Finite Group Databasebeta

← #8374

Subgroups — #8374

Order 256.

356 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 79 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
1C2×#557C211yesmaximal, characteristic
2C4×#101C211yesmaximal, characteristic
3#1528C212yesmaximal
4#1491C212yesmaximal
5#1467C211yesmaximal, characteristic
6#557—24no—
7#557—24no—
8C2×C4⋊Q8—21no—
9C2×C4⋊Q8C411yescharacteristic
10C2×#125—21no—
11C2×#125—21no—
12C2×#125C411yescharacteristic
13C2×#125C2211yescharacteristic
14C2×C4×Q8—21no—
15C2×C4×Q8C411yescharacteristic
16C2×C4×Q8C411yescharacteristic
17C2×C4×Q8C2211yescharacteristic
18C2×C4×Q8C2211yescharacteristic
19#432C2212yes—
20C2×#101—21no—
21C4×M16C2212yes—
22#343—21no—
23#330—24no—
24Q8⋊C8—24no—
25#324—21no—
26#324—21no—
27C22×Q8—21no—
28C22×Q8C2×C411yescharacteristic
29C22×Q8D411yescharacteristic
30C2×M16—22no—
31C4⋊Q8—28no—
32C4⋊Q8—22no—
33C4⋊Q8—22no—
34#125—28no—
35#125—28no—
36#125—22no—
37#125—22no—
38#125—22no—
39#125D414yes—
40C4×Q8—28no—
41C4×Q8—22no—
42C4×Q8—22no—
43C4×Q8—22no—
44C4×Q8—22no—
45C4×Q8—22no—
46C4×Q8—22no—
47C4×Q8—22no—
48C4×Q8D414yes—
49C2×C4⋊C4—21no—
50C2×C4⋊C4—21no—
51C2×C4⋊C4—21no—
52C2×C4⋊C4—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4—21no—
57C2×C4⋊C4C2×C411yescharacteristic
58C2×C4⋊C4C2×C411yescharacteristic
59C2×C4⋊C4C2×C411yescharacteristic
60C2×C4⋊C4D411yescharacteristic
61C2×C4⋊C4D411yescharacteristic
62C2×C4⋊C4D411yescharacteristic
63C2×C42—21no—
64C2×C42—21no—
65C2×C42—21no—
66C2×C42C2×C411yescharacteristic
67C2×C42C2×C411yescharacteristic
68C2×C42C2311yescharacteristic
69C4⋊C8—22no—
70#101—24no—
71C22⋊C8—22no—
72#97—22no—
73#97—22no—
74C4×C8—22no—
75C2×Q8—24no—
76C2×Q8—24no—
77C2×Q8—22no—
78C2×Q8—21no—
79C2×Q8—22no—
80C2×Q8—41no—
81C2×Q8—42no—
82C2×Q8—42no—
83C2×Q8C22⋊C412yes—
84C22×C4—21no—
85C22×C4—21no—
86C22×C4—21no—
87C22×C4—21no—
88C22×C4C22⋊C411yescharacteristic
89C22×C4C22⋊C411yescharacteristic
90C22×C4C22⋊C411yescharacteristic
91C22×C4C22⋊C411yescharacteristic
92C22×C4C22×C411yescharacteristic
93C22×C4C2×D411yescharacteristic
94C22×C4C2×D411yescharacteristic
95M16—24no—
96M16—42no—
97C2×C8—42no—
98C2×C8—42no—
99C4⋊C4—24no—
100C4⋊C4—24no—
101C4⋊C4—24no—
102C4⋊C4—24no—
103C4⋊C4—24no—
104C4⋊C4—21no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—24no—
108C4⋊C4—24no—
109C4⋊C4—24no—
110C4⋊C4—22no—
111C4⋊C4—22no—
112C4⋊C4—22no—
113C4⋊C4C22⋊C412yes—
114C4⋊C4C22⋊C412yes—
115C4⋊C4C22⋊C412yes—
116C42—24no—
117C42—24no—
118C42—21no—
119C42—21no—
120C42—21no—
121C42—21no—
122C42—24no—
123C42C2×D412yes—
124C42C2×D412yes—
125C23C2×C22⋊C411yescharacteristic
126Q8—24no—
127Q8—22no—
128Q8—44no—
129Q8—48no—
130Q8#10114yescomplemented
131C2×C4—24no—
132C2×C4—22no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—22no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—22no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4#10412yes—
155C2×C4C2×C22⋊C411yescharacteristic
156C2×C4C2×C22⋊C411yescharacteristic
157C2×C4#12012yes—
158C2×C4#12012yes—
159C8—44no—
160C8—82no—
161C22—21no—
162C22—21no—
163C22#37911yescharacteristic
164C22C2×#10411yescharacteristic
165C22#42111yescharacteristic
166C4—22no—
167C4—24no—
168C4—21no—
169C4—22no—
170C4—22no—
171C4—41no—
172C4—41no—
173C4—42no—
174C4—41no—
175C4—42no—
176C4—42no—
177C4C2×#10112yes—
178C2—21no—
179C2—21no—
180C2#178411yescharacteristic
181C2#178911yescharacteristic
182C2#179611yescharacteristic
subgroupG/H
center, socleC22#379
commutatorC22×C4C22×C4
Frattini, cosocleC2×C42C23
prime radicalC23C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
130. Q8#101semidirect

Maximal subgroups

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

subgroupindex
C2×#5572
C4×#1012
#15282
#14912
#14672