Finite Group Databasebeta

← #10411

Subgroups — #10411

Order 256.

286 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 71 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#2548C211yesmaximal, characteristic
2#1957C211yesmaximal, characteristic
3#1947C211yesmaximal, characteristic, complemented
4#1803C211yesmaximal, characteristic, complemented
5C2×#331C211yesmaximal, characteristic
6C2×Q8⋊C8C211yesmaximal, characteristic, complemented
7#1279C211yesmaximal, characteristic, complemented
8C2×#127C2211yescharacteristic
9C2×#124—21no—
10C2×C4×Q8C2211yescharacteristic
11C2×#107—21no—
12C2×C4⋊C8C2211yescharacteristic
13C2×C4⋊C8C2211yescharacteristic
14C2×#103—21no—
15C2×#102—22no—
16C2×C4×C8C2211yescharacteristic
17#394—22no—
18#390—21no—
19#390—21no—
20#390—21no—
21#384C2211yescharacteristic
22C4×C4⋊C4C2211yescharacteristic
23#340—21no—
24#340—21no—
25#331—22no—
26Q8⋊C8—22no—
27C22×Q8D411yescharacteristic
28C22×D4—21no—
29C22×D4—21no—
30C22×D4D412yes—
31C22×C8—21no—
32C22×C8—21no—
33C22×C8—21no—
34#127—21no—
35#127—21no—
36#127—21no—
37#127—21no—
38#124—42no—
39#124—42no—
40C4×Q8—21no—
41C4×Q8—21no—
42C4×Q8—21no—
43C4×Q8—21no—
44C2×C4⋊C4—21no—
45C2×C4⋊C4—21no—
46C2×C4⋊C4—21no—
47C2×C4⋊C4—21no—
48C2×C4⋊C4D411yescharacteristic
49C2×C4⋊C4D411yescharacteristic
50C2×C4⋊C4D411yescharacteristic
51C2×C22⋊C4—22no—
52C2×C22⋊C4—22no—
53C2×C22⋊C4—22no—
54C2×C22⋊C4—22no—
55C2×C42—21no—
56C2×C42—21no—
57C2×C42C2311yescharacteristic
58#107—42no—
59C4⋊C8—21no—
60C4⋊C8—21no—
61C4⋊C8—21no—
62C4⋊C8D412yes—
63#103—42no—
64#102—44no—
65C4×C8—21no—
66C4×C8—21no—
67#95—21no—
68C24—22no—
69C2×Q8—21no—
70C2×Q8—21no—
71C2×Q8—21no—
72C2×Q8—21no—
73C2×Q8—21no—
74C2×Q8D812yes—
75C2×D4—22no—
76C2×D4—22no—
77C2×D4—42no—
78C2×D4—42no—
79C2×D4—41no—
80C2×D4—41no—
81C2×D4—41no—
82C2×D4—41no—
83C2×D4—41no—
84C2×D4—41no—
85C2×D4—41no—
86C2×D4—41no—
87C2×D4—41no—
88C2×D4—41no—
89C2×D4—41no—
90C2×D4—41no—
91C22×C4—21no—
92C22×C4—21no—
93C22×C4—21no—
94C22×C4—21no—
95C22×C4—41no—
96C22×C4C2×D411yescharacteristic
97C22×C4C2×D411yescharacteristic
98C22×C4C2×D411yescharacteristic
99C2×C8—22no—
100C2×C8—22no—
101C2×C8—41no—
102C2×C8—41no—
103C2×C8—41no—
104C2×C8—41no—
105C2×C8—41no—
106C2×C8—41no—
107C2×C8—41no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—21no—
111C4⋊C4—21no—
112C4⋊C4—21no—
113C4⋊C4—21no—
114C4⋊C4—42no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4—41no—
119C4⋊C4—41no—
120C4⋊C4—41no—
121C22⋊C4—44no—
122C22⋊C4—44no—
123C22⋊C4—82no—
124C22⋊C4—82no—
125C42—41no—
126C42—41no—
127C42—41no—
128C42—41no—
129C42C2×D411yescharacteristic
130C42#4111yescharacteristic
131C42#4111yescharacteristic
132C42#4111yescharacteristic
133C23—42no—
134C23—42no—
135C23—42no—
136C23—42no—
137C23—42no—
138C23—42no—
139C23—42no—
140C23#12011yescharacteristic
141Q8—22no—
142Q8—22no—
143Q8—41no—
144Q8—41no—
145D4—44no—
146D4—82no—
147D4—81no—
148D4—81no—
149D4—81no—
150D4—81no—
151D4—81no—
152D4—81no—
153D4—81no—
154D4—81no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4#12111yescharacteristic
173C2×C4#12111yescharacteristic
174C2×C4#12111yescharacteristic
175C2×C4#12311yescharacteristic
176C2×C4#12311yescharacteristic
177C2×C4#12411yescharacteristic
178C2×C4C2×D811yescharacteristic
179C2×C4#13511yescharacteristic
180C2×C4#13511yescharacteristic
181C2×C4#13511yescharacteristic
182C2×C4AGL(1,ℤ/8)11yescharacteristic
183C2×C4AGL(1,ℤ/8)11yescharacteristic
184C2×C4#13711yescharacteristic
185C2×C4#13711yescharacteristic
186C8—42no—
187C8—42no—
188C8—81no—
189C22—82no—
190C22—82no—
191C22—82no—
192C22—82no—
193C22—82no—
194C22—82no—
195C22—82no—
196C22#39411yescharacteristic
197C22#44711yescharacteristic
198C22#44911yescharacteristic
199C22#45211yescharacteristic
200C22#45211yescharacteristic
201C22#45311yescharacteristic
202C22#45511yescharacteristic
203C4—21no—
204C4—21no—
205C4—42no—
206C4—81no—
207C4—81no—
208C4—81no—
209C4—161no—
210C4#46311yescharacteristic
211C4#46411yescharacteristic
212C4#46611yescharacteristic
213C4#46811yescharacteristic
214C4#48011yescharacteristic
215C4#48211yescharacteristic
216C4#48811yescharacteristic
217C4#48911yescharacteristic
218C2—162no—
219C2#162111yescharacteristic
220C2#163011yescharacteristic
221C2#164011yescharacteristic
222C2#164111yescharacteristic
223C2#203311yescharacteristic
224C2#203711yescharacteristic
225C2#204211yescharacteristic
subgroupG/H
center, socleC23#120
commutator, Frattini, cosocleC2×C42C23
prime radicalC2×#127C22
LCSG ▷ C2×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
3. #1947C2semidirect
4. #1803C2semidirect
6. C2×Q8⋊C8C2semidirect
7. #1279C2semidirect

Maximal subgroups

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

subgroupindex
#25482
#19572
#19472
#18032
C2×#3312
C2×Q8⋊C82
#12792