Finite Group Databasebeta

← #99333

Subgroups — #99333

Order 512.

320 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 92 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#23372C211yesmaximal, characteristic
2#9872C211yesmaximal, characteristic
3#8808C211yesmaximal, characteristic
4#8786C211yesmaximal, characteristic
5C4×#330C211yesmaximal, characteristic
6#7030C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8C4×#125C2211yescharacteristic
9#1940—21no—
10#1940—21no—
11#1917—21no—
12#1917—21no—
13#1917—21no—
14#1917—21no—
15#1842C2211yescharacteristic
16#1831C2211yescharacteristic
17#1831C2211yescharacteristic
18#1744C2211yescharacteristic
19C4×#97C2211yescharacteristic
20C4×#97C2211yescharacteristic
21C2×#335—21no—
22C2×#334—21no—
23C2×#330C411yescharacteristic
24C2×#330C411yescharacteristic
25#1295C411yescharacteristic
26#1295C411yescharacteristic
27#1279—21no—
28#1279—21no—
29#1277—21no—
30#1277—21no—
31C2×#125C2×C411yescharacteristic
32C2×C4⋊C8—21no—
33C2×C4⋊C8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8D411yescharacteristic
38C2×C4⋊C8D411yescharacteristic
39C2×C4⋊C8D411yescharacteristic
40C2×C4⋊C8D411yescharacteristic
41C2×#97—21no—
42C2×#97—21no—
43C2×#97—21no—
44C2×#97—21no—
45C2×#97C2×C411yescharacteristic
46C2×#97C2×C411yescharacteristic
47C2×#97C2×C411yescharacteristic
48C2×#97C2×C411yescharacteristic
49C2×C4×C8—21no—
50C2×C4×C8—21no—
51C2×C4×C8—21no—
52#389Q811yescharacteristic
53#389Q811yescharacteristic
54#387—21no—
55#387—21no—
56#382C2×C411yescharacteristic
57C4×C4⋊C4—21no—
58C4×C4⋊C4—21no—
59C4×C4⋊C4D411yescharacteristic
60C4×C4⋊C4D411yescharacteristic
61C43C2311yescharacteristic
62#336—21no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
69#336—21no—
70#336—21no—
71#336—21no—
72#335—42no—
73#334—42no—
74#330—22no—
75#330—22no—
76C22×C8—21no—
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—21no—
83C22×C8—21no—
84C22×C8—41no—
85C22×C8—41no—
86#125—21no—
87#125—21no—
88#125—21no—
89#125—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4C4⋊C411yescharacteristic
95C2×C4⋊C4C4⋊C411yescharacteristic
96C2×C4⋊C4C4⋊C411yescharacteristic
97C2×C4⋊C4C4⋊C411yescharacteristic
98C2×C42—21no—
99C2×C42—21no—
100C2×C42C22×C411yescharacteristic
101C2×C42C2×D411yescharacteristic
102C2×C42C2×D411yescharacteristic
103C2×C42C2×D411yescharacteristic
104C2×C42C2×Q811yescharacteristic
105C2×C42#4111yescharacteristic
106C2×C42#4111yescharacteristic
107C4⋊C8—41no—
108C4⋊C8—41no—
109C4⋊C8—41no—
110C4⋊C8—41no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113C4⋊C8—42no—
114C4⋊C8—42no—
115C4⋊C8—81no—
116C4⋊C8—81no—
117#97—21no—
118#97—21no—
119#97—21no—
120#97—21no—
121#97—21no—
122#97—21no—
123#97—42no—
124#97—42no—
125#97—81no—
126#97—81no—
127#97M1612yes—
128#97M1612yes—
129C4×C8—22no—
130C4×C8—22no—
131C4×C8—22no—
132C4×C8—41no—
133C4×C8—41no—
134C4×C8—41no—
135#95—21no—
136#95—21no—
137#95—21no—
138#95—21no—
139#95—21no—
140#95—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4C2×C4⋊C411yescharacteristic
146C22×C4C4×D411yescharacteristic
147C22×C4C4×D411yescharacteristic
148C22×C4#12011yescharacteristic
149C22×C4C22⋊Q811yescharacteristic
150C22×C4C22⋊Q811yescharacteristic
151C22×C4#12311yescharacteristic
152C2×C8—22no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—42no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C2×C8—81no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C42—21no—
195C42—21no—
196C42—21no—
197C42—21no—
198C42—21no—
199C42—21no—
200C42—41no—
201C42—41no—
202C42—41no—
203C42—41no—
204C42—41no—
205C42—41no—
206C42—41no—
207C42C2×M1611yescharacteristic
208C42C2×M1611yescharacteristic
209C42#13111yescharacteristic
210C42#13111yescharacteristic
211C23#38511yescharacteristic
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—21no—
225C2×C4—21no—
226C2×C4—21no—
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—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4#42311yescharacteristic
240C2×C4#42411yescharacteristic
241C2×C4#43511yescharacteristic
242C2×C4#43511yescharacteristic
243C2×C4#43611yescharacteristic
244C2×C4#43611yescharacteristic
245C2×C4#45311yescharacteristic
246C2×C4#45411yescharacteristic
247C2×C4#45411yescharacteristic
248C2×C4#45511yescharacteristic
249C2×C4#45611yescharacteristic
250C2×C4#45611yescharacteristic
251C8—24no—
252C8—42no—
253C8—42no—
254C8—42no—
255C8—82no—
256C8—81no—
257C8—81no—
258C8—81no—
259C8—81no—
260C8—161no—
261C22#185111yescharacteristic
262C22#185711yescharacteristic
263C22#185811yescharacteristic
264C22#185911yescharacteristic
265C22#186011yescharacteristic
266C22#186111yescharacteristic
267C22#186111yescharacteristic
268C4—21no—
269C4—21no—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—81no—
279C4—81no—
280C4—81no—
281C4#165711yescharacteristic
282C4#166111yescharacteristic
283C4#166311yescharacteristic
284C4#166411yescharacteristic
285C2#883811yescharacteristic
286C2#884111yescharacteristic
287C2#884211yescharacteristic
288C2#891211yescharacteristic
289C2#891611yescharacteristic
290C2#891711yescharacteristic
291C2#891911yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#385
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C4 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

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

subgroupindex
#233722
#98722
#88082
#87862
C4×#3302
#70302