Finite Group Databasebeta

← #104163

Subgroups — #104163

Order 512.

594 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 96 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#29951C211yesmaximal, characteristic
2#27950C211yesmaximal, characteristic
3#15240C211yesmaximal, characteristic
4#9711C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7575C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#391—21no—
10C2×#391C2211yescharacteristic
11C2×#384C2211yescharacteristic
12C2×#382—21no—
13#2096—21no—
14#2083—22no—
15#2066—22no—
16#2024—21no—
17#1990—21no—
18#1853—21no—
19#1852—22no—
20#1845—21no—
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23#1787—21no—
24C4×C22⋊C8C2211yescharacteristic
25C2×#328—22no—
26#1445—22no—
27#1445—22no—
28C4×#95C2211yescharacteristic
29#1296—22no—
30#1272—22no—
31C23×Q8D411yescharacteristic
32C2×C4⋊Q8D411yescharacteristic
33C2×C22⋊Q8—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4D412yes—
37C22×C4⋊C4D411yescharacteristic
38C22×C42—21no—
39C22×C42C2311yescharacteristic
40C2×#107—24no—
41C2×#106—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8D412yes—
44C2×#103—22no—
45C2×#103—22no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C4×C8—21no—
50#391—21no—
51#391—21no—
52#391—21no—
53#391—21no—
54#391—21no—
55#391—44no—
56#389—21no—
57#389—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384D411yescharacteristic
63#382—44no—
64#380—21no—
65#380—21no—
66C2×#95—24no—
67C2×#95—24no—
68C2×#95—21no—
69C2×#95—21no—
70C2×#95—21no—
71C2×#95D412yes—
72#340—22no—
73#340—24no—
74#336—21no—
75#336—21no—
76#336D412yes—
77#328—44no—
78C22×Q8—21no—
79C22×Q8—21no—
80C22×Q8—21no—
81C22×Q8—21no—
82C22×Q8—21no—
83C22×Q8—21no—
84C22×Q8—42no—
85C22×Q8—42no—
86C22×Q8Q1612yes—
87C23×C4—21no—
88C23×C4—22no—
89C23×C4—22no—
90C23×C4—21no—
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4C2×D411yescharacteristic
94C22×C8—22no—
95C22×C8—22no—
96C22×C8—41no—
97C4⋊Q8—42no—
98C22⋊Q8—42no—
99C22⋊Q8—42no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—22no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—44no—
110C2×C4⋊C4—42no—
111C2×C4⋊C4—42no—
112C2×C4⋊C4—42no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—41no—
115C2×C4⋊C4—41no—
116C2×C4⋊C4—41no—
117C2×C4⋊C4—41no—
118C2×C4⋊C4—42no—
119C2×C4⋊C4—42no—
120C2×C22⋊C4—41no—
121C2×C42—24no—
122C2×C42—42no—
123C2×C42—42no—
124C2×C42—41no—
125C2×C42—41no—
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42C2×D411yescharacteristic
129C2×C42#4111yescharacteristic
130#107—84no—
131#106—82no—
132C4⋊C8—42no—
133C4⋊C8—42no—
134#103—82no—
135#103—82no—
136C22⋊C8—24no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—42no—
140C4×C8—42no—
141#95—22no—
142#95—22no—
143#95—42no—
144#95—48no—
145#95—48no—
146#95—41no—
147#95—41no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152C24#12011yescharacteristic
153C2×Q8—22no—
154C2×Q8—22no—
155C2×Q8—44no—
156C2×Q8—44no—
157C2×Q8—41no—
158C2×Q8—41no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—42no—
162C2×Q8—82no—
163C2×Q8—82no—
164C2×Q8—81no—
165C2×Q8—81no—
166C2×Q8—81no—
167C2×Q8—81no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—24no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—42no—
181C22×C4—42no—
182C22×C4—41no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—41no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—42no—
190C22×C4—44no—
191C22×C4—42no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4—42no—
196C22×C4—44no—
197C22×C4—42no—
198C22×C4#12011yescharacteristic
199C22×C4#12011yescharacteristic
200C22×C4#12111yescharacteristic
201C22×C4#12111yescharacteristic
202C22×C4#12111yescharacteristic
203C22×C4#12711yescharacteristic
204C22×C4C2×Q1611yescharacteristic
205C22×C4#13511yescharacteristic
206C22×C4#13512yes—
207C22×C4AGL(1,ℤ/8)12yes—
208C22×C4#13711yescharacteristic
209C22×C4#13711yescharacteristic
210C2×C8—24no—
211C2×C8—42no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—81no—
217C2×C8—81no—
218C2×C8—81no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—44no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—81no—
227C4⋊C4—82no—
228C4⋊C4—82no—
229C4⋊C4—82no—
230C4⋊C4—82no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C22⋊C4—82no—
236C42—22no—
237C42—22no—
238C42—41no—
239C42—41no—
240C42—44no—
241C42—44no—
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23#39211yescharacteristic
247C23#44912yes—
248C23#45111yescharacteristic
249C23#45211yescharacteristic
250C23#45612yes—
251Q8—44no—
252Q8—82no—
253Q8—82no—
254Q8—82no—
255Q8—162no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—42no—
279C2×C4—82no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—84no—
287C2×C4—84no—
288C2×C4—84no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—82no—
292C2×C4—82no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—81no—
301C2×C4#45111yescharacteristic
302C2×C4#45211yescharacteristic
303C2×C4#45312yes—
304C2×C4#45512yes—
305C2×C4#45812yes—
306C2×C4#46312yes—
307C2×C4#46711yescharacteristic
308C2×C4#47011yescharacteristic
309C2×C4#49511yescharacteristic
310C2×C4#49611yescharacteristic
311C8—44no—
312C8—82no—
313C8—161no—
314C22—21no—
315C22—21no—
316C22—22no—
317C22—22no—
318C22—22no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22#164812yes—
323C22#165012yes—
324C22#200111yescharacteristic
325C22#200211yescharacteristic
326C22#200411yescharacteristic
327C22#200511yescharacteristic
328C22#200911yescharacteristic
329C22#201211yescharacteristic
330C22#202211yescharacteristic
331C4—22no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—22no—
336C4—21no—
337C4—41no—
338C4—84no—
339C4—82no—
340C4—161no—
341C4—162no—
342C4—161no—
343C4—161no—
344C4#161412yes—
345C4#161812yes—
346C2—22no—
347C2—22no—
348C2#992811yescharacteristic
349C2#995311yescharacteristic
350C2#1007711yescharacteristic
351C2#1010211yescharacteristic
352C2#1025211yescharacteristic
353C2#1028111yescharacteristic
354C2#1033511yescharacteristic
subgroupG/H
center, socleC23#392
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
#299512
#279502
#152402
#97112
#87242
#75752
#70282