Finite Group Databasebeta

← #105059

Subgroups — #105059

Order 512.

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

normal subgroups only

This group has 473 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#29953C211yesmaximal, characteristic
2#11077C211yesmaximal, characteristic
3#9884C211yesmaximal, characteristic
4#9878C211yesmaximal, characteristic
5#9127C211yesmaximal, characteristic
6#8830C211yesmaximal, characteristic
7#7039C211yesmaximal, characteristic
8C22×C4⋊C8C2211yescharacteristic
9C22×#103—21no—
10#2857C2211yescharacteristic
11C2×#391C2211yescharacteristic
12#2095—21no—
13#2068—21no—
14#2068—21no—
15#2024—21no—
16#1852—21no—
17#1797C2211yescharacteristic
18#1797C2211yescharacteristic
19#1787—21no—
20C4×C22⋊C8C2211yescharacteristic
21C2×#340—21no—
22C2×#334—21no—
23C2×#333—21no—
24C4⋊#95C2211yescharacteristic
25#1296—21no—
26#1294—21no—
27#1294—21no—
28#1280—21no—
29#1280—21no—
30#1277—21no—
31C23×Q8D411yescharacteristic
32C23×C8—21no—
33C2×C4⋊Q8D411yescharacteristic
34C2×C22⋊Q8—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4D411yescharacteristic
37C22×C42C2311yescharacteristic
38C2×#107—21no—
39C2×#107—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—42no—
44C2×C4⋊C8D411yescharacteristic
45C2×C4⋊C8D411yescharacteristic
46C2×#103—21no—
47C2×#103—21no—
48C2×#103—21no—
49C2×#103—21no—
50C2×#103—42no—
51C2×#103—42no—
52C2×#103—42no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8D411yescharacteristic
56C2×C22⋊C8D411yescharacteristic
57C2×C4×C8—21no—
58#391—21no—
59#391—21no—
60#391—21no—
61#391—21no—
62#391—21no—
63#389—21no—
64#389—21no—
65#384D411yescharacteristic
66#380—21no—
67#380—21no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95—21no—
72#340—21no—
73#340—21no—
74#340—42no—
75#336—21no—
76#336—21no—
77#336—21no—
78#334—42no—
79#333—42no—
80C22×Q8—21no—
81C22×Q8—21no—
82C22×Q8—21no—
83C22×Q8—21no—
84C22×Q8—21no—
85C22×Q8—21no—
86C22×Q8—41no—
87C22×Q8—41no—
88C22×Q8—41no—
89C22×Q8—41no—
90C22×Q8SD1612yes—
91C23×C4—21no—
92C23×C4—21no—
93C23×C4—41no—
94C23×C4C2×D411yescharacteristic
95C23×C4C2×D411yescharacteristic
96C23×C4#4111yescharacteristic
97C22×C8—21no—
98C22×C8—22no—
99C22×C8—21no—
100C22×C8—21no—
101C22×C8—21no—
102C22×C8—41no—
103C22×C8—41no—
104C22×C8—41no—
105C22×C8—41no—
106C22×C8—41no—
107C22×C8—41no—
108C22×C8—41no—
109C4⋊Q8—41no—
110C4⋊Q8—41no—
111C22⋊Q8—81no—
112C22⋊Q8—81no—
113C2×C4⋊C4—22no—
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—21no—
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×C22⋊C4—41no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42#4111yescharacteristic
135C2×C42#4111yescharacteristic
136#107—81no—
137#107—81no—
138C4⋊C8—22no—
139C4⋊C8—22no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146#103—48no—
147#103—81no—
148#103—81no—
149#103—81no—
150#103—81no—
151C22⋊C8—21no—
152C22⋊C8—21no—
153C22⋊C8—21no—
154C22⋊C8—41no—
155C22⋊C8—41no—
156C22⋊C8—41no—
157C22⋊C8—41no—
158C22⋊C8Q1612yes—
159C4×C8—41no—
160C4×C8—41no—
161#95—41no—
162#95—41no—
163#95—41no—
164#95—41no—
165#95—41no—
166#95—41no—
167#95—41no—
168#95—41no—
169#95—81no—
170C24#12111yescharacteristic
171C2×Q8—22no—
172C2×Q8—22no—
173C2×Q8—42no—
174C2×Q8—42no—
175C2×Q8—42no—
176C2×Q8—42no—
177C2×Q8—42no—
178C2×Q8—42no—
179C2×Q8—42no—
180C2×Q8—41no—
181C2×Q8—41no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—81no—
187C2×Q8—81no—
188C2×Q8—81no—
189C2×Q8—81no—
190C2×Q8—81no—
191C2×Q8—81no—
192C22×C4—21no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—41no—
205C22×C4—42no—
206C22×C4—41no—
207C22×C4—41no—
208C22×C4—41no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—81no—
212C22×C4—81no—
213C22×C4—81no—
214C22×C4—81no—
215C22×C4—81no—
216C22×C4—81no—
217C22×C4—81no—
218C22×C4—81no—
219C22×C4—81no—
220C22×C4—81no—
221C22×C4#12011yescharacteristic
222C22×C4#12111yescharacteristic
223C22×C4#12111yescharacteristic
224C22×C4#12311yescharacteristic
225C22×C4#12311yescharacteristic
226C22×C4#12411yescharacteristic
227C22×C4C2×SD1611yescharacteristic
228C22×C4C2×Q1611yescharacteristic
229C22×C4#13511yescharacteristic
230C22×C4#13511yescharacteristic
231C22×C4#13711yescharacteristic
232C22×C4#13711yescharacteristic
233C22×C4#13711yescharacteristic
234C22×C4#13711yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—42no—
240C2×C8—41no—
241C2×C8—42no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—42no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—81no—
251C2×C8—81no—
252C2×C8—81no—
253C2×C8—81no—
254C2×C8—81no—
255C2×C8—81no—
256C2×C8—81no—
257C4⋊C4—42no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—81no—
267C4⋊C4—81no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—82no—
272C22⋊C4—81no—
273C22⋊C4—81no—
274C42—21no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—41no—
279C42—41no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23#39411yescharacteristic
285C23#46211yescharacteristic
286C23#46411yescharacteristic
287C23#46511yescharacteristic
288C23#47011yescharacteristic
289C23#47111yescharacteristic
290C23#47211yescharacteristic
291Q8—44no—
292Q8—42no—
293Q8—42no—
294Q8—82no—
295Q8—81no—
296Q8—81no—
297Q8—162no—
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—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—82no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—82no—
329C2×C4—82no—
330C2×C4—82no—
331C2×C4—82no—
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—161no—
342C2×C4—161no—
343C2×C4—161no—
344C2×C4—161no—
345C2×C4—161no—
346C2×C4—161no—
347C2×C4#44811yescharacteristic
348C2×C4#45211yescharacteristic
349C2×C4#45311yescharacteristic
350C2×C4#45511yescharacteristic
351C2×C4B(4,𝔽2)11yescharacteristic
352C2×C4#45811yescharacteristic
353C2×C4#46211yescharacteristic
354C2×C4#46411yescharacteristic
355C2×C4#46711yescharacteristic
356C2×C4#47011yescharacteristic
357C2×C4#48311yescharacteristic
358C2×C4#48511yescharacteristic
359C8—42no—
360C8—81no—
361C8—82no—
362C8—81no—
363C8—81no—
364C8—161no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22#167211yescharacteristic
378C22#167811yescharacteristic
379C22#169611yescharacteristic
380C22#170411yescharacteristic
381C22#203511yescharacteristic
382C22#203711yescharacteristic
383C22#204411yescharacteristic
384C22#204911yescharacteristic
385C22#205111yescharacteristic
386C22#205311yescharacteristic
387C22#205611yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—82no—
397C4—162no—
398C4—161no—
399C4—161no—
400C4—161no—
401C4#159611yescharacteristic
402C4#160611yescharacteristic
403C4#160811yescharacteristic
404C4#161811yescharacteristic
405C2—21no—
406C2—21no—
407C2—21no—
408C2—21no—
409C2#1039811yescharacteristic
410C2#1047011yescharacteristic
411C2#1048211yescharacteristic
412C2#1050511yescharacteristic
413C2#1050811yescharacteristic
414C2#1056211yescharacteristic
415C2#1056611yescharacteristic
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
#299532
#110772
#98842
#98782
#91272
#88302
#70392