Finite Group Databasebeta

← #101302

Subgroups — #101302

Order 512.

535 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 535 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#23629C211yesmaximal, characteristic
2#14501C211yesmaximal, characteristic
3#8716C212yesmaximal
4#7595C211yesmaximal, characteristic
5#7037C212yesmaximal
6C2×#419—21no—
7C2×#391—21no—
8C2×#391C2211yescharacteristic
9#2285C2211yescharacteristic
10#2074—22no—
11#2072C414yescomplemented
12#1817C2212yes—
13#1736—21no—
14#1728C2211yescharacteristic
15#1442—22no—
16#1441—21no—
17#1436—22no—
18#1434C2212yes—
19#1294—22no—
20#1294—22no—
21#1272—22no—
22C23×Q8D411yescharacteristic
23C22×M16—21no—
24C2×#117—21no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4—21no—
27C22×C4⋊C4D411yescharacteristic
28C22×C42—21no—
29C22×C42C2311yescharacteristic
30#419—42no—
31#419—42no—
32C2×#103—24no—
33C2×C22⋊C8—22no—
34#391—22no—
35#391—42no—
36#391—42no—
37#391C2×C412yes—
38#391D412yes—
39#384C2×C412yes—
40#382—21no—
41#380—22no—
42C4×C4⋊C4—22no—
43C2×#95—22no—
44C2×#95—22no—
45C2×#95—22no—
46C2×#95—22no—
47C2×#95—22no—
48C2×#95—21no—
49C2×#95D412yes—
50C2×#95D412yes—
51#340—24no—
52#336—21no—
53#336—22no—
54#336—22no—
55#336C2×C412yes—
56C22×Q8—21no—
57C22×Q8—21no—
58C22×Q8—21no—
59C22×Q8—41no—
60C22×Q8—41no—
61C22×Q8—41no—
62C22×Q8—41no—
63C22×Q8C22⋊C412yes—
64C22×Q8D812yes—
65C22×Q8SD1612yes—
66C23×C4—21no—
67C23×C4—21no—
68C23×C4—22no—
69C23×C4—22no—
70C23×C4C2×D411yescharacteristic
71C23×C4C2×D412yes—
72C2×M16—41no—
73C2×M16—41no—
74C2×M16—41no—
75C2×M16—41no—
76C2×M16—41no—
77C2×M16—41no—
78C22×C8—22no—
79C22×C8—42no—
80#117—41no—
81#117—41no—
82#117—41no—
83#117—41no—
84C2×C4⋊C4—22no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4—22no—
87C2×C4⋊C4—22no—
88C2×C4⋊C4—41no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—44no—
91C2×C4⋊C4—42no—
92C2×C4⋊C4—81no—
93C2×C4⋊C4—81no—
94C2×C4⋊C4—81no—
95C2×C4⋊C4C22⋊C412yes—
96C2×C22⋊C4—41no—
97C2×C42—41no—
98C2×C42—41no—
99C2×C42—42no—
100C2×C42—41no—
101C2×C42—81no—
102C2×C42—81no—
103C2×C42C22×C411yescharacteristic
104C2×C42C2×D411yescharacteristic
105C2×C42#4112yes—
106#103—48no—
107C22⋊C8—42no—
108C22⋊C8—42no—
109#95—24no—
110#95—24no—
111#95—42no—
112#95—42no—
113#95—44no—
114#95—44no—
115#95—44no—
116#95—42no—
117#95—42no—
118#95—42no—
119#95—81no—
120C24#12011yescharacteristic
121C2×Q8—22no—
122C2×Q8—22no—
123C2×Q8—22no—
124C2×Q8—42no—
125C2×Q8—42no—
126C2×Q8—42no—
127C2×Q8—42no—
128C2×Q8—42no—
129C2×Q8—42no—
130C2×Q8—81no—
131C2×Q8—81no—
132C2×Q8—81no—
133C2×Q8—81no—
134C2×Q8—81no—
135C2×Q8—81no—
136C2×Q8#10214yes—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—24no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—42no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—41no—
161C22×C4—42no—
162C22×C4—41no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4C2×C22⋊C411yescharacteristic
173C22×C4C4×D412yes—
174C22×C4#12112yes—
175C22×C4#12311yescharacteristic
176C22×C4C2×D811yescharacteristic
177C22×C4C2×SD1611yescharacteristic
178C22×C4AGL(1,ℤ/8)11yescharacteristic
179C22×C4#13711yescharacteristic
180M16—81no—
181M16—81no—
182M16—81no—
183M16—81no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—82no—
188C2×C8—82no—
189C2×C8—82no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C4⋊C4—84no—
197C4⋊C4—84no—
198C22⋊C4—81no—
199C22⋊C4—81no—
200C42—41no—
201C42—41no—
202C42—42no—
203C42—84no—
204C42—81no—
205C42—81no—
206C23—22no—
207C23—22no—
208C23#38611yescharacteristic
209C23#44711yescharacteristic
210C23#44811yescharacteristic
211C23#45511yescharacteristic
212C23#45511yescharacteristic
213C23#45811yescharacteristic
214C23#45811yescharacteristic
215Q8—44no—
216Q8—82no—
217Q8—82no—
218Q8—82no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—24no—
232C2×C4—22no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—44no—
245C2×C4—44no—
246C2×C4—44no—
247C2×C4—42no—
248C2×C4—44no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—81no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4C2×#10211yescharacteristic
269C2×C4#41711yescharacteristic
270C2×C4#48011yescharacteristic
271C2×C4#48111yescharacteristic
272C8—82no—
273C8—162no—
274C22—22no—
275C22—22no—
276C22—21no—
277C22—21no—
278C22—22no—
279C22—22no—
280C22—21no—
281C22—21no—
282C22#160711yescharacteristic
283C22#160711yescharacteristic
284C22#160811yescharacteristic
285C22#160811yescharacteristic
286C22#187411yescharacteristic
287C22#188511yescharacteristic
288C22#189011yescharacteristic
289C22#190512yes—
290C22#190612yes—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—42no—
296C4—42no—
297C4—44no—
298C4—84no—
299C4—82no—
300C4—162no—
301C4—162no—
302C2—21no—
303C2—21no—
304C2—21no—
305C2—21no—
306C2#902511yescharacteristic
307C2#918012yes—
308C2#942611yescharacteristic
309C2#943911yescharacteristic
310C2#952612yes—
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
11. #2072C4semidirect

Maximal subgroups

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

subgroupindex
#236292
#145012
#87162
#75952
#70372