Finite Group Databasebeta

← #121032

Subgroups — #121032

Order 512.

398 conjugacy classes of subgroups.

The subgroup lattice has 309 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#17817C211yesmaximal, characteristic
2#8121C211yesmaximal, characteristic
3#8076C211yesmaximal, characteristic
4#7959C211yesmaximal, characteristic
5C2×#1286C211yesmaximal, characteristic
6#7933C211yesmaximal, characteristic
7#7914C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10C2×#432C2211yescharacteristic
11C2×#431C2211yescharacteristic
12C2×#431C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C2×#382C2211yescharacteristic
15#1574—22no—
16#1573—22no—
17#1567—21no—
18#1566—21no—
19#1307—22no—
20#1301—22no—
21#1286—22no—
22#1286—21no—
23#1286—21no—
24#1283—22no—
25#1280C414yes—
26C22×M16—21no—
27C22×C4⋊C4—21no—
28C22×C42C2311yescharacteristic
29#432—21no—
30#432—21no—
31#432—21no—
32#432—21no—
33#432—21no—
34#432—21no—
35#432—21no—
36#432—21no—
37#431—21no—
38#431—21no—
39#431—21no—
40#431—21no—
41#431—21no—
42#431—21no—
43#431—21no—
44#431—21no—
45#431D412yes—
46#431D412yes—
47#431Q812yes—
48#431Q812yes—
49#423—21no—
50#423—21no—
51#423—21no—
52#423—21no—
53#423D411yescharacteristic
54#423D411yescharacteristic
55#423D412yes—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8—21no—
60C2×C4⋊C8—21no—
61#407—21no—
62#407—21no—
63C2×C22⋊C8—21no—
64C2×C22⋊C8C2×C412yes—
65C2×C22⋊C8C2×C412yes—
66C4×M16—21no—
67C4×M16—21no—
68C2×#97—21no—
69C2×C4×C8—21no—
70C2×C4×C8—21no—
71#382—21no—
72#382—21no—
73#382—21no—
74#382—21no—
75C2×#95—21no—
76C2×#95C2×C412yes—
77#335—24no—
78#334—24no—
79C23×C4—22no—
80C23×C4C22×C411yescharacteristic
81C23×C4#4111yescharacteristic
82C23×C4#4111yescharacteristic
83C2×M16—21no—
84C2×M16—21no—
85C2×M16—22no—
86C2×M16—41no—
87C2×M16—41no—
88C2×M16—81no—
89C2×M16—81no—
90C22×C8—22no—
91C22×C8—22no—
92C22×C8—41no—
93C22×C8—41no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—81no—
97C2×C4⋊C4—81no—
98C2×C42C2×D411yescharacteristic
99C2×C42C2×D411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42C2×D411yescharacteristic
102C2×C42C2×Q811yescharacteristic
103C2×C42C2×Q811yescharacteristic
104C2×C42#4111yescharacteristic
105C2×C42#4111yescharacteristic
106C2×C42#4111yescharacteristic
107C2×C42#4111yescharacteristic
108C2×C42#4111yescharacteristic
109C2×C42#4111yescharacteristic
110C4⋊C8—21no—
111C4⋊C8—22no—
112C4⋊C8—21no—
113C4⋊C8—22no—
114C4⋊C8—22no—
115C4⋊C8—22no—
116C4⋊C8—22no—
117C4⋊C8—22no—
118C4⋊C8—21no—
119C4⋊C8—21no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C22⋊C8—22no—
127C22⋊C8—22no—
128C22⋊C8—22no—
129C22⋊C8—22no—
130C22⋊C8—22no—
131C22⋊C8—41no—
132C22⋊C8—41no—
133C22⋊C8—41no—
134C22⋊C8—41no—
135C22⋊C8C4⋊C414yes—
136#97—41no—
137#97—41no—
138#97—41no—
139#97—41no—
140C4×C8—22no—
141C4×C8—22no—
142C4×C8—22no—
143C4×C8—22no—
144C4×C8—41no—
145C4×C8—41no—
146#95—22no—
147#95—22no—
148#95—41no—
149#95—41no—
150C24#11711yescharacteristic
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—44no—
158C22×C4—81no—
159C22×C4—82no—
160C22×C4—82no—
161C22×C4C2×C4⋊C411yescharacteristic
162C22×C4#11711yescharacteristic
163C22×C4C4×D411yescharacteristic
164C22×C4C4×D411yescharacteristic
165C22×C4C4×D411yescharacteristic
166C22×C4C4×Q811yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4C22⋊Q811yescharacteristic
169C22×C4#12311yescharacteristic
170C22×C4#12311yescharacteristic
171C22×C4#12411yescharacteristic
172C22×C4#12411yescharacteristic
173C22×C4#12411yescharacteristic
174C22×C4#12511yescharacteristic
175C22×C4#12511yescharacteristic
176C22×C4#12511yescharacteristic
177C22×C4#12611yescharacteristic
178C22×C4#12611yescharacteristic
179M16—41no—
180M16—41no—
181M16—41no—
182M16—41no—
183M16—82no—
184M16—81no—
185M16—81no—
186M16—82no—
187C2×C8—24no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—82no—
195C2×C8—82no—
196C2×C8—82no—
197C2×C8—82no—
198C4⋊C4—82no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C42#12011yescharacteristic
202C42#12111yescharacteristic
203C42#12111yescharacteristic
204C42C22⋊Q811yescharacteristic
205C42C22⋊Q811yescharacteristic
206C42C22⋊Q811yescharacteristic
207C42C22⋊Q811yescharacteristic
208C42#12311yescharacteristic
209C42#12311yescharacteristic
210C42#12311yescharacteristic
211C42#12411yescharacteristic
212C42#12511yescharacteristic
213C42#12511yescharacteristic
214C42#12611yescharacteristic
215C42#12611yescharacteristic
216C42C4⋊Q811yescharacteristic
217C23—22no—
218C23—21no—
219C23—21no—
220C23—41no—
221C23#38211yescharacteristic
222C23#38711yescharacteristic
223C23#38811yescharacteristic
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4—164no—
250C2×C4#38511yescharacteristic
251C2×C4#38711yescharacteristic
252C2×C4#38811yescharacteristic
253C2×C4#38911yescharacteristic
254C2×C4#39311yescharacteristic
255C2×C4#39411yescharacteristic
256C2×C4#39711yescharacteristic
257C2×C4#39811yescharacteristic
258C2×C4#39811yescharacteristic
259C2×C4#40011yescharacteristic
260C2×C4#40011yescharacteristic
261C2×C4#40011yescharacteristic
262C2×C4#47111yescharacteristic
263C2×C4#47111yescharacteristic
264C2×C4#47211yescharacteristic
265C2×C4#47311yescharacteristic
266C8—44no—
267C8—82no—
268C8—82no—
269C8—82no—
270C8—82no—
271C8—81no—
272C8—81no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—42no—
281C22—42no—
282C22#144211yescharacteristic
283C22#183312yes—
284C22#193011yescharacteristic
285C22#193111yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—162no—
297C4#205111yescharacteristic
298C4#205211yescharacteristic
299C4#208911yescharacteristic
300C4#209011yescharacteristic
301C2—21no—
302C2—22no—
303C2—21no—
304C2—41no—
305C2#1125911yescharacteristic
306C2#1128011yescharacteristic
307C2#1129011yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#117
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#178172
#81212
#80762
#79592
C2×#12862
#79332
#79142