Finite Group Databasebeta

← #140696

Subgroups — #140696

Order 512.

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

normal subgroups only

This group has 598 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#13910C211yesmaximal, characteristic
2C2×#1325C214yesmaximal
3#8560C211yesmaximal, characteristic
4#8153C211yesmaximal, characteristic
5C2×#389—21no—
6C2×#389—21no—
7C2×#384C411yescharacteristic
8C2×#384C2212yes—
9C2×C4×C4⋊C4C411yescharacteristic
10C2×C4×C4⋊C4C2211yescharacteristic
11#1797—21no—
12#1749—21no—
13C2×#324C2212yes—
14C2×#324C2212yes—
15#1444—21no—
16#1444—21no—
17C4⋊#95C412yes—
18#1325—28no—
19#1280—21no—
20#1280—21no—
21C22×C4⋊C4—21no—
22C22×C4⋊C4—21no—
23C22×C4⋊C4—22no—
24C22×C4⋊C4—22no—
25C22×C4⋊C4—21no—
26C22×C4⋊C4C2×C411yescharacteristic
27C22×C4⋊C4C2×C412yes—
28C22×C4⋊C4C2311yescharacteristic
29C22×C42C2×C411yescharacteristic
30C22×C42C2×C412yes—
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C2×C4⋊C8—41no—
34C2×C22⋊C8—22no—
35C2×C22⋊C8—22no—
36C2×#97—41no—
37#389—44no—
38#389—44no—
39#384—24no—
40#384—24no—
41#384—41no—
42#384—41no—
43C4×C4⋊C4—24no—
44C4×C4⋊C4—41no—
45C4×C4⋊C4—41no—
46C2×#95—21no—
47C2×#95—22no—
48C2×#95—22no—
49C2×#95D411yescharacteristic
50C2×#95D411yescharacteristic
51#336—41no—
52#336—41no—
53#324—22no—
54#324—24no—
55#324D414yes—
56C23×C4—22no—
57C23×C4—22no—
58C23×C4C22⋊C411yescharacteristic
59C23×C4C22⋊C411yescharacteristic
60C23×C4C22⋊C411yescharacteristic
61C23×C4C22⋊C411yescharacteristic
62C23×C4C22×C411yescharacteristic
63C23×C4C2×D411yescharacteristic
64C23×C4C2×D411yescharacteristic
65C22×C8—42no—
66C22×C8—42no—
67C2×C4⋊C4—24no—
68C2×C4⋊C4—24no—
69C2×C4⋊C4—24no—
70C2×C4⋊C4—22no—
71C2×C4⋊C4—22no—
72C2×C4⋊C4—24no—
73C2×C4⋊C4—41no—
74C2×C4⋊C4—41no—
75C2×C4⋊C4—41no—
76C2×C4⋊C4—42no—
77C2×C4⋊C4—42no—
78C2×C4⋊C4—42no—
79C2×C4⋊C4—42no—
80C2×C4⋊C4—42no—
81C2×C4⋊C4—44no—
82C2×C4⋊C4—44no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—41no—
85C2×C4⋊C4—44no—
86C2×C4⋊C4—42no—
87C2×C4⋊C4—42no—
88C2×C4⋊C4—82no—
89C2×C4⋊C4—82no—
90C2×C4⋊C4—82no—
91C2×C4⋊C4C2×D412yes—
92C2×C4⋊C4#4112yes—
93C2×C42—21no—
94C2×C42—21no—
95C2×C42—22no—
96C2×C42—22no—
97C2×C42—24no—
98C2×C42—24no—
99C2×C42—21no—
100C2×C42—21no—
101C2×C42—22no—
102C2×C42—21no—
103C2×C42—21no—
104C2×C42—42no—
105C2×C42—42no—
106C2×C42M1614yes—
107C4⋊C8—82no—
108C22⋊C8—24no—
109C22⋊C8—42no—
110C22⋊C8—42no—
111C22⋊C8—42no—
112#97—82no—
113#95—24no—
114#95—41no—
115#95—41no—
116#95—44no—
117#95—44no—
118C24C2×C22⋊C411yescharacteristic
119C22×C4—21no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—22no—
126C22×C4—22no—
127C22×C4—24no—
128C22×C4—24no—
129C22×C4—21no—
130C22×C4—24no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—21no—
137C22×C4—21no—
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—21no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—42no—
156C22×C4—42no—
157C22×C4—42no—
158C22×C4—42no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4#9911yescharacteristic
163C22×C4#9911yescharacteristic
164C22×C4#10112yes—
165C22×C4#10112yes—
166C22×C4C4×D412yes—
167C22×C4#12112yes—
168C22×C4#12411yescharacteristic
169C22×C4#12711yescharacteristic
170C22×C4C2×M1612yes—
171C22×C4#13112yes—
172C2×C8—44no—
173C2×C8—82no—
174C2×C8—82no—
175C2×C8—82no—
176C2×C8—82no—
177C2×C8—82no—
178C4⋊C4—216no—
179C4⋊C4—42no—
180C4⋊C4—42no—
181C4⋊C4—44no—
182C4⋊C4—84no—
183C4⋊C4—82no—
184C4⋊C4—88no—
185C4⋊C4—84no—
186C4⋊C4—84no—
187C4⋊C4—84no—
188C4⋊C4—82no—
189C42—24no—
190C42—24no—
191C42—28no—
192C42—42no—
193C42—42no—
194C42—44no—
195C42—81no—
196C42—81no—
197C23—21no—
198C23—21no—
199C23—21no—
200C23—21no—
201C23#39011yescharacteristic
202C23#40711yescharacteristic
203C23#40811yescharacteristic
204C23C2×#9911yescharacteristic
205C23#41011yescharacteristic
206C23C2×#10111yescharacteristic
207C23C2×#10111yescharacteristic
208C2×C4—24no—
209C2×C4—24no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—28no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—44no—
227C2×C4—44no—
228C2×C4—44no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—44no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4#35312yes—
262C2×C4#35612yes—
263C2×C4#43514yes—
264C8—84no—
265C8—162no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22#146311yescharacteristic
279C22#146711yescharacteristic
280C22#147011yescharacteristic
281C22#147211yescharacteristic
282C22#195511yescharacteristic
283C22#196411yescharacteristic
284C22#196611yescharacteristic
285C22C2×#35311yescharacteristic
286C22#212811yescharacteristic
287C22C2×#35611yescharacteristic
288C22#213511yescharacteristic
289C4—24no—
290C4—22no—
291C4—22no—
292C4—48no—
293C4—42no—
294C4—42no—
295C4—41no—
296C4—41no—
297C4—42no—
298C4—81no—
299C4—162no—
300C2—21no—
301C2—21no—
302C2—21no—
303C2—21no—
304C2#965411yescharacteristic
305C2#1151211yescharacteristic
306C2#1151611yescharacteristic
307C2#1157011yescharacteristic
308C2#1157411yescharacteristic
309C2#1322311yescharacteristic
310C2#1322711yescharacteristic
subgroupG/H
center, socleC23C2×#99
commutatorC23×C4C22×C4
Frattini, cosocleC22×C4⋊C4C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#139102
C2×#13252
#85602
#81532