Finite Group Databasebeta

← #94222

Subgroups — #94222

Order 512.

255 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 255 conjugacy classes of subgroups — too many to draw. Only its 50 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#12798C211yesmaximal, characteristic
2#8960C211yesmaximal, characteristic
3#8583C211yesmaximal, characteristic
4#2982C411yescharacteristic, complemented
5C4×#124C2211yescharacteristic
6C2×#354—21no—
7#1799—21no—
8#1767—21no—
9C2×#329—21no—
10#1478—21no—
11#1461C411yescharacteristic, complemented
12#1393C412yes—
13#1295C412yescomplemented
14#1276—21no—
15C2×#124D411yescharacteristic
16C2×C4×Q8C2×C411yescharacteristic
17C2×C4×D4D411yescharacteristic
18C8×Q8—42no—
19#431—21no—
20#431—21no—
21#431—41no—
22C2×C4⋊C8—41no—
23C2×#99—22no—
24C2×#97—22no—
25#391Q811yescharacteristic
26#390C2×C411yescharacteristic
27#388—41no—
28#382C2×C411yescharacteristic
29#380—41no—
30C4×C22⋊C4—41no—
31C43D411yescharacteristic
32#354—41no—
33#354—41no—
34#342—41no—
35#336—41no—
36#329—41no—
37#329—41no—
38D4⋊C8—42no—
39#324—41no—
40C22×Q8C4⋊C411yescharacteristic
41C22×D4C22⋊C411yescharacteristic
42C23×C4—21no—
43C22×C8—42no—
44#124—41no—
45#124D811yescharacteristic
46#124SD1611yescharacteristic
47#124SD1611yescharacteristic
48#124Q1611yescharacteristic
49C4×Q8—41no—
50C4×Q8—41no—
51C4×D4—41no—
52C4×D4—41no—
53C2×C4⋊C4—21no—
54C2×C4⋊C4—81no—
55C2×C4⋊C4C4211yescharacteristic
56C2×C4⋊C4C4⋊C411yescharacteristic
57C2×C22⋊C4—21no—
58C2×C22⋊C4—41no—
59C2×C22⋊C4—41no—
60C2×C22⋊C4—42no—
61C2×C42—21no—
62C2×C42—21no—
63C2×C42—21no—
64C2×C42C22⋊C411yescharacteristic
65C2×C42C22⋊C411yescharacteristic
66C2×C42C4⋊C411yescharacteristic
67C4⋊C8—22no—
68C4⋊C8—41no—
69C4⋊C8—44no—
70C4⋊C8—42no—
71#99—42no—
72#99—42no—
73C22⋊C8—41no—
74C22⋊C8—41no—
75#97—42no—
76#97—42no—
77C4×C8—41no—
78C4×C8—41no—
79C4×C8—42no—
80#95—41no—
81#95—41no—
82#95—81no—
83C24—21no—
84C2×Q8—21no—
85C2×Q8—41no—
86C2×Q8—41no—
87C2×Q8#10611yescharacteristic
88C2×Q8#10711yescharacteristic
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92C2×D4#10211yescharacteristic
93C2×D4#10311yescharacteristic
94C22×C4—21no—
95C22×C4—21no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—21no—
99C22×C4—41no—
100C22×C4—41no—
101C22×C4—82no—
102C22×C4—82no—
103C22×C4#9511yescharacteristic
104C22×C4#9911yescharacteristic
105C22×C4#9911yescharacteristic
106C2×C8—44no—
107C2×C8—42no—
108C2×C8—82no—
109C2×C8—82no—
110C2×C8—81no—
111C4⋊C4—41no—
112C4⋊C4—41no—
113C4⋊C4—42no—
114C4⋊C4—162no—
115C22⋊C4—41no—
116C22⋊C4—41no—
117C22⋊C4—41no—
118C22⋊C4—41no—
119C22⋊C4—81no—
120C22⋊C4—82no—
121C22⋊C4—82no—
122C22⋊C4—82no—
123C42—21no—
124C42—21no—
125C42—21no—
126C42—41no—
127C42—42no—
128C42—41no—
129C42—41no—
130C42—81no—
131C42#10211yescharacteristic
132C42#10311yescharacteristic
133C23—21no—
134C23—21no—
135C23—41no—
136C23—41no—
137C23—81no—
138C23—81no—
139C23#34211yescharacteristic
140Q8—41no—
141Q8—41no—
142Q8—42no—
143D4—41no—
144D4—41no—
145D4—81no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—82no—
165C2×C4—81no—
166C2×C4—81no—
167C2×C4—161no—
168C2×C4—162no—
169C2×C4—162no—
170C2×C4—162no—
171C2×C4H(3,ℤ/4)11yescharacteristic
172C2×C4#34011yescharacteristic
173C2×C4AΣL(1,𝔽16)11yescharacteristic
174C2×C4#35211yescharacteristic
175C8—82no—
176C8—84no—
177C8—161no—
178C22—21no—
179C22—21no—
180C22—41no—
181C22—41no—
182C22—81no—
183C22—81no—
184C22—81no—
185C22—81no—
186C22—161no—
187C22#128911yescharacteristic
188C22#139011yescharacteristic
189C22#139511yescharacteristic
190C4—21no—
191C4—21no—
192C4—21no—
193C4—21no—
194C4—41no—
195C4—41no—
196C4—42no—
197C4—41no—
198C4—41no—
199C4—41no—
200C4—81no—
201C4—81no—
202C4—322no—
203C2—21no—
204C2—21no—
205C2—81no—
206C2—81no—
207C2#723611yescharacteristic
208C2#748111yescharacteristic
209C2#748611yescharacteristic
subgroupG/H
center, socleC22#1390
commutatorC2×C4⋊C4C42
Frattini, cosocleC4×#124C22
prime radicalC22×D4C22⋊C4
LCSG ▷ C2×C4⋊C4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×#124 ◁ G
LECSG ▷ C4×#124 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #2982C4semidirect
11. #1461C4semidirect
13. #1295C4semidirect

Maximal subgroups

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

subgroupindex
#127982
#89602
#85832