Finite Group Databasebeta

← #145938

Subgroups — #145938

Order 512.

268 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 94 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#13275C211yesmaximal, characteristic
2#13177C211yesmaximal, characteristic
3C2×#1370C211yesmaximal, characteristic
4C2×#1364C211yesmaximal, characteristic
5#9823C211yesmaximal, characteristic
6#9594C211yesmaximal, characteristic
7#7274C211yesmaximal, characteristic
8C2×#500C2211yescharacteristic
9C2×#367—21no—
10C2×C4⋊C16C2211yescharacteristic
11C2×C4⋊C16C2211yescharacteristic
12#1990—21no—
13#1956—21no—
14#1939—21no—
15#1845C2211yescharacteristic
16C4×#107C2211yescharacteristic
17C2×#335C2211yescharacteristic
18C2×C82C2211yescharacteristic
19#1380—21no—
20#1380—21no—
21#1380—21no—
22#1370—22no—
23#1364—22no—
24#1279—21no—
25C2×C4⋊Q8—21no—
26C22×C16—21no—
27C22×C16—21no—
28#500—21no—
29#500—21no—
30#500—21no—
31#500Q812yes—
32C2×#107—21no—
33C2×#107—21no—
34C2×#107—21no—
35C2×#107—21no—
36C2×#107D411yescharacteristic
37C2×#107D411yescharacteristic
38C2×C4⋊C8—21no—
39C2×C4⋊C8—41no—
40C2×#103—41no—
41C2×#103—41no—
42C2×C4×C8D411yescharacteristic
43C2×C4×C8D411yescharacteristic
44C2×C4×C8C2311yescharacteristic
45#384—21no—
46C4×C4⋊C4—21no—
47#367—42no—
48C4⋊C16—21no—
49C4⋊C16—21no—
50C4⋊C16—21no—
51C4⋊C16D412yes—
52#340—21no—
53#340—42no—
54#336—41no—
55#335—21no—
56#335—21no—
57C82—21no—
58C82—21no—
59C22×Q8—41no—
60C22×C8—21no—
61C22×C8—41no—
62C22×C8D811yescharacteristic
63C22×C8D811yescharacteristic
64C22×C8C2×D411yescharacteristic
65C22×C8#4111yescharacteristic
66C4⋊Q8—22no—
67C4⋊Q8—41no—
68C4⋊Q8—41no—
69C4⋊Q8—41no—
70C2×C4⋊C4—21no—
71C2×C4⋊C4—21no—
72C2×C4⋊C4—41no—
73C2×C4⋊C4—41no—
74C2×C4⋊C4—41no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—41no—
77C2×C42—41no—
78C2×C42C2×D411yescharacteristic
79C2×C16—22no—
80C2×C16—41no—
81C2×C16—41no—
82C2×C16—41no—
83C2×C16—41no—
84C2×C16—41no—
85#107—21no—
86#107—22no—
87#107—22no—
88#107—21no—
89#107—21no—
90#107—41no—
91#107—41no—
92#107—41no—
93#107—41no—
94#107—81no—
95#107Q1612yes—
96C4⋊C8—41no—
97C4⋊C8—41no—
98C4⋊C8—82no—
99#103—82no—
100#103—82no—
101C4×C8—21no—
102C4×C8—21no—
103C4×C8—21no—
104C4×C8—21no—
105C4×C8C2×D411yescharacteristic
106C4×C8C2×Q811yescharacteristic
107C4×C8#4111yescharacteristic
108C4×C8#4111yescharacteristic
109#95—41no—
110C2×Q8—42no—
111C2×Q8—81no—
112C2×Q8—81no—
113C2×Q8—81no—
114C2×Q8—81no—
115C2×Q8—81no—
116C22×C4—41no—
117C22×C4—41no—
118C22×C4—81no—
119C22×C4—81no—
120C22×C4#12111yescharacteristic
121C22×C4C2×D811yescharacteristic
122C22×C4AGL(1,ℤ/8)11yescharacteristic
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—22no—
128C2×C8—21no—
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—41no—
132C2×C8—41no—
133C2×C8—81no—
134C2×C8—81no—
135C2×C8—81no—
136C2×C8SD3212yes—
137C2×C8#12111yescharacteristic
138C2×C8C22⋊Q811yescharacteristic
139C2×C8C22⋊Q811yescharacteristic
140C2×C8#12611yescharacteristic
141C2×C8C2×Q1611yescharacteristic
142C2×C8#13511yescharacteristic
143C2×C8AGL(1,ℤ/8)11yescharacteristic
144C2×C8#13711yescharacteristic
145C4⋊C4—22no—
146C4⋊C4—41no—
147C4⋊C4—42no—
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—42no—
151C4⋊C4—82no—
152C4⋊C4—81no—
153C4⋊C4—81no—
154C4⋊C4—81no—
155C4⋊C4—81no—
156C4⋊C4—81no—
157C4⋊C4—81no—
158C42—81no—
159C42—81no—
160C42#12111yescharacteristic
161C42C22⋊Q811yescharacteristic
162C42#13511yescharacteristic
163C42#13711yescharacteristic
164C16—42no—
165C16—81no—
166C23#45911yescharacteristic
167Q8—82no—
168Q8—82no—
169Q8—161no—
170Q8—161no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—42no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—82no—
177C2×C4—81no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—161no—
181C2×C4—161no—
182C2×C4—161no—
183C2×C4—161no—
184C2×C4—161no—
185C2×C4#39611yescharacteristic
186C2×C4#46411yescharacteristic
187C2×C4#46611yescharacteristic
188C2×C4#46711yescharacteristic
189C2×C4#46811yescharacteristic
190C2×C4#46811yescharacteristic
191C2×C4#47111yescharacteristic
192C2×C4#47311yescharacteristic
193C2×C4#47411yescharacteristic
194C2×C4#47811yescharacteristic
195C2×C4C2×SD3211yescharacteristic
196C2×C4#50811yescharacteristic
197C2×C4#50911yescharacteristic
198C2×C4#50911yescharacteristic
199C8—21no—
200C8—21no—
201C8—22no—
202C8—42no—
203C8—41no—
204C8—161no—
205C8#46211yescharacteristic
206C8#46311yescharacteristic
207C8#47711yescharacteristic
208C8#47911yescharacteristic
209C22#166911yescharacteristic
210C22#168511yescharacteristic
211C22#206711yescharacteristic
212C22#220711yescharacteristic
213C22#221011yescharacteristic
214C22#221211yescharacteristic
215C22#221411yescharacteristic
216C4—21no—
217C4—21no—
218C4—82no—
219C4—162no—
220C4—161no—
221C4—321no—
222C4#168411yescharacteristic
223C4#170011yescharacteristic
224C4#206411yescharacteristic
225C4#206811yescharacteristic
226C4#221711yescharacteristic
227C4#221811yescharacteristic
228C4#222611yescharacteristic
229C4#222811yescharacteristic
230C2#1059211yescharacteristic
231C2#1244611yescharacteristic
232C2#1244911yescharacteristic
233C2#1248411yescharacteristic
234C2#1248911yescharacteristic
235C2#1347611yescharacteristic
236C2#1347911yescharacteristic
subgroupG/H
center, socle, prime radicalC23#459
commutator, Frattini, cosocleC2×C4×C8C23
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C82 ◁ G
LECSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#132752
#131772
C2×#13702
C2×#13642
#98232
#95942
#72742