Finite Group Databasebeta

← #105054

Subgroups — #105054

Order 512.

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

normal subgroups only

This group has 445 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#29757C211yesmaximal, characteristic
2#11228C211yesmaximal, characteristic
3#9885C211yesmaximal, characteristic
4#9879C211yesmaximal, characteristic
5#9131C211yesmaximal, characteristic
6#8829C211yesmaximal, characteristic
7#7039C211yesmaximal, characteristic
8C2×#484—21no—
9C22×C4⋊C8C2211yescharacteristic
10#2857C2211yescharacteristic
11C2×#389C2211yescharacteristic
12#2083—21no—
13#2068—21no—
14#2068—21no—
15#2043—21no—
16#1872—21no—
17#1797C2211yescharacteristic
18#1797C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C2×#340—21no—
21C2×#340—21no—
22C2×#335—21no—
23C2×#332—21no—
24C4⋊#95C2211yescharacteristic
25#1296—21no—
26#1294—21no—
27#1294—21no—
28#1280—21no—
29#1280—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#484—42no—
40#484—42no—
41C2×#107—21no—
42C2×#107—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#335—42no—
79#332—42no—
80C22×Q8—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4—41no—
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4#4111yescharacteristic
87C22×C8—21no—
88C22×C8—22no—
89C22×C8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—41no—
93C22×C8—41no—
94C22×C8—41no—
95C22×C8—41no—
96C22×C8—41no—
97C22×C8—41no—
98C22×C8—41no—
99C4⋊Q8—41no—
100C4⋊Q8—41no—
101C22⋊Q8—41no—
102C22⋊Q8—41no—
103C22⋊Q8—41no—
104C22⋊Q8—41no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—22no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—41no—
119C2×C4⋊C4—41no—
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—82no—
129C2×C4⋊C4D812yes—
130C2×C22⋊C4—41no—
131C2×C42—41no—
132C2×C42—41no—
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42#4111yescharacteristic
136C2×C42#4111yescharacteristic
137#107—42no—
138#107—42no—
139C4⋊C8—22no—
140C4⋊C8—22no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C4⋊C8—41no—
144C4⋊C8—41no—
145C4⋊C8—41no—
146C4⋊C8—41no—
147#103—42no—
148#103—42no—
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—81no—
168C24#12111yescharacteristic
169C2×Q8—41no—
170C2×Q8—41no—
171C2×Q8—41no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—41no—
183C22×C4—41no—
184C22×C4—41no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—41no—
188C22×C4—42no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—81no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4—81no—
200C22×C4—81no—
201C22×C4—81no—
202C22×C4—81no—
203C22×C4—81no—
204C22×C4#12011yescharacteristic
205C22×C4#12111yescharacteristic
206C22×C4#12111yescharacteristic
207C22×C4#12311yescharacteristic
208C22×C4#12311yescharacteristic
209C22×C4#12411yescharacteristic
210C22×C4C2×D811yescharacteristic
211C22×C4C2×Q1611yescharacteristic
212C22×C4#13511yescharacteristic
213C22×C4#13511yescharacteristic
214C22×C4AGL(1,ℤ/8)11yescharacteristic
215C22×C4#13711yescharacteristic
216C22×C4#13711yescharacteristic
217C22×C4#13711yescharacteristic
218C2×C8—22no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—41no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—42no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—81no—
234C2×C8—81no—
235C2×C8—81no—
236C2×C8—81no—
237C2×C8—81no—
238C2×C8—81no—
239C2×C8—81no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—42no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—81no—
253C4⋊C4—81no—
254C4⋊C4—81no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C4⋊C4—82no—
258C4⋊C4—82no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C22⋊C4—81no—
262C22⋊C4—81no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—41no—
268C42—41no—
269C23—21no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23#39411yescharacteristic
274C23#46211yescharacteristic
275C23#46411yescharacteristic
276C23#46611yescharacteristic
277C23#46811yescharacteristic
278C23#47111yescharacteristic
279C23#47311yescharacteristic
280Q8—81no—
281Q8—81no—
282Q8—81no—
283Q8—81no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
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—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—82no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—82no—
315C2×C4—82no—
316C2×C4—82no—
317C2×C4—82no—
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—161no—
328C2×C4—161no—
329C2×C4—161no—
330C2×C4—161no—
331C2×C4—161no—
332C2×C4—161no—
333C2×C4#44711yescharacteristic
334C2×C4#45211yescharacteristic
335C2×C4#45411yescharacteristic
336C2×C4#45611yescharacteristic
337C2×C4B(4,𝔽2)11yescharacteristic
338C2×C4#45811yescharacteristic
339C2×C4#46211yescharacteristic
340C2×C4#46411yescharacteristic
341C2×C4#46711yescharacteristic
342C2×C4#47011yescharacteristic
343C2×C4#48011yescharacteristic
344C2×C4#48211yescharacteristic
345C8—42no—
346C8—81no—
347C8—81no—
348C8—82no—
349C8—81no—
350C8—161no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22#167411yescharacteristic
364C22#168211yescharacteristic
365C22#169211yescharacteristic
366C22#170011yescharacteristic
367C22#203311yescharacteristic
368C22#203811yescharacteristic
369C22#204411yescharacteristic
370C22#204811yescharacteristic
371C22#205211yescharacteristic
372C22#205311yescharacteristic
373C22#205611yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—82no—
383C4—162no—
384C4—161no—
385C4—161no—
386C4—161no—
387C4#159811yescharacteristic
388C4#160311yescharacteristic
389C4#161011yescharacteristic
390C4#161511yescharacteristic
391C2—21no—
392C2—21no—
393C2—21no—
394C2—21no—
395C2#1039711yescharacteristic
396C2#1046411yescharacteristic
397C2#1047811yescharacteristic
398C2#1050611yescharacteristic
399C2#1051111yescharacteristic
400C2#1056111yescharacteristic
401C2#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
#297572
#112282
#98852
#98792
#91312
#88292
#70392