Finite Group Databasebeta

← #145183

Subgroups — #145183

Order 512.

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

normal subgroups only

This group has 327 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#12908C211yesmaximal, 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×#367—21no—
12C2×#366—21no—
13C2×C4⋊C16C2211yescharacteristic
14C2×#358—21no—
15C2×#346C2211yescharacteristic
16#2068—21no—
17#2068—21no—
18#1971—21no—
19#1944—21no—
20#1846C2211yescharacteristic
21#1845C2211yescharacteristic
22#1805—21no—
23#1803—21no—
24C2×#334C2211yescharacteristic
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—
67#367—42no—
68#366—42no—
69C4⋊C16—21no—
70C4⋊C16—21no—
71#358—42no—
72#346—21no—
73#346D412yes—
74#340—21no—
75#340—21no—
76#340—41no—
77#334—21no—
78#334—21no—
79C22×Q8—21no—
80C22×Q8D811yescharacteristic
81C2×Q16—21no—
82C2×Q16—21no—
83C2×Q16—21no—
84C2×Q16—21no—
85C2×Q16—21no—
86C2×Q16Q1612yes—
87C22×C8—21no—
88C22×C8—41no—
89C22×C8C2×D411yescharacteristic
90C22×C8C2×D411yescharacteristic
91C4×Q8—21no—
92C4×Q8—21no—
93C4×Q8—21no—
94C4×Q8—21no—
95C4×Q8—41no—
96C4×Q8—41no—
97C4×Q8—41no—
98C4×Q8—41no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—41no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4D811yescharacteristic
110C2×C42—21no—
111C2×C42—41no—
112C2×C42C2×D411yescharacteristic
113C2×C16—22no—
114C2×C16—22no—
115C2×C16—22no—
116C2×C16—41no—
117C2×C16—41no—
118C2×C16—41no—
119#107—21no—
120#107—21no—
121#107—41no—
122#107—41no—
123#107—41no—
124#107—41no—
125#107—41no—
126#107—41no—
127#106—41no—
128#106—41no—
129C4⋊C8—21no—
130C4⋊C8—21no—
131C4⋊C8—41no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135#103—41no—
136#103—41no—
137#103—81no—
138#103—81no—
139#103—82no—
140#97—41no—
141#97—41no—
142C4×C8C2×D411yescharacteristic
143C4×C8#4111yescharacteristic
144C4×C8#4111yescharacteristic
145C4×C8#4111yescharacteristic
146#95—41no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—41no—
154C2×Q8—22no—
155C2×Q8—21no—
156C2×Q8—21no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—41no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—81no—
171C22×C4#12011yescharacteristic
172C22×C4C2×D811yescharacteristic
173C22×C4AGL(1,ℤ/8)11yescharacteristic
174Q16—22no—
175Q16—22no—
176Q16—41no—
177Q16—41no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8#12111yescharacteristic
187C2×C8#12111yescharacteristic
188C2×C8#12311yescharacteristic
189C2×C8#12411yescharacteristic
190C2×C8C2×Q1611yescharacteristic
191C2×C8#13511yescharacteristic
192C2×C8AGL(1,ℤ/8)11yescharacteristic
193C2×C8#13711yescharacteristic
194C4⋊C4—21no—
195C4⋊C4—21no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—41no—
204C4⋊C4—81no—
205C4⋊C4—81no—
206C4⋊C4—82no—
207C4⋊C4—82no—
208C4⋊C4—81no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—161no—
213C42—41no—
214C42—41no—
215C42—81no—
216C42—81no—
217C42#12111yescharacteristic
218C42#12311yescharacteristic
219C42#13511yescharacteristic
220C42#13711yescharacteristic
221C16—24no—
222C16—81no—
223C23#44711yescharacteristic
224Q8—42no—
225Q8—42no—
226Q8—42no—
227Q8—81no—
228Q8—81no—
229Q8—81no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
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—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—161no—
253C2×C4—161no—
254C2×C4—161no—
255C2×C4#39411yescharacteristic
256C2×C4#44911yescharacteristic
257C2×C4#45111yescharacteristic
258C2×C4#45211yescharacteristic
259C2×C4#45311yescharacteristic
260C2×C4#45611yescharacteristic
261C2×C4#46611yescharacteristic
262C2×C4#46811yescharacteristic
263C2×C4#48011yescharacteristic
264C2×C4#48211yescharacteristic
265C8—21no—
266C8—21no—
267C8—81no—
268C8—161no—
269C8#46711yescharacteristic
270C8#46811yescharacteristic
271C8#48411yescharacteristic
272C8#48511yescharacteristic
273C22#162111yescharacteristic
274C22#164911yescharacteristic
275C22#203311yescharacteristic
276C22#219011yescharacteristic
277C22#219111yescharacteristic
278C22#219311yescharacteristic
279C22#219511yescharacteristic
280C4—21no—
281C4—21no—
282C4—21no—
283C4—21no—
284C4—81no—
285C4—81no—
286C4—82no—
287C4—161no—
288C4—161no—
289C4—161no—
290C4—321no—
291C4#163211yescharacteristic
292C4#165011yescharacteristic
293C4#203611yescharacteristic
294C4#203911yescharacteristic
295C2#1043411yescharacteristic
296C2#1233711yescharacteristic
297C2#1233911yescharacteristic
298C2#1241311yescharacteristic
299C2#1241511yescharacteristic
300C2#1338611yescharacteristic
301C2#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
#129082
#128122
C2×#13382
C2×#13342
#86532
#72752