Finite Group Databasebeta

← #8994

Subgroups — #8994

Order 256.

215 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 215 conjugacy classes of subgroups — too many to draw. Only its 69 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#3076C211yesmaximal, characteristic
2#2925C211yesmaximal, characteristic
3#1493C211yesmaximal, characteristic, complemented
4#1481C211yesmaximal, characteristic, complemented
5#1476C211yesmaximal, characteristic
6#1301C211yesmaximal, characteristic, complemented
7#1277C211yesmaximal, characteristic, complemented
8#533C2211yescharacteristic
9C4×#41C2211yescharacteristic
10#479—21no—
11#478—21no—
12#477C411yescharacteristic
13#476C411yescharacteristic
14#475C411yescharacteristic
15#474C411yescharacteristic
16#433—22no—
17#432—21no—
18#431—21no—
19#431C2211yescharacteristic
20#427—21no—
21#423C2211yescharacteristic
22C2×C4⋊C8C2211yescharacteristic
23C2×C4⋊C8C2211yescharacteristic
24#416—21no—
25#408—21no—
26#405—21no—
27C2×C4×C8C2211yescharacteristic
28Q8⋊C8—21no—
29Q8⋊C8—21no—
30Q8⋊C8—21no—
31Q8⋊C8—22no—
32D4⋊C8—21no—
33C2×#41D411yescharacteristic
34C2×M16—21no—
35C22×C8—21no—
36C22×C8—21no—
37C22×C8—21no—
38C4⋊Q8C2×C411yescharacteristic
39C4⋊Q8C2×C411yescharacteristic
40#125—21no—
41C22⋊Q8—21no—
42C22⋊Q8—21no—
43C4×Q8—21no—
44C4×Q8—21no—
45C4×Q8C2×C411yescharacteristic
46C4×Q8D411yescharacteristic
47C4×D4—21no—
48C4×D4—21no—
49C4×D4C2×C411yescharacteristic
50C4×D4D411yescharacteristic
51#117—21no—
52#117—21no—
53#117D411yescharacteristic
54C2×C42—21no—
55C2×C42C2311yescharacteristic
56#107—21no—
57#107—21no—
58#106—21no—
59#106—21no—
60C4⋊C8—21no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8C2×C411yescharacteristic
65C4⋊C8C2×C411yescharacteristic
66C4⋊C8D411yescharacteristic
67C4⋊C8D411yescharacteristic
68C4⋊C8D412yes—
69#103—21no—
70#103—21no—
71#102—21no—
72#102—21no—
73C22⋊C8—22no—
74C22⋊C8—22no—
75C22⋊C8—21no—
76#97—22no—
77C4×C8—22no—
78C4×C8—21no—
79C4×C8—21no—
80C4×C8—21no—
81#41—21no—
82#41—21no—
83#41—21no—
84#41—21no—
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8C22⋊C411yescharacteristic
88C2×D4—21no—
89C2×D4C22⋊C411yescharacteristic
90C22×C4—21no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4C2×D411yescharacteristic
94C22×C4#4111yescharacteristic
95C22×C4#4111yescharacteristic
96M16—41no—
97M16—41no—
98C2×C8—22no—
99C2×C8—21no—
100C2×C8—21no—
101C2×C8—21no—
102C2×C8—22no—
103C2×C8—21no—
104C2×C8—41no—
105C2×C8—41no—
106C2×C8—41no—
107C2×C8—41no—
108C2×C8—41no—
109C2×C8—41no—
110C2×C8—41no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—21no—
115C4⋊C4—21no—
116C4⋊C4—21no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C4⋊C4C22⋊C411yescharacteristic
120C4⋊C4C22⋊C411yescharacteristic
121C22⋊C4—21no—
122C22⋊C4—21no—
123C22⋊C4—21no—
124C22⋊C4—41no—
125C42—21no—
126C42—21no—
127C42—21no—
128C42—41no—
129C42C22×C411yescharacteristic
130C42C2×D411yescharacteristic
131C42C2×D411yescharacteristic
132C42C2×D411yescharacteristic
133C23—21no—
134C23#12311yescharacteristic
135Q8—21no—
136Q8—21no—
137Q8—42no—
138Q8—41no—
139Q8—41no—
140D4—21no—
141D4—21no—
142D4—41no—
143D4—41no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4C2×C22⋊C411yescharacteristic
158C2×C4C4×D411yescharacteristic
159C2×C4C4×D411yescharacteristic
160C2×C4#12011yescharacteristic
161C2×C4#12111yescharacteristic
162C2×C4#12111yescharacteristic
163C2×C4#13511yescharacteristic
164C2×C4#13511yescharacteristic
165C2×C4#13711yescharacteristic
166C2×C4#13711yescharacteristic
167C8—42no—
168C8—41no—
169C8—41no—
170C8—41no—
171C8—41no—
172C8—42no—
173C8—81no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22#38611yescharacteristic
180C22#48511yescharacteristic
181C22#48511yescharacteristic
182C4—21no—
183C4—21no—
184C4—21no—
185C4—41no—
186C4—41no—
187C4—41no—
188C4—81no—
189C4—81no—
190C4#41611yescharacteristic
191C4#41911yescharacteristic
192C4#44311yescharacteristic
193C4#44411yescharacteristic
194C4#45211yescharacteristic
195C4#45211yescharacteristic
196C2—21no—
197C2—21no—
198C2—81no—
199C2#187311yescharacteristic
200C2#187611yescharacteristic
201C2#188111yescharacteristic
subgroupG/H
centerC2×C4#120
commutatorC42C22×C4
Frattini, cosocleC2×C42C23
socleC22#386
prime radicalC2×#41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #1493C2semidirect
4. #1481C2semidirect
6. #1301C2semidirect
7. #1277C2semidirect

Maximal subgroups

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

subgroupindex
#30762
#29252
#14932
#14812
#14762
#13012
#12772