Finite Group Databasebeta

← #120890

Subgroups — #120890

Order 512.

537 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 537 conjugacy classes of subgroups — too many to draw. Only its 116 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#21935C211yesmaximal, characteristic
2#8112C211yesmaximal, characteristic
3#8104C211yesmaximal, characteristic
4#8100C211yesmaximal, characteristic
5#7927C211yesmaximal, characteristic
6#7927C211yesmaximal, characteristic
7#7927C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12#2280C2211yescharacteristic
13#2280C2211yescharacteristic
14#2280C2211yescharacteristic
15#1851—22no—
16#1851—22no—
17#1798—22no—
18#1306—22no—
19#1305—22no—
20#1304C414yes—
21#1282—22no—
22#1282—22no—
23#1282—22no—
24C24×C4C2311yescharacteristic
25C22×M16—21no—
26C22×M16—21no—
27C22×M16—21no—
28C23×C8Q812yes—
29C2×#117—21no—
30C2×#117—21no—
31C2×#117—21no—
32C2×C4⋊C8—24no—
33#407—21no—
34#407—21no—
35#407—21no—
36#407—21no—
37#407—21no—
38#407—21no—
39#407—21no—
40#407—21no—
41#407—21no—
42#407—21no—
43#407—21no—
44#407D412yes—
45C2×C22⋊C8—21no—
46C2×C22⋊C8—21no—
47C2×C22⋊C8—21no—
48C2×C22⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C2×C22⋊C8—21no—
52C2×C22⋊C8—21no—
53C2×C22⋊C8—21no—
54C2×C22⋊C8—21no—
55C2×C22⋊C8D412yes—
56C2×C22⋊C8D412yes—
57#381—21no—
58#381—21no—
59#381—21no—
60#380—21no—
61#380—21no—
62#380—21no—
63#380—21no—
64#380—21no—
65#380Q812yes—
66#379C2×C412yes—
67#379C2×C412yes—
68#379C2×C412yes—
69C4×C22⋊C4—21no—
70C4×C22⋊C4—21no—
71C4×C22⋊C4—21no—
72C4×C22⋊C4—21no—
73C4×C22⋊C4—21no—
74C4×C22⋊C4D412yes—
75#336—24no—
76C25C22×C411yescharacteristic
77C23×C4—82no—
78C23×C4C2×D411yescharacteristic
79C23×C4C2×D411yescharacteristic
80C23×C4C2×D411yescharacteristic
81C23×C4C2×D411yescharacteristic
82C23×C4C2×Q811yescharacteristic
83C23×C4C2×Q811yescharacteristic
84C23×C4#4111yescharacteristic
85C23×C4#4111yescharacteristic
86C23×C4#4111yescharacteristic
87C23×C4#4111yescharacteristic
88C23×C4#4111yescharacteristic
89C23×C4#4111yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4111yescharacteristic
92C2×M16—22no—
93C2×M16—41no—
94C2×M16—41no—
95C2×M16—41no—
96C2×M16—41no—
97C2×M16—41no—
98C2×M16—82no—
99C2×M16—82no—
100C2×M16—82no—
101C22×C8—22no—
102C22×C8—22no—
103C22×C8—22no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—41no—
107C22×C8—82no—
108#117—82no—
109#117—82no—
110#117—82no—
111C2×C4⋊C4—22no—
112C2×C4⋊C4—41no—
113C2×C4⋊C4—41no—
114C2×C22⋊C4—22no—
115C2×C22⋊C4—22no—
116C2×C22⋊C4—22no—
117C2×C22⋊C4—22no—
118C2×C22⋊C4—22no—
119C2×C22⋊C4—22no—
120C2×C22⋊C4—22no—
121C2×C22⋊C4—22no—
122C2×C22⋊C4C4⋊C414yes—
123C2×C42—22no—
124C2×C42—41no—
125C2×C42—41no—
126C4⋊C8—84no—
127C22⋊C8—22no—
128C22⋊C8—22no—
129C22⋊C8—22no—
130C22⋊C8—22no—
131C22⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—41no—
134C22⋊C8—41no—
135C22⋊C8—41no—
136C22⋊C8—41no—
137C22⋊C8—41no—
138C22⋊C8—41no—
139C22⋊C8—41no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143#95—22no—
144#95—22no—
145#95—41no—
146#95—41no—
147#95—41no—
148#95—41no—
149C24—42no—
150C24—81no—
151C24—81no—
152C24C2×C4⋊C411yescharacteristic
153C24#11711yescharacteristic
154C24#11711yescharacteristic
155C24C4×D411yescharacteristic
156C24C4×D411yescharacteristic
157C24C4×D411yescharacteristic
158C24C4×Q811yescharacteristic
159C22×C4—24no—
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—81no—
170C22×C4—81no—
171C22×C4—81no—
172C22×C4—81no—
173C22×C4—81no—
174C22×C4—81no—
175C22×C4—81no—
176C22×C4#12011yescharacteristic
177C22×C4#12111yescharacteristic
178C22×C4#12111yescharacteristic
179C22×C4#12111yescharacteristic
180C22×C4C22⋊Q811yescharacteristic
181C22×C4C22⋊Q811yescharacteristic
182C22×C4C22⋊Q811yescharacteristic
183C22×C4C22⋊Q811yescharacteristic
184C22×C4C22⋊Q811yescharacteristic
185C22×C4#12311yescharacteristic
186C22×C4#12311yescharacteristic
187C22×C4#12311yescharacteristic
188C22×C4#12311yescharacteristic
189C22×C4#12311yescharacteristic
190C22×C4#12411yescharacteristic
191C22×C4#12411yescharacteristic
192C22×C4#12411yescharacteristic
193C22×C4#12411yescharacteristic
194C22×C4#12511yescharacteristic
195C22×C4#12511yescharacteristic
196C22×C4#12511yescharacteristic
197C22×C4#12511yescharacteristic
198C22×C4#12511yescharacteristic
199C22×C4#12611yescharacteristic
200C22×C4#12611yescharacteristic
201C22×C4#12611yescharacteristic
202C22×C4#12611yescharacteristic
203C22×C4C4⋊Q811yescharacteristic
204M16—82no—
205M16—82no—
206M16—82no—
207M16—82no—
208M16—82no—
209M16—82no—
210C2×C8—44no—
211C2×C8—44no—
212C2×C8—42no—
213C2×C8—42no—
214C2×C8—42no—
215C2×C8—42no—
216C2×C8—82no—
217C2×C8—82no—
218C2×C8—82no—
219C2×C8—82no—
220C4⋊C4—82no—
221C4⋊C4—82no—
222C4⋊C4—82no—
223C22⋊C4—44no—
224C22⋊C4—44no—
225C22⋊C4—44no—
226C22⋊C4—82no—
227C22⋊C4—82no—
228C22⋊C4—82no—
229C22⋊C4—82no—
230C22⋊C4—82no—
231C22⋊C4—82no—
232C42—44no—
233C42—82no—
234C42—82no—
235C23—22no—
236C23—22no—
237C23—22no—
238C23—41no—
239C23—41no—
240C23—41no—
241C23—41no—
242C23—41no—
243C23—41no—
244C23—41no—
245C23—41no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23—41no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—88no—
257C23#38211yescharacteristic
258C23#38511yescharacteristic
259C23#38711yescharacteristic
260C23#38711yescharacteristic
261C23#38811yescharacteristic
262C23#38811yescharacteristic
263C23#38911yescharacteristic
264C2×C4—22no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4—82no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4#39311yescharacteristic
302C2×C4#39411yescharacteristic
303C2×C4#39711yescharacteristic
304C2×C4#39811yescharacteristic
305C2×C4#39811yescharacteristic
306C2×C4#40011yescharacteristic
307C2×C4#40011yescharacteristic
308C2×C4#40011yescharacteristic
309C8—82no—
310C8—82no—
311C8—82no—
312C8—82no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—44no—
334C22—82no—
335C22—82no—
336C22—82no—
337C22—82no—
338C22—82no—
339C22—82no—
340C22#144211yescharacteristic
341C22#186812yes—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—84no—
350C4—162no—
351C4—162no—
352C4#203212yes—
353C2—22no—
354C2—41no—
355C2—41no—
356C2—41no—
357C2—41no—
358C2—41no—
359C2—41no—
360C2#1127911yescharacteristic
361C2#1128011yescharacteristic
362C2#1128811yescharacteristic
subgroupG/H
centerC2×C4#393
commutator, prime radicalC25C22×C4
Frattini, cosocleC24×C4C23
socleC22#1442
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Maximal subgroups

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

subgroupindex
#219352
#81122
#81042
#81002
#79272