Finite Group Databasebeta

← #99415

Subgroups — #99415

Order 512.

308 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 86 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#23371C211yesmaximal, characteristic
2#9876C211yesmaximal, characteristic
3#8812C211yesmaximal, characteristic
4#8789C211yesmaximal, characteristic
5#7568C211yesmaximal, characteristic
6#7030C211yesmaximal, characteristic
7#7030C211yesmaximal, characteristic
8C4×#125C2211yescharacteristic
9#1940—21no—
10#1939—21no—
11#1917—21no—
12#1917—21no—
13#1916—21no—
14#1916—21no—
15#1842C2211yescharacteristic
16#1831C2211yescharacteristic
17#1831C2211yescharacteristic
18#1744C2211yescharacteristic
19#1744C2211yescharacteristic
20C4×#97C2211yescharacteristic
21C2×#335—21no—
22C2×#334—21no—
23#1279—21no—
24#1279—21no—
25#1277—21no—
26#1277—21no—
27#1271C411yescharacteristic
28#1271C411yescharacteristic
29#1271C411yescharacteristic
30#1271C411yescharacteristic
31C2×#125Q811yescharacteristic
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×C4×C8—21no—
45C2×C4×C8—21no—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48#389C2×C411yescharacteristic
49#389C2×C411yescharacteristic
50#387—21no—
51#387—21no—
52#382Q811yescharacteristic
53C4×C4⋊C4—21no—
54C4×C4⋊C4—21no—
55C4×C4⋊C4D411yescharacteristic
56C4×C4⋊C4D411yescharacteristic
57C43C2311yescharacteristic
58#336—21no—
59#336—21no—
60#336—21no—
61#336—21no—
62#336—21no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336C2×C411yescharacteristic
69#336C2×C411yescharacteristic
70#336C2×C411yescharacteristic
71#336C2×C411yescharacteristic
72#335—42no—
73#334—42no—
74C22×C8—21no—
75C22×C8—21no—
76C22×C8—21no—
77C22×C8—21no—
78C22×C8—21no—
79C22×C8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—41no—
83C22×C8—41no—
84#125—22no—
85#125—41no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4C4⋊C411yescharacteristic
91C2×C4⋊C4C4⋊C411yescharacteristic
92C2×C4⋊C4C4⋊C411yescharacteristic
93C2×C4⋊C4C4⋊C411yescharacteristic
94C2×C42—21no—
95C2×C42—21no—
96C2×C42C22×C411yescharacteristic
97C2×C42C2×D411yescharacteristic
98C2×C42C2×D411yescharacteristic
99C2×C42C2×D411yescharacteristic
100C2×C42C2×Q811yescharacteristic
101C2×C42#4111yescharacteristic
102C2×C42#4111yescharacteristic
103C4⋊C8—41no—
104C4⋊C8—41no—
105C4⋊C8—41no—
106C4⋊C8—41no—
107C4⋊C8—41no—
108C4⋊C8—41no—
109C4⋊C8—42no—
110C4⋊C8—42no—
111C4⋊C8—81no—
112C4⋊C8—81no—
113#97—22no—
114#97—22no—
115#97—41no—
116#97—41no—
117#97—81no—
118C4×C8—22no—
119C4×C8—22no—
120C4×C8—22no—
121C4×C8—41no—
122C4×C8—41no—
123C4×C8—41no—
124C4×C8—81no—
125#95—21no—
126#95—21no—
127#95—21no—
128#95—21no—
129#95—21no—
130#95—21no—
131C22×C4—21no—
132C22×C4—21no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4C2×C4⋊C411yescharacteristic
136C22×C4C4×D411yescharacteristic
137C22×C4C4×D411yescharacteristic
138C22×C4#12011yescharacteristic
139C22×C4C22⋊Q811yescharacteristic
140C22×C4C22⋊Q811yescharacteristic
141C22×C4#12311yescharacteristic
142C2×C8—22no—
143C2×C8—22no—
144C2×C8—42no—
145C2×C8—42no—
146C2×C8—42no—
147C2×C8—41no—
148C2×C8—41no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—41no—
154C2×C8—41no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—41no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—81no—
170C2×C8—81no—
171C2×C8—81no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—41no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—41no—
183C4⋊C4#10812yes—
184C42—21no—
185C42—21no—
186C42—21no—
187C42—21no—
188C42—21no—
189C42—21no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—21no—
194C42—21no—
195C42—21no—
196C42—41no—
197C42—41no—
198C42—41no—
199C42—41no—
200C42—41no—
201C23#38511yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4C2×#10811yescharacteristic
230C2×C4#43011yescharacteristic
231C2×C4#44311yescharacteristic
232C2×C4#44311yescharacteristic
233C2×C4#44411yescharacteristic
234C2×C4#44411yescharacteristic
235C2×C4#45311yescharacteristic
236C2×C4#45411yescharacteristic
237C2×C4#45411yescharacteristic
238C2×C4#45511yescharacteristic
239C2×C4#45611yescharacteristic
240C2×C4#45611yescharacteristic
241C8—42no—
242C8—42no—
243C8—44no—
244C8—81no—
245C8—81no—
246C8—81no—
247C8—81no—
248C8—81no—
249C8—81no—
250C8—161no—
251C22#185511yescharacteristic
252C22#185711yescharacteristic
253C22#185911yescharacteristic
254C22#186011yescharacteristic
255C22#186611yescharacteristic
256C22#186611yescharacteristic
257C22#186811yescharacteristic
258C4—21no—
259C4—21no—
260C4—21no—
261C4—21no—
262C4—21no—
263C4—21no—
264C4—41no—
265C4—42no—
266C4—41no—
267C4—41no—
268C4—81no—
269C4—81no—
270C4—81no—
271C4#165711yescharacteristic
272C4#166111yescharacteristic
273C4#166311yescharacteristic
274C4#166411yescharacteristic
275C2#886511yescharacteristic
276C2#887611yescharacteristic
277C2#887711yescharacteristic
278C2#889811yescharacteristic
279C2#890111yescharacteristic
280C2#891211yescharacteristic
281C2#893611yescharacteristic
subgroupG/H
centerC22×C4#120
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
socle, prime radicalC23#385
LCSG ▷ C2×C42 ▷ C23 ▷ 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
#233712
#98762
#88122
#87892
#75682
#70302