Finite Group Databasebeta

← #101770

Subgroups — #101770

Order 512.

564 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 564 conjugacy classes of subgroups — too many to draw. Only its 100 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#28304C211yesmaximal, characteristic
2#14162C211yesmaximal, characteristic
3#9908C212yesmaximal
4#7643C211yesmaximal, characteristic
5#7028C212yesmaximal
6C2×#484—21no—
7C2×#451—21no—
8#2857C2211yescharacteristic
9C2×#391C2211yescharacteristic
10#2095C412yescomplemented
11#2016C412yescomplemented
12#1969—22no—
13#1797C2212yes—
14C4×C22⋊C8C2211yescharacteristic
15#1446—21no—
16#1441—21no—
17#1436—22no—
18#1434—22no—
19C4×#95C2212yes—
20#1294—22no—
21#1294—22no—
22#1272—22no—
23C23×Q8D411yescharacteristic
24C22×Q16—22no—
25C2×C4⋊Q8C2×C411yescharacteristic
26C2×C22⋊Q8—21no—
27C22×C4⋊C4—21no—
28C22×C4⋊C4D411yescharacteristic
29C22×C42—22no—
30C22×C42C2311yescharacteristic
31#484—42no—
32#484—42no—
33#451—42no—
34#451—42no—
35C2×#107—22no—
36C2×C4⋊C8—22no—
37C2×#103—22no—
38C2×#103—22no—
39C2×C22⋊C8—21no—
40C2×C22⋊C8—22no—
41C2×C4×C8—21no—
42#391—22no—
43#391—21no—
44#391C2×C412yes—
45#391D412yes—
46#389—22no—
47#384C2×C411yescharacteristic
48#380—22no—
49C2×#95—22no—
50C2×#95—22no—
51C2×#95—22no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—22no—
55C2×#95—21no—
56C2×#95D412yes—
57C2×#95D412yes—
58#336—22no—
59#336C2×C412yes—
60C22×Q8—21no—
61C22×Q8—21no—
62C22×Q8—42no—
63C22×Q8—41no—
64C22×Q8—41no—
65C22×Q8—81no—
66C22×Q8C22⋊C412yes—
67C23×C4—21no—
68C23×C4—22no—
69C23×C4—21no—
70C23×C4—22no—
71C23×C4C2×D411yescharacteristic
72C23×C4C2×D412yes—
73C2×Q16—44no—
74C2×Q16—44no—
75C2×Q16—82no—
76C22×C8—22no—
77C22×C8—42no—
78C4⋊Q8—81no—
79C22⋊Q8—41no—
80C22⋊Q8—41no—
81C22⋊Q8—41no—
82C22⋊Q8—41no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4—22no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—41no—
88C2×C4⋊C4—41no—
89C2×C4⋊C4—44no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—81no—
92C2×C4⋊C4C22⋊C412yes—
93C2×C22⋊C4—41no—
94C2×C42—44no—
95C2×C42—42no—
96C2×C42—42no—
97C2×C42—81no—
98C2×C42—82no—
99C2×C42C22×C411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42#4112yes—
102#107—44no—
103C4⋊C8—82no—
104#103—44no—
105#103—44no—
106C22⋊C8—22no—
107C22⋊C8—22no—
108C22⋊C8—42no—
109C22⋊C8—42no—
110C4×C8—81no—
111#95—24no—
112#95—24no—
113#95—22no—
114#95—22no—
115#95—22no—
116#95—44no—
117#95—44no—
118#95—42no—
119#95—82no—
120#95—81no—
121#95—81no—
122#95—81no—
123#95Q1614yescomplemented
124C24#12011yescharacteristic
125C2×Q8—22no—
126C2×Q8—22no—
127C2×Q8—42no—
128C2×Q8—42no—
129C2×Q8—42no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—42no—
133C2×Q8—42no—
134C2×Q8—81no—
135C2×Q8—81no—
136C2×Q8—84no—
137C2×Q8—84no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—22no—
141C22×C4—24no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—24no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—41no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—41no—
164C22×C4—42no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4C2×C22⋊C411yescharacteristic
171C22×C4C4×D412yes—
172C22×C4#12112yes—
173C22×C4#12311yescharacteristic
174C22×C4C2×Q1612yes—
175C22×C4#13512yes—
176C22×C4#13712yes—
177C22×C4#13712yes—
178Q16—88no—
179C2×C8—24no—
180C2×C8—42no—
181C2×C8—42no—
182C2×C8—82no—
183C2×C8—82no—
184C2×C8—82no—
185C4⋊C4—42no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—81no—
189C4⋊C4—82no—
190C4⋊C4—82no—
191C4⋊C4—81no—
192C4⋊C4—81no—
193C4⋊C4—84no—
194C22⋊C4—81no—
195C22⋊C4—81no—
196C42—41no—
197C42—42no—
198C42—41no—
199C42—84no—
200C42—84no—
201C23—21no—
202C23—22no—
203C23—21no—
204C23#38611yescharacteristic
205C23#45112yes—
206C23#45212yes—
207C23#45311yescharacteristic
208C23#45311yescharacteristic
209Q8—44no—
210Q8—82no—
211Q8—82no—
212Q8—82no—
213Q8—84no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—44no—
232C2×C4—44no—
233C2×C4—44no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—42no—
238C2×C4—44no—
239C2×C4—42no—
240C2×C4—82no—
241C2×C4—81no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—81no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—82no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—82no—
257C2×C4—81no—
258C2×C4#42112yes—
259C2×C4C4×Q1612yes—
260C2×C4#44112yes—
261C2×C4#46212yes—
262C2×C4#46412yes—
263C8—44no—
264C8—162no—
265C22—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22#163212yes—
274C22#163311yescharacteristic
275C22#163411yescharacteristic
276C22#187812yes—
277C22#188711yescharacteristic
278C22#189711yescharacteristic
279C22#190612yes—
280C22#191311yescharacteristic
281C4—22no—
282C4—22no—
283C4—22no—
284C4—22no—
285C4—22no—
286C4—41no—
287C4—84no—
288C4—84no—
289C4—82no—
290C4—82no—
291C4—161no—
292C4—161no—
293C2—21no—
294C2—22no—
295C2—21no—
296C2#906611yescharacteristic
297C2#923612yes—
298C2#927612yes—
299C2#941311yescharacteristic
300C2#944111yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
10. #2095C4semidirect
11. #2016C4semidirect
123. #95Q16semidirect

Maximal subgroups

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

subgroupindex
#283042
#141622
#99082
#76432
#70282