Finite Group Databasebeta

← #104100

Subgroups — #104100

Order 512.

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

normal subgroups only

This group has 554 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#29968C211yesmaximal, characteristic
2#27972C211yesmaximal, characteristic
3#15153C211yesmaximal, characteristic
4#9908C211yesmaximal, characteristic
5#8724C211yesmaximal, characteristic
6#7573C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8#2857C2211yescharacteristic
9C2×#400—22no—
10C2×#389C2211yescharacteristic
11C2×#384C2211yescharacteristic
12#2100—21no—
13#2088—22no—
14#2072—22no—
15#2058—21no—
16#1956—21no—
17#1872—22no—
18#1853—21no—
19#1834—21no—
20#1823—21no—
21#1797C2211yescharacteristic
22#1797C2211yescharacteristic
23C4×C22⋊C8C2211yescharacteristic
24#1445—22no—
25C4⋊#95—21no—
26C4⋊#95—21no—
27C4×#95C2211yescharacteristic
28#1296—22no—
29#1294—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⋊C4D411yescharacteristic
37C22×C4⋊C4D411yescharacteristic
38C22×C4⋊C4D412yes—
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41C2×#106—22no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8D412yes—
44C2×#103—24no—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C4×C8—21no—
49#400—44no—
50#400—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#384D411yescharacteristic
63#380—21no—
64#380—21no—
65C2×#95—24no—
66C2×#95—24no—
67C2×#95—21no—
68C2×#95—21no—
69C2×#95D412yes—
70#340—22no—
71#340—24no—
72#340—22no—
73#340—22no—
74#336—21no—
75#336—21no—
76#336D412yes—
77C22×Q8—21no—
78C23×C4—21no—
79C23×C4—22no—
80C23×C4—22no—
81C23×C4—21no—
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C22×C8—22no—
86C22×C8—22no—
87C22×C8—41no—
88C4⋊Q8—42no—
89C22⋊Q8—44no—
90C2×C4⋊C4—21no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—22no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—22no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—21no—
104C2×C4⋊C4—44no—
105C2×C4⋊C4—42no—
106C2×C4⋊C4—44no—
107C2×C4⋊C4—41no—
108C2×C4⋊C4—41no—
109C2×C4⋊C4—41no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4—41no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—42no—
116C2×C4⋊C4—42no—
117C2×C4⋊C4—42no—
118C2×C4⋊C4Q1612yes—
119C2×C22⋊C4—41no—
120C2×C42—42no—
121C2×C42—42no—
122C2×C42—42no—
123C2×C42—41no—
124C2×C42—41no—
125C2×C42C2×D411yescharacteristic
126C2×C42C2×D411yescharacteristic
127C2×C42C2×D411yescharacteristic
128C2×C42#4111yescharacteristic
129#106—82no—
130C4⋊C8—42no—
131C4⋊C8—42no—
132#103—84no—
133C22⋊C8—42no—
134C22⋊C8—41no—
135C22⋊C8—41no—
136C22⋊C8—42no—
137C4×C8—42no—
138#95—22no—
139#95—42no—
140#95—48no—
141#95—48no—
142#95—41no—
143#95—41no—
144#95—41no—
145#95—41no—
146#95SD1614yes—
147C24#12011yescharacteristic
148C2×Q8—42no—
149C2×Q8—42no—
150C2×Q8—42no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—24no—
156C22×C4—22no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—41no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—41no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—41no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—44no—
171C22×C4—44no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—42no—
178C22×C4—44no—
179C22×C4—42no—
180C22×C4#12011yescharacteristic
181C22×C4#12011yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4#12111yescharacteristic
185C22×C4#12711yescharacteristic
186C22×C4C2×SD1612yes—
187C22×C4C2×Q1611yescharacteristic
188C22×C4#13511yescharacteristic
189C22×C4AGL(1,ℤ/8)12yes—
190C22×C4#13711yescharacteristic
191C22×C4#13711yescharacteristic
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—42no—
198C2×C8—81no—
199C2×C8—81no—
200C2×C8—81no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—42no—
209C4⋊C4—42no—
210C4⋊C4—81no—
211C4⋊C4—81no—
212C4⋊C4—82no—
213C4⋊C4—81no—
214C4⋊C4—82no—
215C4⋊C4—82no—
216C4⋊C4—82no—
217C4⋊C4—82no—
218C4⋊C4—82no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C4⋊C4—81no—
222C4⋊C4—81no—
223C22⋊C4—82no—
224C42—22no—
225C42—22no—
226C42—41no—
227C42—41no—
228C42—82no—
229C42—82no—
230C23—21no—
231C23—21no—
232C23—21no—
233C23—21no—
234C23#39211yescharacteristic
235C23#45012yes—
236C23#45111yescharacteristic
237C23#45211yescharacteristic
238C23#45412yes—
239Q8—84no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—42no—
256C2×C4—42no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—44no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—82no—
267C2×C4—82no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—88no—
271C2×C4—84no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—82no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4#45111yescharacteristic
285C2×C4#45211yescharacteristic
286C2×C4#45412yes—
287C2×C4#45512yes—
288C2×C4#45812yes—
289C2×C4#46012yes—
290C2×C4#46711yescharacteristic
291C2×C4#47011yescharacteristic
292C2×C4#49211yescharacteristic
293C2×C4#49611yescharacteristic
294C8—82no—
295C8—82no—
296C8—161no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—21no—
303C22—21no—
304C22—22no—
305C22#163512yes—
306C22#163712yes—
307C22#200111yescharacteristic
308C22#200311yescharacteristic
309C22#200311yescharacteristic
310C22#200411yescharacteristic
311C22#200911yescharacteristic
312C22#201411yescharacteristic
313C22#202211yescharacteristic
314C4—22no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—22no—
319C4—21no—
320C4—41no—
321C4—84no—
322C4—82no—
323C4—162no—
324C4—161no—
325C4—161no—
326C4—161no—
327C4#161512yes—
328C4#161712yes—
329C2—22no—
330C2—22no—
331C2#992911yescharacteristic
332C2#996011yescharacteristic
333C2#1006011yescharacteristic
334C2#1009511yescharacteristic
335C2#1025211yescharacteristic
336C2#1029411yescharacteristic
337C2#1033211yescharacteristic
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
#299682
#279722
#151532
#99082
#87242
#75732
#70282