Finite Group Databasebeta

← #101833

Subgroups — #101833

Order 512.

407 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 407 conjugacy classes of subgroups — too many to draw. Only its 102 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#28687C211yesmaximal, characteristic
2#23152C211yesmaximal, characteristic
3#9905C211yesmaximal, characteristic
4#9702C211yesmaximal, characteristic
5#7652C211yesmaximal, characteristic
6#7022C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C2×#498C412yes—
9C2×#446—21no—
10#2868C2211yescharacteristic
11C4×C4⋊Q8C2211yescharacteristic
12#2084—21no—
13#2084—21no—
14#1990C412yes—
15#1985—21no—
16#1948—21no—
17#1948—21no—
18#1940—21no—
19#1917—21no—
20#1916—21no—
21#1831C2211yescharacteristic
22#1831C2211yescharacteristic
23#1771—21no—
24#1767C2211yescharacteristic
25#1767C2211yescharacteristic
26C4×C4⋊C8C2211yescharacteristic
27C2×#333—21no—
28C2×#333—21no—
29#1296—21no—
30#1296—21no—
31#1271—21no—
32#1271—21no—
33C2×C4⋊Q8—21no—
34C2×C4⋊Q8—21no—
35C2×C4⋊Q8C2×C412yes—
36C2×C4⋊Q8C2×C411yescharacteristic
37C2×C4×Q8—21no—
38#498—44no—
39#446—42no—
40#446—42no—
41C2×#106—22no—
42C2×#106—22no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8D411yescharacteristic
49C2×C4⋊C8D411yescharacteristic
50C2×C4⋊C8D411yescharacteristic
51C2×C4⋊C8D411yescharacteristic
52C2×#97—21no—
53C2×#97—21no—
54C2×#97—21no—
55C2×C4×C8—21no—
56C2×C4×C8C2×C412yes—
57#391—21no—
58#389—21no—
59#389D411yescharacteristic
60#389D411yescharacteristic
61#384—21no—
62#384—21no—
63#384—21no—
64#384—21no—
65#384C2×C411yescharacteristic
66C4×C4⋊C4—21no—
67C4×C4⋊C4D411yescharacteristic
68C4×C4⋊C4D411yescharacteristic
69C43C2311yescharacteristic
70#340—22no—
71#340—22no—
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#336—21no—
82#336—21no—
83#333—42no—
84#333—42no—
85C22×Q8—21no—
86C22×Q8—22no—
87C22×C8—22no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—41no—
93C22×C8—41no—
94C4⋊Q8—22no—
95C4⋊Q8—41no—
96C4⋊Q8—42no—
97C4⋊Q8—42no—
98C4⋊Q8—41no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C4⋊Q8—41no—
102C4⋊Q8—82no—
103C4×Q8—41no—
104C4×Q8—41no—
105C4×Q8—41no—
106C4×Q8—41no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—22no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4C22⋊C411yescharacteristic
119C2×C4⋊C4C22⋊C411yescharacteristic
120C2×C4⋊C4C22⋊C411yescharacteristic
121C2×C4⋊C4C22⋊C411yescharacteristic
122C2×C42—21no—
123C2×C42—21no—
124C2×C42C22×C411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130C2×C42#4111yescharacteristic
131#106—44no—
132#106—44no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—21no—
136C4⋊C8—21no—
137C4⋊C8—21no—
138C4⋊C8—21no—
139C4⋊C8—21no—
140C4⋊C8—21no—
141C4⋊C8—42no—
142C4⋊C8—42no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147C4⋊C8SD1612yes—
148C4⋊C8SD1612yes—
149#97—42no—
150#97—41no—
151#97—41no—
152#97—41no—
153#97—41no—
154C4×C8—42no—
155C4×C8—42no—
156#95—21no—
157#95—21no—
158#95—21no—
159#95—21no—
160C2×Q8—42no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×Q8—42no—
164C2×Q8—42no—
165C2×Q8—81no—
166C2×Q8—82no—
167C2×Q8—82no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—42no—
173C22×C4C2×C22⋊C411yescharacteristic
174C22×C4C4×D411yescharacteristic
175C22×C4C4×D411yescharacteristic
176C22×C4#12011yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12111yescharacteristic
179C22×C4#12311yescharacteristic
180C2×C8—24no—
181C2×C8—22no—
182C2×C8—22no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—81no—
196C2×C8—81no—
197C2×C8—81no—
198C2×C8—81no—
199C2×C8—81no—
200C2×C8—81no—
201C4⋊C4—21no—
202C4⋊C4—21no—
203C4⋊C4—21no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C4⋊C4—81no—
216C4⋊C4—82no—
217C4⋊C4—82no—
218C4⋊C4—82no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C4⋊C4#10012yes—
224C42—21no—
225C42—21no—
226C42—21no—
227C42—21no—
228C42—41no—
229C42—41no—
230C42—41no—
231C42—41no—
232C42—41no—
233C42—41no—
234C42—41no—
235C42C2×SD1611yescharacteristic
236C42C2×SD1611yescharacteristic
237C42#13511yescharacteristic
238C42#13511yescharacteristic
239C42AGL(1,ℤ/8)11yescharacteristic
240C42AGL(1,ℤ/8)11yescharacteristic
241C42#13711yescharacteristic
242C42#13711yescharacteristic
243C23#38611yescharacteristic
244Q8—82no—
245Q8—82no—
246Q8—162no—
247Q8—162no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
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—82no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4C2×#10011yescharacteristic
277C2×C4#41311yescharacteristic
278C2×C4C4×SD1611yescharacteristic
279C2×C4C4×SD1611yescharacteristic
280C2×C4#44011yescharacteristic
281C2×C4#44011yescharacteristic
282C2×C4#44811yescharacteristic
283C2×C4#44911yescharacteristic
284C2×C4#45011yescharacteristic
285C2×C4#45211yescharacteristic
286C2×C4#45611yescharacteristic
287C2×C4#45611yescharacteristic
288C2×C4#46011yescharacteristic
289C2×C4#46111yescharacteristic
290C2×C4#46311yescharacteristic
291C2×C4#46411yescharacteristic
292C8—44no—
293C8—42no—
294C8—42no—
295C8—81no—
296C8—81no—
297C8—161no—
298C8—161no—
299C22#187711yescharacteristic
300C22#188011yescharacteristic
301C22#188611yescharacteristic
302C22#190011yescharacteristic
303C22#190211yescharacteristic
304C22#190311yescharacteristic
305C22#190911yescharacteristic
306C4—21no—
307C4—21no—
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—162no—
322C4#165111yescharacteristic
323C4#165211yescharacteristic
324C4#165311yescharacteristic
325C4#165411yescharacteristic
326C2#905911yescharacteristic
327C2#924711yescharacteristic
328C2#925411yescharacteristic
329C2#928711yescharacteristic
330C2#929211yescharacteristic
331C2#942011yescharacteristic
332C2#945211yescharacteristic
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
#286872
#231522
#99052
#97022
#76522
#70222