Finite Group Databasebeta

← #103748

Subgroups — #103748

Order 512.

453 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 453 conjugacy classes of subgroups — too many to draw. Only its 114 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#29218C211yesmaximal, characteristic
3#29208C211yesmaximal, characteristic
4#9691C211yesmaximal, characteristic
5#9673C211yesmaximal, characteristic
6#7571C211yesmaximal, characteristic
7#7031C211yesmaximal, characteristic
8#2868C2211yescharacteristic
9C4×C4⋊Q8C2211yescharacteristic
10C4×C4⋊Q8C2211yescharacteristic
11#2100—22no—
12#2088—22no—
13#2057—22no—
14#1990—21no—
15#1990—21no—
16#1988—21no—
17#1987—22no—
18#1987—21no—
19#1948—21no—
20#1948—21no—
21#1947—22no—
22#1845—21no—
23#1842C2211yescharacteristic
24#1834—21no—
25C4×C4⋊C8C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27C4×C4⋊C8C2211yescharacteristic
28C2×#333—22no—
29C2×Q8⋊C8—22no—
30#1272—22no—
31C2×C4⋊Q8—21no—
32C2×C4⋊Q8—21no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C4⋊Q8D411yescharacteristic
35C2×C4⋊Q8D412yes—
36C2×C4×Q8—21no—
37C2×C4×Q8—21no—
38C2×#107—24no—
39C2×#106—22no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D412yes—
45C2×C4⋊C8D412yes—
46C2×C4×C8—21no—
47C2×C4×C8—21no—
48C2×C4×C8—21no—
49#391—21no—
50#391—21no—
51#389—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#384—21no—
56#384—21no—
57#384—21no—
58#384—21no—
59#384D411yescharacteristic
60#384D411yescharacteristic
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C43C2311yescharacteristic
66#340—24no—
67#340—22no—
68#340—22no—
69#340—22no—
70#340—24no—
71#340—24no—
72#336—21no—
73#336—21no—
74#336D412yes—
75#333—44no—
76Q8⋊C8—44no—
77C22×Q8—21no—
78C22×Q8—21no—
79C22×Q8—22no—
80C22×C8—22no—
81C22×C8—22no—
82C22×C8—22no—
83C22×C8—41no—
84C4⋊Q8—21no—
85C4⋊Q8—21no—
86C4⋊Q8—21no—
87C4⋊Q8—21no—
88C4⋊Q8—21no—
89C4⋊Q8—21no—
90C4⋊Q8—44no—
91C4⋊Q8—42no—
92C4⋊Q8—42no—
93C4⋊Q8—82no—
94C4⋊Q8Q1612yes—
95C4⋊Q8Q1612yes—
96C4×Q8—42no—
97C4×Q8—42no—
98C4×Q8—82no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—22no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C42—41no—
118C2×C42—41no—
119C2×C42C2×D411yescharacteristic
120C2×C42C2×D411yescharacteristic
121C2×C42C2×D411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42#4111yescharacteristic
126#107—84no—
127#106—82no—
128C4⋊C8—22no—
129C4⋊C8—22no—
130C4⋊C8—42no—
131C4⋊C8—41no—
132C4⋊C8—42no—
133C4⋊C8—41no—
134C4⋊C8—41no—
135C4⋊C8—41no—
136C4⋊C8—41no—
137C4⋊C8SD1614yes—
138C4×C8—42no—
139C4×C8—41no—
140C4×C8—41no—
141C4×C8—41no—
142C4×C8—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147C2×Q8—22no—
148C2×Q8—22no—
149C2×Q8—44no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—42no—
153C2×Q8—42no—
154C2×Q8—81no—
155C2×Q8—81no—
156C2×Q8—82no—
157C2×Q8—82no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—42no—
163C22×C4#12011yescharacteristic
164C22×C4#12011yescharacteristic
165C22×C4#12011yescharacteristic
166C22×C4#12111yescharacteristic
167C22×C4#12111yescharacteristic
168C22×C4#12111yescharacteristic
169C22×C4#12711yescharacteristic
170C2×C8—24no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—81no—
181C2×C8—81no—
182C4⋊C4—22no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—42no—
187C4⋊C4—44no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—42no—
197C4⋊C4—44no—
198C4⋊C4—42no—
199C4⋊C4—81no—
200C4⋊C4—82no—
201C4⋊C4—82no—
202C4⋊C4—82no—
203C4⋊C4—81no—
204C4⋊C4—81no—
205C4⋊C4—82no—
206C4⋊C4—81no—
207C4⋊C4—81no—
208C42—21no—
209C42—21no—
210C42—22no—
211C42—22no—
212C42—41no—
213C42—82no—
214C42—82no—
215C42C2×SD1612yes—
216C42C2×Q1611yescharacteristic
217C42C2×Q1611yescharacteristic
218C42#13511yescharacteristic
219C42#13511yescharacteristic
220C42#13712yes—
221C42#13711yescharacteristic
222C42#13711yescharacteristic
223C42#13711yescharacteristic
224C42#13711yescharacteristic
225C23#39211yescharacteristic
226Q8—44no—
227Q8—82no—
228Q8—82no—
229Q8—82no—
230Q8—164no—
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—42no—
241C2×C4—42no—
242C2×C4—81no—
243C2×C4—81no—
244C2×C4—81no—
245C2×C4—81no—
246C2×C4—82no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—82no—
255C2×C4#44812yes—
256C2×C4#45111yescharacteristic
257C2×C4#45111yescharacteristic
258C2×C4#45111yescharacteristic
259C2×C4#45111yescharacteristic
260C2×C4#45211yescharacteristic
261C2×C4#45211yescharacteristic
262C2×C4#45211yescharacteristic
263C2×C4#45211yescharacteristic
264C2×C4#45311yescharacteristic
265C2×C4#45411yescharacteristic
266C2×C4#45512yes—
267C2×C4#46112yes—
268C2×C4#46711yescharacteristic
269C2×C4#46711yescharacteristic
270C2×C4#47011yescharacteristic
271C2×C4#47011yescharacteristic
272C2×C4#47212yes—
273C2×C4#49211yescharacteristic
274C2×C4#49711yescharacteristic
275C8—44no—
276C8—82no—
277C8—82no—
278C8—82no—
279C22#200111yescharacteristic
280C22#200111yescharacteristic
281C22#200411yescharacteristic
282C22#200611yescharacteristic
283C22#200911yescharacteristic
284C22#201311yescharacteristic
285C22#201811yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—21no—
292C4—41no—
293C4—82no—
294C4—82no—
295C4—161no—
296C4—162no—
297C4—161no—
298C4#163011yescharacteristic
299C4#163311yescharacteristic
300C4#163611yescharacteristic
301C4#163611yescharacteristic
302C4#164312yes—
303C4#164512yes—
304C4#167512yes—
305C4#169512yes—
306C2#1007311yescharacteristic
307C2#1011211yescharacteristic
308C2#1019011yescharacteristic
309C2#1020111yescharacteristic
310C2#1023711yescharacteristic
311C2#1025211yescharacteristic
312C2#1027811yescharacteristic
subgroupG/H
center, socle, prime radicalC23#392
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
#292182
#292082
#96912
#96732
#75712
#70312