Finite Group Databasebeta

← #105061

Subgroups — #105061

Order 512.

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

normal subgroups only

This group has 427 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#29969C211yesmaximal, characteristic
2#11228C211yesmaximal, characteristic
3#9884C211yesmaximal, characteristic
4#9879C211yesmaximal, characteristic
5#9127C211yesmaximal, characteristic
6#8829C211yesmaximal, characteristic
7#7039C211yesmaximal, characteristic
8C22×C4⋊C8C2211yescharacteristic
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11#2100—21no—
12#2087—21no—
13#2087—21no—
14#2057—21no—
15#1852—21no—
16#1824—21no—
17#1797C2211yescharacteristic
18#1797C2211yescharacteristic
19C4×C22⋊C8C2211yescharacteristic
20C2×#340—21no—
21C2×#340—21no—
22C2×#335—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×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
39C2×#107—21no—
40C2×#107—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—42no—
45C2×C4⋊C8D411yescharacteristic
46C2×C4⋊C8D411yescharacteristic
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8D411yescharacteristic
50C2×C22⋊C8D411yescharacteristic
51C2×C4×C8—21no—
52#391—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#389—21no—
59#384D411yescharacteristic
60#380—21no—
61#380—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65#340—21no—
66#340—21no—
67#340—21no—
68#340—21no—
69#340—21no—
70#340—21no—
71#340—42no—
72#340—42no—
73#336—21no—
74#336—21no—
75#336—21no—
76#335—42no—
77#333—42no—
78C22×Q8—21no—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—41no—
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4#4111yescharacteristic
85C22×C8—21no—
86C22×C8—22no—
87C22×C8—21no—
88C22×C8—21no—
89C22×C8—21no—
90C22×C8—41no—
91C22×C8—41no—
92C22×C8—41no—
93C22×C8—41no—
94C22×C8—41no—
95C22×C8—41no—
96C22×C8—41no—
97C4⋊Q8—41no—
98C4⋊Q8—41no—
99C22⋊Q8—81no—
100C22⋊Q8—81no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—22no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—21no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
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—82no—
125C2×C4⋊C4Q1612yes—
126C2×C22⋊C4—41no—
127C2×C42—41no—
128C2×C42—41no—
129C2×C42C2×D411yescharacteristic
130C2×C42C2×D411yescharacteristic
131C2×C42#4111yescharacteristic
132C2×C42#4111yescharacteristic
133#107—81no—
134#107—81no—
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—41no—
138C4⋊C8—41no—
139C4⋊C8—41no—
140C4⋊C8—41no—
141C4⋊C8—41no—
142C4⋊C8—41no—
143C22⋊C8—21no—
144C22⋊C8—21no—
145C22⋊C8—21no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8Q1612yes—
151C4×C8—41no—
152C4×C8—41no—
153#95—41no—
154#95—41no—
155#95—41no—
156#95—41no—
157#95—41no—
158#95—41no—
159#95—81no—
160C24#12111yescharacteristic
161C2×Q8—42no—
162C2×Q8—81no—
163C2×Q8—81no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—42no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4—81no—
187C22×C4—81no—
188C22×C4—81no—
189C22×C4—81no—
190C22×C4—81no—
191C22×C4—81no—
192C22×C4—81no—
193C22×C4#12011yescharacteristic
194C22×C4#12111yescharacteristic
195C22×C4#12111yescharacteristic
196C22×C4#12311yescharacteristic
197C22×C4#12311yescharacteristic
198C22×C4#12411yescharacteristic
199C22×C4C2×Q1611yescharacteristic
200C22×C4C2×Q1611yescharacteristic
201C22×C4#13511yescharacteristic
202C22×C4#13511yescharacteristic
203C22×C4AGL(1,ℤ/8)11yescharacteristic
204C22×C4#13711yescharacteristic
205C22×C4#13711yescharacteristic
206C22×C4#13711yescharacteristic
207C2×C8—22no—
208C2×C8—41no—
209C2×C8—41no—
210C2×C8—41no—
211C2×C8—41no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—41no—
215C2×C8—41no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—42no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8—81no—
223C2×C8—81no—
224C2×C8—81no—
225C2×C8—81no—
226C2×C8—81no—
227C2×C8—81no—
228C2×C8—81no—
229C4⋊C4—22no—
230C4⋊C4—22no—
231C4⋊C4—42no—
232C4⋊C4—42no—
233C4⋊C4—42no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—81no—
243C4⋊C4—81no—
244C4⋊C4—81no—
245C4⋊C4—81no—
246C4⋊C4—81no—
247C4⋊C4—82no—
248C4⋊C4—82no—
249C4⋊C4—82no—
250C22⋊C4—81no—
251C22⋊C4—81no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—41no—
257C42—41no—
258C23—21no—
259C23—21no—
260C23—21no—
261C23—21no—
262C23#39411yescharacteristic
263C23#46211yescharacteristic
264C23#46411yescharacteristic
265C23#46711yescharacteristic
266C23#46811yescharacteristic
267C23#47111yescharacteristic
268C23#47211yescharacteristic
269Q8—162no—
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—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—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—82no—
301C2×C4—82no—
302C2×C4—82no—
303C2×C4—82no—
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—161no—
314C2×C4—161no—
315C2×C4—161no—
316C2×C4—161no—
317C2×C4—161no—
318C2×C4—161no—
319C2×C4#44911yescharacteristic
320C2×C4#45111yescharacteristic
321C2×C4#45411yescharacteristic
322C2×C4#45611yescharacteristic
323C2×C4B(4,𝔽2)11yescharacteristic
324C2×C4#45811yescharacteristic
325C2×C4#46211yescharacteristic
326C2×C4#46411yescharacteristic
327C2×C4#46711yescharacteristic
328C2×C4#47011yescharacteristic
329C2×C4#48411yescharacteristic
330C2×C4#48511yescharacteristic
331C8—42no—
332C8—81no—
333C8—81no—
334C8—82no—
335C8—81no—
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#167611yescharacteristic
350C22#168411yescharacteristic
351C22#169211yescharacteristic
352C22#169811yescharacteristic
353C22#203611yescharacteristic
354C22#203811yescharacteristic
355C22#204411yescharacteristic
356C22#204811yescharacteristic
357C22#205111yescharacteristic
358C22#205311yescharacteristic
359C22#205611yescharacteristic
360C4—21no—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—82no—
369C4—162no—
370C4—161no—
371C4—161no—
372C4—161no—
373C4#159711yescharacteristic
374C4#160511yescharacteristic
375C4#160911yescharacteristic
376C4#161711yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—21no—
381C2#1040011yescharacteristic
382C2#1046911yescharacteristic
383C2#1048311yescharacteristic
384C2#1050611yescharacteristic
385C2#1050911yescharacteristic
386C2#1056011yescharacteristic
387C2#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
#299692
#112282
#98842
#98792
#91272
#88292
#70392