Finite Group Databasebeta

← #105182

Subgroups — #105182

Order 512.

579 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 579 conjugacy classes of subgroups — too many to draw. Only its 136 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#17076C211yesmaximal, characteristic
2#11323C211yesmaximal, characteristic
3#11267C212yesmaximal
4#7025C212yesmaximal
5#7025C211yesmaximal, characteristic
6C22×#106—21no—
7C2×#400—21no—
8C2×#384C2211yescharacteristic
9C2×#340—22no—
10C2×#340—22no—
11C2×#340—21no—
12C2×#336C2212yes—
13C2×#336C2211yescharacteristic
14#1444—22no—
15#1442—22no—
16#1441—21no—
17C4⋊#95C2212yes—
18C4⋊#95C2211yescharacteristic
19C23×C8—21no—
20C23×C8—22no—
21C22×C4⋊C4—21no—
22C22×C4⋊C4—22no—
23C22×C4⋊C4—21no—
24C22×C4⋊C4—21no—
25C22×C4⋊C4D412yes—
26C22×C4⋊C4D412yes—
27C22×C4⋊C4D411yescharacteristic
28C22×C4⋊C4D411yescharacteristic
29C22×C42C2311yescharacteristic
30C2×#106—42no—
31C2×#106—42no—
32C2×#106—42no—
33#400—42no—
34#400—42no—
35#384—42no—
36C2×#95—21no—
37C2×#95—22no—
38C2×#95—22no—
39C2×#95—22no—
40C2×#95—22no—
41C2×#95—21no—
42C2×#95—22no—
43#340—44no—
44#340—44no—
45#340—42no—
46#336—21no—
47#336—22no—
48#336Q812yes—
49#336Q814yes—
50C23×C4—21no—
51C23×C4—21no—
52C23×C4—22no—
53C23×C4—22no—
54C23×C4—41no—
55C23×C4C2×D411yescharacteristic
56C23×C4C2×D412yes—
57C22×C8—22no—
58C22×C8—22no—
59C22×C8—22no—
60C22×C8—24no—
61C22×C8—41no—
62C22×C8—41no—
63C22×C8—41no—
64C22×C8—41no—
65C22×C8—42no—
66C22×C8—42no—
67C22×C8—42no—
68C22×C8—42no—
69C22×C8—42no—
70C22×C8—42no—
71C2×C4⋊C4—24no—
72C2×C4⋊C4—22no—
73C2×C4⋊C4—22no—
74C2×C4⋊C4—22no—
75C2×C4⋊C4—21no—
76C2×C4⋊C4—21no—
77C2×C4⋊C4—22no—
78C2×C4⋊C4—22no—
79C2×C4⋊C4—41no—
80C2×C4⋊C4—42no—
81C2×C4⋊C4—42no—
82C2×C4⋊C4—42no—
83C2×C4⋊C4—41no—
84C2×C4⋊C4—42no—
85C2×C4⋊C4—41no—
86C2×C4⋊C4—41no—
87C2×C4⋊C4—42no—
88C2×C4⋊C4—42no—
89C2×C4⋊C4—41no—
90C2×C4⋊C4—41no—
91C2×C4⋊C4—41no—
92C2×C4⋊C4—42no—
93C2×C4⋊C4—42no—
94C2×C4⋊C4—41no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—81no—
99C2×C4⋊C4—81no—
100C2×C4⋊C4—81no—
101C2×C4⋊C4—82no—
102C2×C4⋊C4SD1612yes—
103C2×C4⋊C4SD1612yes—
104C2×C42—41no—
105C2×C42—41no—
106C2×C42C2×Q811yescharacteristic
107C2×C42C2×Q812yes—
108C2×C42#4111yescharacteristic
109#106—48no—
110#95—42no—
111#95—44no—
112#95—42no—
113#95—42no—
114#95—42no—
115#95—42no—
116#95—42no—
117#95—42no—
118#95—82no—
119#95—81no—
120C24#12011yescharacteristic
121C22×C4—21no—
122C22×C4—22no—
123C22×C4—22no—
124C22×C4—21no—
125C22×C4—21no—
126C22×C4—22no—
127C22×C4—21no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—42no—
132C22×C4—42no—
133C22×C4—41no—
134C22×C4—41no—
135C22×C4—42no—
136C22×C4—42no—
137C22×C4—41no—
138C22×C4—41no—
139C22×C4—42no—
140C22×C4—42no—
141C22×C4—42no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4—42no—
146C22×C4—42no—
147C22×C4—42no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4—42no—
151C22×C4—42no—
152C22×C4—42no—
153C22×C4—42no—
154C22×C4—81no—
155C22×C4—82no—
156C22×C4—81no—
157C22×C4—82no—
158C22×C4C22⋊Q811yescharacteristic
159C22×C4C22⋊Q812yes—
160C22×C4C4⋊Q811yescharacteristic
161C22×C4C4⋊Q812yes—
162C22×C4C2×SD1611yescharacteristic
163C22×C4C2×SD1611yescharacteristic
164C22×C4#13512yes—
165C22×C4#13512yes—
166C22×C4AGL(1,ℤ/8)11yescharacteristic
167C22×C4AGL(1,ℤ/8)12yes—
168C22×C4#13711yescharacteristic
169C22×C4#13712yes—
170C2×C8—24no—
171C2×C8—42no—
172C2×C8—42no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8—44no—
178C2×C8—44no—
179C2×C8—44no—
180C2×C8—82no—
181C2×C8—82no—
182C2×C8—82no—
183C2×C8—82no—
184C4⋊C4—42no—
185C4⋊C4—42no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—44no—
189C4⋊C4—44no—
190C4⋊C4—44no—
191C4⋊C4—44no—
192C4⋊C4—81no—
193C4⋊C4—81no—
194C4⋊C4—82no—
195C4⋊C4—82no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C4⋊C4—82no—
199C4⋊C4—82no—
200C4⋊C4—84no—
201C4⋊C4—84no—
202C42—41no—
203C42—42no—
204C42—41no—
205C23#39511yescharacteristic
206C23#44811yescharacteristic
207C23#44912yes—
208C23#45011yescharacteristic
209C23#45212yes—
210C23#45311yescharacteristic
211C23#45412yes—
212C23#45512yes—
213C23#45611yescharacteristic
214C23B(4,𝔽2)11yescharacteristic
215C23#45811yescharacteristic
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—42no—
241C2×C4—42no—
242C2×C4—44no—
243C2×C4—44no—
244C2×C4—82no—
245C2×C4—82no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4—82no—
251C2×C4—84no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4—82no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—161no—
267C2×C4—162no—
268C2×C4—161no—
269C2×C4#47511yescharacteristic
270C2×C4#47611yescharacteristic
271C2×C4#47812yes—
272C2×C4#47912yes—
273C2×C4#49811yescharacteristic
274C2×C4#49912yes—
275C2×C4#50111yescharacteristic
276C2×C4#50112yes—
277C8—44no—
278C8—84no—
279C22#159611yescharacteristic
280C22#159712yes—
281C22#160411yescharacteristic
282C22#160612yes—
283C22#161111yescharacteristic
284C22#161212yes—
285C22#161311yescharacteristic
286C22#161512yes—
287C22#162411yescharacteristic
288C22#162612yes—
289C22#163011yescharacteristic
290C22#163512yes—
291C22#164212yes—
292C22#164312yes—
293C22#165212yes—
294C22#165711yescharacteristic
295C22#165911yescharacteristic
296C22#166412yes—
297C22#205811yescharacteristic
298C22#205912yes—
299C22#206011yescharacteristic
300C22#206112yes—
301C22#206211yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—22no—
307C4—22no—
308C4—22no—
309C4—22no—
310C4—82no—
311C4—82no—
312C4—162no—
313C4—162no—
314C4—162no—
315C2#774311yescharacteristic
316C2#775511yescharacteristic
317C2#777612yes—
318C2#781011yescharacteristic
319C2#781812yes—
320C2#782411yescharacteristic
321C2#1057011yescharacteristic
322C2#1057112yes—
323C2#1057711yescharacteristic
324C2#1058212yes—
325C2#1058411yescharacteristic
subgroupG/H
center, socle, prime radicalC24#120
commutator, Frattini, cosocleC22×C42C23
LCSG ▷ C22×C42 ▷ C23 ▷ C1
UCSC1 ◁ C24 ◁ 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
#170762
#113232
#112672
#70252