Finite Group Databasebeta

← #104146

Subgroups — #104146

Order 512.

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

normal subgroups only

This group has 544 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#27961C211yesmaximal, characteristic
3#15197C211yesmaximal, characteristic
4#9909C211yesmaximal, characteristic
5#8725C211yesmaximal, characteristic
6#7576C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8C2×#484—21no—
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11C2×#384C2211yescharacteristic
12#2100—22no—
13#2083—21no—
14#2068—22no—
15#2043—21no—
16#1990—21no—
17#1872—21no—
18#1834—21no—
19#1824—22no—
20#1797C2211yescharacteristic
21#1797C2211yescharacteristic
22C4×C22⋊C8C2211yescharacteristic
23#1442—22no—
24#1441—22no—
25C4⋊#95—21no—
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⋊C4D411yescharacteristic
37C22×C4⋊C4D412yes—
38C22×C4⋊C4D411yescharacteristic
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41#484—42no—
42#484—42no—
43C2×#107—22no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D412yes—
46C2×#103—22no—
47C2×#103—22no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C4×C8—21no—
52#391—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384—21no—
63#384D411yescharacteristic
64#380—21no—
65#380—21no—
66C2×#95—21no—
67C2×#95—21no—
68C2×#95—24no—
69C2×#95—24no—
70C2×#95D412yes—
71#340—22no—
72#340—24no—
73#340—24no—
74#336—21no—
75#336—21no—
76#336D412yes—
77C22×Q8—21no—
78C23×C4—21no—
79C23×C4—22no—
80C23×C4—22no—
81C23×C4—21no—
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C22×C8—22no—
86C22×C8—22no—
87C22×C8—41no—
88C4⋊Q8—42no—
89C22⋊Q8—41no—
90C22⋊Q8—41no—
91C22⋊Q8—41no—
92C22⋊Q8—41no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—22no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—44no—
108C2×C4⋊C4—42no—
109C2×C4⋊C4—44no—
110C2×C4⋊C4—44no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—82no—
119C2×C4⋊C4SD1612yes—
120C2×C22⋊C4—41no—
121C2×C42—42no—
122C2×C42—42no—
123C2×C42—42no—
124C2×C42—41no—
125C2×C42—41no—
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130#107—44no—
131C4⋊C8—42no—
132C4⋊C8—42no—
133#103—44no—
134#103—82no—
135C22⋊C8—42no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—42no—
139C4×C8—42no—
140#95—22no—
141#95—42no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—84no—
147#95—84no—
148#95Q1614yes—
149C24#12011yescharacteristic
150C2×Q8—41no—
151C2×Q8—41no—
152C2×Q8—42no—
153C2×Q8—42no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—24no—
160C22×C4—41no—
161C22×C4—41no—
162C22×C4—41no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—41no—
170C22×C4—42no—
171C22×C4—41no—
172C22×C4—42no—
173C22×C4—44no—
174C22×C4—44no—
175C22×C4—42no—
176C22×C4—42no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—44no—
183C22×C4#12011yescharacteristic
184C22×C4#12011yescharacteristic
185C22×C4#12111yescharacteristic
186C22×C4#12111yescharacteristic
187C22×C4#12111yescharacteristic
188C22×C4#12711yescharacteristic
189C22×C4C2×SD1611yescharacteristic
190C22×C4C2×Q1612yes—
191C22×C4#13511yescharacteristic
192C22×C4AGL(1,ℤ/8)11yescharacteristic
193C22×C4#13711yescharacteristic
194C22×C4#13712yes—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—42no—
199C2×C8—42no—
200C2×C8—42no—
201C2×C8—81no—
202C2×C8—81no—
203C2×C8—81no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—44no—
207C4⋊C4—42no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—42no—
213C4⋊C4—42no—
214C4⋊C4—81no—
215C4⋊C4—81no—
216C4⋊C4—82no—
217C4⋊C4—81no—
218C4⋊C4—82no—
219C4⋊C4—82no—
220C4⋊C4—82no—
221C4⋊C4—82no—
222C4⋊C4—82no—
223C4⋊C4—82no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C22⋊C4—81no—
227C22⋊C4—81no—
228C42—22no—
229C42—22no—
230C42—41no—
231C42—41no—
232C42—82no—
233C42—82no—
234C23—21no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23#39211yescharacteristic
239C23#44811yescharacteristic
240C23#44911yescharacteristic
241C23#45112yes—
242C23#45512yes—
243Q8—82no—
244Q8—82no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—44no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—84no—
276C2×C4—88no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—82no—
282C2×C4—81no—
283C2×C4—82no—
284C2×C4—81no—
285C2×C4—82no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4#45011yescharacteristic
290C2×C4#45211yescharacteristic
291C2×C4#45412yes—
292C2×C4#45412yes—
293C2×C4#45812yes—
294C2×C4#46212yes—
295C2×C4#46511yescharacteristic
296C2×C4#46811yescharacteristic
297C2×C4#49411yescharacteristic
298C2×C4#49711yescharacteristic
299C8—82no—
300C8—82no—
301C8—161no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22—22no—
306C22—22no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22#164412yes—
311C22#164512yes—
312C22#200011yescharacteristic
313C22#200311yescharacteristic
314C22#200311yescharacteristic
315C22#200411yescharacteristic
316C22#200811yescharacteristic
317C22#201611yescharacteristic
318C22#202211yescharacteristic
319C4—22no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—22no—
324C4—21no—
325C4—41no—
326C4—84no—
327C4—82no—
328C4—161no—
329C4—161no—
330C4—162no—
331C4—161no—
332C4#161512yes—
333C4#161612yes—
334C2—22no—
335C2—22no—
336C2#992111yescharacteristic
337C2#995911yescharacteristic
338C2#1006511yescharacteristic
339C2#1009711yescharacteristic
340C2#1024111yescharacteristic
341C2#1029511yescharacteristic
342C2#1033211yescharacteristic
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
#279612
#151972
#99092
#87252
#75762
#70282