Finite Group Databasebeta

← #152243

Subgroups — #152243

Order 512.

313 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 313 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#491C211yesmaximal, characteristic
2C2×#1413C212yesmaximal
3#12802C212yesmaximal
4#7505C212yesmaximal
5C2×#491C2211yescharacteristic
6C4×C4⋊Q8C2211yescharacteristic
7C4×#125C411yescharacteristic
8C2×#356C2214yes—
9#1992C411yescharacteristic
10#1960C2211yescharacteristic
11#1935—22no—
12#1836C411yescharacteristic
13#1801—22no—
14C4×#103—22no—
15C4×#97C411yescharacteristic
16#1413—24no—
17#1394—22no—
18C2×C4⋊Q8C2311yescharacteristic
19C2×#125C2×C411yescharacteristic
20C2×C4×Q8D412yes—
21#491—22no—
22#491D412yes—
23#491Q812yes—
24#423—42no—
25C2×#103—22no—
26C2×#103—22no—
27C2×#101—24no—
28C2×#97—21no—
29C2×#97C2×C411yescharacteristic
30C2×#97C2×C411yescharacteristic
31C2×C4×C8—21no—
32#391D412yes—
33#389—21no—
34#389—41no—
35#387—41no—
36#384C2×C411yescharacteristic
37#382C2×C411yescharacteristic
38C4×C4⋊C4—21no—
39C4×C4⋊C4—41no—
40C4×C4⋊C4—41no—
41C43C2×C411yescharacteristic
42#356—24no—
43#356—24no—
44#343—42no—
45#340—22no—
46#340—22no—
47C22×Q8C2×D412yes—
48C2×M16—44no—
49C22×C8—21no—
50C22×C8—21no—
51C4⋊Q8—41no—
52C4⋊Q8C2×D411yescharacteristic
53C4⋊Q8C2×Q811yescharacteristic
54C4⋊Q8#4112yes—
55#125—21no—
56#125—41no—
57#125C4⋊C412yes—
58C4×Q8—42no—
59C4×Q8—42no—
60C2×C4⋊C4—21no—
61C2×C4⋊C4—21no—
62C2×C4⋊C4—22no—
63C2×C4⋊C4—41no—
64C2×C4⋊C4—41no—
65C2×C4⋊C4—41no—
66C2×C4⋊C4—41no—
67C2×C4⋊C4C22⋊C412yes—
68C2×C42—22no—
69C2×C42—21no—
70C2×C42—21no—
71C2×C42—41no—
72C2×C42C22⋊C411yescharacteristic
73C2×C42C22⋊C411yescharacteristic
74C2×C42C22×C411yescharacteristic
75C4⋊C8—82no—
76C4⋊C8—82no—
77#103—24no—
78#103—24no—
79#103—44no—
80#101—44no—
81#101—44no—
82#97—21no—
83#97—41no—
84#97—42no—
85#97C4⋊C412yes—
86C4×C8—41no—
87C4×C8—41no—
88#95—42no—
89#95—41no—
90#95—41no—
91#95—41no—
92C2×Q8—22no—
93C2×Q8—42no—
94C2×Q8—42no—
95C2×Q8#12112yes—
96C2×Q8C22⋊Q812yes—
97C22×C4—21no—
98C22×C4—22no—
99C22×C4—21no—
100C22×C4—22no—
101C22×C4—41no—
102C22×C4—41no—
103C22×C4#9911yescharacteristic
104C22×C4#9911yescharacteristic
105C22×C4C2×C22⋊C411yescharacteristic
106M16—84no—
107M16—84no—
108C2×C8—22no—
109C2×C8—22no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8—41no—
113C2×C8—41no—
114C2×C8—84no—
115C4⋊C4—22no—
116C4⋊C4—41no—
117C4⋊C4—41no—
118C4⋊C4—42no—
119C4⋊C4—42no—
120C4⋊C4—42no—
121C4⋊C4—42no—
122C4⋊C4—42no—
123C4⋊C4—41no—
124C4⋊C4—82no—
125C4⋊C4—82no—
126C4⋊C4—82no—
127C42—21no—
128C42—21no—
129C42—21no—
130C42—41no—
131C42—42no—
132C42—42no—
133C42—42no—
134C42—82no—
135C42—81no—
136C42C2×C4⋊C411yescharacteristic
137C42#11711yescharacteristic
138C23C2×#9911yescharacteristic
139Q8—42no—
140Q8—42no—
141Q8—82no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—22no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—42no—
153C2×C4—42no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—42no—
159C2×C4—41no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—82no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—81no—
166C2×C4#35411yescharacteristic
167C2×C4#35411yescharacteristic
168C2×C4#38011yescharacteristic
169C2×C4#41011yescharacteristic
170C8—42no—
171C8—42no—
172C8—164no—
173C22—21no—
174C22—21no—
175C22#179911yescharacteristic
176C22C2×#35411yescharacteristic
177C22#212611yescharacteristic
178C4—21no—
179C4—21no—
180C4—21no—
181C4—41no—
182C4—41no—
183C4—41no—
184C4—42no—
185C4—42no—
186C4—81no—
187C4—82no—
188C4—82no—
189C4—161no—
190C4#141312yescomplemented
191C2—21no—
192C2—21no—
193C2#1279811yescharacteristic
194C2C2×#141311yescharacteristic
195C2#1359811yescharacteristic
subgroupG/H
center, socleC22C2×#354
commutatorC2×C42C22×C4
Frattini, cosocleC2×C4⋊Q8C23
prime radicalC23C2×#99
LCSG ▷ C2×C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊Q8 ◁ G
LECSG ▷ C2×C4⋊Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
190. C4#1413semidirect

Maximal subgroups

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

subgroupindex
C4×#4912
C2×#14132
#128022
#75052