Finite Group Databasebeta

← #105148

Subgroups — #105148

Order 512.

336 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 84 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#29147C211yesmaximal, characteristic
2#9697C211yesmaximal, characteristic
3#9604C211yesmaximal, characteristic
4#8589C211yesmaximal, characteristic
5#7662C211yesmaximal, characteristic
6#7570C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8#2862C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10#2024—21no—
11#2024—21no—
12#1960—21no—
13#1842C2211yescharacteristic
14#1836—21no—
15#1831C2211yescharacteristic
16#1805—21no—
17#1805—21no—
18#1767C2211yescharacteristic
19C4×C4⋊C8C2211yescharacteristic
20C4×C4⋊C8C2211yescharacteristic
21C2×#335—21no—
22C2×#333—21no—
23C2×#332—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×C4⋊C8—21no—
36C2×C4⋊C8—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—21no—
39C2×C4⋊C8—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8D411yescharacteristic
42C2×C4⋊C8D411yescharacteristic
43C2×#103—21no—
44C2×#103—21no—
45C2×#103—21no—
46C2×#103—21no—
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#335—42no—
74#333—42no—
75#332—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⋊Q8Q1612yes—
95C4×Q8—41no—
96C4×Q8—41no—
97C4×Q8—41no—
98C4×Q8—41no—
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—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—41no—
109C2×C42—41no—
110C2×C42C2×D411yescharacteristic
111C2×C42C2×D411yescharacteristic
112C2×C42C2×D411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116C2×C42#4111yescharacteristic
117C4⋊C8—22no—
118C4⋊C8—21no—
119C4⋊C8—21no—
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—
132#103—81no—
133#103—81no—
134#103—81no—
135#103—81no—
136#97—41no—
137#97—41no—
138C4×C8—41no—
139C4×C8—41no—
140C4×C8—81no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147C2×Q8—22no—
148C2×Q8—42no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—81no—
157C2×Q8—81no—
158C2×Q8—81no—
159C2×Q8—81no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4#12011yescharacteristic
165C22×C4#12111yescharacteristic
166C22×C4#12111yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12311yescharacteristic
169C22×C4#12311yescharacteristic
170C22×C4#12411yescharacteristic
171C2×C8—22no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—42no—
175C2×C8—41no—
176C2×C8—41no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—81no—
185C2×C8—81no—
186C2×C8—81no—
187C2×C8—81no—
188C2×C8—81no—
189C2×C8—81no—
190C2×C8—81no—
191C2×C8—81no—
192C4⋊C4—22no—
193C4⋊C4—22no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—81no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—41no—
213C42—41no—
214C42—41no—
215C42—81no—
216C42—81no—
217C42C2×Q1611yescharacteristic
218C42#13511yescharacteristic
219C42#13511yescharacteristic
220C42#13511yescharacteristic
221C42AGL(1,ℤ/8)11yescharacteristic
222C42AGL(1,ℤ/8)11yescharacteristic
223C42#13711yescharacteristic
224C42#13711yescharacteristic
225C23#39411yescharacteristic
226Q8—42no—
227Q8—42no—
228Q8—81no—
229Q8—81no—
230Q8—161no—
231Q8—161no—
232Q8—162no—
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—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4#44911yescharacteristic
259C2×C4#44911yescharacteristic
260C2×C4#45111yescharacteristic
261C2×C4#45211yescharacteristic
262C2×C4#45311yescharacteristic
263C2×C4#45511yescharacteristic
264C2×C4#46311yescharacteristic
265C2×C4#46411yescharacteristic
266C2×C4#46711yescharacteristic
267C2×C4#46811yescharacteristic
268C2×C4#47111yescharacteristic
269C2×C4#47311yescharacteristic
270C2×C4#48411yescharacteristic
271C2×C4#48511yescharacteristic
272C2×C4#48811yescharacteristic
273C2×C4#48911yescharacteristic
274C8—42no—
275C8—81no—
276C8—82no—
277C8—81no—
278C8—81no—
279C8—161no—
280C8—161no—
281C22#203611yescharacteristic
282C22#203711yescharacteristic
283C22#204211yescharacteristic
284C22#204911yescharacteristic
285C22#205011yescharacteristic
286C22#205211yescharacteristic
287C22#205311yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—41no—
299C4—82no—
300C4—161no—
301C4—161no—
302C4—161no—
303C4#162411yescharacteristic
304C4#163211yescharacteristic
305C4#164411yescharacteristic
306C4#164611yescharacteristic
307C2#1041311yescharacteristic
308C2#1046311yescharacteristic
309C2#1047111yescharacteristic
310C2#1049811yescharacteristic
311C2#1051011yescharacteristic
312C2#1054711yescharacteristic
313C2#1055411yescharacteristic
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
#291472
#96972
#96042
#85892
#76622
#75702
#70222