Finite Group Databasebeta

← #94245

Subgroups — #94245

Order 512.

258 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 52 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#12801C211yesmaximal, characteristic
2#12798C211yesmaximal, characteristic
3#9639C211yesmaximal, characteristic
4C4×#124C2211yescharacteristic
5C2×#355—21no—
6C2×#354—21no—
7#1831C411yescharacteristic, complemented
8#1801—21no—
9#1799—21no—
10C42×C8C411yescharacteristic, complemented
11C2×Q8⋊C8—21no—
12C2×D4⋊C8—21no—
13#1394C412yescomplemented
14#1393C412yes—
15C2×#124D411yescharacteristic
16C2×C4×Q8D411yescharacteristic
17C2×C4×D4D411yescharacteristic
18#423—41no—
19C2×C4⋊C8—21no—
20C2×#101—22no—
21C2×#99—22no—
22C2×C4×C8—21no—
23C2×C4×C8—41no—
24#391C2×C411yescharacteristic
25#390C2×C411yescharacteristic
26#388—41no—
27#382Q811yescharacteristic
28#380—41no—
29C4×C22⋊C4—41no—
30C43C2×C411yescharacteristic
31#355—41no—
32#355—41no—
33#354—41no—
34#354—41no—
35#343—41no—
36#342—41no—
37#336—41no—
38Q8⋊C8—42no—
39D4⋊C8—42no—
40C22×Q8C22⋊C411yescharacteristic
41C22×D4C22⋊C411yescharacteristic
42C23×C4—21no—
43C2×M16—42no—
44C22×C8—41no—
45C22×C8—41no—
46#124—41no—
47#124D811yescharacteristic
48#124SD1611yescharacteristic
49#124SD1611yescharacteristic
50#124Q1611yescharacteristic
51C4×Q8—41no—
52C4×Q8—41no—
53C4×D4—41no—
54C4×D4—41no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4—81no—
57C2×C4⋊C4C4⋊C411yescharacteristic
58C2×C4⋊C4C4⋊C411yescharacteristic
59C2×C22⋊C4—21no—
60C2×C22⋊C4—41no—
61C2×C22⋊C4—41no—
62C2×C22⋊C4—42no—
63C2×C42—21no—
64C2×C42—21no—
65C2×C42—21no—
66C2×C42C4211yescharacteristic
67C2×C42C22⋊C411yescharacteristic
68C2×C42C4⋊C411yescharacteristic
69C4⋊C8—41no—
70C4⋊C8—41no—
71C4⋊C8—81no—
72C4⋊C8—81no—
73#101—42no—
74#101—42no—
75#99—42no—
76#99—42no—
77C4×C8—22no—
78C4×C8—41no—
79C4×C8—44no—
80#95—41no—
81#95—41no—
82#95—81no—
83C24—21no—
84C2×Q8—21no—
85C2×Q8—41no—
86C2×Q8—41no—
87C2×Q8#10211yescharacteristic
88C2×Q8#10311yescharacteristic
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92C2×D4#10211yescharacteristic
93C2×D4#10311yescharacteristic
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—41no—
100C22×C4—41no—
101C22×C4—82no—
102C22×C4—82no—
103C22×C4#9511yescharacteristic
104C22×C4#9911yescharacteristic
105C22×C4#9911yescharacteristic
106M16—82no—
107M16—82no—
108C2×C8—42no—
109C2×C8—44no—
110C2×C8—82no—
111C2×C8—82no—
112C2×C8—81no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—81no—
116C4⋊C4—162no—
117C22⋊C4—41no—
118C22⋊C4—41no—
119C22⋊C4—41no—
120C22⋊C4—41no—
121C22⋊C4—81no—
122C22⋊C4—82no—
123C22⋊C4—82no—
124C22⋊C4—82no—
125C42—21no—
126C42—21no—
127C42—21no—
128C42—41no—
129C42—42no—
130C42—42no—
131C42—41no—
132C42—41no—
133C42#10611yescharacteristic
134C42#10711yescharacteristic
135C23—21no—
136C23—21no—
137C23—41no—
138C23—41no—
139C23—81no—
140C23—81no—
141C23#34211yescharacteristic
142Q8—41no—
143Q8—41no—
144Q8—81no—
145D4—41no—
146D4—41no—
147D4—81no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—82no—
167C2×C4—81no—
168C2×C4—81no—
169C2×C4—161no—
170C2×C4—162no—
171C2×C4—162no—
172C2×C4—162no—
173C2×C4H(3,ℤ/4)11yescharacteristic
174C2×C4#34011yescharacteristic
175C2×C4#35311yescharacteristic
176C2×C4#35411yescharacteristic
177C8—44no—
178C8—161no—
179C8—162no—
180C22—21no—
181C22—21no—
182C22—41no—
183C22—41no—
184C22—81no—
185C22—81no—
186C22—81no—
187C22—81no—
188C22—161no—
189C22#128911yescharacteristic
190C22#139111yescharacteristic
191C22#139311yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—41no—
196C4—41no—
197C4—42no—
198C4—41no—
199C4—41no—
200C4—41no—
201C4—81no—
202C4—81no—
203C4—322no—
204C4#141412yes—
205C2—21no—
206C2—21no—
207C2—81no—
208C2—81no—
209C2#723711yescharacteristic
210C2#749711yescharacteristic
211C2#750211yescharacteristic
subgroupG/H
center, socleC22#1393
commutatorC2×C42C42
Frattini, cosocleC4×#124C22
prime radicalC22×D4C22⋊C4
LCSG ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×#124 ◁ G
LECSG ▷ C4×#124 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
7. #1831C4semidirect
10. C42×C8C4semidirect
13. #1394C4semidirect

Maximal subgroups

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

subgroupindex
#128012
#127982
#96392