Finite Group Databasebeta

← #10182

Subgroups — #10182

Order 256.

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

normal subgroups only

This group has 254 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#3209C211yesmaximal, characteristic, complemented
2#3077C211yesmaximal, characteristic
3C2×#476C211yesmaximal, characteristic
4#1549C211yesmaximal, characteristic, complemented
5#1481C211yesmaximal, characteristic, complemented
6#1460C211yesmaximal, characteristic
7#1301C211yesmaximal, characteristic, complemented
8#533C2211yescharacteristic
9C2×C4⋊Q8C2211yescharacteristic
10C2×C4×D4C2211yescharacteristic
11#494—21no—
12#487—21no—
13#478—22no—
14#476—21no—
15#476—22no—
16#476—22no—
17#474—21no—
18#462—22no—
19#451—22no—
20#431C2211yescharacteristic
21#431C2211yescharacteristic
22#428—21no—
23C2×#106—21no—
24#423C2211yescharacteristic
25C2×C4⋊C8C2211yescharacteristic
26#418—21no—
27C2×#102—21no—
28#332—22no—
29Q8⋊C8—22no—
30#323—22no—
31C22×Q8—21no—
32C22×D4D411yescharacteristic
33C23×C4—21no—
34C2×Q16—24no—
35C2×M16—21no—
36C22×C8—21no—
37C4⋊Q8—21no—
38C4⋊Q8—21no—
39C4⋊Q8—21no—
40C4⋊Q8D412yes—
41C4⋊Q8D411yescharacteristic
42C4⋊Q8D411yescharacteristic
43#125—21no—
44C22⋊Q8—21no—
45C22⋊Q8—21no—
46C4×Q8—21no—
47C4×Q8—21no—
48C4×D4—21no—
49C4×D4—21no—
50C4×D4—21no—
51C4×D4—21no—
52#117—21no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4D411yescharacteristic
56C2×C22⋊C4—21no—
57C2×C42C2311yescharacteristic
58#107—22no—
59#106—24no—
60#106—22no—
61C4⋊C8—21no—
62C4⋊C8—21no—
63C4⋊C8—21no—
64C4⋊C8—21no—
65C4⋊C8D412yes—
66C4⋊C8D412yes—
67#103—24no—
68#102—24no—
69#102—22no—
70#102—22no—
71C22⋊C8—21no—
72C22⋊C8D412yes—
73C4×C8—21no—
74C4×C8—21no—
75C24—21no—
76C2×Q8—22no—
77C2×Q8—21no—
78C2×Q8—21no—
79C2×Q8—41no—
80C2×Q8—82no—
81C2×D4—21no—
82C2×D4—21no—
83C2×D4—21no—
84C2×D4—21no—
85C2×D4—21no—
86C2×D4Q1612yescomplemented
87C22×C4—21no—
88C22×C4—41no—
89C22×C4—41no—
90C22×C4—41no—
91C22×C4—82no—
92C22×C4C2×D411yescharacteristic
93C22×C4C2×D411yescharacteristic
94C22×C4#4111yescharacteristic
95Q16—84no—
96M16—41no—
97M16—41no—
98C2×C8—22no—
99C2×C8—22no—
100C2×C8—22no—
101C2×C8—41no—
102C2×C8—41no—
103C2×C8—41no—
104C4⋊C4—22no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—21no—
110C4⋊C4—22no—
111C4⋊C4—21no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C22⋊C4—41no—
117C22⋊C4—41no—
118C22⋊C4—41no—
119C42—41no—
120C42C2×D411yescharacteristic
121C42C2×D411yescharacteristic
122C42C2×D411yescharacteristic
123C42C2×D411yescharacteristic
124C23—22no—
125C23—41no—
126C23—41no—
127C23—81no—
128C23—81no—
129C23#12111yescharacteristic
130Q8—42no—
131Q8—44no—
132Q8—42no—
133Q8—82no—
134D4—22no—
135D4—22no—
136D4—41no—
137D4—41no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—82no—
145C2×C4—82no—
146C2×C4—82no—
147C2×C4—81no—
148C2×C4#12011yescharacteristic
149C2×C4#12011yescharacteristic
150C2×C4#12011yescharacteristic
151C2×C4#12111yescharacteristic
152C2×C4#12111yescharacteristic
153C2×C4#12711yescharacteristic
154C2×C4C2×Q1611yescharacteristic
155C2×C4#13511yescharacteristic
156C2×C4#13711yescharacteristic
157C2×C4#13711yescharacteristic
158C8—42no—
159C8—42no—
160C8—42no—
161C8—81no—
162C22—21no—
163C22—21no—
164C22—42no—
165C22—82no—
166C22—82no—
167C22—81no—
168C22—81no—
169C22#39211yescharacteristic
170C22#46711yescharacteristic
171C22#47011yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—82no—
176C4—81no—
177C4—81no—
178C4—81no—
179C4#45111yescharacteristic
180C4#45111yescharacteristic
181C4#45211yescharacteristic
182C4#45211yescharacteristic
183C4#47112yes—
184C2—21no—
185C2—21no—
186C2—82no—
187C2#200111yescharacteristic
188C2#200811yescharacteristic
189C2#201911yescharacteristic
subgroupG/H
center, socleC22#392
commutator, Frattini, cosocleC2×C42C23
prime radicalC22×D4D4
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
1. #3209C2semidirect
4. #1549C2semidirect
5. #1481C2semidirect
7. #1301C2semidirect
86. C2×D4Q16semidirect

Maximal subgroups

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

subgroupindex
#32092
#30772
C2×#4762
#15492
#14812
#14602
#13012