Finite Group Databasebeta

← #10003

Subgroups — #10003

Order 256.

250 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 59 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#3104C211yesmaximal, characteristic
2#3078C211yesmaximal, characteristic
3#2581C211yesmaximal, characteristic
4#1518C211yesmaximal, characteristic
5#1487C211yesmaximal, characteristic
6#1479C211yesmaximal, characteristic
7#1286C211yesmaximal, characteristic
8#533C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10C2×C4×Q8C2211yescharacteristic
11#484—21no—
12#479—22no—
13#477—21no—
14#477—21no—
15#475—21no—
16#462—21no—
17#451—21no—
18C4×Q16—22no—
19#431C2211yescharacteristic
20#431C2211yescharacteristic
21#428—21no—
22#423C2211yescharacteristic
23#419—21no—
24#400—21no—
25#395—21no—
26#391—21no—
27#389—21no—
28#387—22no—
29#382C2211yescharacteristic
30#328—22no—
31Q8⋊C8—22no—
32Q8⋊C8—22no—
33C22×Q8D411yescharacteristic
34C22×Q8D411yescharacteristic
35C2×Q16—22no—
36C2×M16—21no—
37C4⋊Q8D411yescharacteristic
38C4⋊Q8D411yescharacteristic
39#125—21no—
40C22⋊Q8—21no—
41C22⋊Q8—21no—
42C4×Q8—21no—
43C4×Q8—21no—
44C4×Q8—21no—
45C4×Q8—21no—
46C4×Q8—21no—
47C4×Q8—21no—
48C4×Q8—21no—
49C4×Q8—21no—
50C4×Q8—21no—
51C4×Q8—21no—
52#117—21no—
53C2×C4⋊C4—22no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—21no—
56C2×C4⋊C4—21no—
57C2×C4⋊C4D411yescharacteristic
58C2×C4⋊C4D411yescharacteristic
59C2×C42—21no—
60C2×C42—21no—
61C2×C42C2311yescharacteristic
62#107—22no—
63#107—22no—
64#106—22no—
65C4⋊C8—21no—
66C4⋊C8—21no—
67C4⋊C8—21no—
68C4⋊C8D412yes—
69#103—22no—
70#103—22no—
71#103—22no—
72#103—22no—
73C22⋊C8—21no—
74C22⋊C8—21no—
75C4×C8—21no—
76C4×C8D412yes—
77#95—22no—
78#95—22no—
79#95—22no—
80#95—21no—
81#95D412yes—
82C2×Q8—21no—
83C2×Q8—21no—
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—21no—
88C2×Q8—21no—
89C2×Q8—21no—
90C2×Q8—21no—
91C2×Q8—42no—
92C2×Q8Q1612yescomplemented
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—22no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C2×D411yescharacteristic
99C22×C4C2×D411yescharacteristic
100C22×C4C2×D411yescharacteristic
101Q16—44no—
102M16—41no—
103M16—41no—
104C2×C8—22no—
105C2×C8—22no—
106C2×C8—41no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—44no—
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—41no—
121C4⋊C4—41no—
122C4⋊C4—41no—
123C4⋊C4—41no—
124C22⋊C4—41no—
125C42—41no—
126C42—41no—
127C42—41no—
128C42—41no—
129C42—41no—
130C42C2×D411yescharacteristic
131C42C2×D411yescharacteristic
132C42C2×D411yescharacteristic
133C42#4111yescharacteristic
134C23#12011yescharacteristic
135Q8—22no—
136Q8—22no—
137Q8—22no—
138Q8—22no—
139Q8—41no—
140Q8—41no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—81no—
145C2×C4—22no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—42no—
154C2×C4—42no—
155C2×C4—42no—
156C2×C4—42no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4#12011yescharacteristic
163C2×C4#12011yescharacteristic
164C2×C4#12111yescharacteristic
165C2×C4#12111yescharacteristic
166C2×C4#12111yescharacteristic
167C2×C4#12711yescharacteristic
168C2×C4C2×Q1611yescharacteristic
169C2×C4#13511yescharacteristic
170C2×C4#13711yescharacteristic
171C2×C4#13711yescharacteristic
172C8—42no—
173C8—42no—
174C8—81no—
175C22—21no—
176C22—21no—
177C22#39211yescharacteristic
178C22#45111yescharacteristic
179C22#45211yescharacteristic
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—42no—
185C4—42no—
186C4—82no—
187C4—81no—
188C4—81no—
189C4—81no—
190C4—81no—
191C4#45111yescharacteristic
192C4#45211yescharacteristic
193C4#46711yescharacteristic
194C4#47011yescharacteristic
195C2—21no—
196C2—21no—
197C2#200111yescharacteristic
198C2#200911yescharacteristic
199C2#201011yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC2×C42C23
prime radicalC23#120
LCSG ▷ C2×C42 ▷ 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
92. C2×Q8Q16semidirect

Maximal subgroups

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

subgroupindex
#31042
#30782
#25812
#15182
#14872
#14792
#12862