Finite Group Databasebeta

← #138374

Subgroups — #138374

Order 512.

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

normal subgroups only

This group has 416 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
1#33130C211yesmaximal, characteristic
2C2×#1837C211yesmaximal, characteristic
3#12844C211yesmaximal, characteristic
4C2×#1350C212yesmaximal
5#7259C212yesmaximal
6C2×#467C2211yescharacteristic
7C2×#423—21no—
8C22×C4×C8C2211yescharacteristic
9#2855—21no—
10C2×C22⋊C16C2212yes—
11#1969C411yescharacteristic
12#1969C411yescharacteristic
13#1942C411yescharacteristic
14#1942C411yescharacteristic
15#1933—21no—
16#1933—21no—
17#1892—21no—
18#1837—24no—
19#1808C2211yescharacteristic
20C2×#341—21no—
21C2×#341C2212yes—
22#1374—21no—
23#1374—21no—
24#1350—24no—
25C22×Q16C2×C411yescharacteristic
26C22×M16—22no—
27C23×C8D411yescharacteristic
28C23×C8C2311yescharacteristic
29C2×C22⋊Q8—21no—
30C22×C42D411yescharacteristic
31C22×C16—22no—
32#467—22no—
33#467—22no—
34C2×#107C2×C411yescharacteristic
35C2×#107C2×C411yescharacteristic
36C2×#107C2×C411yescharacteristic
37#423—24no—
38#423—42no—
39C2×C4⋊C8—41no—
40C2×C4⋊C8—41no—
41C2×#103—21no—
42C2×#103—21no—
43C2×#103—21no—
44C2×C4×C8—22no—
45C2×C4×C8—22no—
46C2×C4×C8C2×C411yescharacteristic
47C2×C4×C8C2×C411yescharacteristic
48C2×C4×C8D411yescharacteristic
49C2×C4×C8D411yescharacteristic
50#391—21no—
51#391—21no—
52#389—21no—
53#389—21no—
54#387—41no—
55#387—41no—
56#385—41no—
57#381—41no—
58#380—21no—
59C22⋊C16—22no—
60C22⋊C16—22no—
61#341—24no—
62#341—22no—
63#341D414yes—
64#340—21no—
65#340—21no—
66#340—21no—
67C22×Q8—21no—
68C23×C4SD1611yescharacteristic
69C23×C4SD1611yescharacteristic
70C23×C4C2×D411yescharacteristic
71C2×Q16—22no—
72C2×Q16—41no—
73C2×Q16—41no—
74C2×M16—24no—
75C2×M16—42no—
76C2×M16—42no—
77C2×M16—42no—
78C2×M16—42no—
79C2×M16—42no—
80C22×C8—21no—
81C22×C8—21no—
82C22×C8—41no—
83C22×C8—41no—
84C22×C8—41no—
85C22×C8—41no—
86C22×C8—42no—
87C22×C8C22⋊C411yescharacteristic
88C22×C8C22⋊C411yescharacteristic
89C22×C8C22×C411yescharacteristic
90C22×C8C2×D411yescharacteristic
91C22×C8C2×D412yes—
92C22×C8#4112yes—
93C22⋊Q8—41no—
94C22⋊Q8—41no—
95C22⋊Q8—41no—
96C22⋊Q8—41no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4—21no—
100C2×C4⋊C4—41no—
101C2×C4⋊C4—41no—
102C2×C4⋊C4—41no—
103C2×C22⋊C4—41no—
104C2×C22⋊C4—41no—
105C2×C42—21no—
106C2×C42—21no—
107C2×C42—21no—
108C2×C42—21no—
109C2×C42C22⋊C411yescharacteristic
110C2×C42C22⋊C411yescharacteristic
111C2×C42D811yescharacteristic
112C2×C42D811yescharacteristic
113C2×C16—42no—
114C2×C16—42no—
115C2×C16—42no—
116#107—22no—
117#107—41no—
118#107—41no—
119C4⋊C8—44no—
120C4⋊C8—44no—
121#103—42no—
122#103—42no—
123#103—42no—
124C4×C8—22no—
125C4×C8—22no—
126C4×C8—22no—
127C4×C8—22no—
128#95—41no—
129#95—41no—
130#95—41no—
131#95—41no—
132#95—41no—
133#95—41no—
134#95—41no—
135C24C2×SD1611yescharacteristic
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8—41no—
140C2×Q8—41no—
141C2×Q8—41no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—21no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—21no—
149C22×C4—21no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—41no—
155C22×C4—41no—
156C22×C4—41no—
157C22×C4—41no—
158C22×C4#10211yescharacteristic
159C22×C4#10211yescharacteristic
160C22×C4#10211yescharacteristic
161C22×C4#10211yescharacteristic
162C22×C4C2×C22⋊C411yescharacteristic
163C22×C4#12011yescharacteristic
164C22×C4#12311yescharacteristic
165C22×C4C2×D811yescharacteristic
166C22×C4AGL(1,ℤ/8)11yescharacteristic
167C22×C4#13711yescharacteristic
168Q16—82no—
169M16—44no—
170M16—44no—
171M16—82no—
172M16—82no—
173C2×C8—21no—
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—21no—
183C2×C8—42no—
184C2×C8—42no—
185C2×C8—42no—
186C2×C8—42no—
187C2×C8—44no—
188C2×C8—82no—
189C2×C8—82no—
190C2×C8C4×D412yes—
191C2×C8#12112yes—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—41no—
198C4⋊C4—82no—
199C4⋊C4—82no—
200C4⋊C4—81no—
201C4⋊C4—81no—
202C22⋊C4—82no—
203C22⋊C4—81no—
204C22⋊C4—81no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—21no—
210C42—21no—
211C42—21no—
212C42—21no—
213C16—82no—
214C23—21no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23C2×#10211yescharacteristic
221C23#44811yescharacteristic
222C23#48111yescharacteristic
223Q8—81no—
224Q8—81no—
225Q8—81no—
226Q8—81no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
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—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4—81no—
254C2×C4—81no—
255C2×C4—81no—
256C2×C4—81no—
257C2×C4—81no—
258C2×C4—81no—
259C2×C4—81no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—81no—
263C2×C4#35912yes—
264C2×C4#36212yes—
265C2×C4#38611yescharacteristic
266C2×C4#41011yescharacteristic
267C2×C4#41011yescharacteristic
268C2×C4#41711yescharacteristic
269C2×C4#42111yescharacteristic
270C2×C4#42111yescharacteristic
271C2×C4#44711yescharacteristic
272C2×C4#48011yescharacteristic
273C8—22no—
274C8—22no—
275C8—41no—
276C8—41no—
277C8—84no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—41no—
285C22—41no—
286C22—41no—
287C22—41no—
288C22#151711yescharacteristic
289C22#151711yescharacteristic
290C22#187411yescharacteristic
291C22C2×#35911yescharacteristic
292C22#214311yescharacteristic
293C22C2×#36211yescharacteristic
294C22#214811yescharacteristic
295C4—22no—
296C4—21no—
297C4—21no—
298C4—22no—
299C4—41no—
300C4—41no—
301C4—161no—
302C4—161no—
303C4—161no—
304C4—161no—
305C4#151211yescharacteristic
306C4#151211yescharacteristic
307C4#189711yescharacteristic
308C4#189911yescharacteristic
309C2—41no—
310C2—41no—
311C2#915611yescharacteristic
312C2#1186111yescharacteristic
313C2#1186311yescharacteristic
314C2#1186511yescharacteristic
315C2#1186611yescharacteristic
316C2#1299011yescharacteristic
317C2#1300311yescharacteristic
subgroupG/H
center, socleC23C2×#102
commutatorC22×C8C22×C4
Frattini, cosocleC23×C8C23
prime radicalC24C2×SD16
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×C8 ◁ G
LECSG ▷ C23×C8 ▷ C2×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
#331302
C2×#18372
#128442
C2×#13502
#72592