Finite Group Databasebeta

← #105055

Subgroups — #105055

Order 512.

455 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 455 conjugacy classes of subgroups — too many to draw. Only its 92 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#29756C211yesmaximal, characteristic
2#11227C211yesmaximal, characteristic
3#9885C211yesmaximal, characteristic
4#9650C211yesmaximal, characteristic
5#9131C211yesmaximal, characteristic
6#8830C211yesmaximal, characteristic
7#7039C211yesmaximal, characteristic
8C2×#483—21no—
9C22×C4⋊C8C2211yescharacteristic
10#2857C2211yescharacteristic
11C2×#389C2211yescharacteristic
12#2084—21no—
13#2066—21no—
14#2066—21no—
15#2043—21no—
16#1872—21no—
17#1797C2211yescharacteristic
18#1797C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C2×#340—21no—
21C2×#340—21no—
22C2×#334—21no—
23C2×#332—21no—
24C2×#324—21no—
25C2×#324—21no—
26C4⋊#95C2211yescharacteristic
27#1296—21no—
28#1294—21no—
29#1294—21no—
30#1277—21no—
31C23×C8—21no—
32C2×C4⋊Q8D411yescharacteristic
33C2×C22⋊Q8—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C42C2311yescharacteristic
39#483—42no—
40#483—42no—
41C2×#106—21no—
42C2×#106—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×C4⋊C8—42no—
47C2×C4⋊C8D411yescharacteristic
48C2×C4⋊C8D411yescharacteristic
49C2×#103—21no—
50C2×#103—21no—
51C2×#103—21no—
52C2×#103—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8D411yescharacteristic
56C2×C22⋊C8D411yescharacteristic
57C2×C4×C8—21no—
58#391—21no—
59#389—21no—
60#389—21no—
61#389—21no—
62#389—21no—
63#389—21no—
64#389—21no—
65#384D411yescharacteristic
66#380—21no—
67#380—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71#340—21no—
72#340—21no—
73#340—42no—
74#340—42no—
75#336—21no—
76#336—21no—
77#336—21no—
78#334—42no—
79#332—42no—
80#324—42no—
81#324—42no—
82C22×Q8—21no—
83C23×C4—21no—
84C23×C4—21no—
85C23×C4—41no—
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C23×C4#4111yescharacteristic
89C22×C8—21no—
90C22×C8—22no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—41no—
95C22×C8—41no—
96C22×C8—41no—
97C22×C8—41no—
98C22×C8—41no—
99C22×C8—41no—
100C22×C8—41no—
101C4⋊Q8—41no—
102C4⋊Q8—41no—
103C22⋊Q8—41no—
104C22⋊Q8—41no—
105C22⋊Q8—41no—
106C22⋊Q8—41no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—22no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—41no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—41no—
128C2×C4⋊C4—41no—
129C2×C4⋊C4—41no—
130C2×C4⋊C4—41no—
131C2×C4⋊C4—41no—
132C2×C4⋊C4—41no—
133C2×C4⋊C4—41no—
134C2×C4⋊C4SD1612yes—
135C2×C22⋊C4—41no—
136C2×C42—41no—
137C2×C42—41no—
138C2×C42C2×D411yescharacteristic
139C2×C42C2×D411yescharacteristic
140C2×C42#4111yescharacteristic
141C2×C42#4111yescharacteristic
142#106—42no—
143#106—42no—
144C4⋊C8—22no—
145C4⋊C8—22no—
146C4⋊C8—41no—
147C4⋊C8—41no—
148C4⋊C8—41no—
149C4⋊C8—41no—
150C4⋊C8—41no—
151C4⋊C8—41no—
152#103—42no—
153#103—42no—
154#103—81no—
155#103—81no—
156C22⋊C8—21no—
157C22⋊C8—21no—
158C22⋊C8—21no—
159C22⋊C8—41no—
160C22⋊C8—41no—
161C22⋊C8—41no—
162C22⋊C8—41no—
163C22⋊C8SD1612yes—
164C4×C8—41no—
165C4×C8—41no—
166#95—41no—
167#95—41no—
168#95—41no—
169#95—41no—
170#95—41no—
171#95—41no—
172#95—81no—
173C24#12111yescharacteristic
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—41no—
178C2×Q8—41no—
179C2×Q8—41no—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—22no—
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—42no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—81no—
204C22×C4—81no—
205C22×C4—81no—
206C22×C4—81no—
207C22×C4—81no—
208C22×C4—81no—
209C22×C4—81no—
210C22×C4—81no—
211C22×C4#12011yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4#12311yescharacteristic
215C22×C4#12311yescharacteristic
216C22×C4#12411yescharacteristic
217C22×C4C2×SD1611yescharacteristic
218C22×C4C2×SD1611yescharacteristic
219C22×C4#13511yescharacteristic
220C22×C4#13511yescharacteristic
221C22×C4AGL(1,ℤ/8)11yescharacteristic
222C22×C4AGL(1,ℤ/8)11yescharacteristic
223C22×C4AGL(1,ℤ/8)11yescharacteristic
224C22×C4#13711yescharacteristic
225C2×C8—22no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—42no—
231C2×C8—42no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—42no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—81no—
241C2×C8—81no—
242C2×C8—81no—
243C2×C8—81no—
244C2×C8—81no—
245C2×C8—81no—
246C2×C8—81no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—42no—
250C4⋊C4—42no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C22⋊C4—81no—
271C22⋊C4—81no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—41no—
277C42—41no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23#39411yescharacteristic
283C23#46111yescharacteristic
284C23#46311yescharacteristic
285C23#46511yescharacteristic
286C23#46911yescharacteristic
287C23#47111yescharacteristic
288C23#47311yescharacteristic
289Q8—81no—
290Q8—81no—
291Q8—81no—
292Q8—81no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—81no—
326C2×C4—82no—
327C2×C4—82no—
328C2×C4—82no—
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—161no—
339C2×C4—161no—
340C2×C4—161no—
341C2×C4—161no—
342C2×C4—161no—
343C2×C4—161no—
344C2×C4#44911yescharacteristic
345C2×C4#45011yescharacteristic
346C2×C4#45411yescharacteristic
347C2×C4#45611yescharacteristic
348C2×C4B(4,𝔽2)11yescharacteristic
349C2×C4#45811yescharacteristic
350C2×C4#46011yescharacteristic
351C2×C4#46411yescharacteristic
352C2×C4#46511yescharacteristic
353C2×C4#46811yescharacteristic
354C2×C4#48111yescharacteristic
355C2×C4#48211yescharacteristic
356C8—42no—
357C8—81no—
358C8—82no—
359C8—81no—
360C8—81no—
361C8—161no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22#167111yescharacteristic
375C22#167911yescharacteristic
376C22#169311yescharacteristic
377C22#170111yescharacteristic
378C22#203411yescharacteristic
379C22#203811yescharacteristic
380C22#204411yescharacteristic
381C22#204911yescharacteristic
382C22#205211yescharacteristic
383C22#205311yescharacteristic
384C22#205511yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—21no—
390C4—21no—
391C4—41no—
392C4—41no—
393C4—82no—
394C4—162no—
395C4—161no—
396C4—161no—
397C4—161no—
398C4#159711yescharacteristic
399C4#160411yescharacteristic
400C4#160911yescharacteristic
401C4#161611yescharacteristic
402C2—21no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2#1039611yescharacteristic
407C2#1046711yescharacteristic
408C2#1047711yescharacteristic
409C2#1050711yescharacteristic
410C2#1051111yescharacteristic
411C2#1056311yescharacteristic
412C2#1056511yescharacteristic
subgroupG/H
center, socleC23#394
commutator, Frattini, cosocleC22×C42C23
prime radicalC24#121
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
#297562
#112272
#98852
#96502
#91312
#88302
#70392