Finite Group Databasebeta

← #10355

Subgroups — #10355

Order 256.

226 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 73 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#2552C211yesmaximal, characteristic
2#1987C211yesmaximal, characteristic
3#1987C211yesmaximal, characteristic
4#1956C211yesmaximal, characteristic
5#1296C211yesmaximal, characteristic
6#1279C211yesmaximal, characteristic
7#1279C211yesmaximal, characteristic
8C2×C4⋊Q8C2211yescharacteristic
9C2×#125—21no—
10C2×C4⋊C8C2211yescharacteristic
11C2×C4⋊C8C2211yescharacteristic
12C2×#103—22no—
13C2×C4×C8C2211yescharacteristic
14#398—22no—
15#389—21no—
16#389—21no—
17#384—21no—
18#384C2211yescharacteristic
19C4×C4⋊C4C2211yescharacteristic
20C4×C4⋊C4C2211yescharacteristic
21#340—21no—
22#340—21no—
23#340—21no—
24#340—21no—
25C22×Q8—21no—
26C22×C8—21no—
27C22×C8—21no—
28C22×C8—21no—
29C4⋊Q8—21no—
30C4⋊Q8—21no—
31C4⋊Q8—21no—
32C4⋊Q8Q812yes—
33#125—42no—
34#125—42no—
35C2×C4⋊C4—21no—
36C2×C4⋊C4—21no—
37C2×C4⋊C4—22no—
38C2×C4⋊C4—22no—
39C2×C4⋊C4—21no—
40C2×C4⋊C4—21no—
41C2×C4⋊C4—22no—
42C2×C4⋊C4D411yescharacteristic
43C2×C4⋊C4D411yescharacteristic
44C2×C4⋊C4D411yescharacteristic
45C2×C4⋊C4D411yescharacteristic
46C2×C4⋊C4D412yes—
47C2×C42—21no—
48C2×C42—21no—
49C2×C42C2311yescharacteristic
50C4⋊C8—21no—
51C4⋊C8—21no—
52C4⋊C8—21no—
53C4⋊C8—21no—
54#103—44no—
55C4×C8—21no—
56C4×C8—21no—
57#95—22no—
58#95—21no—
59#95—21no—
60C2×Q8—22no—
61C2×Q8—42no—
62C2×Q8—42no—
63C2×Q8—41no—
64C22×C4—21no—
65C22×C4—21no—
66C22×C4—21no—
67C22×C4—21no—
68C22×C4—22no—
69C22×C4—41no—
70C22×C4C2×D411yescharacteristic
71C22×C4C2×D411yescharacteristic
72C22×C4C2×D411yescharacteristic
73C2×C8—22no—
74C2×C8—41no—
75C2×C8—41no—
76C2×C8—41no—
77C2×C8—41no—
78C2×C8—41no—
79C2×C8—41no—
80C2×C8—41no—
81C2×C8—41no—
82C4⋊C4—21no—
83C4⋊C4—21no—
84C4⋊C4—22no—
85C4⋊C4—22no—
86C4⋊C4—21no—
87C4⋊C4—21no—
88C4⋊C4—21no—
89C4⋊C4—21no—
90C4⋊C4—42no—
91C4⋊C4—44no—
92C4⋊C4—44no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C4⋊C4—41no—
96C4⋊C4—41no—
97C4⋊C4—41no—
98C4⋊C4—41no—
99C4⋊C4—82no—
100C4⋊C4SD1612yes—
101C4⋊C4Q1612yes—
102C42—41no—
103C42—41no—
104C42—41no—
105C42—41no—
106C42C2×Q811yescharacteristic
107C42#4111yescharacteristic
108C42#4111yescharacteristic
109C42#4111yescharacteristic
110C23#12011yescharacteristic
111Q8—44no—
112Q8—82no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—42no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—42no—
128C2×C4—42no—
129C2×C4—41no—
130C2×C4—41no—
131C2×C4—81no—
132C2×C4—81no—
133C2×C4C22⋊Q811yescharacteristic
134C2×C4C22⋊Q811yescharacteristic
135C2×C4C22⋊Q811yescharacteristic
136C2×C4#12411yescharacteristic
137C2×C4#12411yescharacteristic
138C2×C4#12411yescharacteristic
139C2×C4C2×SD1611yescharacteristic
140C2×C4C2×Q1611yescharacteristic
141C2×C4#13511yescharacteristic
142C2×C4#13511yescharacteristic
143C2×C4AGL(1,ℤ/8)11yescharacteristic
144C2×C4#13711yescharacteristic
145C2×C4#13711yescharacteristic
146C2×C4#13711yescharacteristic
147C8—42no—
148C8—81no—
149C8—81no—
150C22#39311yescharacteristic
151C22#45011yescharacteristic
152C22#45111yescharacteristic
153C22#45211yescharacteristic
154C22#45211yescharacteristic
155C22#45311yescharacteristic
156C22#45411yescharacteristic
157C4—21no—
158C4—21no—
159C4—42no—
160C4—42no—
161C4—81no—
162C4—82no—
163C4—81no—
164C4—82no—
165C4#47511yescharacteristic
166C4#47711yescharacteristic
167C4#47911yescharacteristic
168C4#47911yescharacteristic
169C4#48711yescharacteristic
170C4#48811yescharacteristic
171C4#48911yescharacteristic
172C4#49111yescharacteristic
173C2#163111yescharacteristic
174C2#163211yescharacteristic
175C2#163511yescharacteristic
176C2#163611yescharacteristic
177C2#202411yescharacteristic
178C2#202611yescharacteristic
179C2#202711yescharacteristic
subgroupG/H
center, socle, prime radicalC23#120
commutator, Frattini, cosocleC2×C42C23
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#25522
#19872
#19562
#12962
#12792