Finite Group Databasebeta

← #145584

Subgroups — #145584

Order 512.

346 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 74 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#19616C211yesmaximal, characteristic
2#11947C212yesmaximal, complemented
3#11742C212yesmaximal, complemented
4#9598C211yesmaximal, characteristic, complemented
5#7145C211yesmaximal, characteristic, complemented
6#3169—21no—
7#3169C2212yes—
8#3147—21no—
9#2162C2212yes—
10#1939—21no—
11C4×#107C2211yescharacteristic
12#1722—22no—
13#1721—22no—
14C2×#335C2211yescharacteristic
15C2×#322C2211yescharacteristic
16#1364—22no—
17#1361—22no—
18#1347—22no—
19#1347—22no—
20#1279—21no—
21C2×#135—41no—
22C2×#135—41no—
23#532—22no—
24#500—21no—
25#500D412yes—
26#495—41no—
27#495—41no—
28#494—21no—
29#493—21no—
30#493—21no—
31#493D412yes—
32#492—22no—
33#486—22no—
34#486—22no—
35#466—22no—
36#466—22no—
37#466—42no—
38C4×D8—22no—
39C4×D8—22no—
40C4×D8—42no—
41C2×#107—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—41no—
44C2×C4×C8D411yescharacteristic
45C2×C4×C8D411yescharacteristic
46C2×C4×C8C2311yescharacteristic
47C4×C4⋊C4—21no—
48C4⋊C16—22no—
49C22⋊C16—22no—
50C4×C16—22no—
51#340D411yescharacteristic
52#340D411yescharacteristic
53#336—41no—
54#335—22no—
55#322—22no—
56C2×#41—42no—
57#135—82no—
58#135—82no—
59#135—82no—
60#135—82no—
61C2×Q16—41no—
62C2×Q16—41no—
63C2×SD16—42no—
64C2×SD16—42no—
65C2×D8—22no—
66C2×D8—22no—
67C2×D8—41no—
68C2×D8—41no—
69C2×D8—42no—
70C22×C8—21no—
71C22×C8—41no—
72C22×C8D811yescharacteristic
73C22×C8D811yescharacteristic
74C22×C8C2×D411yescharacteristic
75C22×C8#4111yescharacteristic
76C4⋊Q8—22no—
77#127—22no—
78#124—42no—
79#121—42no—
80#121—42no—
81C4×D4—42no—
82C4×D4—42no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C42—41no—
86C2×C42C2×D411yescharacteristic
87C2×C16—42no—
88#107—22no—
89#107—22no—
90#107—42no—
91#107—42no—
92C4⋊C8—41no—
93C4⋊C8—41no—
94C4⋊C8—82no—
95#102—44no—
96#102—42no—
97#102—42no—
98C4×C8—21no—
99C4×C8—21no—
100C4×C8—21no—
101C4×C8SD1612yes—
102C4×C8C2×D412yes—
103C4×C8#4112yes—
104#95—41no—
105#41—82no—
106#41—82no—
107#41—82no—
108#41—82no—
109C2×Q8—42no—
110C2×D4—42no—
111C2×D4—42no—
112C2×D4—42no—
113C2×D4—82no—
114C22×C4—41no—
115C22×C4—41no—
116C22×C4—82no—
117C22×C4#12111yescharacteristic
118C22×C4C2×D811yescharacteristic
119C22×C4AGL(1,ℤ/8)11yescharacteristic
120Q16—82no—
121Q16—82no—
122SD16—84no—
123SD16—84no—
124D8—82no—
125D8—82no—
126D8—82no—
127D8—82no—
128D8—84no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—22no—
134C2×C8—41no—
135C2×C8—41no—
136C2×C8—81no—
137C2×C8—81no—
138C2×C8—81no—
139C2×C8—81no—
140C2×C8D1612yes—
141C2×C8SD3212yes—
142C2×C8#12112yes—
143C2×C8#12312yes—
144C4⋊C4—22no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—41no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C22⋊C4—82no—
151C22⋊C4—82no—
152C42—81no—
153C42—81no—
154C42#12011yescharacteristic
155C42#12411yescharacteristic
156C42C2×SD1611yescharacteristic
157C42AGL(1,ℤ/8)11yescharacteristic
158C16—82no—
159C23—82no—
160C23#45911yescharacteristic
161Q8—82no—
162Q8—82no—
163D4—84no—
164D4—82no—
165D4—82no—
166D4—82no—
167D4—82no—
168D4—162no—
169D4—162no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—81no—
179C2×C4—82no—
180C2×C4—162no—
181C2×C4—162no—
182C2×C4#39411yescharacteristic
183C2×C4#44711yescharacteristic
184C2×C4#45011yescharacteristic
185C2×C4#46011yescharacteristic
186C2×C4#48611yescharacteristic
187C2×C4#49011yescharacteristic
188C2×C4C2×D1611yescharacteristic
189C2×C4C2×SD3211yescharacteristic
190C2×C4#50911yescharacteristic
191C2×C4#50911yescharacteristic
192C8—22no—
193C8—22no—
194C8—22no—
195C8—22no—
196C8—42no—
197C8—161no—
198C22—21no—
199C22—21no—
200C22—162no—
201C22—162no—
202C22—162no—
203C22#204111yescharacteristic
204C22#220611yescharacteristic
205C22#220711yescharacteristic
206C4—21no—
207C4—21no—
208C4—21no—
209C4—82no—
210C4—161no—
211C4—162no—
212C4#205011yescharacteristic
213C4#205311yescharacteristic
214C4#218411yescharacteristic
215C4#218711yescharacteristic
216C4#224011yescharacteristic
217C4#224411yescharacteristic
218C2—21no—
219C2—21no—
220C2—322no—
221C2#1054611yescharacteristic
222C2#1340711yescharacteristic
223C2#1341611yescharacteristic
subgroupG/H
centerC2×C4#486
commutator, Frattini, cosocleC2×C4×C8C23
socleC22#2041
prime radical#19616C2
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×#322 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #11947C2semidirect
3. #11742C2semidirect
4. #9598C2semidirect
5. #7145C2semidirect

Maximal subgroups

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

subgroupindex
#196162
#119472
#117422
#95982
#71452