Finite Group Databasebeta

← #101488

Subgroups — #101488

Order 512.

361 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 361 conjugacy classes of subgroups — too many to draw. Only its 90 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#29280C211yesmaximal, characteristic
2#22373C211yesmaximal, characteristic
3#9868C211yesmaximal, characteristic
4#8582C211yesmaximal, characteristic
5#7624C211yesmaximal, characteristic
6#7041C211yesmaximal, characteristic
7#7022C211yesmaximal, characteristic
8C4×C4⋊Q8C2211yescharacteristic
9C4×#125C2211yescharacteristic
10#2099C411yescharacteristic
11#2099C411yescharacteristic
12#2058C411yescharacteristic
13#2057C411yescharacteristic
14#1989—21no—
15#1949—21no—
16#1939—21no—
17#1921—21no—
18#1920—21no—
19#1916—21no—
20#1916—21no—
21#1916—21no—
22#1916—21no—
23#1839C2211yescharacteristic
24#1831C2211yescharacteristic
25C8×C4⋊C4—21no—
26#1767C2211yescharacteristic
27#1767C2211yescharacteristic
28C4×C4⋊C8C2211yescharacteristic
29C2×#330—21no—
30#1295—21no—
31#1279—21no—
32#1279—21no—
33#1272—21no—
34#1272—21no—
35C2×C4⋊Q8C2×C411yescharacteristic
36C2×#125D411yescharacteristic
37C2×C4×Q8—21no—
38C2×#107—21no—
39C2×#106—21no—
40C2×C4⋊C8—21no—
41C2×C4⋊C8—21no—
42C2×C4⋊C8—21no—
43C2×C4⋊C8—21no—
44C2×C4⋊C8—21no—
45C2×C4⋊C8—21no—
46C2×#97—21no—
47C2×#97—21no—
48C2×C4×C8—21no—
49C2×C4×C8—21no—
50C2×C4×C8D411yescharacteristic
51C2×C4×C8D411yescharacteristic
52#391—21no—
53#389—21no—
54#389—21no—
55#389C2×C411yescharacteristic
56#389C2×C411yescharacteristic
57#387—21no—
58#387—21no—
59#384C2×C411yescharacteristic
60#382D411yescharacteristic
61C4×C4⋊C4—21no—
62C4×C4⋊C4—21no—
63C4×C4⋊C4—21no—
64C4×C4⋊C4—21no—
65C4×C4⋊C4D411yescharacteristic
66C4×C4⋊C4D411yescharacteristic
67C43C2311yescharacteristic
68#340—21no—
69#340—21no—
70#340—21no—
71#340—21no—
72#340—21no—
73#340—21no—
74#336—21no—
75#336—21no—
76#336—21no—
77#336—21no—
78#336—21no—
79#336—21no—
80#336—21no—
81#336—21no—
82#336—21no—
83#336—21no—
84#336C2×C411yescharacteristic
85#336C2×C411yescharacteristic
86#336D411yescharacteristic
87#336D411yescharacteristic
88#330—42no—
89C22×Q8—21no—
90C22×C8—21no—
91C22×C8—21no—
92C22×C8—21no—
93C22×C8—21no—
94C22×C8—21no—
95C22×C8—21no—
96C22×C8—41no—
97C22×C8—41no—
98C4⋊Q8—42no—
99#125—21no—
100#125—21no—
101#125SD1612yes—
102#125Q1612yes—
103C4×Q8—82no—
104C2×C4⋊C4—21no—
105C2×C4⋊C4—21no—
106C2×C4⋊C4—21no—
107C2×C4⋊C4—21no—
108C2×C4⋊C4—21no—
109C2×C4⋊C4—21no—
110C2×C4⋊C4—21no—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4—41no—
114C2×C4⋊C4C22⋊C411yescharacteristic
115C2×C4⋊C4C22⋊C411yescharacteristic
116C2×C4⋊C4C22⋊C411yescharacteristic
117C2×C4⋊C4C22⋊C411yescharacteristic
118C2×C42—21no—
119C2×C42—21no—
120C2×C42—41no—
121C2×C42C22×C411yescharacteristic
122C2×C42C2×D411yescharacteristic
123C2×C42C2×D411yescharacteristic
124C2×C42C2×D411yescharacteristic
125C2×C42C2×D411yescharacteristic
126C2×C42#4111yescharacteristic
127C2×C42#4111yescharacteristic
128#107—42no—
129#106—42no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8—41no—
133C4⋊C8—41no—
134C4⋊C8—42no—
135C4⋊C8—42no—
136C4⋊C8—41no—
137C4⋊C8—41no—
138C4⋊C8—81no—
139#97—41no—
140#97—41no—
141#97—41no—
142#97—41no—
143C4×C8—41no—
144C4×C8—41no—
145C4×C8—42no—
146C4×C8—81no—
147#95—21no—
148#95—21no—
149#95—21no—
150#95—21no—
151#95—21no—
152#95—21no—
153#95—41no—
154#95—41no—
155C2×Q8—22no—
156C2×Q8—41no—
157C2×Q8—81no—
158C2×Q8—81no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—21no—
163C22×C4—41no—
164C22×C4—41no—
165C22×C4C2×C22⋊C411yescharacteristic
166C22×C4C4×D411yescharacteristic
167C22×C4C4×D411yescharacteristic
168C22×C4#12011yescharacteristic
169C22×C4#12111yescharacteristic
170C22×C4#12111yescharacteristic
171C22×C4#12311yescharacteristic
172C2×C8—22no—
173C2×C8—41no—
174C2×C8—41no—
175C2×C8—41no—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—41no—
179C2×C8—41no—
180C2×C8—41no—
181C2×C8—41no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8—41no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—41no—
190C2×C8—41no—
191C2×C8—41no—
192C2×C8—81no—
193C2×C8—81no—
194C2×C8—81no—
195C2×C8—81no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—42no—
209C4⋊C4—41no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—81no—
214C4⋊C4—81no—
215C4⋊C4—82no—
216C4⋊C4#10312yes—
217C4⋊C4#10312yes—
218C42—21no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—41no—
223C42—41no—
224C42—41no—
225C42—41no—
226C42—41no—
227C42—41no—
228C42—41no—
229C42—41no—
230C42—82no—
231C42C2×SD1611yescharacteristic
232C42C2×Q1611yescharacteristic
233C42#13511yescharacteristic
234C42#13511yescharacteristic
235C23#38611yescharacteristic
236Q8—82no—
237Q8—82no—
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—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—81no—
270C2×C4—81no—
271C2×C4—81no—
272C2×C4C2×#10311yescharacteristic
273C2×C4#41611yescharacteristic
274C2×C4#44311yescharacteristic
275C2×C4#44411yescharacteristic
276C2×C4#45511yescharacteristic
277C2×C4#45611yescharacteristic
278C2×C4#46511yescharacteristic
279C2×C4#46511yescharacteristic
280C2×C4#46711yescharacteristic
281C2×C4#46711yescharacteristic
282C8—42no—
283C8—81no—
284C8—81no—
285C8—81no—
286C8—81no—
287C8—81no—
288C8—82no—
289C8—82no—
290C22#187611yescharacteristic
291C22#188211yescharacteristic
292C22#189111yescharacteristic
293C22#189211yescharacteristic
294C22#190311yescharacteristic
295C22#190611yescharacteristic
296C22#191211yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—41no—
308C4—41no—
309C4—42no—
310C4—42no—
311C4—81no—
312C4—82no—
313C4—81no—
314C4—161no—
315C2#905111yescharacteristic
316C2#920711yescharacteristic
317C2#928411yescharacteristic
318C2#931511yescharacteristic
319C2#938011yescharacteristic
320C2#948411yescharacteristic
321C2#953211yescharacteristic
subgroupG/H
center, socle, prime radicalC23#386
commutatorC2×C42C22×C4
Frattini, cosocleC43C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ C43 ◁ G
LECSG ▷ C43 ▷ C23 ▷ C1

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#292802
#223732
#98682
#85822
#76242
#70412
#70222