Finite Group Databasebeta

← #145913

Subgroups — #145913

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#13276C211yesmaximal, characteristic
2#13177C211yesmaximal, characteristic
3C2×#1367C211yesmaximal, characteristic
4C2×#1365C211yesmaximal, 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#1367—22no—
23#1365—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—42no—
41C2×C4×C8D411yescharacteristic
42C2×C4×C8D411yescharacteristic
43C2×C4×C8C2311yescharacteristic
44#384—21no—
45C4×C4⋊C4—21no—
46#367—42no—
47C4⋊C16—21no—
48C4⋊C16—21no—
49C4⋊C16—21no—
50C4⋊C16D412yes—
51#340—21no—
52#340—41no—
53#340—41no—
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#107SD1612yes—
96C4⋊C8—41no—
97C4⋊C8—41no—
98C4⋊C8—82no—
99#103—84no—
100C4×C8—21no—
101C4×C8—21no—
102C4×C8—21no—
103C4×C8—21no—
104C4×C8C2×D411yescharacteristic
105C4×C8C2×Q811yescharacteristic
106C4×C8#4111yescharacteristic
107C4×C8#4111yescharacteristic
108#95—41no—
109C2×Q8—42no—
110C2×Q8—82no—
111C2×Q8—82no—
112C2×Q8—81no—
113C22×C4—41no—
114C22×C4—41no—
115C22×C4—81no—
116C22×C4—81no—
117C22×C4#12111yescharacteristic
118C22×C4C2×D811yescharacteristic
119C22×C4AGL(1,ℤ/8)11yescharacteristic
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—22no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—41no—
129C2×C8—41no—
130C2×C8—81no—
131C2×C8—81no—
132C2×C8—81no—
133C2×C8SD3212yes—
134C2×C8#12111yescharacteristic
135C2×C8C22⋊Q811yescharacteristic
136C2×C8C22⋊Q811yescharacteristic
137C2×C8#12611yescharacteristic
138C2×C8C2×SD1611yescharacteristic
139C2×C8#13511yescharacteristic
140C2×C8#13711yescharacteristic
141C2×C8#13711yescharacteristic
142C4⋊C4—22no—
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—42no—
148C4⋊C4—82no—
149C4⋊C4—81no—
150C4⋊C4—81no—
151C4⋊C4—81no—
152C4⋊C4—81no—
153C4⋊C4—81no—
154C4⋊C4—81no—
155C42—81no—
156C42—81no—
157C42#12111yescharacteristic
158C42C22⋊Q811yescharacteristic
159C42#13511yescharacteristic
160C42#13711yescharacteristic
161C16—42no—
162C16—81no—
163C23#45911yescharacteristic
164Q8—84no—
165Q8—162no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—42no—
169C2×C4—81no—
170C2×C4—81no—
171C2×C4—82no—
172C2×C4—81no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4—161no—
176C2×C4—161no—
177C2×C4—161no—
178C2×C4—161no—
179C2×C4—161no—
180C2×C4#39611yescharacteristic
181C2×C4#46411yescharacteristic
182C2×C4#46511yescharacteristic
183C2×C4#46611yescharacteristic
184C2×C4#46811yescharacteristic
185C2×C4#47011yescharacteristic
186C2×C4#47111yescharacteristic
187C2×C4#47311yescharacteristic
188C2×C4#47411yescharacteristic
189C2×C4#47811yescharacteristic
190C2×C4C2×SD3211yescharacteristic
191C2×C4#50811yescharacteristic
192C2×C4#51011yescharacteristic
193C2×C4#51011yescharacteristic
194C8—21no—
195C8—21no—
196C8—22no—
197C8—42no—
198C8—41no—
199C8—161no—
200C8#46111yescharacteristic
201C8#46411yescharacteristic
202C8#47511yescharacteristic
203C8#47911yescharacteristic
204C22#166511yescharacteristic
205C22#168911yescharacteristic
206C22#206711yescharacteristic
207C22#220811yescharacteristic
208C22#221111yescharacteristic
209C22#221211yescharacteristic
210C22#221311yescharacteristic
211C4—21no—
212C4—21no—
213C4—82no—
214C4—162no—
215C4—161no—
216C4—321no—
217C4#168011yescharacteristic
218C4#170411yescharacteristic
219C4#206411yescharacteristic
220C4#206611yescharacteristic
221C4#221711yescharacteristic
222C4#221911yescharacteristic
223C4#222511yescharacteristic
224C4#222911yescharacteristic
225C2#1058811yescharacteristic
226C2#1241911yescharacteristic
227C2#1242011yescharacteristic
228C2#1249911yescharacteristic
229C2#1250211yescharacteristic
230C2#1347711yescharacteristic
231C2#1347811yescharacteristic
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
#132762
#131772
C2×#13672
C2×#13652
#98232
#95942
#72742