Finite Group Databasebeta

← #97041

Subgroups — #97041

Order 512.

588 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 98 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
1C2×#2645C211yesmaximal, characteristic
2#8699C211yesmaximal, characteristic
3#8699C211yesmaximal, characteristic
4#7595C212yesmaximal
5#7593C212yesmaximal
6#2645—24no—
7#2645—24no—
8C2×#401—21no—
9C2×#400—21no—
10C2×#400—21no—
11C2×#400—21no—
12C2×#391C411yescharacteristic
13C2×#391C411yescharacteristic
14C2×#391C2211yescharacteristic
15C2×#389C411yescharacteristic
16C2×#389C411yescharacteristic
17C2×#389C2211yescharacteristic
18C2×#376C2211yescharacteristic
19#1817C2212yes—
20#1817C2212yes—
21#1280—21no—
22#1280—21no—
23#1280—21no—
24#1280—21no—
25#1272—24no—
26#1271—24no—
27C23×Q8C2×C411yescharacteristic
28C22×C4⋊C4—21no—
29C22×C4⋊C4—21no—
30C22×C4⋊C4—21no—
31C22×C4⋊C4C2×C411yescharacteristic
32C22×C4⋊C4C2×C411yescharacteristic
33C22×C4⋊C4C2×C411yescharacteristic
34C22×C42C2×C411yescharacteristic
35C22×C42C2×C411yescharacteristic
36C22×C42C2311yescharacteristic
37C2×C22⋊C8—22no—
38C2×C22⋊C8—22no—
39#401—28no—
40#400—28no—
41#400—28no—
42#400—28no—
43#391—22no—
44#391—22no—
45#391—22no—
46#391—22no—
47#391—22no—
48#391D414yes—
49#389—22no—
50#389—22no—
51#389—22no—
52#389—22no—
53#389—22no—
54#389D414yes—
55#376—22no—
56#376—22no—
57C2×#95—21no—
58C2×#95—21no—
59C2×#95—21no—
60C2×#95—21no—
61C2×#95—21no—
62C2×#95—21no—
63C2×#95—21no—
64C2×#95—21no—
65C2×#95—21no—
66C2×#95D411yescharacteristic
67C2×#95D411yescharacteristic
68C2×#95D411yescharacteristic
69C2×#95D411yescharacteristic
70#336—22no—
71#336—22no—
72#336—22no—
73#336—22no—
74C22×Q8—21no—
75C22×Q8—24no—
76C22×Q8—42no—
77C22×Q8—42no—
78C22×Q8C22⋊C412yes—
79C23×C4—21no—
80C23×C4—21no—
81C23×C4—21no—
82C23×C4—21no—
83C23×C4C22⋊C411yescharacteristic
84C23×C4C22⋊C411yescharacteristic
85C23×C4C22⋊C411yescharacteristic
86C23×C4C22⋊C411yescharacteristic
87C23×C4C22×C411yescharacteristic
88C23×C4C2×D411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C22×C8—42no—
91C22×C8—42no—
92C2×C4⋊C4—24no—
93C2×C4⋊C4—21no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—21no—
96C2×C4⋊C4—24no—
97C2×C4⋊C4—24no—
98C2×C4⋊C4—24no—
99C2×C4⋊C4—42no—
100C2×C4⋊C4—42no—
101C2×C4⋊C4—82no—
102C2×C4⋊C4—82no—
103C2×C4⋊C4—82no—
104C2×C4⋊C4C22⋊C412yes—
105C2×C4⋊C4C22⋊C412yes—
106C2×C4⋊C4C22⋊C412yes—
107C2×C42—21no—
108C2×C42—21no—
109C2×C42—21no—
110C2×C42—21no—
111C2×C42—24no—
112C2×C42—42no—
113C2×C42—42no—
114C2×C42C2×D412yes—
115C2×C42C2×D412yes—
116C22⋊C8—44no—
117C22⋊C8—44no—
118#95—24no—
119#95—24no—
120#95—24no—
121#95—24no—
122#95—24no—
123#95—24no—
124#95—24no—
125#95—24no—
126#95—24no—
127#95—22no—
128#95—22no—
129#95—22no—
130#95—22no—
131C24C2×C22⋊C411yescharacteristic
132C2×Q8—24no—
133C2×Q8—42no—
134C2×Q8—42no—
135C2×Q8—42no—
136C2×Q8—42no—
137C2×Q8—42no—
138C2×Q8—88no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—22no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4—41no—
159C22×C4—42no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—42no—
163C22×C4—42no—
164C22×C4—42no—
165C22×C4—42no—
166C22×C4—42no—
167C22×C4—42no—
168C22×C4—42no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—41no—
172C22×C4—41no—
173C22×C4—41no—
174C22×C4—41no—
175C22×C4—41no—
176C22×C4—41no—
177C22×C4—41no—
178C22×C4—41no—
179C22×C4C2×C22⋊C411yescharacteristic
180C22×C4C2×C22⋊C411yescharacteristic
181C22×C4#12012yes—
182C22×C4#12012yes—
183C22×C4#13114yes—
184C2×C8—82no—
185C2×C8—82no—
186C2×C8—82no—
187C2×C8—82no—
188C2×C8—82no—
189C2×C8—82no—
190C4⋊C4—24no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—84no—
197C4⋊C4—84no—
198C4⋊C4—84no—
199C42—42no—
200C42—42no—
201C42—42no—
202C42—42no—
203C42—42no—
204C42—42no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23#37911yescharacteristic
210C23#40812yes—
211C23#41012yes—
212C23#41312yes—
213Q8—84no—
214Q8—84no—
215C2×C4—28no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—42no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—41no—
241C2×C4—41no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—82no—
251C2×C4—82no—
252C2×C4—84no—
253C2×C4—84no—
254C2×C4—84no—
255C2×C4—84no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4—82no—
259C2×C4—82no—
260C2×C4#40812yes—
261C2×C4#40812yes—
262C8—162no—
263C8—162no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—22no—
268C22—22no—
269C22—22no—
270C22#147314yes—
271C22#178011yescharacteristic
272C22#178211yescharacteristic
273C22#178511yescharacteristic
274C22#179511yescharacteristic
275C22#179611yescharacteristic
276C22#179611yescharacteristic
277C22#179611yescharacteristic
278C4—22no—
279C4—22no—
280C4—42no—
281C4—42no—
282C4—82no—
283C4—81no—
284C4—82no—
285C4—81no—
286C4—82no—
287C4—81no—
288C4—82no—
289C4—81no—
290C2—24no—
291C2#830911yescharacteristic
292C2#832511yescharacteristic
293C2#832711yescharacteristic
294C2#851911yescharacteristic
295C2#852111yescharacteristic
296C2#852311yescharacteristic
297C2#852711yescharacteristic
subgroupG/H
center, socleC23#379
commutatorC23×C4C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24C2×C22⋊C4
LCSG ▷ C23×C4 ▷ C22 ▷ 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
C2×#26452
#86992
#75952
#75932