Finite Group Databasebeta

← #145173

Subgroups — #145173

Order 512.

319 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 319 conjugacy classes of subgroups — too many to draw. Only its 84 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#28271C211yesmaximal, characteristic
2#12890C211yesmaximal, characteristic
3#12812C211yesmaximal, characteristic
4C2×#1338C211yesmaximal, characteristic
5C2×#1334C211yesmaximal, characteristic
6#8653C211yesmaximal, characteristic
7#7275C211yesmaximal, characteristic
8C2×#446C2211yescharacteristic
9C2×C4×Q16C2211yescharacteristic
10#2581—21no—
11C2×C4⋊C16C2211yescharacteristic
12C2×#358—21no—
13C2×#346C2211yescharacteristic
14#2068—21no—
15#2068—21no—
16#1971—21no—
17#1944—21no—
18#1846C2211yescharacteristic
19#1845C2211yescharacteristic
20#1805—21no—
21#1803—21no—
22C2×#334C2211yescharacteristic
23#1380—21no—
24#1380—21no—
25#1380—21no—
26#1338—22no—
27#1334—22no—
28#1296—21no—
29C22×Q16D411yescharacteristic
30C2×C4×Q8—21no—
31C2×C4×Q8D411yescharacteristic
32C22×C16—21no—
33C22×C16—21no—
34#446—21no—
35#446—21no—
36#446—21no—
37#446—21no—
38C4×Q16—21no—
39C4×Q16—21no—
40C4×Q16—21no—
41C4×Q16—21no—
42C2×#107—21no—
43C2×#107—21no—
44C2×#107D411yescharacteristic
45C2×#107D411yescharacteristic
46C2×#107D411yescharacteristic
47C2×#106—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8D411yescharacteristic
51C2×#103—21no—
52C2×#103—21no—
53C2×#103—21no—
54C2×#103—41no—
55C2×#97—21no—
56C2×C4×C8C2311yescharacteristic
57#400—41no—
58#395—41no—
59#391—21no—
60#391—21no—
61#389—21no—
62#389—21no—
63#387—41no—
64#387—41no—
65#384—21no—
66#382—21no—
67C4⋊C16—21no—
68C4⋊C16—21no—
69#358—42no—
70#346—21no—
71#346D412yes—
72#340—21no—
73#340—21no—
74#340—41no—
75#334—21no—
76#334—21no—
77C22×Q8—21no—
78C22×Q8D811yescharacteristic
79C2×Q16—21no—
80C2×Q16—21no—
81C2×Q16—21no—
82C2×Q16—21no—
83C2×Q16—21no—
84C2×Q16SD1612yes—
85C22×C8—21no—
86C22×C8—41no—
87C22×C8C2×D411yescharacteristic
88C22×C8C2×D411yescharacteristic
89C4×Q8—21no—
90C4×Q8—21no—
91C4×Q8—21no—
92C4×Q8—21no—
93C4×Q8—41no—
94C4×Q8—41no—
95C4×Q8—41no—
96C4×Q8—41no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4D811yescharacteristic
108C2×C42—21no—
109C2×C42—41no—
110C2×C42C2×D411yescharacteristic
111C2×C16—22no—
112C2×C16—41no—
113C2×C16—41no—
114C2×C16—41no—
115C2×C16—41no—
116C2×C16—41no—
117#107—21no—
118#107—21no—
119#107—41no—
120#107—41no—
121#107—42no—
122#107—41no—
123#107—41no—
124#106—41no—
125#106—41no—
126C4⋊C8—21no—
127C4⋊C8—21no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132#103—41no—
133#103—41no—
134#103—81no—
135#103—81no—
136#103—82no—
137#97—41no—
138#97—41no—
139C4×C8C2×D411yescharacteristic
140C4×C8#4111yescharacteristic
141C4×C8#4111yescharacteristic
142C4×C8#4111yescharacteristic
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151C2×Q8—22no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—81no—
168C22×C4#12011yescharacteristic
169C22×C4C2×D811yescharacteristic
170C22×C4AGL(1,ℤ/8)11yescharacteristic
171Q16—22no—
172Q16—22no—
173Q16—41no—
174Q16—41no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8#12111yescharacteristic
184C2×C8#12111yescharacteristic
185C2×C8#12311yescharacteristic
186C2×C8#12411yescharacteristic
187C2×C8C2×SD1611yescharacteristic
188C2×C8#13511yescharacteristic
189C2×C8#13711yescharacteristic
190C2×C8#13711yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—82no—
204C4⋊C4—82no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C4⋊C4—81no—
209C4⋊C4—161no—
210C42—41no—
211C42—41no—
212C42—81no—
213C42—81no—
214C42#12111yescharacteristic
215C42#12311yescharacteristic
216C42#13511yescharacteristic
217C42#13711yescharacteristic
218C16—42no—
219C16—81no—
220C23#44711yescharacteristic
221Q8—42no—
222Q8—42no—
223Q8—42no—
224Q8—81no—
225Q8—81no—
226Q8—81no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—161no—
250C2×C4—161no—
251C2×C4—161no—
252C2×C4#39411yescharacteristic
253C2×C4#44811yescharacteristic
254C2×C4#45211yescharacteristic
255C2×C4#45211yescharacteristic
256C2×C4#45411yescharacteristic
257C2×C4#45511yescharacteristic
258C2×C4#46611yescharacteristic
259C2×C4#46811yescharacteristic
260C2×C4#48011yescharacteristic
261C2×C4#48211yescharacteristic
262C8—21no—
263C8—21no—
264C8—81no—
265C8—161no—
266C8#46511yescharacteristic
267C8#47011yescharacteristic
268C8#48311yescharacteristic
269C8#48511yescharacteristic
270C22#162711yescharacteristic
271C22#164111yescharacteristic
272C22#203311yescharacteristic
273C22#219011yescharacteristic
274C22#219111yescharacteristic
275C22#219311yescharacteristic
276C22#219511yescharacteristic
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—81no—
282C4—81no—
283C4—82no—
284C4—161no—
285C4—161no—
286C4—161no—
287C4—321no—
288C4#163811yescharacteristic
289C4#164311yescharacteristic
290C4#203511yescharacteristic
291C4#204011yescharacteristic
292C2#1043311yescharacteristic
293C2#1236111yescharacteristic
294C2#1236311yescharacteristic
295C2#1238911yescharacteristic
296C2#1239111yescharacteristic
297C2#1338611yescharacteristic
298C2#1338811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#447
commutator, Frattini, cosocleC2×C4×C8C23
LCSG ▷ C2×C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#446 ◁ 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
#282712
#128902
#128122
C2×#13382
C2×#13342
#86532
#72752