Finite Group Databasebeta

← #94228

Subgroups — #94228

Order 512.

238 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 52 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#12802C211yesmaximal, characteristic
2#8958C211yesmaximal, characteristic
3#8587C211yesmaximal, characteristic
4#2982C411yescharacteristic
5C4×C4⋊Q8C2211yescharacteristic
6C2×#356—21no—
7#1842—21no—
8#1801—21no—
9C2×#333—21no—
10#1479—21no—
11#1461C411yescharacteristic
12#1394C412yes—
13#1296C412yes—
14#1276—21no—
15C2×C4⋊Q8D411yescharacteristic
16C2×C4×Q8C2×C411yescharacteristic
17C2×C4×Q8D411yescharacteristic
18C8×Q8—42no—
19#431—21no—
20#431—21no—
21#431—41no—
22#423—41no—
23C2×C4⋊C8—22no—
24C2×C4⋊C8—41no—
25C2×C4⋊C8—41no—
26C2×#101—22no—
27#391C2×C411yescharacteristic
28#391Q811yescharacteristic
29#389—41no—
30#384C2×C411yescharacteristic
31C4×C4⋊C4—41no—
32C43D411yescharacteristic
33#356—41no—
34#356—41no—
35#343—41no—
36#333—41no—
37#333—41no—
38Q8⋊C8—42no—
39#324—41no—
40C22×Q8C22⋊C411yescharacteristic
41C22×Q8C4⋊C411yescharacteristic
42C2×M16—42no—
43C22×C8—42no—
44C4⋊Q8—41no—
45C4⋊Q8D811yescharacteristic
46C4⋊Q8SD1611yescharacteristic
47C4⋊Q8SD1611yescharacteristic
48C4⋊Q8Q1611yescharacteristic
49C4×Q8—41no—
50C4×Q8—41no—
51C4×Q8—41no—
52C4×Q8—41no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—21no—
55C2×C4⋊C4—41no—
56C2×C4⋊C4—41no—
57C2×C4⋊C4C4211yescharacteristic
58C2×C4⋊C4C4⋊C411yescharacteristic
59C2×C42—21no—
60C2×C42—21no—
61C2×C42—21no—
62C2×C42—21no—
63C2×C42C22⋊C411yescharacteristic
64C2×C42C22⋊C411yescharacteristic
65C2×C42C4⋊C411yescharacteristic
66C4⋊C8—22no—
67C4⋊C8—42no—
68C4⋊C8—41no—
69C4⋊C8—42no—
70C4⋊C8—42no—
71C4⋊C8—82no—
72C4⋊C8—82no—
73C4⋊C8—81no—
74C4⋊C8—81no—
75#101—42no—
76#101—42no—
77C22⋊C8—41no—
78C22⋊C8—41no—
79C4×C8—41no—
80C4×C8—41no—
81C4×C8—42no—
82#95—41no—
83#95—41no—
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—41no—
87C2×Q8—41no—
88C2×Q8—41no—
89C2×Q8—41no—
90C2×Q8#10211yescharacteristic
91C2×Q8#10311yescharacteristic
92C2×Q8#10611yescharacteristic
93C2×Q8#10711yescharacteristic
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—21no—
100C22×C4#9511yescharacteristic
101C22×C4#9911yescharacteristic
102C22×C4#9911yescharacteristic
103M16—82no—
104M16—82no—
105C2×C8—42no—
106C2×C8—81no—
107C2×C8—82no—
108C2×C8—82no—
109C2×C8—82no—
110C2×C8—82no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—41no—
114C4⋊C4—41no—
115C4⋊C4—41no—
116C4⋊C4—41no—
117C4⋊C4—42no—
118C4⋊C4—81no—
119C4⋊C4—81no—
120C4⋊C4—81no—
121C42—22no—
122C42—22no—
123C42—21no—
124C42—21no—
125C42—21no—
126C42—41no—
127C42—41no—
128C42—41no—
129C42—41no—
130C42—41no—
131C42—41no—
132C42—41no—
133C42#10211yescharacteristic
134C42#10311yescharacteristic
135C23#34211yescharacteristic
136Q8—41no—
137Q8—41no—
138Q8—41no—
139Q8—41no—
140Q8—42no—
141Q8—81no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—41no—
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—81no—
167C2×C4—81no—
168C2×C4H(3,ℤ/4)11yescharacteristic
169C2×C4#34011yescharacteristic
170C2×C4AΣL(1,𝔽16)11yescharacteristic
171C2×C4#35211yescharacteristic
172C8—82no—
173C8—162no—
174C8—161no—
175C8—162no—
176C22—21no—
177C22—21no—
178C22#128911yescharacteristic
179C22#139011yescharacteristic
180C22#139511yescharacteristic
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—21no—
186C4—21no—
187C4—21no—
188C4—42no—
189C4—41no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—41no—
194C4—81no—
195C4—81no—
196C4#140512yes—
197C2—21no—
198C2—21no—
199C2#723611yescharacteristic
200C2#749111yescharacteristic
201C2#749611yescharacteristic
subgroupG/H
center, socleC22#1390
commutatorC2×C4⋊C4C42
Frattini, cosocleC4×C4⋊Q8C22
prime radicalC23#342
LCSG ▷ C2×C4⋊C4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C4×C4⋊Q8 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#128022
#89582
#85872