Finite Group Databasebeta

← #120388

Subgroups — #120388

Order 512.

443 conjugacy classes of subgroups.

The subgroup lattice has 293 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21366C211yesmaximal, characteristic
2#17810C211yesmaximal, characteristic
3#8116C211yesmaximal, characteristic
4#8092C211yesmaximal, characteristic
5#7980C211yesmaximal, characteristic
6#7954C211yesmaximal, characteristic
7#7940C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12#2283C2211yescharacteristic
13#2283C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1949—22no—
16#1854—22no—
17#1776—22no—
18#1573C414yescomplemented
19#1572—22no—
20#1565—22no—
21#1306—22no—
22#1303—22no—
23#1289—22no—
24#1285—22no—
25#1284—22no—
26C2×#117—21no—
27C22×C42C2311yescharacteristic
28#432—21no—
29#432—21no—
30#432—21no—
31#432—21no—
32#432C2×C412yes—
33#432D412yes—
34#432Q812yes—
35#432Q812yes—
36#431—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431C2×C412yes—
44C2×#107—22no—
45C2×#106—22no—
46#423—21no—
47#423—21no—
48C2×C4⋊C8C2×C412yes—
49C2×C4⋊C8D412yes—
50#407—21no—
51#407D412yes—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C4×M16—21no—
55C4×M16—21no—
56C2×#97—21no—
57C2×C4×C8—21no—
58#383—21no—
59#383—21no—
60#382—21no—
61#382—21no—
62#381—21no—
63#381—21no—
64#380—21no—
65#380D412yes—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4D412yes—
70C4×C22⋊C4—21no—
71C4×C22⋊C4—21no—
72C4×C22⋊C4—21no—
73C4×C22⋊C4—21no—
74#376—21no—
75#376—21no—
76#376Q812yes—
77C43—21no—
78#340—24no—
79#335—24no—
80#334—24no—
81C23×C4C2×D411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4#4111yescharacteristic
84C2×M16—22no—
85C2×M16—41no—
86C22×C8—22no—
87C22×C8—22no—
88#117—44no—
89C2×C4⋊C4—22no—
90C2×C4⋊C4—22no—
91C2×C4⋊C4—41no—
92C2×C22⋊C4—22no—
93C2×C22⋊C4—41no—
94C2×C22⋊C4—41no—
95C2×C42—22no—
96C2×C42—22no—
97C2×C42—41no—
98C2×C42—41no—
99C2×C42—41no—
100C2×C42C22×C411yescharacteristic
101C2×C42C2×D411yescharacteristic
102C2×C42C2×D411yescharacteristic
103C2×C42C2×D411yescharacteristic
104C2×C42C2×Q811yescharacteristic
105C2×C42C2×Q811yescharacteristic
106C2×C42C2×Q811yescharacteristic
107C2×C42#4111yescharacteristic
108C2×C42#4111yescharacteristic
109C2×C42#4111yescharacteristic
110C2×C42#4111yescharacteristic
111C2×C42#4111yescharacteristic
112#107—44no—
113#106—44no—
114C4⋊C8—22no—
115C4⋊C8—22no—
116C4⋊C8—22no—
117C4⋊C8—22no—
118C4⋊C8—22no—
119C4⋊C8—22no—
120C4⋊C8—41no—
121C4⋊C8C22⋊C414yes—
122C22⋊C8—22no—
123C22⋊C8—22no—
124C22⋊C8—22no—
125C22⋊C8—22no—
126C22⋊C8—41no—
127C22⋊C8—41no—
128C22⋊C8—41no—
129C22⋊C8C4⋊C414yes—
130#97—22no—
131#97—22no—
132#97—22no—
133#97—22no—
134C4×C8—22no—
135C4×C8—41no—
136C4×C8—41no—
137C4×C8—41no—
138#95—22no—
139#95—22no—
140#95—22no—
141#95—22no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147#95—41no—
148C24#12111yescharacteristic
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—81no—
155C22×C4C2×C4⋊C411yescharacteristic
156C22×C4C4×D411yescharacteristic
157C22×C4C4×Q811yescharacteristic
158C22×C4#12011yescharacteristic
159C22×C4#12111yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12111yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4C22⋊Q811yescharacteristic
164C22×C4C22⋊Q811yescharacteristic
165C22×C4C22⋊Q811yescharacteristic
166C22×C4C22⋊Q811yescharacteristic
167C22×C4#12311yescharacteristic
168C22×C4#12311yescharacteristic
169C22×C4#12411yescharacteristic
170C22×C4#12511yescharacteristic
171C22×C4#12611yescharacteristic
172C22×C4C4⋊Q811yescharacteristic
173M16—44no—
174M16—82no—
175C2×C8—24no—
176C2×C8—24no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—82no—
182C4⋊C4—24no—
183C4⋊C4—42no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—82no—
187C22⋊C4—44no—
188C22⋊C4—82no—
189C22⋊C4—82no—
190C42—44no—
191C42—82no—
192C42—82no—
193C42—82no—
194C42—82no—
195C42C2×C22⋊C411yescharacteristic
196C42#11711yescharacteristic
197C42C4×D411yescharacteristic
198C42C4×Q811yescharacteristic
199C42#12111yescharacteristic
200C42C22⋊Q811yescharacteristic
201C42C22⋊Q811yescharacteristic
202C42C22⋊Q811yescharacteristic
203C42C22⋊Q811yescharacteristic
204C42#12311yescharacteristic
205C42#12511yescharacteristic
206C42#12511yescharacteristic
207C42#12511yescharacteristic
208C42#12611yescharacteristic
209C42C4⋊Q811yescharacteristic
210C42C4⋊Q811yescharacteristic
211C23—22no—
212C23—41no—
213C23—41no—
214C23#38911yescharacteristic
215C23#39411yescharacteristic
216C23#39611yescharacteristic
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—44no—
236C2×C4—82no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—82no—
241C2×C4—82no—
242C2×C4—82no—
243C2×C4—82no—
244C2×C4#38011yescharacteristic
245C2×C4#38611yescharacteristic
246C2×C4#38711yescharacteristic
247C2×C4#38711yescharacteristic
248C2×C4#38911yescharacteristic
249C2×C4#39111yescharacteristic
250C2×C4#39511yescharacteristic
251C2×C4#39611yescharacteristic
252C2×C4#39811yescharacteristic
253C2×C4#39811yescharacteristic
254C2×C4#39811yescharacteristic
255C2×C4#40011yescharacteristic
256C8—44no—
257C8—44no—
258C8—82no—
259C8—82no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—82no—
269C22#144111yescharacteristic
270C22#205312yes—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—21no—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—21no—
281C4—21no—
282C4—84no—
283C4—162no—
284C4—162no—
285C4#190612yes—
286C2—22no—
287C2—41no—
288C2—41no—
289C2#1121511yescharacteristic
290C2#1123611yescharacteristic
291C2#1124711yescharacteristic
subgroupG/H
center, socleC22#1441
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#121
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
18. #1573C4semidirect

Maximal subgroups

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

subgroupindex
#213662
#178102
#81162
#80922
#79802
#79542
#79402