Finite Group Databasebeta

← #104116

Subgroups — #104116

Order 512.

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

normal subgroups only

This group has 562 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#29968C211yesmaximal, characteristic
2#27910C211yesmaximal, characteristic
3#15197C211yesmaximal, characteristic
4#9908C211yesmaximal, characteristic
5#8725C211yesmaximal, characteristic
6#7573C211yesmaximal, characteristic
7#7028C211yesmaximal, characteristic
8C2×#484—22no—
9#2857C2211yescharacteristic
10C2×#389C2211yescharacteristic
11C2×#384C2211yescharacteristic
12#2100—21no—
13#2095—22no—
14#2088—22no—
15#2058—21no—
16#1956—21no—
17#1853—21no—
18#1845—21no—
19#1823—21no—
20#1797C2211yescharacteristic
21#1797C2211yescharacteristic
22C4×C22⋊C8C2211yescharacteristic
23#1442—22no—
24#1441—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⋊C4D412yes—
38C22×C4⋊C4D411yescharacteristic
39C22×C42—21no—
40C22×C42C2311yescharacteristic
41#484—48no—
42C2×#107—24no—
43C2×#106—22no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8D412yes—
46C2×#103—24no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C4×C8—21no—
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—21no—
66C2×#95—21no—
67C2×#95—24no—
68C2×#95—24no—
69C2×#95D412yes—
70#340—22no—
71#340—22no—
72#340—22no—
73#336—21no—
74#336—21no—
75#336D412yes—
76C22×Q8—21no—
77C23×C4—21no—
78C23×C4—22no—
79C23×C4—22no—
80C23×C4—21no—
81C23×C4C2×D411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C22×C8—22no—
85C22×C8—22no—
86C22×C8—41no—
87C4⋊Q8—42no—
88C22⋊Q8—44no—
89C2×C4⋊C4—21no—
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—22no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4—21no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4—44no—
104C2×C4⋊C4—42no—
105C2×C4⋊C4—44no—
106C2×C4⋊C4—41no—
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—42no—
114C2×C4⋊C4—42no—
115C2×C4⋊C4—82no—
116C2×C4⋊C4Q1612yes—
117C2×C22⋊C4—41no—
118C2×C42—42no—
119C2×C42—42no—
120C2×C42—42no—
121C2×C42—41no—
122C2×C42—41no—
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42#4111yescharacteristic
127#107—48no—
128#106—82no—
129C4⋊C8—42no—
130C4⋊C8—42no—
131#103—48no—
132C22⋊C8—24no—
133C22⋊C8—41no—
134C22⋊C8—41no—
135C22⋊C8—42no—
136C4×C8—42no—
137#95—24no—
138#95—22no—
139#95—22no—
140#95—41no—
141#95—41no—
142#95—41no—
143#95—41no—
144#95—84no—
145#95—84no—
146C24#12011yescharacteristic
147C2×Q8—42no—
148C2×Q8—42no—
149C2×Q8—42no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—24no—
155C22×C4—22no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—41no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—41no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—44no—
171C22×C4—44no—
172C22×C4—42no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—42no—
177C22×C4—42no—
178C22×C4—44no—
179C22×C4#12011yescharacteristic
180C22×C4#12011yescharacteristic
181C22×C4#12111yescharacteristic
182C22×C4#12111yescharacteristic
183C22×C4#12111yescharacteristic
184C22×C4#12711yescharacteristic
185C22×C4C2×Q1611yescharacteristic
186C22×C4#13511yescharacteristic
187C22×C4#13512yes—
188C22×C4#13711yescharacteristic
189C22×C4#13711yescharacteristic
190C22×C4#13712yes—
191C2×C8—24no—
192C2×C8—42no—
193C2×C8—42no—
194C2×C8—42no—
195C2×C8—42no—
196C2×C8—42no—
197C2×C8—81no—
198C2×C8—81no—
199C2×C8—81no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—44no—
203C4⋊C4—42no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—42no—
208C4⋊C4—42no—
209C4⋊C4—81no—
210C4⋊C4—81no—
211C4⋊C4—82no—
212C4⋊C4—81no—
213C4⋊C4—82no—
214C4⋊C4—82no—
215C4⋊C4—82no—
216C4⋊C4—82no—
217C4⋊C4—82no—
218C4⋊C4—82no—
219C4⋊C4—81no—
220C4⋊C4—81no—
221C22⋊C4—82no—
222C42—22no—
223C42—22no—
224C42—41no—
225C42—41no—
226C42—82no—
227C42—82no—
228C23—21no—
229C23—21no—
230C23—21no—
231C23—21no—
232C23#39211yescharacteristic
233C23#45111yescharacteristic
234C23#45212yes—
235C23#45211yescharacteristic
236C23#45312yes—
237Q8—84no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—44no—
256C2×C4—44no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—82no—
262C2×C4—82no—
263C2×C4—82no—
264C2×C4—82no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—88no—
269C2×C4—84no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4—82no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—81no—
276C2×C4—82no—
277C2×C4—81no—
278C2×C4—81no—
279C2×C4—81no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4#45111yescharacteristic
283C2×C4#45211yescharacteristic
284C2×C4#45412yes—
285C2×C4#45612yes—
286C2×C4#45812yes—
287C2×C4#46412yes—
288C2×C4#46711yescharacteristic
289C2×C4#47011yescharacteristic
290C2×C4#49511yescharacteristic
291C2×C4#49711yescharacteristic
292C8—44no—
293C8—82no—
294C8—161no—
295C22—21no—
296C22—21no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—21no—
301C22—21no—
302C22—22no—
303C22#163212yes—
304C22#163412yes—
305C22#200111yescharacteristic
306C22#200211yescharacteristic
307C22#200311yescharacteristic
308C22#200511yescharacteristic
309C22#200811yescharacteristic
310C22#201511yescharacteristic
311C22#202211yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—22no—
317C4—21no—
318C4—41no—
319C4—84no—
320C4—82no—
321C4—161no—
322C4—161no—
323C4—162no—
324C4—161no—
325C4#161512yes—
326C4#161712yes—
327C2—22no—
328C2—22no—
329C2#992911yescharacteristic
330C2#995811yescharacteristic
331C2#1005611yescharacteristic
332C2#1008911yescharacteristic
333C2#1025311yescharacteristic
334C2#1029611yescharacteristic
335C2#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
#299682
#279102
#151972
#99082
#87252
#75732
#70282