Finite Group Databasebeta

← #101456

Subgroups — #101456

Order 512.

373 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 373 conjugacy classes of subgroups — too many to draw. Only its 96 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#29276C211yesmaximal, characteristic
2#22242C211yesmaximal, characteristic
3#9874C211yesmaximal, characteristic
4#8589C211yesmaximal, characteristic
5#7653C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic
7#7018C211yesmaximal, characteristic
8C2×#446—21no—
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2100C412yes—
12#2058C412yes—
13#1988—21no—
14#1984—21no—
15#1948—21no—
16#1920—22no—
17#1917—22no—
18#1917—22no—
19#1842C2211yescharacteristic
20#1831C2211yescharacteristic
21#1831C2211yescharacteristic
22#1831C2211yescharacteristic
23#1744C2211yescharacteristic
24C2×#332—21no—
25#1296—21no—
26#1279—21no—
27#1279—21no—
28#1272—22no—
29C2×C4⋊Q8C2×C411yescharacteristic
30C2×C4⋊Q8D411yescharacteristic
31C2×C4×Q8—21no—
32C2×C4×Q8—21no—
33#446—42no—
34#446—42no—
35C2×#106—22no—
36C2×C4⋊C8—22no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×#97—22no—
44C2×C4×C8D411yescharacteristic
45C2×C4×C8D411yescharacteristic
46#391—21no—
47#391—21no—
48#389—21no—
49#389—21no—
50#389—21no—
51#389C2×C412yes—
52#384C2×C411yescharacteristic
53#384D411yescharacteristic
54C4×C4⋊C4—21no—
55C4×C4⋊C4—21no—
56C4×C4⋊C4—21no—
57C4×C4⋊C4D412yes—
58C43C2311yescharacteristic
59#340—22no—
60#340—22no—
61#340—22no—
62#336—24no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
69#336C2×C412yes—
70#336D412yes—
71#332—42no—
72C22×Q8—21no—
73C22×Q8—21no—
74C22×C8—21no—
75C22×C8—22no—
76C22×C8—21no—
77C22×C8—22no—
78C22×C8—41no—
79C22×C8—41no—
80C4⋊Q8—21no—
81C4⋊Q8—21no—
82C4⋊Q8—21no—
83C4⋊Q8—21no—
84C4⋊Q8—42no—
85C4×Q8—41no—
86C4×Q8—41no—
87C4×Q8—41no—
88C4×Q8—41no—
89C4×Q8—81no—
90C4×Q8—81no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—22no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4C22⋊C412yes—
102C2×C4⋊C4C22⋊C412yes—
103C2×C42—22no—
104C2×C42—41no—
105C2×C42C22×C411yescharacteristic
106C2×C42C2×D411yescharacteristic
107C2×C42C2×D411yescharacteristic
108C2×C42C2×D411yescharacteristic
109C2×C42C2×D411yescharacteristic
110C2×C42#4111yescharacteristic
111C2×C42#4111yescharacteristic
112#106—44no—
113C4⋊C8—44no—
114C4⋊C8—41no—
115C4⋊C8—41no—
116C4⋊C8—41no—
117C4⋊C8—41no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—81no—
125#97—44no—
126C4×C8—21no—
127C4×C8—21no—
128C4×C8—21no—
129C4×C8SD1612yes—
130#95—22no—
131#95—22no—
132#95—41no—
133#95—41no—
134C2×Q8—22no—
135C2×Q8—41no—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—81no—
143C2×Q8—81no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—41no—
147C22×C4—41no—
148C22×C4C2×C22⋊C411yescharacteristic
149C22×C4C4×D411yescharacteristic
150C22×C4C4×D411yescharacteristic
151C22×C4#12011yescharacteristic
152C22×C4#12111yescharacteristic
153C22×C4#12111yescharacteristic
154C22×C4#12311yescharacteristic
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—42no—
159C2×C8—41no—
160C2×C8—42no—
161C2×C8—42no—
162C2×C8—41no—
163C2×C8—42no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—41no—
167C2×C8—81no—
168C2×C8—81no—
169C2×C8—81no—
170C2×C8—81no—
171C2×C8—81no—
172C2×C8—81no—
173C4⋊C4—22no—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—42no—
178C4⋊C4—41no—
179C4⋊C4—41no—
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—81no—
189C4⋊C4—81no—
190C4⋊C4—82no—
191C42—21no—
192C42—21no—
193C42—41no—
194C42—41no—
195C42—41no—
196C42—41no—
197C42—42no—
198C42—42no—
199C42—81no—
200C42—81no—
201C42C2×SD1611yescharacteristic
202C42#13511yescharacteristic
203C42AGL(1,ℤ/8)11yescharacteristic
204C42AGL(1,ℤ/8)11yescharacteristic
205C42#13711yescharacteristic
206C42#13711yescharacteristic
207C42#13711yescharacteristic
208C42#13711yescharacteristic
209C23#38611yescharacteristic
210Q8—82no—
211Q8—82no—
212Q8—81no—
213Q8—81no—
214Q8—81no—
215Q8—81no—
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—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—81no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4#41711yescharacteristic
243C2×C4#41911yescharacteristic
244C2×C4C4×SD1611yescharacteristic
245C2×C4#44011yescharacteristic
246C2×C4#45011yescharacteristic
247C2×C4#45211yescharacteristic
248C2×C4#46111yescharacteristic
249C2×C4#46311yescharacteristic
250C2×C4#46811yescharacteristic
251C2×C4#46811yescharacteristic
252C2×C4#47011yescharacteristic
253C2×C4#47011yescharacteristic
254C2×C4#47111yescharacteristic
255C2×C4#47211yescharacteristic
256C8—42no—
257C8—82no—
258C8—82no—
259C8—81no—
260C8—161no—
261C8—161no—
262C22#187711yescharacteristic
263C22#188111yescharacteristic
264C22#189111yescharacteristic
265C22#189411yescharacteristic
266C22#190511yescharacteristic
267C22#190711yescharacteristic
268C22#191211yescharacteristic
269C4—21no—
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—21no—
277C4—41no—
278C4—41no—
279C4—82no—
280C4—82no—
281C4—82no—
282C4—161no—
283C4#169111yescharacteristic
284C4#169511yescharacteristic
285C4#169711yescharacteristic
286C4#170311yescharacteristic
287C2#904711yescharacteristic
288C2#922311yescharacteristic
289C2#929611yescharacteristic
290C2#930811yescharacteristic
291C2#937211yescharacteristic
292C2#948811yescharacteristic
293C2#953011yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ 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
#292762
#222422
#98742
#85892
#76532
#70402
#70182