Finite Group Databasebeta

← #104144

Subgroups — #104144

Order 512.

622 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 100 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#29756C211yesmaximal, characteristic
2#27960C211yesmaximal, characteristic
3#15145C211yesmaximal, characteristic
4#9909C211yesmaximal, characteristic
5#8723C211yesmaximal, characteristic
6#7573C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8C2×#483—21no—
9#2857C2211yescharacteristic
10C2×#398—22no—
11C2×#389C2211yescharacteristic
12C2×#384—21no—
13C2×#384C2211yescharacteristic
14#2099—22no—
15#2084—21no—
16#2066—22no—
17#2043—21no—
18#1990—21no—
19#1872—21no—
20#1834—21no—
21#1823—22no—
22#1797C2211yescharacteristic
23#1797C2211yescharacteristic
24C4×C22⋊C8C2211yescharacteristic
25#1444—22no—
26C4⋊#95—21no—
27C4×#95C2211yescharacteristic
28#1296—22no—
29#1294—22no—
30#1271—22no—
31C2×C4⋊Q8D411yescharacteristic
32C2×C22⋊Q8—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—24no—
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D412yes—
39C22×C4⋊C4D411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42#483—42no—
43#483—42no—
44C2×#106—22no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8D412yes—
47C2×#103—22no—
48C2×#103—22no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C4×C8—21no—
53#398—44no—
54#398—44no—
55#391—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#384—21no—
63#384—21no—
64#384—21no—
65#384—21no—
66#384—42no—
67#384—42no—
68#384D411yescharacteristic
69#380—21no—
70#380—21no—
71C2×#95—21no—
72C2×#95—24no—
73C2×#95—21no—
74C2×#95D412yes—
75#340—22no—
76#340—24no—
77#340—24no—
78#336—21no—
79#336—21no—
80#336D412yes—
81C22×Q8—21no—
82C23×C4—22no—
83C23×C4—21no—
84C23×C4—22no—
85C23×C4—21no—
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C22×C8—22no—
90C22×C8—22no—
91C22×C8—41no—
92C4⋊Q8—42no—
93C22⋊Q8—41no—
94C22⋊Q8—41no—
95C22⋊Q8—41no—
96C22⋊Q8—41no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—22no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—44no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—48no—
114C2×C4⋊C4—48no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—42no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—84no—
131C2×C4⋊C4D812yes—
132C2×C22⋊C4—41no—
133C2×C42—24no—
134C2×C42—42no—
135C2×C42—42no—
136C2×C42—41no—
137C2×C42—41no—
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42C2×D411yescharacteristic
141C2×C42#4111yescharacteristic
142#106—44no—
143C4⋊C8—42no—
144C4⋊C8—42no—
145#103—44no—
146#103—82no—
147C22⋊C8—42no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—42no—
151C4×C8—42no—
152#95—24no—
153#95—22no—
154#95—48no—
155#95—41no—
156#95—41no—
157#95—41no—
158#95—41no—
159#95SD1614yes—
160C24#12011yescharacteristic
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—42no—
164C2×Q8—42no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—24no—
168C22×C4—24no—
169C22×C4—24no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4—44no—
194C22×C4—44no—
195C22×C4#12011yescharacteristic
196C22×C4#12011yescharacteristic
197C22×C4#12111yescharacteristic
198C22×C4#12111yescharacteristic
199C22×C4#12111yescharacteristic
200C22×C4#12711yescharacteristic
201C22×C4C2×D811yescharacteristic
202C22×C4C2×SD1612yes—
203C22×C4#13511yescharacteristic
204C22×C4AGL(1,ℤ/8)11yescharacteristic
205C22×C4AGL(1,ℤ/8)11yescharacteristic
206C22×C4AGL(1,ℤ/8)12yes—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—81no—
214C2×C8—81no—
215C2×C8—81no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—44no—
219C4⋊C4—42no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C4⋊C4—82no—
229C4⋊C4—81no—
230C4⋊C4—816no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C4⋊C4—82no—
234C4⋊C4—82no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C4⋊C4—81no—
238C4⋊C4—81no—
239C4⋊C4—81no—
240C4⋊C4—81no—
241C4⋊C4—81no—
242C4⋊C4—81no—
243C22⋊C4—81no—
244C22⋊C4—81no—
245C42—22no—
246C42—22no—
247C42—41no—
248C42—41no—
249C42—44no—
250C42—44no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23#39211yescharacteristic
256C23#44711yescharacteristic
257C23#44911yescharacteristic
258C23#45012yes—
259C23#45512yes—
260Q8—82no—
261Q8—82no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—28no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—44no—
285C2×C4—44no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—82no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—84no—
293C2×C4—84no—
294C2×C4—84no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—82no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4#44711yescharacteristic
308C2×C4#44911yescharacteristic
309C2×C4#45612yes—
310C2×C4#45612yes—
311C2×C4#45812yes—
312C2×C4#46012yes—
313C2×C4#46611yescharacteristic
314C2×C4#46911yescharacteristic
315C2×C4#49211yescharacteristic
316C2×C4#49611yescharacteristic
317C8—82no—
318C8—82no—
319C8—161no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—21no—
326C22—21no—
327C22—22no—
328C22#163912yes—
329C22#164212yes—
330C22#199911yescharacteristic
331C22#200411yescharacteristic
332C22#200511yescharacteristic
333C22#200511yescharacteristic
334C22#200911yescharacteristic
335C22#201411yescharacteristic
336C22#202211yescharacteristic
337C4—22no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—22no—
342C4—21no—
343C4—48no—
344C4—41no—
345C4—82no—
346C4—161no—
347C4—162no—
348C4—161no—
349C4—161no—
350C4#160912yes—
351C4#161012yes—
352C2—22no—
353C2—22no—
354C2#991911yescharacteristic
355C2#996011yescharacteristic
356C2#1006211yescharacteristic
357C2#1009911yescharacteristic
358C2#1024311yescharacteristic
359C2#1029911yescharacteristic
360C2#1033511yescharacteristic
subgroupG/H
center, socleC23#392
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#120
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#297562
#279602
#151452
#99092
#87232
#75732
#70282