Finite Group Databasebeta

← #104739

Subgroups — #104739

Order 512.

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

normal subgroups only

This group has 471 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#15251C211yesmaximal, characteristic
2#11370C211yesmaximal, characteristic
3#8716C211yesmaximal, characteristic
4#8716C211yesmaximal, characteristic
5#7037C211yesmaximal, characteristic
6#7037C211yesmaximal, characteristic
7#7017C211yesmaximal, characteristic
8C2×#387—21no—
9#2285C2211yescharacteristic
10#1817C2211yescharacteristic
11#1817C2211yescharacteristic
12C2×#339—21no—
13C2×#339—21no—
14#1728C2211yescharacteristic
15#1444—21no—
16#1442—21no—
17#1441—21no—
18#1441—21no—
19C4⋊#95—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×C4⋊C4—21no—
32C22×C4⋊C4—21no—
33C22×C42D411yescharacteristic
34C22×C42D411yescharacteristic
35C22×C42C2311yescharacteristic
36C2×C22⋊C8—21no—
37C2×C22⋊C8—21no—
38#387—42no—
39#387—42no—
40#384Q811yescharacteristic
41#384Q811yescharacteristic
42#382—21no—
43#380—21no—
44#380—21no—
45C4×C4⋊C4—21no—
46C4×C4⋊C4—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×#95—21no—
57C2×#95D411yescharacteristic
58C2×#95D411yescharacteristic
59C2×#95D411yescharacteristic
60C2×#95D411yescharacteristic
61#339—42no—
62#339—42no—
63#336—21no—
64#336—21no—
65#336—21no—
66#336—21no—
67#336—21no—
68#336—21no—
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—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—42no—
98C2×C4⋊C4—42no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—42no—
101C2×C4⋊C4—42no—
102C2×C4⋊C4—42no—
103C2×C4⋊C4—42no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—81no—
106C2×C4⋊C4—81no—
107C2×C4⋊C4—81no—
108C2×C4⋊C4—81no—
109C2×C22⋊C4—41no—
110C2×C42—21no—
111C2×C42—21no—
112C2×C42—41no—
113C2×C42—41no—
114C2×C42—41no—
115C2×C42—41no—
116C2×C42—41no—
117C2×C42—41no—
118C2×C42—41no—
119C2×C42D812yes—
120C2×C42SD1612yes—
121C2×C42C2×Q811yescharacteristic
122C2×C42#4111yescharacteristic
123C2×C42#4111yescharacteristic
124C2×C42#4111yescharacteristic
125C22⋊C8—41no—
126C22⋊C8—41no—
127C22⋊C8—41no—
128C22⋊C8—41no—
129#95—41no—
130#95—41no—
131#95—41no—
132#95—41no—
133#95—42no—
134#95—42no—
135#95—42no—
136#95—42no—
137#95—42no—
138#95—42no—
139#95—42no—
140#95—42no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95—41no—
147C24#12011yescharacteristic
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—21no—
158C22×C4—21no—
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×C4C22⋊Q811yescharacteristic
205C22×C4C22⋊Q811yescharacteristic
206C22×C4C22⋊Q811yescharacteristic
207C22×C4#12411yescharacteristic
208C22×C4#12411yescharacteristic
209C22×C4#12411yescharacteristic
210C22×C4C2×D811yescharacteristic
211C22×C4C2×SD1611yescharacteristic
212C22×C4AGL(1,ℤ/8)11yescharacteristic
213C22×C4#13711yescharacteristic
214M16—42no—
215M16—42no—
216M16—81no—
217M16—81no—
218C2×C8—42no—
219C2×C8—81no—
220C2×C8—81no—
221C2×C8—81no—
222C2×C8—81no—
223C2×C8—81no—
224C2×C8—81no—
225C2×C8—81no—
226C2×C8—81no—
227C4⋊C4—48no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C4⋊C4—84no—
237C4⋊C4—84no—
238C4⋊C4—84no—
239C22⋊C4—81no—
240C22⋊C4—81no—
241C42—41no—
242C42—41no—
243C42—41no—
244C42—41no—
245C42—42no—
246C42—42no—
247C42—81no—
248C42—81no—
249C42—81no—
250C42—81no—
251C23—21no—
252C23—21no—
253C23—21no—
254C23—21no—
255C23#39311yescharacteristic
256C23#44711yescharacteristic
257C23#44811yescharacteristic
258C23#45511yescharacteristic
259C23#45611yescharacteristic
260C23#45811yescharacteristic
261C23#45811yescharacteristic
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—24no—
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—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—42no—
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—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—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—81no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4#47411yescharacteristic
339C2×C4#47611yescharacteristic
340C2×C4#48611yescharacteristic
341C2×C4#48911yescharacteristic
342C8—82no—
343C8—161no—
344C8—161no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22#160711yescharacteristic
358C22#160811yescharacteristic
359C22#161011yescharacteristic
360C22#161111yescharacteristic
361C22#202311yescharacteristic
362C22#202811yescharacteristic
363C22#203011yescharacteristic
364C22#203111yescharacteristic
365C22#203111yescharacteristic
366C22#203111yescharacteristic
367C22#203111yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—44no—
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—82no—
378C4—82no—
379C4—82no—
380C4—161no—
381C4—161no—
382C4—161no—
383C4—161no—
384C2—21no—
385C2—21no—
386C2—21no—
387C2—21no—
388C2#1034211yescharacteristic
389C2#1036411yescharacteristic
390C2#1037011yescharacteristic
391C2#1037911yescharacteristic
392C2#1038111yescharacteristic
393C2#1038711yescharacteristic
394C2#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
#152512
#113702
#87162
#70372
#70172