Finite Group Databasebeta

← #145191

Subgroups — #145191

Order 512.

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

normal subgroups only

This group has 316 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#28268C211yesmaximal, characteristic
2#12904C211yesmaximal, characteristic
3#12819C211yesmaximal, characteristic
4#11607C211yesmaximal, characteristic
5#11594C211yesmaximal, characteristic
6#8659C211yesmaximal, characteristic
7#7279C211yesmaximal, characteristic
8C2×C8×Q8C2211yescharacteristic
9C2×C4×Q16C2211yescharacteristic
10#2581—21no—
11C2×#365—22no—
12#2150C2211yescharacteristic
13C2×#362—21no—
14C4×M32C2211yescharacteristic
15#2066—22no—
16#1969—21no—
17#1942—21no—
18#1848C2211yescharacteristic
19#1846C2211yescharacteristic
20#1805—21no—
21#1564C2211yescharacteristic
22#1487—21no—
23#1387—21no—
24Q8⋊C16—22no—
25#1332—22no—
26#1301—21no—
27C22×Q16D411yescharacteristic
28C2×C4×Q8—21no—
29C2×C4×Q8D411yescharacteristic
30C2×M32—21no—
31C2×M32—21no—
32C8×Q8—21no—
33C8×Q8—21no—
34C8×Q8—21no—
35C8×Q8—21no—
36C4×Q16—21no—
37C4×Q16—21no—
38C4×Q16—21no—
39C4×Q16—21no—
40#431—21no—
41C2×#108—21no—
42C2×#108—21no—
43C2×#107—21no—
44C2×#107D411yescharacteristic
45C2×#106D412yes—
46#423—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8D411yescharacteristic
49C2×#103—21no—
50C2×#103—22no—
51C2×C4×C8—21no—
52C2×C4×C8C2311yescharacteristic
53#400—41no—
54#395—41no—
55#391—22no—
56#389—22no—
57#387—42no—
58#382—21no—
59#365—44no—
60C4⋊C16—21no—
61C4⋊C16—21no—
62#362—42no—
63#346—21no—
64C4×C16D412yes—
65#340—22no—
66#335—21no—
67#334—21no—
68Q8⋊C8—42no—
69C22×Q8—21no—
70C22×Q8SD1611yescharacteristic
71C2×Q16—21no—
72C2×Q16—21no—
73C2×Q16—21no—
74C2×Q16—21no—
75C2×Q16—21no—
76C2×Q16SD1612yes—
77C2×M16—41no—
78C22×C8—21no—
79C22×C8C2×D411yescharacteristic
80C22×C8C2×D411yescharacteristic
81C4×Q8—21no—
82C4×Q8—21no—
83C4×Q8—21no—
84C4×Q8—21no—
85C4×Q8—41no—
86C4×Q8—41no—
87C4×Q8—41no—
88C4×Q8—41no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—42no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4SD1611yescharacteristic
95C2×C42—21no—
96C2×C42—41no—
97C2×C42C2×D411yescharacteristic
98M32—22no—
99M32—22no—
100M32—41no—
101M32—41no—
102C2×C16—22no—
103C2×C16—41no—
104#108—42no—
105#108—41no—
106#108—41no—
107#107—21no—
108#107—21no—
109#107—41no—
110#107—41no—
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—41no—
120#103—41no—
121#103—82no—
122C22⋊C8—41no—
123C4×C8—41no—
124C4×C8—41no—
125C4×C8—41no—
126C4×C8C2×D411yescharacteristic
127C4×C8#4111yescharacteristic
128C4×C8#4111yescharacteristic
129C4×C8#4111yescharacteristic
130#95—42no—
131#95—42no—
132#95—42no—
133#95—41no—
134#95—41no—
135C2×Q8—22no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—42no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—41no—
147C22×C4—42no—
148C22×C4—41no—
149C22×C4#12011yescharacteristic
150C22×C4C2×SD1611yescharacteristic
151C22×C4AGL(1,ℤ/8)11yescharacteristic
152Q16—22no—
153Q16—22no—
154Q16—41no—
155Q16—41no—
156M16—81no—
157M16—81no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—81no—
164C2×C8—81no—
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—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—84no—
182C4⋊C4—81no—
183C4⋊C4—81no—
184C42—41no—
185C42—41no—
186C42—81no—
187C42—81no—
188C42#12111yescharacteristic
189C42#12311yescharacteristic
190C42#13511yescharacteristic
191C42AGL(1,ℤ/8)11yescharacteristic
192C16—24no—
193C16—81no—
194C23#45011yescharacteristic
195Q8—22no—
196Q8—22no—
197Q8—41no—
198Q8—41no—
199Q8—42no—
200Q8—42no—
201Q8—81no—
202Q8—81no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—41no—
211C2×C4—81no—
212C2×C4—81no—
213C2×C4—82no—
214C2×C4—82no—
215C2×C4—82no—
216C2×C4—82no—
217C2×C4—81no—
218C2×C4#39411yescharacteristic
219C2×C4#44811yescharacteristic
220C2×C4#44911yescharacteristic
221C2×C4#45211yescharacteristic
222C2×C4#45311yescharacteristic
223C2×C4#45611yescharacteristic
224C2×C4#46511yescharacteristic
225C2×C4#46911yescharacteristic
226C2×C4#48111yescharacteristic
227C2×C4#48211yescharacteristic
228C8—21no—
229C8—21no—
230C8—81no—
231C8—161no—
232C8—161no—
233C8#46511yescharacteristic
234C8#47011yescharacteristic
235C8#48311yescharacteristic
236C8#48511yescharacteristic
237C22—21no—
238C22—21no—
239C22#163111yescharacteristic
240C22#165111yescharacteristic
241C22#203411yescharacteristic
242C4—21no—
243C4—21no—
244C4—21no—
245C4—21no—
246C4—42no—
247C4—81no—
248C4—82no—
249C4—162no—
250C4—161no—
251C4#162211yescharacteristic
252C4#165211yescharacteristic
253C4#203511yescharacteristic
254C4#203911yescharacteristic
255C2—21no—
256C2—21no—
257C2#1043511yescharacteristic
258C2#1339511yescharacteristic
259C2#1339711yescharacteristic
subgroupG/H
center, socleC22#2034
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#450
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
#282682
#129042
#128192
#116072
#115942
#86592
#72792