Finite Group Databasebeta

← #104158

Subgroups — #104158

Order 512.

620 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 100 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#29967C211yesmaximal, characteristic
2#27948C211yesmaximal, characteristic
3#15145C211yesmaximal, characteristic
4#9711C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7576C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#398—22no—
10C2×#389C2211yescharacteristic
11C2×#384—21no—
12C2×#384C2211yescharacteristic
13#2099—21no—
14#2088—22no—
15#2084—22no—
16#2058—21no—
17#1990—21no—
18#1853—21no—
19#1853—22no—
20#1844—21no—
21#1824—21no—
22#1797C2211yescharacteristic
23#1797C2211yescharacteristic
24C4×C22⋊C8C2211yescharacteristic
25C2×#328—22no—
26#1444—22no—
27C4⋊#95—21no—
28C4×#95C2211yescharacteristic
29#1296—22no—
30#1271—22no—
31C2×C4⋊Q8D411yescharacteristic
32C2×C22⋊Q8—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—24no—
36C22×C4⋊C4—21no—
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D412yes—
39C22×C4⋊C4D411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42C2×#106—22no—
43C2×#106—24no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D412yes—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C4×C8—21no—
50#398—48no—
51#391—21no—
52#389—21no—
53#389—21no—
54#389—21no—
55#389—21no—
56#389—21no—
57#389—21no—
58#384—21no—
59#384—21no—
60#384—21no—
61#384—21no—
62#384—42no—
63#384—42no—
64#384D411yescharacteristic
65#380—21no—
66#380—21no—
67C2×#95—21no—
68C2×#95—24no—
69C2×#95—21no—
70C2×#95D412yes—
71#340—22no—
72#340—22no—
73#340—24no—
74#340—22no—
75#336—21no—
76#336—21no—
77#336D412yes—
78#328—44no—
79C22×Q8—21no—
80C23×C4—22no—
81C23×C4—21no—
82C23×C4—22no—
83C23×C4—21no—
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C22×C8—22no—
88C22×C8—22no—
89C22×C8—41no—
90C4⋊Q8—42no—
91C22⋊Q8—42no—
92C22⋊Q8—42no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—22no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—42no—
108C2×C4⋊C4—44no—
109C2×C4⋊C4—48no—
110C2×C4⋊C4—44no—
111C2×C4⋊C4—48no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
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—82no—
124C2×C4⋊C4—84no—
125C2×C4⋊C4SD1612yes—
126C2×C22⋊C4—41no—
127C2×C42—24no—
128C2×C42—42no—
129C2×C42—42no—
130C2×C42—41no—
131C2×C42—41no—
132C2×C42C2×D411yescharacteristic
133C2×C42C2×D411yescharacteristic
134C2×C42C2×D411yescharacteristic
135C2×C42#4111yescharacteristic
136#106—84no—
137#106—82no—
138C4⋊C8—42no—
139C4⋊C8—42no—
140C22⋊C8—24no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C22⋊C8—42no—
144C4×C8—42no—
145#95—24no—
146#95—22no—
147#95—48no—
148#95—41no—
149#95—41no—
150#95—41no—
151#95—41no—
152#95SD1614yes—
153C24#12011yescharacteristic
154C2×Q8—42no—
155C2×Q8—81no—
156C2×Q8—81no—
157C22×C4—22no—
158C22×C4—22no—
159C22×C4—24no—
160C22×C4—24no—
161C22×C4—24no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—22no—
165C22×C4—41no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—42no—
177C22×C4—44no—
178C22×C4—42no—
179C22×C4—44no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4#12011yescharacteristic
188C22×C4#12011yescharacteristic
189C22×C4#12111yescharacteristic
190C22×C4#12111yescharacteristic
191C22×C4#12111yescharacteristic
192C22×C4#12711yescharacteristic
193C22×C4C2×SD1611yescharacteristic
194C22×C4C2×SD1612yes—
195C22×C4#13511yescharacteristic
196C22×C4AGL(1,ℤ/8)11yescharacteristic
197C22×C4#13711yescharacteristic
198C22×C4#13712yes—
199C2×C8—24no—
200C2×C8—42no—
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—81no—
206C2×C8—81no—
207C2×C8—81no—
208C4⋊C4—22no—
209C4⋊C4—22no—
210C4⋊C4—42no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—42no—
214C4⋊C4—44no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—81no—
220C4⋊C4—82no—
221C4⋊C4—82no—
222C4⋊C4—82no—
223C4⋊C4—82no—
224C4⋊C4—816no—
225C4⋊C4—81no—
226C4⋊C4—81no—
227C4⋊C4—82no—
228C4⋊C4—81no—
229C4⋊C4—81no—
230C4⋊C4—81no—
231C4⋊C4—81no—
232C22⋊C4—82no—
233C42—22no—
234C42—22no—
235C42—41no—
236C42—41no—
237C42—44no—
238C42—44no—
239C23—21no—
240C23—21no—
241C23—21no—
242C23—21no—
243C23#39211yescharacteristic
244C23#44812yes—
245C23#45011yescharacteristic
246C23#45211yescharacteristic
247C23#45612yes—
248Q8—162no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—28no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—42no—
276C2×C4—82no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—84no—
280C2×C4—84no—
281C2×C4—84no—
282C2×C4—82no—
283C2×C4—82no—
284C2×C4—81no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—81no—
288C2×C4—82no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4#44811yescharacteristic
295C2×C4#44911yescharacteristic
296C2×C4#45312yes—
297C2×C4#45612yes—
298C2×C4#45812yes—
299C2×C4#46112yes—
300C2×C4#46511yescharacteristic
301C2×C4#46811yescharacteristic
302C2×C4#49211yescharacteristic
303C2×C4#49711yescharacteristic
304C8—44no—
305C8—82no—
306C8—161no—
307C22—21no—
308C22—21no—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22#165112yes—
316C22#165312yes—
317C22#200011yescharacteristic
318C22#200211yescharacteristic
319C22#200511yescharacteristic
320C22#200511yescharacteristic
321C22#200811yescharacteristic
322C22#201311yescharacteristic
323C22#202211yescharacteristic
324C4—22no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—22no—
329C4—21no—
330C4—48no—
331C4—41no—
332C4—82no—
333C4—162no—
334C4—161no—
335C4—161no—
336C4—161no—
337C4#160912yes—
338C4#161112yes—
339C2—22no—
340C2—22no—
341C2#992711yescharacteristic
342C2#995111yescharacteristic
343C2#1007511yescharacteristic
344C2#1010111yescharacteristic
345C2#1024611yescharacteristic
346C2#1028311yescharacteristic
347C2#1033111yescharacteristic
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
#299672
#279482
#151452
#97112
#87242
#75762
#70282