Finite Group Databasebeta

← #104751

Subgroups — #104751

Order 512.

435 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 435 conjugacy classes of subgroups — too many to draw. Only its 72 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#15248C211yesmaximal, characteristic
2#11370C211yesmaximal, characteristic
3#8716C211yesmaximal, characteristic
4#8716C211yesmaximal, characteristic
5#7037C211yesmaximal, characteristic
6#7037C211yesmaximal, characteristic
7#7017C211yesmaximal, characteristic
8#2285C2211yescharacteristic
9#1817C2211yescharacteristic
10#1817C2211yescharacteristic
11C2×#339—21no—
12C2×#339—21no—
13#1728C2211yescharacteristic
14#1445—21no—
15#1443—21no—
16#1442—21no—
17#1441—21no—
18#1436—21no—
19#1436—21no—
20#1434C2211yescharacteristic
21#1434C2211yescharacteristic
22C4×#95C2211yescharacteristic
23#1294—21no—
24#1294—21no—
25#1294—21no—
26#1294—21no—
27C22×M16—21no—
28C2×#117—21no—
29C22×C4⋊C4—21no—
30C22×C4⋊C4—21no—
31C22×C42D411yescharacteristic
32C22×C42D411yescharacteristic
33C22×C42C2311yescharacteristic
34C2×C22⋊C8—21no—
35C2×C22⋊C8—21no—
36#384Q811yescharacteristic
37#384Q811yescharacteristic
38#382—21no—
39#380—21no—
40#380—21no—
41C4×C4⋊C4—21no—
42C4×C4⋊C4—21no—
43C2×#95—21no—
44C2×#95—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×#95D411yescharacteristic
56C2×#95D411yescharacteristic
57C2×#95D411yescharacteristic
58C2×#95D411yescharacteristic
59#339—42no—
60#339—42no—
61#336—21no—
62#336—21no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67C23×C4—21no—
68C23×C4—21no—
69C23×C4—21no—
70C23×C4—21no—
71C23×C4—21no—
72C23×C4—21no—
73C23×C4C2×D411yescharacteristic
74C23×C4C2×D411yescharacteristic
75C23×C4C2×D411yescharacteristic
76C2×M16—22no—
77C2×M16—41no—
78C2×M16—41no—
79C2×M16—41no—
80C2×M16—41no—
81C2×M16—41no—
82C22×C8—41no—
83C22×C8—41no—
84C22×C8—41no—
85#117—41no—
86#117—41no—
87#117—41no—
88#117—41no—
89C2×C4⋊C4—21no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—42no—
96C2×C4⋊C4—42no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—42no—
99C2×C4⋊C4—81no—
100C2×C4⋊C4—81no—
101C2×C22⋊C4—41no—
102C2×C42—21no—
103C2×C42—21no—
104C2×C42—21no—
105C2×C42—21no—
106C2×C42—41no—
107C2×C42—41no—
108C2×C42—41no—
109C2×C42—41no—
110C2×C42—41no—
111C2×C42—41no—
112C2×C42—41no—
113C2×C42C2×Q811yescharacteristic
114C2×C42#4111yescharacteristic
115C2×C42#4111yescharacteristic
116C2×C42#4111yescharacteristic
117C22⋊C8—41no—
118C22⋊C8—41no—
119C22⋊C8—41no—
120C22⋊C8—41no—
121#95—41no—
122#95—41no—
123#95—41no—
124#95—41no—
125#95—42no—
126#95—42no—
127#95—42no—
128#95—42no—
129#95—42no—
130#95—42no—
131#95—42no—
132#95—42no—
133#95—41no—
134#95—41no—
135#95—41no—
136#95—41no—
137#95—41no—
138#95—41no—
139#95—81no—
140#95—81no—
141C24#12011yescharacteristic
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—41no—
161C22×C4—41no—
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×C4C22⋊Q811yescharacteristic
199C22×C4C22⋊Q811yescharacteristic
200C22×C4C22⋊Q811yescharacteristic
201C22×C4#12411yescharacteristic
202C22×C4#12411yescharacteristic
203C22×C4#12411yescharacteristic
204C22×C4#13511yescharacteristic
205C22×C4#13511yescharacteristic
206C22×C4AGL(1,ℤ/8)11yescharacteristic
207C22×C4AGL(1,ℤ/8)11yescharacteristic
208M16—42no—
209M16—42no—
210M16—81no—
211M16—81no—
212C2×C8—42no—
213C2×C8—81no—
214C2×C8—81no—
215C2×C8—81no—
216C2×C8—81no—
217C2×C8—81no—
218C2×C8—81no—
219C2×C8—81no—
220C2×C8—81no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C4⋊C4—81no—
228C4⋊C4—81no—
229C4⋊C4—84no—
230C4⋊C4—84no—
231C22⋊C4—81no—
232C22⋊C4—81no—
233C42—41no—
234C42—41no—
235C42—41no—
236C42—41no—
237C42—42no—
238C42—42no—
239C42—81no—
240C42—81no—
241C42—81no—
242C42—81no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23#39311yescharacteristic
248C23#44911yescharacteristic
249C23#44911yescharacteristic
250C23#45511yescharacteristic
251C23#45611yescharacteristic
252C23#45811yescharacteristic
253C23#45811yescharacteristic
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—21no—
266C2×C4—21no—
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—42no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
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#47811yescharacteristic
331C2×C4#47811yescharacteristic
332C2×C4#48811yescharacteristic
333C2×C4#49011yescharacteristic
334C8—82no—
335C8—161no—
336C8—161no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22#160911yescharacteristic
350C22#160911yescharacteristic
351C22#161211yescharacteristic
352C22#161211yescharacteristic
353C22#202511yescharacteristic
354C22#202811yescharacteristic
355C22#203011yescharacteristic
356C22#203111yescharacteristic
357C22#203111yescharacteristic
358C22#203111yescharacteristic
359C22#203111yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—41no—
367C4—41no—
368C4—82no—
369C4—82no—
370C4—82no—
371C4—82no—
372C4—161no—
373C4—161no—
374C4—161no—
375C4—161no—
376C2—21no—
377C2—21no—
378C2—21no—
379C2—21no—
380C2#1034611yescharacteristic
381C2#1036811yescharacteristic
382C2#1037211yescharacteristic
383C2#1037911yescharacteristic
384C2#1038111yescharacteristic
385C2#1038711yescharacteristic
386C2#1038911yescharacteristic
subgroupG/H
center, socleC23#393
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
#152482
#113702
#87162
#70372
#70172