Finite Group Databasebeta

← #121155

Subgroups — #121155

Order 512.

377 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 377 conjugacy classes of subgroups — too many to draw. Only its 110 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#8119C211yesmaximal, characteristic
2#8097C211yesmaximal, characteristic
3#8097C211yesmaximal, characteristic
4#8078C211yesmaximal, characteristic
5#8004C211yesmaximal, characteristic
6#7969C211yesmaximal, characteristic
7#7856C211yesmaximal, characteristic
8#2920C2211yescharacteristic
9#2920C2211yescharacteristic
10#2920C2211yescharacteristic
11#2920C2211yescharacteristic
12C2×#423C2211yescharacteristic
13C2×#423C2211yescharacteristic
14C4×#117C2211yescharacteristic
15#1307—22no—
16#1303—22no—
17#1303—22no—
18#1301—22no—
19#1292—22no—
20#1287—22no—
21#1274C414yes—
22C22×M16—21no—
23C22×M16—21no—
24C2×#117—21no—
25C22×C42C2311yescharacteristic
26#432—21no—
27#432—21no—
28#432—21no—
29#432—21no—
30#432—21no—
31#432—21no—
32#432—21no—
33#432Q812yes—
34#431—21no—
35#431—21no—
36#431—21no—
37#431—21no—
38#431—21no—
39#431C2×C412yes—
40#431C2×C412yes—
41#431D412yes—
42#423—21no—
43#423—21no—
44#423—21no—
45#423—21no—
46#423—21no—
47#423—21no—
48#423—21no—
49#423—21no—
50#423—21no—
51#423—21no—
52#423—21no—
53#423D412yes—
54C2×C4⋊C8—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8D412yes—
58#407—21no—
59#407—21no—
60#407—21no—
61#407—21no—
62C4×M16—21no—
63C4×M16—21no—
64C4×M16—21no—
65C4×M16—21no—
66C4×C4⋊C4—21no—
67C4×C4⋊C4—21no—
68C4×C22⋊C4—21no—
69C4×C22⋊C4—21no—
70#376C2×C412yes—
71C43—21no—
72C23×C4#4111yescharacteristic
73C23×C4#4111yescharacteristic
74C23×C4#4111yescharacteristic
75C2×M16—22no—
76C2×M16—41no—
77C2×M16—41no—
78C2×M16—41no—
79C2×M16—41no—
80C2×M16—41no—
81C2×M16—41no—
82C2×M16—41no—
83C2×M16—82no—
84C2×M16—82no—
85C22×C8—22no—
86C22×C8—41no—
87#117—44no—
88C2×C4⋊C4—41no—
89C2×C22⋊C4—41no—
90C2×C42—22no—
91C2×C42—41no—
92C2×C42—41no—
93C2×C42C22×C411yescharacteristic
94C2×C42C2×D411yescharacteristic
95C2×C42C2×D411yescharacteristic
96C2×C42C2×D411yescharacteristic
97C2×C42C2×Q811yescharacteristic
98C2×C42#4111yescharacteristic
99C2×C42#4111yescharacteristic
100C2×C42#4111yescharacteristic
101C2×C42#4111yescharacteristic
102C2×C42#4111yescharacteristic
103C2×C42#4111yescharacteristic
104C2×C42#4111yescharacteristic
105C4⋊C8—22no—
106C4⋊C8—22no—
107C4⋊C8—22no—
108C4⋊C8—22no—
109C4⋊C8—22no—
110C4⋊C8—22no—
111C4⋊C8—22no—
112C4⋊C8—22no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C22⋊C8—22no—
122C22⋊C8—22no—
123C22⋊C8—22no—
124C22⋊C8—22no—
125C22⋊C8—41no—
126C22⋊C8—41no—
127C22⋊C8—41no—
128C22⋊C8—41no—
129#97—22no—
130#97—41no—
131#97—41no—
132#97—41no—
133C4×C8—22no—
134C4×C8—22no—
135C4×C8—22no—
136C4×C8—41no—
137#95—22no—
138#95—22no—
139C24#12611yescharacteristic
140C22×C4—42no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4—42no—
146C22×C4#11711yescharacteristic
147C22×C4C4×D411yescharacteristic
148C22×C4C4×D411yescharacteristic
149C22×C4#12111yescharacteristic
150C22×C4C22⋊Q811yescharacteristic
151C22×C4#12311yescharacteristic
152C22×C4#12311yescharacteristic
153C22×C4#12411yescharacteristic
154C22×C4#12411yescharacteristic
155C22×C4#12511yescharacteristic
156C22×C4#12511yescharacteristic
157C22×C4#12611yescharacteristic
158C22×C4#12611yescharacteristic
159C22×C4#12611yescharacteristic
160C22×C4#12611yescharacteristic
161C22×C4#12611yescharacteristic
162C22×C4#12611yescharacteristic
163C22×C4#12611yescharacteristic
164M16—81no—
165M16—81no—
166M16—81no—
167M16—81no—
168M16—82no—
169M16—82no—
170M16—82no—
171M16—82no—
172M16—82no—
173M16—82no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—82no—
181C2×C8—82no—
182C4⋊C4—44no—
183C22⋊C4—44no—
184C42—24no—
185C42—42no—
186C42—81no—
187C42—81no—
188C42—81no—
189C42—81no—
190C42#11711yescharacteristic
191C42#11711yescharacteristic
192C42C4×D411yescharacteristic
193C42C4×Q811yescharacteristic
194C42#12111yescharacteristic
195C42#12111yescharacteristic
196C42C22⋊Q811yescharacteristic
197C42C22⋊Q811yescharacteristic
198C42#12311yescharacteristic
199C42#12311yescharacteristic
200C42#12311yescharacteristic
201C42#12311yescharacteristic
202C42#12411yescharacteristic
203C42#12511yescharacteristic
204C42#12611yescharacteristic
205C42#12611yescharacteristic
206C23—41no—
207C23—41no—
208C23—41no—
209C23#38811yescharacteristic
210C23#40011yescharacteristic
211C23#40111yescharacteristic
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
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—41no—
236C2×C4—44no—
237C2×C4—82no—
238C2×C4—82no—
239C2×C4#38311yescharacteristic
240C2×C4#38711yescharacteristic
241C2×C4#38711yescharacteristic
242C2×C4#38711yescharacteristic
243C2×C4#38811yescharacteristic
244C2×C4#38811yescharacteristic
245C2×C4#39611yescharacteristic
246C2×C4#39711yescharacteristic
247C2×C4#39711yescharacteristic
248C2×C4#39711yescharacteristic
249C2×C4#40011yescharacteristic
250C2×C4#40011yescharacteristic
251C8—82no—
252C8—82no—
253C8—82no—
254C8—82no—
255C8—82no—
256C8—82no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22—21no—
264C22—21no—
265C22—21no—
266C22—82no—
267C22#144311yescharacteristic
268C4—21no—
269C4—21no—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—21no—
277C4—84no—
278C4#184112yes—
279C4#208111yescharacteristic
280C4#208111yescharacteristic
281C4#208211yescharacteristic
282C4#208211yescharacteristic
283C2—41no—
284C2—41no—
285C2—41no—
286C2#1129911yescharacteristic
287C2#1130811yescharacteristic
288C2#1130811yescharacteristic
subgroupG/H
center, socleC22#1443
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#126
LCSG ▷ C2×C42 ▷ 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
#81192
#80972
#80782
#80042
#79692
#78562