Finite Group Databasebeta

← #105152

Subgroups — #105152

Order 512.

336 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 88 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#29211C211yesmaximal, characteristic
2#9697C211yesmaximal, characteristic
3#9605C211yesmaximal, characteristic
4#8590C211yesmaximal, characteristic
5#7662C211yesmaximal, characteristic
6#7570C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8#2862C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2058—21no—
11#2057—21no—
12#1993—21no—
13#1949—21no—
14#1949—21no—
15#1847—21no—
16#1842C2211yescharacteristic
17#1831C2211yescharacteristic
18#1767C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C4×C4⋊C8C2211yescharacteristic
21C2×#334—21no—
22C2×#333—21no—
23C2×#333—21no—
24C2×#332—21no—
25#1296—21no—
26#1277—21no—
27#1272—21no—
28#1272—21no—
29#1271—21no—
30#1271—21no—
31C2×C4⋊Q8D411yescharacteristic
32C2×C4⋊Q8D411yescharacteristic
33C2×C4⋊Q8D411yescharacteristic
34C2×C4×Q8—21no—
35C2×#107—21no—
36C2×#107—21no—
37C2×#106—21no—
38C2×#106—21no—
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×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×#97—21no—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50#391—21no—
51#391—21no—
52#391—21no—
53#391—21no—
54#391—21no—
55#389—21no—
56#389—21no—
57#384D411yescharacteristic
58#382—21no—
59#382—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62C43C2311yescharacteristic
63#340—21no—
64#340—21no—
65#340—21no—
66#340—21no—
67#336—21no—
68#336—21no—
69#336—21no—
70#336—21no—
71#336D411yescharacteristic
72#336D411yescharacteristic
73#334—42no—
74#333—42no—
75#333—42no—
76#332—42no—
77C22×Q8—21no—
78C22×Q8—21no—
79C22×Q8—21no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—21no—
83C22×C8—21no—
84C22×C8—41no—
85C22×C8—41no—
86C22×C8—41no—
87C4⋊Q8—21no—
88C4⋊Q8—21no—
89C4⋊Q8—21no—
90C4⋊Q8—41no—
91C4⋊Q8—41no—
92C4⋊Q8—41no—
93C4⋊Q8—41no—
94C4⋊Q8SD1612yes—
95C4×Q8—81no—
96C4×Q8—81no—
97C2×C4⋊C4—21no—
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—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—41no—
107C2×C42—41no—
108C2×C42C2×D411yescharacteristic
109C2×C42C2×D411yescharacteristic
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42#4111yescharacteristic
113C2×C42#4111yescharacteristic
114C2×C42#4111yescharacteristic
115#107—81no—
116#107—81no—
117#106—81no—
118#106—81no—
119C4⋊C8—22no—
120C4⋊C8—21no—
121C4⋊C8—21no—
122C4⋊C8—41no—
123C4⋊C8—41no—
124C4⋊C8—41no—
125C4⋊C8—42no—
126C4⋊C8—41no—
127C4⋊C8—41no—
128C4⋊C8—41no—
129C4⋊C8—41no—
130C4⋊C8—41no—
131C4⋊C8—41no—
132C4⋊C8SD1612yes—
133C4⋊C8Q1612yes—
134#97—41no—
135#97—41no—
136C4×C8—41no—
137C4×C8—41no—
138C4×C8—81no—
139#95—41no—
140#95—41no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—41no—
145C2×Q8—22no—
146C2×Q8—42no—
147C2×Q8—41no—
148C2×Q8—41no—
149C2×Q8—41no—
150C2×Q8—81no—
151C2×Q8—81no—
152C2×Q8—81no—
153C2×Q8—81no—
154C2×Q8—81no—
155C2×Q8—81no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4#12011yescharacteristic
161C22×C4#12111yescharacteristic
162C22×C4#12111yescharacteristic
163C22×C4#12111yescharacteristic
164C22×C4#12311yescharacteristic
165C22×C4#12311yescharacteristic
166C22×C4#12411yescharacteristic
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—22no—
170C2×C8—41no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—42no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—81no—
181C2×C8—81no—
182C2×C8—81no—
183C2×C8—81no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—42no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—81no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C4⋊C4—81no—
203C4⋊C4—81no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—41no—
209C42—41no—
210C42—41no—
211C42—82no—
212C42C2×SD1611yescharacteristic
213C42C2×SD1611yescharacteristic
214C42C2×Q1611yescharacteristic
215C42#13511yescharacteristic
216C42#13711yescharacteristic
217C42#13711yescharacteristic
218C42#13711yescharacteristic
219C42#13711yescharacteristic
220C23#39411yescharacteristic
221Q8—82no—
222Q8—82no—
223Q8—161no—
224Q8—161no—
225Q8—162no—
226C2×C4—21no—
227C2×C4—21no—
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—42no—
240C2×C4—81no—
241C2×C4—81no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4#44811yescharacteristic
252C2×C4#44811yescharacteristic
253C2×C4#45111yescharacteristic
254C2×C4#45211yescharacteristic
255C2×C4#45311yescharacteristic
256C2×C4#45511yescharacteristic
257C2×C4#46111yescharacteristic
258C2×C4#46211yescharacteristic
259C2×C4#46511yescharacteristic
260C2×C4#47011yescharacteristic
261C2×C4#47111yescharacteristic
262C2×C4#47211yescharacteristic
263C2×C4#48311yescharacteristic
264C2×C4#48511yescharacteristic
265C2×C4#48711yescharacteristic
266C2×C4#49111yescharacteristic
267C8—42no—
268C8—42no—
269C8—42no—
270C8—81no—
271C8—82no—
272C8—161no—
273C8—161no—
274C22#203511yescharacteristic
275C22#203711yescharacteristic
276C22#204311yescharacteristic
277C22#204911yescharacteristic
278C22#205011yescharacteristic
279C22#205111yescharacteristic
280C22#205311yescharacteristic
281C4—21no—
282C4—21no—
283C4—21no—
284C4—21no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—41no—
292C4—82no—
293C4—161no—
294C4—161no—
295C4—161no—
296C4#162311yescharacteristic
297C4#163211yescharacteristic
298C4#164311yescharacteristic
299C4#164511yescharacteristic
300C2#1041511yescharacteristic
301C2#1046011yescharacteristic
302C2#1047011yescharacteristic
303C2#1049811yescharacteristic
304C2#1050811yescharacteristic
305C2#1054811yescharacteristic
306C2#1055611yescharacteristic
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
#292112
#96972
#96052
#85902
#76622
#75702
#70222