Finite Group Databasebeta

← #102176

Subgroups — #102176

Order 512.

394 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 110 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#33258C211yesmaximal, characteristic
2#9686C212yesmaximal
3#8274C211yesmaximal, characteristic
4C8×#97C211yesmaximal, characteristic
5#7680C212yesmaximal
6#2859C2212yes—
7#1942—21no—
8#1942—21no—
9#1942—21no—
10#1942—21no—
11#1845C411yescharacteristic
12#1845C411yescharacteristic
13#1834C412yes—
14#1767C2212yes—
15#1744C2211yescharacteristic
16C4×#97C2211yescharacteristic
17C42×C8C2211yescharacteristic
18C2×#335—21no—
19C2×#330—24no—
20C2×#322—21no—
21C2×C82—21no—
22#1277—21no—
23#1271—24no—
24C2×#125—22no—
25C2×#107—21no—
26C2×#107—21no—
27C2×#107—21no—
28C2×#107—21no—
29C2×C4⋊C8—22no—
30C2×#97—21no—
31C2×#97—22no—
32C2×#97D412yes—
33C2×C4×C8—21no—
34C2×C4×C8—21no—
35C2×C4×C8C2×C411yescharacteristic
36C2×C4×C8C2×C411yescharacteristic
37C2×C4×C8D411yescharacteristic
38C2×C4×C8D411yescharacteristic
39C2×C4×C8D411yescharacteristic
40C2×C4×C8D411yescharacteristic
41#389—22no—
42#389—22no—
43#389—22no—
44#389—22no—
45#384C2×C412yes—
46#384C2×C412yes—
47#382—22no—
48C43C2311yescharacteristic
49#340—22no—
50#340—22no—
51#336—22no—
52#336—21no—
53#336D412yes—
54#335—24no—
55#330—48no—
56#322—24no—
57C82—24no—
58C22×C8—22no—
59C22×C8—22no—
60C22×C8—42no—
61C22×C8C22⋊C411yescharacteristic
62C22×C8C22⋊C411yescharacteristic
63C22×C8C22⋊C411yescharacteristic
64C22×C8C22⋊C411yescharacteristic
65#125—44no—
66#125—44no—
67C2×C4⋊C4—22no—
68C2×C4⋊C4—22no—
69C2×C4⋊C4—22no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—42no—
74C2×C4⋊C4—42no—
75C2×C42C22×C411yescharacteristic
76C2×C42C2×D411yescharacteristic
77C2×C42C2×D411yescharacteristic
78C2×C42C2×D411yescharacteristic
79C2×C42C2×D411yescharacteristic
80C2×C42#4111yescharacteristic
81C2×C42#4111yescharacteristic
82#107—42no—
83#107—42no—
84#107—42no—
85#107—42no—
86C4⋊C8—24no—
87C4⋊C8—42no—
88#97—24no—
89#97—22no—
90#97—44no—
91#97D814yes—
92C4×C8—22no—
93C4×C8—22no—
94C4×C8—22no—
95C4×C8—22no—
96C4×C8—22no—
97C4×C8—22no—
98C4×C8—22no—
99C4×C8—22no—
100C4×C8—22no—
101C4×C8—41no—
102#95—42no—
103#95—42no—
104C22×C4—42no—
105C22×C4—42no—
106C22×C4C2×C22⋊C411yescharacteristic
107C22×C4C4×D411yescharacteristic
108C22×C4C4×D411yescharacteristic
109C22×C4#12111yescharacteristic
110C22×C4#12111yescharacteristic
111C22×C4#12411yescharacteristic
112C22×C4#12711yescharacteristic
113C2×C8—24no—
114C2×C8—24no—
115C2×C8—21no—
116C2×C8—21no—
117C2×C8—21no—
118C2×C8—21no—
119C2×C8—24no—
120C2×C8—24no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—42no—
125C2×C8—42no—
126C2×C8—44no—
127C2×C8—82no—
128C2×C8—82no—
129C2×C8#10112yes—
130C2×C8#10112yes—
131C2×C8#10412yes—
132C2×C8#10412yes—
133C2×C8#10412yes—
134C4⋊C4—42no—
135C4⋊C4—42no—
136C4⋊C4—42no—
137C4⋊C4—42no—
138C4⋊C4—44no—
139C4⋊C4—44no—
140C4⋊C4—44no—
141C4⋊C4—82no—
142C4⋊C4—84no—
143C4⋊C4—82no—
144C4⋊C4—82no—
145C42—21no—
146C42—21no—
147C42—21no—
148C42—21no—
149C42—21no—
150C42—21no—
151C42—22no—
152C42—22no—
153C42—41no—
154C42C2×D812yes—
155C42#13512yes—
156C23#39011yescharacteristic
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—82no—
171C2×C4—82no—
172C2×C4—82no—
173C2×C4—82no—
174C2×C4—82no—
175C2×C4—82no—
176C2×C4C2×#10111yescharacteristic
177C2×C4C2×#10111yescharacteristic
178C2×C4C2×#10411yescharacteristic
179C2×C4C2×#10411yescharacteristic
180C2×C4C2×#10411yescharacteristic
181C2×C4#42111yescharacteristic
182C2×C4C4×D812yes—
183C2×C4#44312yes—
184C2×C4#46612yes—
185C2×C4#47312yes—
186C2×C4#49311yescharacteristic
187C2×C4#49511yescharacteristic
188C8—28no—
189C8—22no—
190C8—22no—
191C8—44no—
192C8—41no—
193C8—84no—
194C8#33014yescomplemented
195C22#196211yescharacteristic
196C22#196611yescharacteristic
197C22#197011yescharacteristic
198C22#197411yescharacteristic
199C22#197611yescharacteristic
200C22#197911yescharacteristic
201C22#198011yescharacteristic
202C4—22no—
203C4—22no—
204C4—22no—
205C4—22no—
206C4—21no—
207C4—21no—
208C4—41no—
209C4—162no—
210C4—162no—
211C4C2×#33011yescharacteristic
212C4#152611yescharacteristic
213C4#152811yescharacteristic
214C4#153111yescharacteristic
215C2#968611yescharacteristic
216C2#971911yescharacteristic
217C2#972511yescharacteristic
218C2#976311yescharacteristic
219C2#978811yescharacteristic
220C2#979911yescharacteristic
221C2#984411yescharacteristic
subgroupG/H
center, socle, prime radicalC23#390
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Complements

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

NH ≅ G/Ntype
194. C8#330semidirect

Maximal subgroups

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

subgroupindex
#332582
#96862
#82742
C8×#972
#76802