Finite Group Databasebeta

← #8986

Subgroups — #8986

Order 256.

266 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 85 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×#462C211yesmaximal, characteristic
2#2355C211yesmaximal, characteristic
3#1990C211yesmaximal, characteristic
4#1988C211yesmaximal, characteristic
5C2×Q8⋊C8C211yesmaximal, characteristic
6#1296C211yesmaximal, characteristic
7#1279C211yesmaximal, characteristic
8C22×Q16—21no—
9C2×C4⋊Q8C2211yescharacteristic
10C2×C4×Q8C2211yescharacteristic
11#462—22no—
12#462C414yescomplemented
13C2×C4⋊C8C2211yescharacteristic
14C2×C4⋊C8C2211yescharacteristic
15C2×#103—21no—
16C2×C4×C8C2211yescharacteristic
17#391—21no—
18#387—22no—
19#384C2211yescharacteristic
20#382—21no—
21C4×C4⋊C4—21no—
22C4×C4⋊C4—21no—
23C4×C4⋊C4C2211yescharacteristic
24#340—21no—
25#340—21no—
26#340—22no—
27Q8⋊C8—22no—
28C22×Q8—21no—
29C22×Q8D411yescharacteristic
30C2×Q16—24no—
31C2×Q16—42no—
32C2×Q16—42no—
33C22×C8—21no—
34C22×C8—21no—
35C22×C8—21no—
36C4⋊Q8—21no—
37C4⋊Q8—21no—
38C4⋊Q8—21no—
39C4⋊Q8C2×C412yes—
40C4×Q8—21no—
41C4×Q8—21no—
42C4×Q8C2×C412yes—
43C4×Q8D412yes—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4—21no—
49C2×C4⋊C4D411yescharacteristic
50C2×C4⋊C4D411yescharacteristic
51C2×C4⋊C4D411yescharacteristic
52C2×C4⋊C4D412yes—
53C2×C42—21no—
54C2×C42—21no—
55C2×C42—22no—
56C2×C42C2311yescharacteristic
57C4⋊C8—21no—
58C4⋊C8—21no—
59C4⋊C8—21no—
60C4⋊C8C2×C412yes—
61#103—24no—
62C4×C8—21no—
63C4×C8—21no—
64#95—22no—
65#95—22no—
66#95—22no—
67#95—21no—
68C2×Q8—21no—
69C2×Q8—22no—
70C2×Q8—21no—
71C2×Q8—21no—
72C2×Q8—21no—
73C2×Q8—21no—
74C2×Q8—41no—
75C2×Q8—41no—
76C2×Q8—41no—
77C2×Q8—41no—
78C2×Q8—41no—
79C2×Q8C22⋊C412yes—
80C22×C4—21no—
81C22×C4—21no—
82C22×C4—21no—
83C22×C4—21no—
84C22×C4—22no—
85C22×C4—41no—
86C22×C4C2×D411yescharacteristic
87C22×C4C2×D411yescharacteristic
88C22×C4C2×D411yescharacteristic
89Q16—48no—
90C2×C8—22no—
91C2×C8—22no—
92C2×C8—41no—
93C2×C8—41no—
94C2×C8—41no—
95C2×C8—41no—
96C2×C8—41no—
97C2×C8—41no—
98C2×C8—41no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—21no—
102C4⋊C4—21no—
103C4⋊C4—22no—
104C4⋊C4—22no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—42no—
108C4⋊C4—41no—
109C4⋊C4—41no—
110C4⋊C4—41no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4C22⋊C412yes—
115C4⋊C4Q1612yescomplemented
116C42—22no—
117C42—22no—
118C42—41no—
119C42—41no—
120C42—82no—
121C42C22×C411yescharacteristic
122C42C2×D411yescharacteristic
123C42#4111yescharacteristic
124C42#4111yescharacteristic
125C23#12011yescharacteristic
126Q8—22no—
127Q8—22no—
128Q8—41no—
129Q8—41no—
130Q8—42no—
131Q8—42no—
132Q8—81no—
133Q8—81no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—41no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—42no—
151C2×C4—41no—
152C2×C4—81no—
153C2×C4—81no—
154C2×C4C2×C22⋊C411yescharacteristic
155C2×C4C4×D411yescharacteristic
156C2×C4C4×D411yescharacteristic
157C2×C4#12111yescharacteristic
158C2×C4#12111yescharacteristic
159C2×C4#12311yescharacteristic
160C2×C4C2×Q1611yescharacteristic
161C2×C4#13511yescharacteristic
162C2×C4#13511yescharacteristic
163C2×C4#13511yescharacteristic
164C2×C4AGL(1,ℤ/8)11yescharacteristic
165C2×C4AGL(1,ℤ/8)11yescharacteristic
166C2×C4#13711yescharacteristic
167C2×C4#13711yescharacteristic
168C8—42no—
169C8—42no—
170C8—81no—
171C22#38611yescharacteristic
172C22#44911yescharacteristic
173C22#44911yescharacteristic
174C22#45111yescharacteristic
175C22#45211yescharacteristic
176C22#45511yescharacteristic
177C22#45611yescharacteristic
178C4—21no—
179C4—21no—
180C4—42no—
181C4—42no—
182C4—42no—
183C4—82no—
184C4—82no—
185C4—81no—
186C4#41611yescharacteristic
187C4#41811yescharacteristic
188C4C4×Q1611yescharacteristic
189C4#44111yescharacteristic
190C4#46211yescharacteristic
191C4#46411yescharacteristic
192C4#48211yescharacteristic
193C4#48211yescharacteristic
194C2#164011yescharacteristic
195C2#164411yescharacteristic
196C2#164811yescharacteristic
197C2#165211yescharacteristic
198C2#187511yescharacteristic
199C2#187811yescharacteristic
200C2#188211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#120
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
12. #462C4semidirect
115. C4⋊C4Q16semidirect

Maximal subgroups

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

subgroupindex
C2×#4622
#23552
#19902
#19882
C2×Q8⋊C82
#12962
#12792