Finite Group Databasebeta

← #120864

Subgroups — #120864

Order 512.

571 conjugacy classes of subgroups.

The subgroup lattice has 383 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21932C211yesmaximal, characteristic
2#8057C211yesmaximal, characteristic
3C2×#1298C211yesmaximal, characteristic
4C2×#1298C211yesmaximal, characteristic
5#8008C211yesmaximal, characteristic
6#7929C211yesmaximal, characteristic
7C2×#1282C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C2×#407C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12C22×C22⋊C8C2211yescharacteristic
13C22×C22⋊C8C2211yescharacteristic
14C2×C4×C22⋊C4C2211yescharacteristic
15#1851—22no—
16#1850—22no—
17#1797—22no—
18#1298—22no—
19#1298—22no—
20#1298—22no—
21#1293—22no—
22#1282—22no—
23#1282C412yes—
24#1282C412yes—
25C24×C4C2311yescharacteristic
26C22×M16—21no—
27C22×M16—21no—
28C22×M16Q812yes—
29C23×C8—21no—
30C23×C8—21no—
31C23×C8—21no—
32C22×C22⋊C4Q812yes—
33C22×C42—21no—
34C2×C4⋊C8—24no—
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#407—21no—
45#407—21no—
46#407D412yes—
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⋊C8—21no—
56C2×C22⋊C8—21no—
57C2×C22⋊C8—21no—
58C2×C22⋊C8—21no—
59C2×C22⋊C8—21no—
60C2×C22⋊C8—21no—
61C2×C22⋊C8—21no—
62C2×C22⋊C8—21no—
63C2×C22⋊C8—21no—
64C2×C22⋊C8—21no—
65C2×C22⋊C8—21no—
66C2×C22⋊C8—21no—
67C2×C22⋊C8C2×C412yes—
68C2×C22⋊C8C2×C412yes—
69C2×C22⋊C8D412yes—
70C2×C22⋊C8D412yes—
71C4×C22⋊C4—21no—
72C4×C22⋊C4—21no—
73C4×C22⋊C4C2×C411yescharacteristic
74C4×C22⋊C4C2×C411yescharacteristic
75C4×C22⋊C4D412yes—
76C2×#95—21no—
77#336—24no—
78C25C2×Q811yescharacteristic
79C23×C4—22no—
80C23×C4—82no—
81C23×C4C22×C411yescharacteristic
82C23×C4C2×D411yescharacteristic
83C23×C4C2×D411yescharacteristic
84C23×C4C2×D411yescharacteristic
85C23×C4C2×D411yescharacteristic
86C23×C4C2×Q811yescharacteristic
87C23×C4#4111yescharacteristic
88C23×C4#4111yescharacteristic
89C23×C4#4111yescharacteristic
90C23×C4#4111yescharacteristic
91C23×C4#4111yescharacteristic
92C23×C4#4111yescharacteristic
93C23×C4#4111yescharacteristic
94C23×C4#4111yescharacteristic
95C2×M16—22no—
96C2×M16—22no—
97C2×M16—22no—
98C2×M16—41no—
99C2×M16—41no—
100C2×M16—41no—
101C2×M16—82no—
102C2×M16—82no—
103C2×M16—82no—
104C22×C8—22no—
105C22×C8—22no—
106C22×C8—22no—
107C22×C8—22no—
108C22×C8—22no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—41no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—82no—
117C22×C8—82no—
118C22×C8—82no—
119C2×C22⋊C4—24no—
120C2×C22⋊C4—22no—
121C2×C22⋊C4—42no—
122C2×C22⋊C4C4⋊C412yes—
123C2×C22⋊C4C4⋊C412yes—
124C2×C42—22no—
125C2×C42—21no—
126C2×C42—21no—
127C2×C42—82no—
128C4⋊C8—84no—
129C22⋊C8—22no—
130C22⋊C8—22no—
131C22⋊C8—22no—
132C22⋊C8—22no—
133C22⋊C8—22no—
134C22⋊C8—22no—
135C22⋊C8—22no—
136C22⋊C8—22no—
137C22⋊C8—22no—
138C22⋊C8—22no—
139C22⋊C8—41no—
140C22⋊C8—41no—
141C22⋊C8—41no—
142C22⋊C8—41no—
143C22⋊C8—41no—
144C22⋊C8—41no—
145C22⋊C8—41no—
146C22⋊C8—41no—
147C22⋊C8—41no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C22⋊C8—41no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153#95—21no—
154#95—21no—
155#95—22no—
156C24—22no—
157C24—22no—
158C24—42no—
159C24—81no—
160C24C2×C4⋊C411yescharacteristic
161C24C22⋊Q811yescharacteristic
162C24C22⋊Q811yescharacteristic
163C24#12511yescharacteristic
164C24#12511yescharacteristic
165C24#12511yescharacteristic
166C24C4⋊Q811yescharacteristic
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—42no—
170C22×C4—42no—
171C22×C4—42no—
172C22×C4—42no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4—44no—
177C22×C4—44no—
178C22×C4—81no—
179C22×C4—81no—
180C22×C4—81no—
181C22×C4—81no—
182C22×C4—81no—
183C22×C4—81no—
184C22×C4—81no—
185C22×C4—82no—
186C22×C4#11711yescharacteristic
187C22×C4#11711yescharacteristic
188C22×C4C4×D411yescharacteristic
189C22×C4C4×D411yescharacteristic
190C22×C4C4×D411yescharacteristic
191C22×C4C4×Q811yescharacteristic
192C22×C4#12011yescharacteristic
193C22×C4#12111yescharacteristic
194C22×C4#12111yescharacteristic
195C22×C4#12111yescharacteristic
196C22×C4C22⋊Q811yescharacteristic
197C22×C4C22⋊Q811yescharacteristic
198C22×C4C22⋊Q811yescharacteristic
199C22×C4#12311yescharacteristic
200C22×C4#12311yescharacteristic
201C22×C4#12311yescharacteristic
202C22×C4#12311yescharacteristic
203C22×C4#12311yescharacteristic
204C22×C4#12411yescharacteristic
205C22×C4#12411yescharacteristic
206C22×C4#12411yescharacteristic
207C22×C4#12411yescharacteristic
208C22×C4#12511yescharacteristic
209C22×C4#12511yescharacteristic
210C22×C4#12611yescharacteristic
211C22×C4#12611yescharacteristic
212C22×C4#12611yescharacteristic
213C22×C4#12611yescharacteristic
214M16—82no—
215M16—82no—
216M16—82no—
217M16—82no—
218M16—82no—
219M16—82no—
220C2×C8—44no—
221C2×C8—44no—
222C2×C8—42no—
223C2×C8—42no—
224C2×C8—42no—
225C2×C8—42no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—82no—
229C2×C8—82no—
230C2×C8—82no—
231C2×C8—82no—
232C2×C8—82no—
233C2×C8—82no—
234C2×C8—82no—
235C2×C8—82no—
236C2×C8—82no—
237C2×C8—82no—
238C22⋊C4—22no—
239C22⋊C4—22no—
240C22⋊C4—22no—
241C22⋊C4—44no—
242C22⋊C4#10814yes—
243C42—44no—
244C42—81no—
245C42—81no—
246C23—21no—
247C23—21no—
248C23—22no—
249C23—22no—
250C23—22no—
251C23—22no—
252C23—22no—
253C23—21no—
254C23—21no—
255C23—22no—
256C23—22no—
257C23—41no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—84no—
269C23—84no—
270C23#38211yescharacteristic
271C23#38511yescharacteristic
272C23#38911yescharacteristic
273C23#39811yescharacteristic
274C23#39811yescharacteristic
275C23#40011yescharacteristic
276C23#40011yescharacteristic
277C23C2×#10812yes—
278C23#43012yes—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—88no—
314C2×C4#38711yescharacteristic
315C2×C4#38711yescharacteristic
316C2×C4#38811yescharacteristic
317C2×C4#38811yescharacteristic
318C2×C4#39311yescharacteristic
319C2×C4#39411yescharacteristic
320C2×C4#39711yescharacteristic
321C2×C4#40011yescharacteristic
322C8—82no—
323C8—82no—
324C8—82no—
325C8—82no—
326C8—82no—
327C8—82no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—42no—
346C22—42no—
347C22—44no—
348C22—42no—
349C22—42no—
350C22—44no—
351C22—82no—
352C22—81no—
353C22—81no—
354C22—82no—
355C22#144211yescharacteristic
356C22#183711yescharacteristic
357C22#183811yescharacteristic
358C22#185512yes—
359C22#195012yes—
360C22#210312yes—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—44no—
369C4—82no—
370C4#203212yes—
371C2—22no—
372C2—22no—
373C2—21no—
374C2—21no—
375C2—22no—
376C2—41no—
377C2—41no—
378C2—41no—
379C2#1126411yescharacteristic
380C2#1126911yescharacteristic
381C2#1127911yescharacteristic
subgroupG/H
centerC2×C4#393
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
socleC22#1442
prime radicalC25C2×Q8
LCSG ▷ C23×C4 ▷ 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
#219322
#80572
C2×#12982
#80082
#79292
C2×#12822