Finite Group Databasebeta

← #101374

Subgroups — #101374

Order 512.

357 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 357 conjugacy classes of subgroups — too many to draw. Only its 76 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#27612C211yesmaximal, characteristic
2#21915C211yesmaximal, characteristic
3#8721C211yesmaximal, characteristic
4#8709C211yesmaximal, characteristic
5#7613C211yesmaximal, characteristic
6#7038C211yesmaximal, characteristic
7#7021C211yesmaximal, characteristic
8#2296C2211yescharacteristic
9#2285C2211yescharacteristic
10#2100C411yescharacteristic
11#2100C411yescharacteristic
12#2084C411yescharacteristic
13#2083C411yescharacteristic
14#1920—21no—
15#1918—21no—
16#1917—22no—
17#1916—22no—
18#1854—21no—
19#1825—21no—
20#1818—21no—
21#1817C2211yescharacteristic
22#1798—21no—
23#1797C2211yescharacteristic
24#1749C2211yescharacteristic
25#1749C2211yescharacteristic
26C4×C22⋊C8C2211yescharacteristic
27#1295—22no—
28#1279—22no—
29#1271—21no—
30#1271—21no—
31C2×#117—21no—
32C2×#117D411yescharacteristic
33C2×#117D411yescharacteristic
34C22×C42C2311yescharacteristic
35C2×#107—21no—
36C2×#106—21no—
37C2×C4⋊C8—21no—
38C2×C4⋊C8—22no—
39C2×C22⋊C8—21no—
40C2×C22⋊C8—21no—
41C2×C22⋊C8—21no—
42C2×C22⋊C8—21no—
43C2×C22⋊C8—21no—
44C2×#97—21no—
45C2×#97D412yes—
46C2×C4×C8D412yes—
47#389C2×C411yescharacteristic
48#389C2×C411yescharacteristic
49#389D411yescharacteristic
50#389D411yescharacteristic
51#385—21no—
52#385—21no—
53#384C2×C411yescharacteristic
54#384C2×C411yescharacteristic
55#382—21no—
56#380—21no—
57#380—21no—
58C4×C4⋊C4—21no—
59C4×C4⋊C4—21no—
60C4×C4⋊C4—21no—
61C4×C4⋊C4—21no—
62#340—21no—
63#340—21no—
64#340—21no—
65#340—21no—
66#340—21no—
67#340—21no—
68#336—22no—
69#336—24no—
70#336—21no—
71#336—21no—
72#336—21no—
73#336—21no—
74#336—21no—
75#336C2×C411yescharacteristic
76#336C2×C411yescharacteristic
77C23×C4C2×D411yescharacteristic
78C23×C4#4111yescharacteristic
79C23×C4#4111yescharacteristic
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—22no—
83C22×C8—22no—
84C22×C8—41no—
85C22×C8—41no—
86#117—41no—
87#117—41no—
88#117—42no—
89#117—81no—
90#117—81no—
91C2×C4⋊C4—21no—
92C2×C4⋊C4—21no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—21no—
101C2×C4⋊C4C22⋊C411yescharacteristic
102C2×C4⋊C4C22⋊C411yescharacteristic
103C2×C4⋊C4C22⋊C411yescharacteristic
104C2×C4⋊C4C22⋊C411yescharacteristic
105C2×C22⋊C4—21no—
106C2×C22⋊C4—21no—
107C2×C22⋊C4—41no—
108C2×C42—21no—
109C2×C42—21no—
110C2×C42—42no—
111C2×C42—41no—
112C2×C42C22×C411yescharacteristic
113C2×C42C2×D411yescharacteristic
114C2×C42C2×D411yescharacteristic
115C2×C42C2×D411yescharacteristic
116#107—42no—
117#106—42no—
118C4⋊C8—42no—
119C4⋊C8—82no—
120C22⋊C8—22no—
121C22⋊C8—41no—
122C22⋊C8—41no—
123C22⋊C8—41no—
124C22⋊C8—41no—
125C22⋊C8—41no—
126C22⋊C8—42no—
127C22⋊C8—81no—
128#97—42no—
129#97—42no—
130C4×C8—42no—
131#95—21no—
132#95—21no—
133#95—21no—
134#95—21no—
135#95—41no—
136#95—41no—
137C24#12311yescharacteristic
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—22no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—41no—
150C22×C4—41no—
151C22×C4—41no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4C2×C22⋊C411yescharacteristic
157C22×C4C4×D411yescharacteristic
158C22×C4C4×D411yescharacteristic
159C22×C4#12011yescharacteristic
160C22×C4#12111yescharacteristic
161C22×C4#12111yescharacteristic
162C2×C8—42no—
163C2×C8—41no—
164C2×C8—41no—
165C2×C8—42no—
166C2×C8—42no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—42no—
170C2×C8—42no—
171C2×C8—41no—
172C2×C8—41no—
173C2×C8—42no—
174C2×C8—42no—
175C2×C8—81no—
176C2×C8—81no—
177C2×C8—81no—
178C2×C8—81no—
179C2×C8—81no—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—41no—
185C4⋊C4—41no—
186C4⋊C4—42no—
187C4⋊C4—42no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—41no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C4⋊C4—81no—
199C4⋊C4—81no—
200C22⋊C4—42no—
201C22⋊C4—81no—
202C22⋊C4—82no—
203C42—22no—
204C42—22no—
205C42—41no—
206C42—41no—
207C42—42no—
208C42—42no—
209C42—81no—
210C42—81no—
211C23—21no—
212C23—21no—
213C23—21no—
214C23—21no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23#38611yescharacteristic
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—42no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—81no—
250C2×C4—81no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4#42111yescharacteristic
258C2×C4#42111yescharacteristic
259C2×C4#44311yescharacteristic
260C2×C4#44411yescharacteristic
261C2×C4#45812yes—
262C2×C4#47111yescharacteristic
263C2×C4#47211yescharacteristic
264C8—82no—
265C8—82no—
266C8—81no—
267C8—81no—
268C8—82no—
269C8—161no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22#187611yescharacteristic
278C22#188111yescharacteristic
279C22#189011yescharacteristic
280C22#189711yescharacteristic
281C22#190211yescharacteristic
282C22#190711yescharacteristic
283C22#191211yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—21no—
290C4—21no—
291C4—41no—
292C4—41no—
293C4—81no—
294C4—81no—
295C4—81no—
296C4—81no—
297C4—161no—
298C4—161no—
299C2—81no—
300C2#903811yescharacteristic
301C2#921311yescharacteristic
302C2#928611yescharacteristic
303C2#931411yescharacteristic
304C2#937211yescharacteristic
305C2#948211yescharacteristic
306C2#952211yescharacteristic
subgroupG/H
center, socleC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#123
LCSG ▷ C2×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
#276122
#219152
#87212
#87092
#76132
#70382
#70212