Finite Group Databasebeta

← #136479

Subgroups — #136479

Order 512.

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

normal subgroups only

This group has 255 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#18062C211yesmaximal, characteristic
2#12025C211yesmaximal, characteristic
3#11658C211yesmaximal, characteristic
4#11600C211yesmaximal, characteristic
5#9636C211yesmaximal, characteristic
6#7289C211yesmaximal, characteristic
7#7166C211yesmaximal, characteristic
8#2984—21no—
9C2×C4×Q16C2211yescharacteristic
10#2162C2211yescharacteristic
11C4×M32C2211yescharacteristic
12#1593—21no—
13#1584—21no—
14#1584—21no—
15#1579—21no—
16#1574—21no—
17#1568C2211yescharacteristic
18#1567C2211yescharacteristic
19#1564C2211yescharacteristic
20#1491—21no—
21#1451C2211yescharacteristic
22#1372—21no—
23#1371—21no—
24#1334C411yescharacteristic
25#1334C411yescharacteristic
26#1334C411yescharacteristic
27#1334C411yescharacteristic
28#1332—21no—
29#1332—21no—
30#1299—21no—
31C22×Q16Q811yescharacteristic
32C2×C4×Q8—21no—
33C2×M32—21no—
34#446—21no—
35#446—21no—
36#446—41no—
37#446—41no—
38C8×Q8—21no—
39C8×Q8—21no—
40C4×Q16—21no—
41C4×Q16—21no—
42C4×Q16C2×C411yescharacteristic
43C4×Q16C2×C411yescharacteristic
44C4×Q16D411yescharacteristic
45C4×Q16D411yescharacteristic
46#432—21no—
47#432—41no—
48#431—21no—
49#431—41no—
50#431D411yescharacteristic
51C2×#107Q811yescharacteristic
52#423—21no—
53C2×#103—21no—
54C4×M16D411yescharacteristic
55C2×C4×C8C2311yescharacteristic
56C4⋊C16—21no—
57C22⋊C16—21no—
58#346C2×C411yescharacteristic
59#346C2×C411yescharacteristic
60C4×C16—21no—
61C4×C16—21no—
62#335—21no—
63#335—21no—
64#335—21no—
65#335—41no—
66#335D411yescharacteristic
67#335D411yescharacteristic
68#334—21no—
69#334—41no—
70#334C2×C411yescharacteristic
71#334C2×C411yescharacteristic
72Q8⋊C8—21no—
73Q8⋊C8—21no—
74Q8⋊C8—21no—
75Q8⋊C8—21no—
76#322—21no—
77#322—21no—
78C22×Q8—21no—
79C2×Q16—22no—
80C2×Q16—21no—
81C2×Q16—41no—
82C2×Q16C4⋊C411yescharacteristic
83C2×Q16C4⋊C411yescharacteristic
84C2×M16—21no—
85C2×M16—41no—
86C22×C8C2×Q811yescharacteristic
87C22×C8#4111yescharacteristic
88C4×Q8—21no—
89C4×Q8—21no—
90C4×Q8—21no—
91C4×Q8—21no—
92C4×Q8—41no—
93C4×Q8—41no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—41no—
96C2×C42—41no—
97C2×C42C2×D411yescharacteristic
98M32—42no—
99C2×C16—21no—
100C2×C16—21no—
101C2×C16—41no—
102#107—21no—
103#107C4⋊C411yescharacteristic
104#107C4⋊C411yescharacteristic
105C4⋊C8—21no—
106C4⋊C8—21no—
107C4⋊C8—21no—
108C4⋊C8—21no—
109C4⋊C8—41no—
110C4⋊C8—41no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8D811yescharacteristic
116C4⋊C8D811yescharacteristic
117#103—21no—
118#103—21no—
119#103—21no—
120#103—21no—
121C22⋊C8—21no—
122C22⋊C8—41no—
123C22⋊C8—41no—
124#97—21no—
125#97—41no—
126#97—41no—
127#97—41no—
128C4×C8—21no—
129C4×C8—21no—
130C4×C8—41no—
131C4×C8—41no—
132C4×C8—41no—
133C4×C8C22×C411yescharacteristic
134C4×C8C2×D411yescharacteristic
135C4×C8C2×D411yescharacteristic
136C4×C8#4111yescharacteristic
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—42no—
140C2×Q8—41no—
141C2×Q8—81no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4C22⋊Q811yescharacteristic
145C22×C4#13511yescharacteristic
146C22×C4AGL(1,ℤ/8)11yescharacteristic
147Q16—21no—
148Q16—21no—
149Q16—21no—
150Q16—42no—
151Q16#10812yes—
152M16—81no—
153M16—161no—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—81no—
165C2×C8C2×C4⋊C411yescharacteristic
166C2×C8C4×D411yescharacteristic
167C2×C8C22⋊Q811yescharacteristic
168C2×C8#12311yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C42—41no—
177C42—41no—
178C42—41no—
179C42—41no—
180C42C4×D411yescharacteristic
181C42#12011yescharacteristic
182C42C2×D811yescharacteristic
183C42#13711yescharacteristic
184C16—22no—
185C16—41no—
186C16—81no—
187C23#47811yescharacteristic
188Q8—22no—
189Q8—41no—
190Q8—41no—
191Q8—41no—
192Q8—82no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—82no—
203C2×C4—82no—
204C2×C4#38511yescharacteristic
205C2×C4C4×D811yescharacteristic
206C2×C4#44011yescharacteristic
207C2×C4#44711yescharacteristic
208C2×C4#45211yescharacteristic
209C2×C4#47411yescharacteristic
210C8—21no—
211C8—21no—
212C8—21no—
213C8—41no—
214C8—41no—
215C8—81no—
216C8—81no—
217C8—81no—
218C8—81no—
219C8—81no—
220C8—161no—
221C8C2×#10811yescharacteristic
222C8#43011yescharacteristic
223C22—21no—
224C22—21no—
225C22—21no—
226C22#186211yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—21no—
231C4—42no—
232C4—81no—
233C4—81no—
234C4—81no—
235C4#185511yescharacteristic
236C4#186111yescharacteristic
237C4#219311yescharacteristic
238C4#219511yescharacteristic
239C2—41no—
240C2#890611yescharacteristic
241C2#1294111yescharacteristic
242C2#1294411yescharacteristic
subgroupG/H
centerC2×C4#447
commutatorC4×C8C22×C4
Frattini, cosocleC2×C4×C8C23
socleC22#1862
prime radicalC23#478
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1451 ◁ 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
#180622
#120252
#116582
#116002
#96362
#72892
#71662