Finite Group Databasebeta

← #145839

Subgroups — #145839

Order 512.

455 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 455 conjugacy classes of subgroups — too many to draw. Only its 76 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#17003C211yesmaximal, characteristic
2#11296C211yesmaximal, characteristic
3#8857C211yesmaximal, characteristic
4#8856C211yesmaximal, characteristic
5#7251C211yesmaximal, characteristic
6#7251C211yesmaximal, characteristic
7#7189C211yesmaximal, characteristic
8#2316C2211yescharacteristic
9#1853—21no—
10#1852—21no—
11C2×#343C2211yescharacteristic
12#1736—21no—
13C2×#339—21no—
14C2×#324C2211yescharacteristic
15C2×#324C2211yescharacteristic
16#1445—21no—
17#1444—21no—
18#1444—21no—
19#1441—21no—
20#1441—21no—
21#1441C2211yescharacteristic
22#1441C2211yescharacteristic
23#1436—21no—
24C4⋊#95C2211yescharacteristic
25#1294—21no—
26#1294—21no—
27C22×M16—21no—
28C2×#117—21no—
29C22×C4⋊C4—21no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4—21no—
32C22×C4⋊C4D411yescharacteristic
33C22×C4⋊C4D411yescharacteristic
34C22×C4⋊C4D411yescharacteristic
35C22×C4⋊C4C2311yescharacteristic
36C22×C42D411yescharacteristic
37C2×#107—41no—
38C2×#106—41no—
39C2×C22⋊C8—21no—
40C2×C22⋊C8—21no—
41#389—41no—
42#389—41no—
43#380—21no—
44#380—21no—
45C2×#95—21no—
46C2×#95—21no—
47C2×#95—21no—
48C2×#95—21no—
49C2×#95—21no—
50C2×#95—21no—
51C2×#95—21no—
52C2×#95—21no—
53C2×#95—21no—
54C2×#95—21no—
55C2×#95—21no—
56C2×#95D411yescharacteristic
57C2×#95D411yescharacteristic
58#343—21no—
59#343Q812yes—
60#340—41no—
61#340—41no—
62#340—41no—
63#340—41no—
64#339—42no—
65#324—21no—
66#324—21no—
67#324Q812yes—
68#324Q812yes—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4—21no—
74C23×C4—21no—
75C23×C4C2×D411yescharacteristic
76C23×C4C2×D411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C2×M16—22no—
79C2×M16—41no—
80C2×M16—41no—
81C2×M16—41no—
82C2×M16—41no—
83C2×M16—41no—
84C22×C8—41no—
85C22×C8—41no—
86C22×C8—41no—
87#117—41no—
88#117—41no—
89#117—41no—
90#117—41no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—24no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C4⋊C4—41no—
104C2×C4⋊C4—41no—
105C2×C4⋊C4—41no—
106C2×C4⋊C4—42no—
107C2×C4⋊C4—81no—
108C2×C4⋊C4—81no—
109C2×C4⋊C4—81no—
110C2×C4⋊C4—81no—
111C2×C4⋊C4—81no—
112C2×C4⋊C4—81no—
113C2×C4⋊C4—81no—
114C2×C4⋊C4—81no—
115C2×C4⋊C4—81no—
116C2×C4⋊C4C2×Q811yescharacteristic
117C2×C4⋊C4C2×Q811yescharacteristic
118C2×C4⋊C4C2×Q811yescharacteristic
119C2×C4⋊C4#4111yescharacteristic
120C2×C22⋊C4—41no—
121C2×C42—21no—
122C2×C42—21no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42—41no—
126#107—82no—
127#106—82no—
128C22⋊C8—22no—
129C22⋊C8—22no—
130C22⋊C8—41no—
131C22⋊C8—41no—
132#95—41no—
133#95—41no—
134#95—42no—
135#95—42no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—41no—
140#95—41no—
141#95—41no—
142#95—81no—
143#95—81no—
144#95—81no—
145#95—81no—
146#95—81no—
147#95—81no—
148#95—81no—
149C24#12011yescharacteristic
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—22no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—41no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C22⋊Q811yescharacteristic
207C22×C4C22⋊Q811yescharacteristic
208C22×C4C22⋊Q811yescharacteristic
209C22×C4C4⋊Q811yescharacteristic
210C22×C4C4⋊Q811yescharacteristic
211C22×C4C4⋊Q811yescharacteristic
212C22×C4#13511yescharacteristic
213C22×C4#13511yescharacteristic
214C22×C4AGL(1,ℤ/8)11yescharacteristic
215C22×C4#13711yescharacteristic
216M16—42no—
217M16—42no—
218M16—81no—
219M16—81no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—81no—
224C2×C8—81no—
225C2×C8—81no—
226C2×C8—81no—
227C2×C8—81no—
228C2×C8—81no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—81no—
241C4⋊C4—84no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4—81no—
247C4⋊C4—81no—
248C4⋊C4—84no—
249C4⋊C4—84no—
250C22⋊C4—81no—
251C22⋊C4—81no—
252C42—42no—
253C42—81no—
254C42—81no—
255C42—81no—
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23#39511yescharacteristic
261C23#44911yescharacteristic
262C23#45211yescharacteristic
263C23#45411yescharacteristic
264C23#45511yescharacteristic
265C23B(4,𝔽2)11yescharacteristic
266C23#45811yescharacteristic
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—81no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4#47811yescharacteristic
342C2×C4#47911yescharacteristic
343C2×C4#49911yescharacteristic
344C2×C4#50111yescharacteristic
345C8—82no—
346C8—82no—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22#159711yescharacteristic
361C22#160611yescharacteristic
362C22#161211yescharacteristic
363C22#161511yescharacteristic
364C22#205911yescharacteristic
365C22#206111yescharacteristic
366C22#206211yescharacteristic
367C22#219711yescharacteristic
368C22#220011yescharacteristic
369C22#220211yescharacteristic
370C22#220511yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—82no—
380C4—82no—
381C4—82no—
382C4—82no—
383C4—161no—
384C4—161no—
385C4—161no—
386C4—161no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2—21no—
391C2#1057111yescharacteristic
392C2#1214111yescharacteristic
393C2#1214611yescharacteristic
394C2#1227311yescharacteristic
395C2#1227411yescharacteristic
396C2#1346211yescharacteristic
397C2#1346411yescharacteristic
subgroupG/H
center, socleC23B(4,𝔽2)
commutator, Frattini, cosocleC22×C4⋊C4C23
prime radicalC24#120
LCSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C24 ◁ C22×C4⋊C4 ◁ G
LECSG ▷ C22×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#170032
#112962
#88572
#88562
#72512
#71892