411yescharacteristic
78C22×C8C2×D411yescharacteristic
79C4⋊Q8SD1611yescharacteristic
80C4⋊Q8SD1611yescharacteristic
81#125—21no—
82C22⋊Q8—21no—
83C22⋊Q8—21no—
84C4×Q8—21no—
85C4×Q8—21no—
86C4×Q8—41no—
87C4×Q8—41no—
88C4×Q8—41no—
89C4×Q8—41no—
90#117—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—41no—
93C2×C4⋊C4—41no—
94C2×C42—41no—
95C2×C42C2×D411yescharacteristic
96M32—41no—
97M32—41no—
98C2×C16—22no—
99C2×C16—41no—
100C2×C16—41no—
101C2×C16—41no—
102#108—42no—
103#108—41no—
104#108—41no—
105#107—21no—
106#107—21no—
107#107—42no—
108#107—41no—
109#107—41no—
110#106—42no—
111#106—42no—
112C4⋊C8—21no—
113C4⋊C8—21no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119#103—42no—
120#103—42no—
121#103—41no—
122#103—41no—
123#101—82no—
124C22⋊C8—41no—
125#97—41no—
126C4×C8—41no—
127C4×C8—41no—
128C4×C8C2×D411yescharacteristic
129C4×C8#4111yescharacteristic
130C4×C8#4111yescharacteristic
131C4×C8#4111yescharacteristic
132#95—41no—
133#95—41no—
134C2×Q8—22no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—81no—
145C22×C4#12011yescharacteristic
146C22×C4#13511yescharacteristic
147C22×C4AGL(1,ℤ/8)11yescharacteristic
148Q16—22no—
149Q16—22no—
150Q16—41no—
151Q16—41no—
152M16—42no—
153M16—41no—
154M16—41no—
155M16—42no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—41no—
159C2×C8—42no—
160C2×C8—81no—
161C2×C8#12111yescharacteristic
162C2×C8#12111yescharacteristic
163C2×C8#12311yescharacteristic
164C2×C8#12411yescharacteristic
165C2×C8C2×Q1611yescharacteristic
166C2×C8#13511yescharacteristic
167C2×C8AGL(1,ℤ/8)11yescharacteristic
168C2×C8#13711yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—81no—
178C4⋊C4—81no—
179C4⋊C4—81no—
180C4⋊C4—81no—
181C22⋊C4—41no—
182C42—41no—
183C42—81no—
184C42—81no—
185C42#12111yescharacteristic
186C42#12311yescharacteristic
187C42C2×SD1611yescharacteristic
188C42AGL(1,ℤ/8)11yescharacteristic
189C16—42no—
190C16—81no—
191C23#44911yescharacteristic
192Q8—42no—
193Q8—42no—
194Q8—42no—
195Q8—81no—
196Q8—81no—
197Q8—81no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—81no—
204C2×C4—81no—
205C2×C4—81no—
206C2×C4—161no—
207C2×C4—161no—
208C2×C4—161no—
209C2×C4—161no—
210C2×C4#39411yescharacteristic
211C2×C4#44911yescharacteristic
212C2×C4#45011yescharacteristic
213C2×C4#45111yescharacteristic
214C2×C4#45411yescharacteristic
215C2×C4#45511yescharacteristic
216C2×C4#46511yescharacteristic
217C2×C4#46911yescharacteristic
218C2×C4#48111yescharacteristic
219C2×C4#48211yescharacteristic
220C8—21no—
221C8—21no—
222C8—82no—
223C8—81no—
224C8—161no—
225C8#46711yescharacteristic
226C8#46811yescharacteristic
227C8#48411yescharacteristic
228C8#48511yescharacteristic
229C22—21no—
230C22—21no—
231C22#162811yescharacteristic
232C22#164411yescharacteristic
233C22#203411yescharacteristic
234C4—21no—
235C4—21no—
236C4—21no—
237C4—21no—
238C4—81no—
239C4—81no—
240C4—82no—
241C4—161no—
242C4—321no—
243C4#163711yescharacteristic
244C4#164211yescharacteristic
245C4#203611yescharacteristic
246C4#204011yescharacteristic
247C2—21no—
248C2—21no—
249C2#1043611yescharacteristic
250C2#1340511yescharacteristic
251C2#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
#128872
#128142
#116062
#115942
#86772
#72762