Finite Group Databasebeta

← #100596

Subgroups — #100596

Order 512.

384 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 98 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#29866C211yesmaximal, characteristic
2#22824C211yesmaximal, characteristic
3#9705C211yesmaximal, characteristic
4#9692C211yesmaximal, characteristic
5#7577C211yesmaximal, characteristic
6#7040C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#475—21no—
9#2868C2211yescharacteristic
10#2295C2211yescharacteristic
11#2084—21no—
12#2084C412yes—
13#2072—21no—
14#2072C412yes—
15#1988—21no—
16#1985—21no—
17#1917—21no—
18#1916—21no—
19#1842C2211yescharacteristic
20#1832—21no—
21#1831C2211yescharacteristic
22#1831C2211yescharacteristic
23#1771—21no—
24#1768—21no—
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27C2×#332—21no—
28C2×#332—21no—
29C2×#332—21no—
30C2×#332—21no—
31#1272—21no—
32#1271—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8—21no—
36C2×C4×Q8D411yescharacteristic
37#475—42no—
38#475—42no—
39C2×#106—22no—
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×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×#103—22no—
50C2×#97—21no—
51C2×#97—21no—
52C2×C4×C8—21no—
53C2×C4×C8—21no—
54#391C2×C411yescharacteristic
55#391D411yescharacteristic
56#389C2×C411yescharacteristic
57#389D411yescharacteristic
58#387—21no—
59#387—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384C2×C412yes—
64C4×C4⋊C4—21no—
65C4×C4⋊C4D411yescharacteristic
66#376—21no—
67C43C2311yescharacteristic
68#340—22no—
69#340—22no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336C2×C412yes—
82#332—42no—
83#332—42no—
84#332—42no—
85#332—42no—
86C22×Q8—41no—
87C22×Q8C22⋊C411yescharacteristic
88C22×C8—21no—
89C22×C8—22no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—41no—
94C22×C8—41no—
95C4⋊Q8—41no—
96C4⋊Q8—41no—
97C4⋊Q8—41no—
98C4⋊Q8—41no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—41no—
102C4⋊Q8—41no—
103C4⋊Q8—41no—
104C4⋊Q8—41no—
105C4⋊Q8—41no—
106C4⋊Q8—41no—
107C4×Q8—21no—
108C4×Q8—21no—
109C4×Q8—21no—
110C4×Q8—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—22no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C4⋊C4C22⋊C411yescharacteristic
122C2×C4⋊C4C22⋊C411yescharacteristic
123C2×C42—21no—
124C2×C42—21no—
125C2×C42C22×C411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42C2×D411yescharacteristic
130C2×C42#4111yescharacteristic
131C2×C42#4111yescharacteristic
132#106—44no—
133C4⋊C8—22no—
134C4⋊C8—21no—
135C4⋊C8—21no—
136C4⋊C8—21no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8SD1612yes—
149#103—44no—
150#97—41no—
151#97—41no—
152#97—81no—
153C4×C8—81no—
154C4×C8—81no—
155#95—21no—
156#95—21no—
157#95—21no—
158#95—21no—
159#95—21no—
160#95—21no—
161#95—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—81no—
167C2×Q8—81no—
168C2×Q8—81no—
169C2×Q8—81no—
170C2×Q8—81no—
171C2×Q8—81no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—42no—
177C22×C4C2×C22⋊C411yescharacteristic
178C22×C4C4×D411yescharacteristic
179C22×C4C4×D411yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4#12311yescharacteristic
184C2×C8—22no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—42no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—81no—
201C2×C8—81no—
202C2×C8—81no—
203C2×C8—81no—
204C2×C8—81no—
205C4⋊C4—21no—
206C4⋊C4—21no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C4⋊C4—81no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—41no—
231C42—41no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42C2×SD1611yescharacteristic
238C42#13511yescharacteristic
239C42#13511yescharacteristic
240C42#13511yescharacteristic
241C42AGL(1,ℤ/8)11yescharacteristic
242C42AGL(1,ℤ/8)11yescharacteristic
243C42AGL(1,ℤ/8)11yescharacteristic
244C42#13711yescharacteristic
245C23#38611yescharacteristic
246Q8—42no—
247Q8—81no—
248Q8—161no—
249Q8—161no—
250Q8—161no—
251Q8—161no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—82no—
280C2×C4#41611yescharacteristic
281C2×C4#41811yescharacteristic
282C2×C4C4×SD1611yescharacteristic
283C2×C4#44011yescharacteristic
284C2×C4#44811yescharacteristic
285C2×C4#44911yescharacteristic
286C2×C4#44911yescharacteristic
287C2×C4#44911yescharacteristic
288C2×C4#45311yescharacteristic
289C2×C4#45411yescharacteristic
290C2×C4#46011yescharacteristic
291C2×C4#46411yescharacteristic
292C2×C4#47111yescharacteristic
293C2×C4#47311yescharacteristic
294C2×C4#48211yescharacteristic
295C2×C4#48211yescharacteristic
296C8—42no—
297C8—82no—
298C8—82no—
299C8—81no—
300C8—81no—
301C8—81no—
302C8—161no—
303C22#187511yescharacteristic
304C22#188011yescharacteristic
305C22#188311yescharacteristic
306C22#190211yescharacteristic
307C22#190811yescharacteristic
308C22#190911yescharacteristic
309C22#191511yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—41no—
321C4—81no—
322C4—81no—
323C4—81no—
324C4—81no—
325C4—162no—
326C4#162011yescharacteristic
327C4#162211yescharacteristic
328C4#162611yescharacteristic
329C4#162811yescharacteristic
330C2#897811yescharacteristic
331C2#917211yescharacteristic
332C2#919611yescharacteristic
333C2#927211yescharacteristic
334C2#929211yescharacteristic
335C2#933911yescharacteristic
336C2#937711yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ 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
#298662
#228242
#97052
#96922
#75772
#70402
#70222