Finite Group Databasebeta

← #145048

Subgroups — #145048

Order 512.

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

normal subgroups only

This group has 308 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#28762C211yesmaximal, characteristic
2#13212C211yesmaximal, characteristic
3#13179C211yesmaximal, characteristic
4C2×#1362C211yesmaximal, characteristic
5#11606C211yesmaximal, characteristic
6#8685C211yesmaximal, characteristic
7#7176C211yesmaximal, characteristic
8C2×#494C2211yescharacteristic
9#3139—21no—
10#2960C2211yescharacteristic
11C2×#368—21no—
12C2×C4⋊C16C2211yescharacteristic
13C2×#362—22no—
14C4×M32C2211yescharacteristic
15#2047—22no—
16#1979—21no—
17#1979—21no—
18#1966—21no—
19#1848C2211yescharacteristic
20C4×#108C2211yescharacteristic
21C2×#335C2211yescharacteristic
22#1550—21no—
23#1381—21no—
24#1362—22no—
25Q8⋊C16—22no—
26#1292—21no—
27C22×Q16—21no—
28C22×Q16D412yes—
29#533D411yescharacteristic
30C2×C4⋊Q8—21no—
31C2×M32—21no—
32C22×C16—21no—
33#494—21no—
34#494—21no—
35#494—21no—
36#494—21no—
37#491—42no—
38#487—41no—
39#487—41no—
40#446—21no—
41#446—21no—
42C8×Q8—21no—
43C8×Q8—21no—
44C2×#108—21no—
45C2×#108—21no—
46C2×#108D411yescharacteristic
47C2×#108D411yescharacteristic
48#424—21no—
49#423—21no—
50#423D411yescharacteristic
51C2×C4⋊C8—21no—
52#419—22no—
53#419—22no—
54C2×#101—22no—
55C2×#101—22no—
56#405—21no—
57C4×M16—21no—
58C2×C4×C8C2311yescharacteristic
59#368—42no—
60C4⋊C16—21no—
61C4⋊C16D412yes—
62#362—44no—
63#346—21no—
64C4×C16—21no—
65#341—21no—
66#335—21no—
67#335—21no—
68#333—41no—
69#332—41no—
70C22×Q8—22no—
71C2×Q16—22no—
72C2×Q16—22no—
73C2×Q16—42no—
74C2×Q16—42no—
75C2×Q16—41no—
76C2×Q16—41no—
77C2×Q16—41no—
78C2×Q16—41no—
79C2×Q16—41no—
80C2×Q16—41no—
81C2×M16—21no—
82C2×M16—21no—
83C2×M16—21no—
84C2×M16—41no—
85C22×C8—41no—
86C22×C8C2×D411yescharacteristic
87C22×C8C2×D411yescharacteristic
88C4⋊Q8—41no—
89C4⋊Q8—41no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92C4⋊Q8D811yescharacteristic
93C4⋊Q8D811yescharacteristic
94#125—21no—
95C22⋊Q8—21no—
96C22⋊Q8—21no—
97C4×Q8—21no—
98C4×Q8—21no—
99#117—21no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C42C2×D411yescharacteristic
103M32—22no—
104M32—41no—
105C2×C16—22no—
106C2×C16—41no—
107C2×C16—41no—
108C2×C16—41no—
109#108—21no—
110#108—21no—
111#108—21no—
112#108—21no—
113#108—42no—
114#108—41no—
115#108—41no—
116C4⋊C8—21no—
117C4⋊C8—21no—
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—42no—
127#103—42no—
128#101—82no—
129#101—82no—
130#97—41no—
131#97—41no—
132C4×C8—41no—
133C4×C8—41no—
134C4×C8C2×D411yescharacteristic
135C4×C8#4111yescharacteristic
136C4×C8#4111yescharacteristic
137C4×C8#4111yescharacteristic
138C2×Q8—21no—
139C2×Q8—21no—
140C2×Q8—42no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8—42no—
145C2×Q8—42no—
146C22×C4—42no—
147C22×C4#12011yescharacteristic
148C22×C4#13511yescharacteristic
149C22×C4#13711yescharacteristic
150Q16—44no—
151Q16—82no—
152Q16—81no—
153Q16—81no—
154Q16—81no—
155Q16—81no—
156M16—41no—
157M16—41no—
158M16—41no—
159M16—41no—
160M16—41no—
161M16—41no—
162M16—81no—
163M16—81no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—81no—
170C2×C8—81no—
171C2×C8—161no—
172C2×C8#12111yescharacteristic
173C2×C8#12111yescharacteristic
174C2×C8#12311yescharacteristic
175C2×C8#12411yescharacteristic
176C2×C8#13511yescharacteristic
177C2×C8#13511yescharacteristic
178C2×C8AGL(1,ℤ/8)11yescharacteristic
179C2×C8#13711yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—81no—
187C4⋊C4—81no—
188C4⋊C4—81no—
189C4⋊C4—81no—
190C22⋊C4—41no—
191C42—41no—
192C42#12111yescharacteristic
193C42#12311yescharacteristic
194C42C2×D811yescharacteristic
195C42AGL(1,ℤ/8)11yescharacteristic
196C16—42no—
197C16—42no—
198C23#45211yescharacteristic
199Q8—41no—
200Q8—41no—
201Q8—81no—
202Q8—82no—
203Q8—82no—
204Q8—82no—
205Q8—82no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—82no—
214C2×C4#39411yescharacteristic
215C2×C4#44711yescharacteristic
216C2×C4#44911yescharacteristic
217C2×C4#45211yescharacteristic
218C2×C4#45311yescharacteristic
219C2×C4#45511yescharacteristic
220C2×C4#46611yescharacteristic
221C2×C4#46811yescharacteristic
222C2×C4#48011yescharacteristic
223C2×C4#48211yescharacteristic
224C8—21no—
225C8—21no—
226C8—81no—
227C8—81no—
228C8—81no—
229C8—161no—
230C8—161no—
231C8#46311yescharacteristic
232C8#46411yescharacteristic
233C8#48811yescharacteristic
234C8#48911yescharacteristic
235C22—21no—
236C22—21no—
237C22#163011yescharacteristic
238C22#164011yescharacteristic
239C22#203311yescharacteristic
240C4—21no—
241C4—21no—
242C4—21no—
243C4—81no—
244C4—81no—
245C4—162no—
246C4#162111yescharacteristic
247C4#164111yescharacteristic
248C4#203711yescharacteristic
249C4#204211yescharacteristic
250C4#222211yescharacteristic
251C4#222311yescharacteristic
252C2—21no—
253C2—21no—
254C2#1041111yescharacteristic
255C2#1339011yescharacteristic
256C2#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
#287622
#132122
#131792
C2×#13622
#116062
#86852
#71762