Finite Group Databasebeta

← #13228

Subgroups — #13228

Order 256.

245 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 245 conjugacy classes of subgroups — too many to draw. Only its 61 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#2545C211yesmaximal, characteristic
2C2×#356C212yesmaximal, complemented
3C2×#355C212yesmaximal
4#1801C211yesmaximal, characteristic, complemented
5C4×#101C211yesmaximal, characteristic, complemented
6C2×C4⋊Q8C2211yescharacteristic
7C2×#124C411yescharacteristic
8C2×#124C2211yescharacteristic
9C2×C4×Q8C2211yescharacteristic
10#423—21no—
11C2×#101C2212yes—
12C2×#101C2212yes—
13C4×M16—21no—
14#396—21no—
15#396—21no—
16#391C411yescharacteristic
17#390C411yescharacteristic
18#388—21no—
19#388—21no—
20C4×C4⋊C4C411yescharacteristic
21#356—24no—
22#355—24no—
23#343—21no—
24#343—21no—
25C22×Q8C2×C411yescharacteristic
26C22×Q8C2311yescharacteristic
27C22×D4C2×C411yescharacteristic
28C2×M16—22no—
29C2×M16—22no—
30C4⋊Q8—22no—
31C4⋊Q8—22no—
32#124—22no—
33#124—22no—
34#124—41no—
35#124—41no—
36C4×Q8—41no—
37C4×Q8—41no—
38C2×C4⋊C4—21no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4C2×C411yescharacteristic
42C2×C4⋊C4D411yescharacteristic
43C2×C4⋊C4D411yescharacteristic
44C2×C22⋊C4—21no—
45C2×C22⋊C4—21no—
46C2×C22⋊C4—21no—
47C2×C22⋊C4—21no—
48C2×C22⋊C4—21no—
49C2×C22⋊C4—21no—
50C2×C42C2×C411yescharacteristic
51C2×C42C2×C411yescharacteristic
52C2×C42C2×C411yescharacteristic
53C2×C42D411yescharacteristic
54C2×C42D411yescharacteristic
55C4⋊C8—41no—
56C4⋊C8—41no—
57#101—22no—
58#101—22no—
59#101—22no—
60#101D414yes—
61#97—41no—
62C4×C8—41no—
63#95—21no—
64#95—21no—
65#95—21no—
66C24—21no—
67C2×Q8—22no—
68C2×Q8—41no—
69C2×Q8—41no—
70C2×Q8—41no—
71C2×Q8—41no—
72C2×Q8C2×D412yes—
73C2×Q8#4112yes—
74C2×D4—22no—
75C2×D4—41no—
76C2×D4—41no—
77C22×C4—21no—
78C22×C4—21no—
79C22×C4—21no—
80C22×C4C22⋊C411yescharacteristic
81C22×C4C22⋊C411yescharacteristic
82C22×C4C22⋊C411yescharacteristic
83C22×C4C22⋊C411yescharacteristic
84C22×C4C22×C411yescharacteristic
85C22×C4C2×D411yescharacteristic
86C22×C4C2×D411yescharacteristic
87M16—24no—
88M16—42no—
89M16—42no—
90M16—42no—
91C2×C8—42no—
92C2×C8—42no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—42no—
97C4⋊C4—42no—
98C4⋊C4—41no—
99C4⋊C4—41no—
100C22⋊C4—42no—
101C22⋊C4—42no—
102C22⋊C4—42no—
103C22⋊C4—41no—
104C22⋊C4—41no—
105C22⋊C4—42no—
106C22⋊C4—41no—
107C22⋊C4—41no—
108C42—21no—
109C42—21no—
110C42—21no—
111C42—21no—
112C42—21no—
113C42—21no—
114C42—22no—
115C42—22no—
116C23—41no—
117C23—41no—
118C23—41no—
119C23—41no—
120C23—41no—
121C23—41no—
122C23—41no—
123C23C2×C22⋊C411yescharacteristic
124Q8—42no—
125Q8—42no—
126Q8—82no—
127D4—82no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—21no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—22no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4#9911yescharacteristic
151C2×C4#9911yescharacteristic
152C2×C4C4×D412yes—
153C2×C4#12112yes—
154C2×C4#12411yescharacteristic
155C2×C4#12711yescharacteristic
156C8—44no—
157C8—82no—
158C22—21no—
159C22—21no—
160C22—81no—
161C22—81no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22—81no—
167C22#39011yescharacteristic
168C22C2×#9911yescharacteristic
169C22#41011yescharacteristic
170C4—21no—
171C4—21no—
172C4—22no—
173C4—21no—
174C4—22no—
175C4—21no—
176C4—42no—
177C4—41no—
178C4—41no—
179C4—41no—
180C4—81no—
181C4—81no—
182C2—21no—
183C2—21no—
184C2—161no—
185C2#196411yescharacteristic
186C2#213211yescharacteristic
187C2#213311yescharacteristic
subgroupG/H
center, socleC22C2×#99
commutatorC22×C4C22×C4
Frattini, cosocleC22×Q8C23
prime radicalC22×D4C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ G
LECSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. C2×#356C2semidirect
4. #1801C2semidirect
5. C4×#101C2semidirect

Maximal subgroups

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

subgroupindex
#25452
C2×#3562
C2×#3552
#18012
C4×#1012