Finite Group Databasebeta

← #102340

Subgroups — #102340

Order 512.

516 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 118 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#33172C211yesmaximal, characteristic
2#10864C211yesmaximal, characteristic
3C8×C22⋊C8C211yesmaximal, characteristic
4#7685C214yesmaximal
5C2×#494C411yescharacteristic
6C2×#467—21no—
7C2×#467—21no—
8C22×#108—21no—
9C22×C4×C8C2211yescharacteristic
10#2857C2212yes—
11#1969—21no—
12#1969—21no—
13#1956C412yes—
14#1845C411yescharacteristic
15C4×C22⋊C8C2212yes—
16C2×#341—21no—
17#1728C2212yes—
18C2×C82—21no—
19#1273—21no—
20#1271—28no—
21C22×Q16—21no—
22C22×Q16—21no—
23C22×M16—22no—
24C23×C8D411yescharacteristic
25C23×C8D411yescharacteristic
26C2×C4⋊Q8C2×C412yes—
27C2×C22⋊Q8—22no—
28C22×C42C2311yescharacteristic
29#494—42no—
30#467—42no—
31#467—42no—
32#467—42no—
33#467—42no—
34C2×#108—24no—
35C2×#108—42no—
36C2×#108—42no—
37C2×#107—21no—
38C2×#107—21no—
39C2×#103—22no—
40C2×#103—22no—
41C2×C22⋊C8—22no—
42C2×C4×C8—22no—
43C2×C4×C8—42no—
44C2×C4×C8C2×C411yescharacteristic
45C2×C4×C8C2×C411yescharacteristic
46C2×C4×C8D411yescharacteristic
47C2×C4×C8D411yescharacteristic
48#391—22no—
49#389—24no—
50#384C2×C412yes—
51#380—24no—
52#341—42no—
53#336—24no—
54#336D414yes—
55C82—42no—
56C22×Q8—22no—
57C23×C4C2×D411yescharacteristic
58C23×C4#4112yes—
59C2×Q16—42no—
60C2×Q16—42no—
61C2×Q16—42no—
62C2×Q16—42no—
63C2×Q16—42no—
64C2×Q16—42no—
65C2×M16—24no—
66C2×M16—42no—
67C2×M16—42no—
68C2×M16—42no—
69C2×M16—42no—
70C2×M16—42no—
71C22×C8—22no—
72C22×C8—22no—
73C22×C8—24no—
74C22×C8—41no—
75C22×C8—41no—
76C22×C8—42no—
77C22×C8C22⋊C411yescharacteristic
78C22×C8C22⋊C411yescharacteristic
79C22×C8C22⋊C411yescharacteristic
80C22×C8C22⋊C411yescharacteristic
81C22×C8D812yes—
82C22×C8D812yes—
83C22×C8SD1612yes—
84C22×C8SD1612yes—
85C4⋊Q8—42no—
86C4⋊Q8—42no—
87C22⋊Q8—42no—
88C22⋊Q8—42no—
89C22⋊Q8—42no—
90C22⋊Q8—42no—
91C2×C4⋊C4—22no—
92C2×C4⋊C4—24no—
93C2×C4⋊C4—24no—
94C2×C4⋊C4—42no—
95C2×C22⋊C4—42no—
96C2×C42—41no—
97C2×C42—41no—
98C2×C42C22×C411yescharacteristic
99C2×C42C2×D411yescharacteristic
100C2×C42C2×D412yes—
101#108—48no—
102#107—42no—
103#107—42no—
104#103—44no—
105#103—44no—
106C22⋊C8—28no—
107C4×C8—22no—
108C4×C8—22no—
109C4×C8—41no—
110C4×C8—41no—
111C4×C8—42no—
112C4×C8—42no—
113#95—44no—
114C24#12411yescharacteristic
115C2×Q8—42no—
116C2×Q8—42no—
117C2×Q8—42no—
118C2×Q8—42no—
119C2×Q8—42no—
120C2×Q8—42no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—24no—
126C22×C4—24no—
127C22×C4—42no—
128C22×C4—42no—
129C22×C4—42no—
130C22×C4C2×C22⋊C411yescharacteristic
131C22×C4C4×D412yes—
132C22×C4#12112yes—
133C22×C4#12711yescharacteristic
134C22×C4C2×D811yescharacteristic
135C22×C4C2×D811yescharacteristic
136C22×C4C2×SD1611yescharacteristic
137C22×C4C2×SD1611yescharacteristic
138Q16—84no—
139Q16—84no—
140M16—44no—
141M16—44no—
142M16—82no—
143M16—82no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—21no—
147C2×C8—21no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—24no—
151C2×C8—24no—
152C2×C8—28no—
153C2×C8—42no—
154C2×C8—42no—
155C2×C8—44no—
156C2×C8—44no—
157C2×C8—44no—
158C2×C8—82no—
159C2×C8—82no—
160C2×C8#9912yes—
161C2×C8#10212yes—
162C2×C8#10212yes—
163C2×C8#10212yes—
164C2×C8#10212yes—
165C2×C8#10412yes—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—48no—
169C4⋊C4—84no—
170C4⋊C4—82no—
171C4⋊C4—82no—
172C22⋊C4—82no—
173C22⋊C4—82no—
174C42—21no—
175C42—21no—
176C42—21no—
177C42—21no—
178C42—42no—
179C23—21no—
180C23—22no—
181C23—22no—
182C23—21no—
183C23#39011yescharacteristic
184C23#48611yescharacteristic
185C23#48611yescharacteristic
186Q8—82no—
187Q8—82no—
188Q8—82no—
189Q8—82no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—48no—
205C2×C4—82no—
206C2×C4—82no—
207C2×C4—82no—
208C2×C4—84no—
209C2×C4—82no—
210C2×C4C2×#9911yescharacteristic
211C2×C4#41011yescharacteristic
212C2×C4C2×#10211yescharacteristic
213C2×C4C2×#10211yescharacteristic
214C2×C4C2×#10411yescharacteristic
215C2×C4#42111yescharacteristic
216C2×C4#44314yes—
217C2×C4#47314yes—
218C2×C4#49211yescharacteristic
219C2×C4#49311yescharacteristic
220C8—22no—
221C8—22no—
222C8—22no—
223C8—48no—
224C8—84no—
225C8#32714yes—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—21no—
230C22—21no—
231C22—21no—
232C22—42no—
233C22—42no—
234C22#195711yescharacteristic
235C22#196411yescharacteristic
236C22#197412yes—
237C22#197912yes—
238C22#198011yescharacteristic
239C4—24no—
240C4—24no—
241C4—21no—
242C4—21no—
243C4—162no—
244C4—162no—
245C4C2×#32711yescharacteristic
246C4#150211yescharacteristic
247C4#151711yescharacteristic
248C4#151911yescharacteristic
249C2—41no—
250C2—41no—
251C2#968011yescharacteristic
252C2#972512yes—
253C2#977211yescharacteristic
254C2#981412yes—
255C2#985611yescharacteristic
subgroupG/H
center, socleC23#390
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#331722
#108642
C8×C22⋊C82
#76852