Finite Group Databasebeta

← #94145

Subgroups — #94145

Order 512.

248 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 56 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
1C4×#356C211yesmaximal, characteristic
2#8958C211yesmaximal, characteristic
3#7571C211yesmaximal, characteristic
4#2982C411yescharacteristic
5C4×C4⋊Q8C2211yescharacteristic
6C2×#356C412yes—
7C4×C4⋊C8—21no—
8C4×#101—21no—
9#1479—21no—
10#1461C411yescharacteristic
11#1394—21no—
12#1276—21no—
13#1272—21no—
14#1272C412yes—
15C2×C4⋊Q8C2×C411yescharacteristic
16C2×C4×Q8C2×C411yescharacteristic
17C2×C4×Q8D411yescharacteristic
18C8×Q8—42no—
19#431—21no—
20#431—21no—
21#431—41no—
22C2×C4⋊C8—41no—
23C2×#101—22no—
24C4×M16—41no—
25C2×C4×C8—41no—
26#391C2×C411yescharacteristic
27#391D411yescharacteristic
28#389—41no—
29#384Q811yescharacteristic
30C4×C4⋊C4—41no—
31C43D411yescharacteristic
32#356—22no—
33#356C814yescomplemented
34#343—41no—
35#336—22no—
36Q8⋊C8—42no—
37#324—41no—
38C22×Q8C4211yescharacteristic
39C22×Q8C22⋊C411yescharacteristic
40C2×M16—42no—
41C22×C8—42no—
42C4⋊Q8—41no—
43C4⋊Q8C2×C812yes—
44C4⋊Q8M1612yes—
45C4×Q8—41no—
46C4×Q8—41no—
47C4×Q8—41no—
48C4×Q8—41no—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—41no—
52C2×C4⋊C4—41no—
53C2×C4⋊C4C4⋊C411yescharacteristic
54C2×C4⋊C4C4⋊C411yescharacteristic
55C2×C42—21no—
56C2×C42—21no—
57C2×C42—21no—
58C2×C42—21no—
59C2×C42C22⋊C411yescharacteristic
60C2×C42C22⋊C411yescharacteristic
61C2×C42C4⋊C411yescharacteristic
62C4⋊C8—22no—
63C4⋊C8—41no—
64C4⋊C8—42no—
65C4⋊C8—44no—
66#101—24no—
67#101—42no—
68C22⋊C8—41no—
69C22⋊C8—41no—
70#97—81no—
71C4×C8—41no—
72C4×C8—41no—
73C4×C8—42no—
74C4×C8—82no—
75C4×C8—81no—
76#95—41no—
77#95—41no—
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—41no—
81C2×Q8—41no—
82C2×Q8—41no—
83C2×Q8—41no—
84C2×Q8C4×C811yescharacteristic
85C2×Q8#9711yescharacteristic
86C2×Q8C22⋊C812yes—
87C22×C4—21no—
88C22×C4—21no—
89C22×C4—21no—
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4#9511yescharacteristic
94C22×C4#9911yescharacteristic
95C22×C4#9911yescharacteristic
96M16—44no—
97M16—82no—
98C2×C8—44no—
99C2×C8—42no—
100C2×C8—82no—
101C2×C8—82no—
102C2×C8—82no—
103C2×C8—81no—
104C4⋊C4—42no—
105C4⋊C4—42no—
106C4⋊C4—41no—
107C4⋊C4—41no—
108C4⋊C4—42no—
109C4⋊C4—81no—
110C4⋊C4—82no—
111C42—22no—
112C42—22no—
113C42—21no—
114C42—21no—
115C42—21no—
116C42—41no—
117C42—42no—
118C42—41no—
119C42—41no—
120C42—41no—
121C42—41no—
122C42C4⋊C812yes—
123C23#34211yescharacteristic
124Q8—41no—
125Q8—41no—
126Q8—42no—
127Q8—42no—
128Q8—81no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—81no—
151C2×C4—81no—
152C2×C4#33611yescharacteristic
153C2×C4#34411yescharacteristic
154C2×C4AΣL(1,𝔽16)11yescharacteristic
155C2×C4#35211yescharacteristic
156C8—84no—
157C8—84no—
158C8—82no—
159C8—161no—
160C22—21no—
161C22—21no—
162C22#128211yescharacteristic
163C22#139011yescharacteristic
164C22#139111yescharacteristic
165C4—24no—
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—42no—
172C4—41no—
173C4—41no—
174C4—41no—
175C4—81no—
176C4—81no—
177C4#140512yes—
178C2—21no—
179C2—21no—
180C2#720411yescharacteristic
181C2#749111yescharacteristic
182C2#749211yescharacteristic
subgroupG/H
centerC2×C4AΣL(1,𝔽16)
commutatorC2×Q8C4×C8
Frattini, cosocleC4×C4⋊Q8C22
socleC22#1390
prime radicalC23#342
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C4×C4⋊Q8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
33. #356C8semidirect

Maximal subgroups

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

subgroupindex
C4×#3562
#89582
#75712