Finite Group Databasebeta

← #104126

Subgroups — #104126

Order 512.

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

normal subgroups only

This group has 630 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#29757C211yesmaximal, characteristic
2#27950C211yesmaximal, characteristic
3#15145C211yesmaximal, characteristic
4#9909C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7576C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8C2×#484—21no—
9#2857C2211yescharacteristic
10C2×#398—22no—
11C2×#389C2211yescharacteristic
12C2×#384—21no—
13C2×#384C2211yescharacteristic
14#2083—21no—
15#2083—22no—
16#2068—22no—
17#2043—21no—
18#1990—21no—
19#1872—21no—
20#1852—22no—
21#1845—21no—
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—24no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D412yes—
39C22×C4⋊C4D411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42#484—42no—
43#484—42no—
44C2×#107—22no—
45C2×#107—24no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8D412yes—
48C2×#103—22no—
49C2×#103—22no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C4×C8—21no—
54#398—48no—
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#336—21no—
78#336—21no—
79#336D412yes—
80C22×Q8—21no—
81C23×C4—22no—
82C23×C4—21no—
83C23×C4—22no—
84C23×C4—21no—
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C22×C8—22no—
89C22×C8—22no—
90C22×C8—41no—
91C4⋊Q8—42no—
92C22⋊Q8—41no—
93C22⋊Q8—41no—
94C22⋊Q8—41no—
95C22⋊Q8—41no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—22no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—44no—
112C2×C4⋊C4—48no—
113C2×C4⋊C4—44no—
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—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—82no—
127C2×C4⋊C4—84no—
128C2×C4⋊C4D812yes—
129C2×C22⋊C4—41no—
130C2×C42—24no—
131C2×C42—42no—
132C2×C42—42no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42#4111yescharacteristic
139#107—44no—
140#107—84no—
141C4⋊C8—42no—
142C4⋊C8—42no—
143#103—44no—
144#103—82no—
145C22⋊C8—24no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—42no—
149C4×C8—42no—
150#95—24no—
151#95—22no—
152#95—48no—
153#95—41no—
154#95—41no—
155#95—41no—
156#95—41no—
157#95Q1614yes—
158C24#12011yescharacteristic
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—42no—
162C2×Q8—42no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—24no—
166C22×C4—24no—
167C22×C4—24no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—42no—
183C22×C4—44no—
184C22×C4—42no—
185C22×C4—44no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—42no—
190C22×C4—42no—
191C22×C4—42no—
192C22×C4—42no—
193C22×C4#12011yescharacteristic
194C22×C4#12011yescharacteristic
195C22×C4#12111yescharacteristic
196C22×C4#12111yescharacteristic
197C22×C4#12111yescharacteristic
198C22×C4#12711yescharacteristic
199C22×C4C2×D811yescharacteristic
200C22×C4C2×Q1612yes—
201C22×C4#13511yescharacteristic
202C22×C4AGL(1,ℤ/8)11yescharacteristic
203C22×C4AGL(1,ℤ/8)11yescharacteristic
204C22×C4#13712yes—
205C2×C8—24no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—42no—
211C2×C8—81no—
212C2×C8—81no—
213C2×C8—81no—
214C4⋊C4—22no—
215C4⋊C4—22no—
216C4⋊C4—42no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—42no—
222C4⋊C4—44no—
223C4⋊C4—42no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C4⋊C4—82no—
227C4⋊C4—81no—
228C4⋊C4—82no—
229C4⋊C4—82no—
230C4⋊C4—82no—
231C4⋊C4—816no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—82no—
235C4⋊C4—81no—
236C4⋊C4—81no—
237C4⋊C4—81no—
238C4⋊C4—81no—
239C22⋊C4—81no—
240C22⋊C4—81no—
241C42—22no—
242C42—22no—
243C42—41no—
244C42—41no—
245C42—44no—
246C42—44no—
247C23—21no—
248C23—21no—
249C23—21no—
250C23—21no—
251C23#39211yescharacteristic
252C23#44711yescharacteristic
253C23#44911yescharacteristic
254C23#45112yes—
255C23#45612yes—
256Q8—82no—
257Q8—82no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—28no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—42no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4—44no—
282C2×C4—44no—
283C2×C4—44no—
284C2×C4—42no—
285C2×C4—82no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—84no—
289C2×C4—84no—
290C2×C4—84no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—82no—
294C2×C4—82no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4#44711yescharacteristic
304C2×C4#44911yescharacteristic
305C2×C4#45312yes—
306C2×C4#45612yes—
307C2×C4#45812yes—
308C2×C4#46212yes—
309C2×C4#46611yescharacteristic
310C2×C4#46911yescharacteristic
311C2×C4#49411yescharacteristic
312C2×C4#49711yescharacteristic
313C8—44no—
314C8—82no—
315C8—161no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—21no—
323C22—21no—
324C22#164812yes—
325C22#164912yes—
326C22#199911yescharacteristic
327C22#200211yescharacteristic
328C22#200511yescharacteristic
329C22#200511yescharacteristic
330C22#200811yescharacteristic
331C22#201611yescharacteristic
332C22#202211yescharacteristic
333C4—22no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—48no—
340C4—41no—
341C4—82no—
342C4—161no—
343C4—161no—
344C4—161no—
345C4—162no—
346C4#160912yes—
347C4#161012yes—
348C2—22no—
349C2—22no—
350C2#991911yescharacteristic
351C2#995911yescharacteristic
352C2#1006711yescharacteristic
353C2#1010111yescharacteristic
354C2#1023811yescharacteristic
355C2#1029311yescharacteristic
356C2#1033111yescharacteristic
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
#297572
#279502
#151452
#99092
#87242
#75762
#70282