Finite Group Databasebeta

← #104176

Subgroups — #104176

Order 512.

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

normal subgroups only

This group has 612 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#29966C211yesmaximal, characteristic
2#27960C211yesmaximal, characteristic
3#15145C211yesmaximal, characteristic
4#9711C211yesmaximal, characteristic
5#8723C211yesmaximal, characteristic
6#7573C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#398—22no—
10C2×#389C2211yescharacteristic
11C2×#384—21no—
12C2×#384C2211yescharacteristic
13#2099—21no—
14#2099—22no—
15#2086—22no—
16#2057—21no—
17#1990—21no—
18#1852—21no—
19#1834—21no—
20#1823—21no—
21#1823—22no—
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—21no—
36C22×C4⋊C4—24no—
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D412yes—
39C22×C4⋊C4D411yescharacteristic
40C22×C42—21no—
41C22×C42C2311yescharacteristic
42C2×#107—22no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8D412yes—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C4×C8—21no—
49#398—44no—
50#398—44no—
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—24no—
75#340—22no—
76#336—21no—
77#336—21no—
78#336D412yes—
79#328—44no—
80C22×Q8—21no—
81C23×C4—22no—
82C23×C4—21no—
83C23×C4—22no—
84C23×C4—21no—
85C23×C4C2×D411yescharacteristic
86C23×C4C2×D411yescharacteristic
87C23×C4C2×D411yescharacteristic
88C22×C8—22no—
89C22×C8—22no—
90C22×C8—41no—
91C4⋊Q8—42no—
92C22⋊Q8—42no—
93C22⋊Q8—42no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—22no—
100C2×C4⋊C4—21no—
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—44no—
109C2×C4⋊C4—42no—
110C2×C4⋊C4—48no—
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—42no—
120C2×C4⋊C4—42no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4—41no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—42no—
125C2×C4⋊C4—42no—
126C2×C4⋊C4—41no—
127C2×C4⋊C4—84no—
128C2×C4⋊C4SD1612yes—
129C2×C22⋊C4—41no—
130C2×C42—24no—
131C2×C42—42no—
132C2×C42—42no—
133C2×C42—41no—
134C2×C42—41no—
135C2×C42C2×D411yescharacteristic
136C2×C42C2×D411yescharacteristic
137C2×C42C2×D411yescharacteristic
138C2×C42#4111yescharacteristic
139#107—82no—
140C4⋊C8—42no—
141C4⋊C8—42no—
142C22⋊C8—42no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—42no—
146C4×C8—42no—
147#95—24no—
148#95—22no—
149#95—48no—
150#95—41no—
151#95—41no—
152#95—41no—
153#95—41no—
154#95D814yes—
155C24#12011yescharacteristic
156C2×Q8—42no—
157C2×Q8—81no—
158C2×Q8—81no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—24no—
162C22×C4—24no—
163C22×C4—24no—
164C22×C4—22no—
165C22×C4—22no—
166C22×C4—22no—
167C22×C4—41no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—41no—
175C22×C4—42no—
176C22×C4—41no—
177C22×C4—42no—
178C22×C4—42no—
179C22×C4—42no—
180C22×C4—41no—
181C22×C4—41no—
182C22×C4—41no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—44no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—44no—
189C22×C4#12011yescharacteristic
190C22×C4#12011yescharacteristic
191C22×C4#12111yescharacteristic
192C22×C4#12111yescharacteristic
193C22×C4#12111yescharacteristic
194C22×C4#12711yescharacteristic
195C22×C4C2×D812yes—
196C22×C4C2×SD1611yescharacteristic
197C22×C4#13511yescharacteristic
198C22×C4AGL(1,ℤ/8)11yescharacteristic
199C22×C4AGL(1,ℤ/8)12yes—
200C22×C4#13711yescharacteristic
201C2×C8—42no—
202C2×C8—42no—
203C2×C8—42no—
204C2×C8—42no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—81no—
208C2×C8—81no—
209C2×C8—81no—
210C4⋊C4—22no—
211C4⋊C4—22no—
212C4⋊C4—44no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—41no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C4⋊C4—42no—
221C4⋊C4—81no—
222C4⋊C4—82no—
223C4⋊C4—816no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C4⋊C4—82no—
227C4⋊C4—82no—
228C4⋊C4—81no—
229C4⋊C4—81no—
230C4⋊C4—81no—
231C4⋊C4—81no—
232C4⋊C4—81no—
233C4⋊C4—81no—
234C4⋊C4—81no—
235C4⋊C4—81no—
236C22⋊C4—82no—
237C42—22no—
238C42—22no—
239C42—41no—
240C42—41no—
241C42—44no—
242C42—44no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—21no—
247C23#39211yescharacteristic
248C23#44712yes—
249C23#45011yescharacteristic
250C23#45211yescharacteristic
251C23#45512yes—
252Q8—162no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—28no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—44no—
272C2×C4—44no—
273C2×C4—44no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—44no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—42no—
280C2×C4—82no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—84no—
284C2×C4—84no—
285C2×C4—84no—
286C2×C4—82no—
287C2×C4—82no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—82no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—81no—
298C2×C4#44811yescharacteristic
299C2×C4#44911yescharacteristic
300C2×C4#45612yes—
301C2×C4#45612yes—
302C2×C4#45812yes—
303C2×C4#45912yes—
304C2×C4#46511yescharacteristic
305C2×C4#46811yescharacteristic
306C2×C4#49311yescharacteristic
307C2×C4#49611yescharacteristic
308C8—82no—
309C8—82no—
310C8—161no—
311C22—21no—
312C22—21no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—21no—
317C22—21no—
318C22—22no—
319C22#163912yes—
320C22#164112yes—
321C22#200011yescharacteristic
322C22#200411yescharacteristic
323C22#200511yescharacteristic
324C22#200511yescharacteristic
325C22#200911yescharacteristic
326C22#201111yescharacteristic
327C22#202211yescharacteristic
328C4—22no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—22no—
333C4—21no—
334C4—48no—
335C4—41no—
336C4—82no—
337C4—161no—
338C4—162no—
339C4—161no—
340C4—161no—
341C4#160912yes—
342C4#161112yes—
343C2—22no—
344C2—22no—
345C2#992711yescharacteristic
346C2#995211yescharacteristic
347C2#1007011yescharacteristic
348C2#1009911yescharacteristic
349C2#1025111yescharacteristic
350C2#1028911yescharacteristic
351C2#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
#299662
#279602
#151452
#97112
#87232
#75732
#70282