Finite Group Databasebeta

← #145107

Subgroups — #145107

Order 512.

313 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 313 conjugacy classes of subgroups — too many to draw. Only its 78 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#28538C211yesmaximal, characteristic
2#13289C211yesmaximal, characteristic
3#12819C211yesmaximal, characteristic
4#11935C211yesmaximal, characteristic
5#11600C211yesmaximal, characteristic
6#9630C211yesmaximal, characteristic
7#7168C211yesmaximal, characteristic
8C2×#499C2211yescharacteristic
9C2×#479—21no—
10C2×C4×Q16C2211yescharacteristic
11#2565—21no—
12#2150C2211yescharacteristic
13C2×#362—21no—
14C4×M32C2211yescharacteristic
15#2097—21no—
16#2095—21no—
17#1971—21no—
18#1848C2211yescharacteristic
19#1847—21no—
20#1770C2211yescharacteristic
21#1571—21no—
22#1564C2211yescharacteristic
23#1387—21no—
24#1387—21no—
25#1387—21no—
26#1363—22no—
27#1334—22no—
28#1303—21no—
29C22×Q16D411yescharacteristic
30C2×#125—21no—
31C2×C4×Q8—21no—
32C2×M32—21no—
33C2×M32—21no—
34#499—21no—
35#499—21no—
36#499—21no—
37#499—21no—
38#479—42no—
39#479—42no—
40C4×Q16—21no—
41C4×Q16—21no—
42C4×Q16—21no—
43C4×Q16—21no—
44#431—21no—
45C2×#108—21no—
46C2×#108—21no—
47C2×#107—21no—
48C2×#107D411yescharacteristic
49C2×#107D411yescharacteristic
50C2×#107D411yescharacteristic
51C2×#106—21no—
52C2×#106—21no—
53#423—21no—
54C2×C4⋊C8D411yescharacteristic
55C2×#103—21no—
56C2×#103—21no—
57C2×#103—21no—
58C2×#97—21no—
59C2×C4×C8C2311yescharacteristic
60#398—42no—
61#391—21no—
62#391—21no—
63#387—42no—
64#384—21no—
65#382—21no—
66C4×C4⋊C4D411yescharacteristic
67C4⋊C16—21no—
68C4⋊C16—21no—
69#362—42no—
70#346—21no—
71C4×C16—21no—
72#336—21no—
73#335—21no—
74#335—42no—
75#334D412yes—
76C22×Q8—21no—
77C2×Q16—21no—
78C2×Q16—21no—
79C2×Q16—21no—
80C2×Q16—21no—
81C2×Q16—21no—
82C2×Q16Q1612yes—
83C2×M16—41no—
84C22×C8—21no—
85C22×C8C2×D411yescharacteristic
86C22×C8C2×D411yescharacteristic
87#125—41no—
88#125—41no—
89#125—41no—
90#125—41no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—41no—
94C4×Q8—41no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C42—21no—
104C2×C42—41no—
105C2×C42C2×D411yescharacteristic
106M32—22no—
107M32—41no—
108M32—41no—
109M32—41no—
110C2×C16—41no—
111C2×C16—41no—
112#108—42no—
113#108—41no—
114#108—41no—
115#107—21no—
116#107—21no—
117#107—21no—
118#107—21no—
119#107—21no—
120#107—21no—
121#107—42no—
122#106—42no—
123#106—41no—
124#106—41no—
125C4⋊C8—22no—
126C4⋊C8—21no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8D812yes—
130#103—42no—
131#103—42no—
132#103—41no—
133#103—41no—
134C22⋊C8—41no—
135#97—41no—
136#97—41no—
137C4×C8—41no—
138C4×C8C2×D411yescharacteristic
139C4×C8#4111yescharacteristic
140C4×C8#4111yescharacteristic
141C4×C8#4111yescharacteristic
142#95—42no—
143#95—42no—
144#95—42no—
145#95SD1612yes—
146C2×Q8—22no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C22×C4—22no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4#12011yescharacteristic
158C22×C4C2×SD1611yescharacteristic
159C22×C4AGL(1,ℤ/8)11yescharacteristic
160Q16—22no—
161Q16—22no—
162Q16—41no—
163Q16—41no—
164M16—81no—
165M16—81no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—22no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—42no—
172C2×C8—81no—
173C2×C8#12111yescharacteristic
174C2×C8#12111yescharacteristic
175C2×C8#12311yescharacteristic
176C2×C8#12311yescharacteristic
177C2×C8C2×Q1611yescharacteristic
178C2×C8#13511yescharacteristic
179C2×C8AGL(1,ℤ/8)11yescharacteristic
180C2×C8#13711yescharacteristic
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—81no—
188C4⋊C4—84no—
189C4⋊C4—81no—
190C4⋊C4—81no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C42—41no—
196C42—41no—
197C42—81no—
198C42—81no—
199C42#12111yescharacteristic
200C42#12411yescharacteristic
201C42C2×D811yescharacteristic
202C42AGL(1,ℤ/8)11yescharacteristic
203C16—42no—
204C16—81no—
205C23#45011yescharacteristic
206Q8—42no—
207Q8—42no—
208Q8—81no—
209Q8—81no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—82no—
219C2×C4—82no—
220C2×C4—82no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4#39411yescharacteristic
225C2×C4#44711yescharacteristic
226C2×C4#44911yescharacteristic
227C2×C4#45111yescharacteristic
228C2×C4#45411yescharacteristic
229C2×C4#45611yescharacteristic
230C2×C4#45911yescharacteristic
231C2×C4#46011yescharacteristic
232C2×C4#48611yescharacteristic
233C2×C4#49011yescharacteristic
234C8—21no—
235C8—21no—
236C8—42no—
237C8—82no—
238C8—161no—
239C8#46711yescharacteristic
240C8#46811yescharacteristic
241C8#48411yescharacteristic
242C8#48511yescharacteristic
243C22—21no—
244C22—21no—
245C22#163711yescharacteristic
246C22#165411yescharacteristic
247C22#204111yescharacteristic
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—82no—
253C4—82no—
254C4—161no—
255C4—161no—
256C4—161no—
257C4#162511yescharacteristic
258C4#164911yescharacteristic
259C4#203611yescharacteristic
260C4#203811yescharacteristic
261C2—21no—
262C2—21no—
263C2#1042111yescharacteristic
264C2#1341611yescharacteristic
265C2#1341811yescharacteristic
subgroupG/H
center, socleC22#2041
commutator, Frattini, cosocleC2×C4×C8C23
prime radicalC23#450
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1770 ◁ 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
#285382
#132892
#128192
#119352
#116002
#96302
#71682