Finite Group Databasebeta

← #104969

Subgroups — #104969

Order 512.

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

normal subgroups only

This group has 335 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#29287C211yesmaximal, characteristic
2#8810C211yesmaximal, characteristic
3#8591C211yesmaximal, characteristic
4#8590C211yesmaximal, characteristic
5#7591C211yesmaximal, characteristic
6#7590C211yesmaximal, characteristic
7#7040C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2088—22no—
11#1988—21no—
12#1987—21no—
13#1948—21no—
14#1948—21no—
15#1842C2211yescharacteristic
16#1842C2211yescharacteristic
17#1831C2211yescharacteristic
18#1831C2211yescharacteristic
19#1744C2211yescharacteristic
20C2×#335—22no—
21C2×#333—21no—
22C2×#332—21no—
23#1296—21no—
24#1296—21no—
25#1272—22no—
26#1271—22no—
27C2×C4⋊Q8D411yescharacteristic
28C2×C4⋊Q8D411yescharacteristic
29C2×C4×Q8—21no—
30C2×C4×Q8—21no—
31C2×#106—22no—
32C2×C4⋊C8—21no—
33C2×C4⋊C8—21no—
34C2×C4⋊C8—21no—
35C2×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8D412yes—
40C2×C4×C8—21no—
41#391—21no—
42#391—21no—
43#389—21no—
44#389—21no—
45#389—21no—
46#389—21no—
47#384D411yescharacteristic
48#384D411yescharacteristic
49C4×C4⋊C4—21no—
50C4×C4⋊C4—21no—
51C4×C4⋊C4—21no—
52C4×C4⋊C4—21no—
53C43C2311yescharacteristic
54#340—22no—
55#340—22no—
56#340—22no—
57#336—21no—
58#336—21no—
59#336—21no—
60#336—21no—
61#336—21no—
62#336D412yes—
63#335—44no—
64#333—42no—
65#332—42no—
66C22×Q8—21no—
67C22×Q8—21no—
68C22×C8—22no—
69C22×C8—22no—
70C22×C8—41no—
71C22×C8—41no—
72C22×C8—41no—
73C4⋊Q8—21no—
74C4⋊Q8—21no—
75C4⋊Q8—21no—
76C4⋊Q8—21no—
77C4⋊Q8—21no—
78C4⋊Q8—21no—
79C4⋊Q8Q1612yes—
80C4⋊Q8Q1612yes—
81C4×Q8—82no—
82C4×Q8—82no—
83C2×C4⋊C4—21no—
84C2×C4⋊C4—21no—
85C2×C4⋊C4—21no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4—21no—
88C2×C4⋊C4—21no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—41no—
94C2×C4⋊C4—41no—
95C2×C42—41no—
96C2×C42—41no—
97C2×C42C2×D411yescharacteristic
98C2×C42C2×D411yescharacteristic
99C2×C42C2×D411yescharacteristic
100C2×C42C2×D411yescharacteristic
101C2×C42#4111yescharacteristic
102C2×C42#4111yescharacteristic
103C2×C42#4111yescharacteristic
104#106—82no—
105C4⋊C8—42no—
106C4⋊C8—42no—
107C4⋊C8—41no—
108C4⋊C8—41no—
109C4⋊C8—41no—
110C4⋊C8—41no—
111C4⋊C8—41no—
112C4⋊C8—41no—
113C4⋊C8—41no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4×C8—22no—
120C4×C8—22no—
121#95—41no—
122#95—41no—
123#95—41no—
124#95—41no—
125C2×Q8—22no—
126C2×Q8—22no—
127C2×Q8—41no—
128C2×Q8—41no—
129C2×Q8—81no—
130C2×Q8—81no—
131C2×Q8—81no—
132C2×Q8—81no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4—41no—
136C22×C4—41no—
137C22×C4#12011yescharacteristic
138C22×C4#12111yescharacteristic
139C22×C4#12111yescharacteristic
140C22×C4#12111yescharacteristic
141C22×C4#12311yescharacteristic
142C22×C4#12311yescharacteristic
143C22×C4#12411yescharacteristic
144C2×C8—24no—
145C2×C8—42no—
146C2×C8—42no—
147C2×C8—42no—
148C2×C8—42no—
149C2×C8—42no—
150C2×C8—81no—
151C2×C8—81no—
152C2×C8—81no—
153C2×C8—81no—
154C2×C8—81no—
155C2×C8—81no—
156C2×C8—81no—
157C2×C8—81no—
158C2×C8—81no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—81no—
172C4⋊C4—81no—
173C4⋊C4—81no—
174C4⋊C4—81no—
175C4⋊C4—82no—
176C4⋊C4—82no—
177C42—21no—
178C42—21no—
179C42—22no—
180C42—41no—
181C42—41no—
182C42—41no—
183C42—82no—
184C42—82no—
185C42C2×Q1611yescharacteristic
186C42C2×Q1611yescharacteristic
187C42#13511yescharacteristic
188C42#13511yescharacteristic
189C42AGL(1,ℤ/8)11yescharacteristic
190C42AGL(1,ℤ/8)11yescharacteristic
191C42#13711yescharacteristic
192C42#13711yescharacteristic
193C23#39411yescharacteristic
194Q8—82no—
195Q8—82no—
196Q8—82no—
197Q8—82no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
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—21no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—81no—
214C2×C4—81no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4—81no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—81no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4#44911yescharacteristic
224C2×C4#44911yescharacteristic
225C2×C4#45111yescharacteristic
226C2×C4#45111yescharacteristic
227C2×C4#45311yescharacteristic
228C2×C4#45611yescharacteristic
229C2×C4#46711yescharacteristic
230C2×C4#46711yescharacteristic
231C2×C4#46811yescharacteristic
232C2×C4#46811yescharacteristic
233C2×C4#47112yes—
234C2×C4#48411yescharacteristic
235C2×C4#48411yescharacteristic
236C2×C4#48511yescharacteristic
237C2×C4#48511yescharacteristic
238C8—44no—
239C8—82no—
240C8—161no—
241C8—161no—
242C8—161no—
243C22#203611yescharacteristic
244C22#203611yescharacteristic
245C22#203911yescharacteristic
246C22#204611yescharacteristic
247C22#204811yescharacteristic
248C22#204911yescharacteristic
249C22#205311yescharacteristic
250C4—22no—
251C4—21no—
252C4—21no—
253C4—21no—
254C4—21no—
255C4—21no—
256C4—21no—
257C4—21no—
258C4—21no—
259C4—41no—
260C4—82no—
261C4—82no—
262C4—161no—
263C4—161no—
264C4#162011yescharacteristic
265C4#163311yescharacteristic
266C4#164811yescharacteristic
267C4#164811yescharacteristic
268C2#1043911yescharacteristic
269C2#1045111yescharacteristic
270C2#1045311yescharacteristic
271C2#1046911yescharacteristic
272C2#1047111yescharacteristic
273C2#1051411yescharacteristic
274C2#1052611yescharacteristic
subgroupG/H
center, socle, prime radicalC23#394
commutator, Frattini, cosocleC43C23
LCSG ▷ C43 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ 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
#292872
#88102
#85912
#85902
#75912
#75902
#70402