Finite Group Databasebeta

← #101460

Subgroups — #101460

Order 512.

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

normal subgroups only

This group has 391 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#28205C211yesmaximal, characteristic
2#22242C211yesmaximal, characteristic
3#9874C211yesmaximal, characteristic
4#8589C211yesmaximal, characteristic
5#7652C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic
7#7018C211yesmaximal, characteristic
8C2×#475—21no—
9C2×#446—21no—
10C4×C4⋊Q8C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2084C412yes—
13#2043C412yes—
14#1984—21no—
15#1927—22no—
16#1917—22no—
17#1917—22no—
18#1842C2211yescharacteristic
19#1831C2211yescharacteristic
20#1831C2211yescharacteristic
21#1831C2211yescharacteristic
22#1803—21no—
23#1744C2211yescharacteristic
24C2×#332—21no—
25#1296—21no—
26#1279—21no—
27#1279—21no—
28#1271—22no—
29C2×C4⋊Q8C2×C411yescharacteristic
30C2×C4⋊Q8D411yescharacteristic
31C2×C4×Q8—21no—
32C2×C4×Q8—21no—
33#475—42no—
34#475—42no—
35#446—42no—
36#446—42no—
37C2×#106—22no—
38C2×C4⋊C8—22no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×#103—22no—
46C2×#103—22no—
47C2×#97—22no—
48C2×C4×C8D411yescharacteristic
49C2×C4×C8D411yescharacteristic
50#391—21no—
51#391—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389C2×C412yes—
56#384C2×C411yescharacteristic
57#384D411yescharacteristic
58C4×C4⋊C4—21no—
59C4×C4⋊C4—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4D412yes—
62C43C2311yescharacteristic
63#340—22no—
64#336—24no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
69#336—21no—
70#336—21no—
71#336C2×C412yes—
72#336D412yes—
73#332—42no—
74C22×Q8—21no—
75C22×Q8—21no—
76C22×C8—21no—
77C22×C8—22no—
78C22×C8—21no—
79C22×C8—22no—
80C22×C8—41no—
81C22×C8—41no—
82C4⋊Q8—21no—
83C4⋊Q8—21no—
84C4⋊Q8—21no—
85C4⋊Q8—21no—
86C4⋊Q8—42no—
87C4×Q8—41no—
88C4×Q8—41no—
89C4×Q8—41no—
90C4×Q8—41no—
91C4×Q8—41no—
92C4×Q8—41no—
93C4×Q8—41no—
94C4×Q8—41no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—22no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4C22⋊C412yes—
106C2×C4⋊C4C22⋊C412yes—
107C2×C42—22no—
108C2×C42—41no—
109C2×C42C22×C411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116#106—44no—
117C4⋊C8—44no—
118C4⋊C8—41no—
119C4⋊C8—41no—
120C4⋊C8—41no—
121C4⋊C8—41no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—41no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—81no—
129#103—44no—
130#103—44no—
131#97—44no—
132C4×C8—21no—
133C4×C8—21no—
134C4×C8—21no—
135C4×C8SD1612yes—
136#95—22no—
137#95—22no—
138#95—41no—
139#95—41no—
140C2×Q8—22no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8—41no—
146C2×Q8—41no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4C2×C22⋊C411yescharacteristic
157C22×C4C4×D411yescharacteristic
158C22×C4C4×D411yescharacteristic
159C22×C4#12011yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12111yescharacteristic
162C22×C4#12311yescharacteristic
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—42no—
167C2×C8—41no—
168C2×C8—42no—
169C2×C8—41no—
170C2×C8—42no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—41no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—81no—
180C2×C8—81no—
181C4⋊C4—22no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—41no—
187C4⋊C4—41no—
188C4⋊C4—42no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C42—21no—
202C42—21no—
203C42—41no—
204C42—41no—
205C42—41no—
206C42—41no—
207C42—42no—
208C42—42no—
209C42—81no—
210C42—81no—
211C42C2×SD1611yescharacteristic
212C42#13511yescharacteristic
213C42AGL(1,ℤ/8)11yescharacteristic
214C42AGL(1,ℤ/8)11yescharacteristic
215C42AGL(1,ℤ/8)11yescharacteristic
216C42AGL(1,ℤ/8)11yescharacteristic
217C42#13711yescharacteristic
218C42#13711yescharacteristic
219C23#38611yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—81no—
223Q8—81no—
224Q8—81no—
225Q8—81no—
226Q8—81no—
227Q8—81no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4#41711yescharacteristic
255C2×C4#41811yescharacteristic
256C2×C4C4×SD1611yescharacteristic
257C2×C4#44011yescharacteristic
258C2×C4#45011yescharacteristic
259C2×C4#45211yescharacteristic
260C2×C4#46111yescharacteristic
261C2×C4#46311yescharacteristic
262C2×C4#46811yescharacteristic
263C2×C4#46811yescharacteristic
264C2×C4#46911yescharacteristic
265C2×C4#46911yescharacteristic
266C2×C4#47111yescharacteristic
267C2×C4#47311yescharacteristic
268C8—42no—
269C8—82no—
270C8—82no—
271C8—81no—
272C8—161no—
273C8—161no—
274C22#187711yescharacteristic
275C22#188111yescharacteristic
276C22#189111yescharacteristic
277C22#189511yescharacteristic
278C22#190511yescharacteristic
279C22#190811yescharacteristic
280C22#191211yescharacteristic
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—82no—
292C4—82no—
293C4—82no—
294C4—161no—
295C4#169111yescharacteristic
296C4#169311yescharacteristic
297C4#169911yescharacteristic
298C4#170111yescharacteristic
299C2#904711yescharacteristic
300C2#922511yescharacteristic
301C2#929611yescharacteristic
302C2#931011yescharacteristic
303C2#937411yescharacteristic
304C2#949011yescharacteristic
305C2#952811yescharacteristic
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
#282052
#222422
#98742
#85892
#76522
#70402
#70182