Finite Group Databasebeta

← #121033

Subgroups — #121033

Order 512.

573 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21941C211yesmaximal, characteristic
2#8107C211yesmaximal, characteristic
3C2×#1298C211yesmaximal, characteristic
4#7983C211yesmaximal, characteristic
5C2×#1289C211yesmaximal, characteristic
6#7925C211yesmaximal, characteristic
7#7915C211yesmaximal, characteristic
8C2×#407C2211yescharacteristic
9C2×#407C2211yescharacteristic
10C22×C22⋊C8C2211yescharacteristic
11C22×C22⋊C8C2211yescharacteristic
12#2280C2211yescharacteristic
13C2×#380C2211yescharacteristic
14C2×#380C2211yescharacteristic
15#1854—22no—
16#1853—21no—
17#1852—21no—
18#1808—21no—
19#1807—21no—
20#1305—22no—
21#1298—21no—
22#1298—21no—
23#1289—22no—
24#1289—21no—
25#1289—21no—
26#1282—22no—
27#1280C414yescomplemented
28C24×C4C2311yescharacteristic
29C22×M16—21no—
30C22×M16Q812yes—
31C23×C8—21no—
32C23×C8—21no—
33C2×#117—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C22⋊C4—21no—
37C22×C22⋊C4—21no—
38C2×#107—22no—
39C2×#106—22no—
40#407—21no—
41#407—21no—
42#407—21no—
43#407—21no—
44#407—21no—
45#407—21no—
46#407—21no—
47#407—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⋊C8C2×C412yes—
60C2×C22⋊C8C2×C412yes—
61C2×C22⋊C8D412yes—
62C2×C22⋊C8D411yescharacteristic
63C2×C22⋊C8D411yescharacteristic
64C2×C22⋊C8Q812yes—
65#381—21no—
66#380—21no—
67#380—21no—
68#380—21no—
69#380—21no—
70#380—21no—
71#380—21no—
72#380—21no—
73#380—21no—
74#380D411yescharacteristic
75#380D411yescharacteristic
76#380D412yes—
77#379—21no—
78C4×C22⋊C4—21no—
79C4×C22⋊C4—21no—
80C2×#95—21no—
81C2×#95C2×C412yes—
82#340—22no—
83#340—22no—
84C25#4111yescharacteristic
85C23×C4—22no—
86C23×C4—41no—
87C23×C4—82no—
88C23×C4C22×C411yescharacteristic
89C23×C4C2×D411yescharacteristic
90C23×C4C2×D411yescharacteristic
91C23×C4C2×D411yescharacteristic
92C23×C4C2×D411yescharacteristic
93C23×C4C2×Q811yescharacteristic
94C23×C4C2×Q811yescharacteristic
95C23×C4#4111yescharacteristic
96C23×C4#4111yescharacteristic
97C23×C4#4111yescharacteristic
98C23×C4#4111yescharacteristic
99C23×C4#4111yescharacteristic
100C23×C4#4111yescharacteristic
101C23×C4#4111yescharacteristic
102C2×M16—22no—
103C2×M16—22no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16—82no—
107C2×M16—82no—
108C22×C8—21no—
109C22×C8—21no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—22no—
113C22×C8—22no—
114C22×C8—22no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—82no—
118C22×C8—82no—
119#117—82no—
120C2×C4⋊C4—22no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—21no—
123C2×C4⋊C4—41no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—82no—
127C2×C4⋊C4—82no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4—21no—
130C2×C22⋊C4—22no—
131C2×C22⋊C4—41no—
132C2×C22⋊C4—41no—
133C2×C22⋊C4—41no—
134C2×C22⋊C4—41no—
135C2×C22⋊C4—41no—
136C2×C22⋊C4—81no—
137C2×C22⋊C4—81no—
138C2×C22⋊C4—81no—
139C2×C22⋊C4—81no—
140C2×C42—41no—
141#107—82no—
142#106—82no—
143C22⋊C8—22no—
144C22⋊C8—22no—
145C22⋊C8—21no—
146C22⋊C8—21no—
147C22⋊C8—22no—
148C22⋊C8—22no—
149C22⋊C8—22no—
150C22⋊C8—22no—
151C22⋊C8—41no—
152C22⋊C8—41no—
153C22⋊C8—41no—
154C22⋊C8—41no—
155C22⋊C8—41no—
156C22⋊C8—41no—
157C22⋊C8—41no—
158C22⋊C8—41no—
159C22⋊C8C4⋊C412yes—
160C22⋊C8C4⋊C412yes—
161#95—22no—
162#95—22no—
163#95—22no—
164#95—21no—
165#95—21no—
166#95—41no—
167#95—41no—
168C24—21no—
169C24—21no—
170C24—21no—
171C24—21no—
172C24—42no—
173C24—81no—
174C24#11711yescharacteristic
175C24#12111yescharacteristic
176C24#12311yescharacteristic
177C24#12411yescharacteristic
178C24#12511yescharacteristic
179C24#12511yescharacteristic
180C24#12611yescharacteristic
181C22×C4—42no—
182C22×C4—42no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—42no—
186C22×C4—42no—
187C22×C4—42no—
188C22×C4—42no—
189C22×C4—41no—
190C22×C4—41no—
191C22×C4—42no—
192C22×C4—44no—
193C22×C4—81no—
194C22×C4—81no—
195C22×C4—81no—
196C22×C4—81no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4—81no—
200C22×C4—82no—
201C22×C4—82no—
202C22×C4—82no—
203C22×C4—82no—
204C22×C4—82no—
205C22×C4C2×C4⋊C411yescharacteristic
206C22×C4#11711yescharacteristic
207C22×C4C4×D411yescharacteristic
208C22×C4C4×D411yescharacteristic
209C22×C4C4×D411yescharacteristic
210C22×C4C4×Q811yescharacteristic
211C22×C4#12011yescharacteristic
212C22×C4#12111yescharacteristic
213C22×C4#12111yescharacteristic
214C22×C4C22⋊Q811yescharacteristic
215C22×C4C22⋊Q811yescharacteristic
216C22×C4C22⋊Q811yescharacteristic
217C22×C4C22⋊Q811yescharacteristic
218C22×C4C22⋊Q811yescharacteristic
219C22×C4#12311yescharacteristic
220C22×C4#12311yescharacteristic
221C22×C4#12311yescharacteristic
222C22×C4#12311yescharacteristic
223C22×C4#12411yescharacteristic
224C22×C4#12411yescharacteristic
225C22×C4#12411yescharacteristic
226C22×C4#12511yescharacteristic
227C22×C4#12511yescharacteristic
228C22×C4#12511yescharacteristic
229C22×C4#12611yescharacteristic
230C22×C4#12611yescharacteristic
231C22×C4#12611yescharacteristic
232C22×C4C4⋊Q811yescharacteristic
233M16—82no—
234M16—82no—
235M16—82no—
236M16—82no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—42no—
240C2×C8—42no—
241C2×C8—42no—
242C2×C8—42no—
243C2×C8—42no—
244C2×C8—82no—
245C2×C8—82no—
246C2×C8—82no—
247C2×C8—82no—
248C2×C8—82no—
249C2×C8—82no—
250C2×C8—82no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—42no—
255C4⋊C4—82no—
256C4⋊C4—82no—
257C4⋊C4—82no—
258C22⋊C4—41no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—82no—
263C22⋊C4—82no—
264C22⋊C4—82no—
265C22⋊C4—81no—
266C22⋊C4—81no—
267C22⋊C4—81no—
268C22⋊C4—81no—
269C22⋊C4—82no—
270C42—82no—
271C23—21no—
272C23—21no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—82no—
298C23—82no—
299C23—82no—
300C23—82no—
301C23#38211yescharacteristic
302C23#38711yescharacteristic
303C23#38811yescharacteristic
304C23#39411yescharacteristic
305C23#39811yescharacteristic
306C23#40011yescharacteristic
307C23#40011yescharacteristic
308C23#47111yescharacteristic
309C23#47111yescharacteristic
310C23#47211yescharacteristic
311C23#47311yescharacteristic
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—82no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—82no—
350C2×C4—81no—
351C2×C4—82no—
352C2×C4—164no—
353C2×C4—164no—
354C2×C4#38511yescharacteristic
355C2×C4#38711yescharacteristic
356C2×C4#38811yescharacteristic
357C2×C4#38911yescharacteristic
358C2×C4#39311yescharacteristic
359C2×C4#39711yescharacteristic
360C2×C4#39811yescharacteristic
361C2×C4#40011yescharacteristic
362C8—42no—
363C8—42no—
364C8—82no—
365C8—82no—
366C8—82no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—42no—
389C22—42no—
390C22—42no—
391C22—42no—
392C22—42no—
393C22—42no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—81no—
398C22—81no—
399C22—81no—
400C22#144211yescharacteristic
401C22#183312yes—
402C22#193011yescharacteristic
403C22#193111yescharacteristic
404C22#205111yescharacteristic
405C22#205211yescharacteristic
406C22#208911yescharacteristic
407C22#209011yescharacteristic
408C4—21no—
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—161no—
416C4—161no—
417C4—162no—
418C4—162no—
419C4#203212yes—
420C2—21no—
421C2—21no—
422C2—21no—
423C2—22no—
424C2—21no—
425C2—21no—
426C2—21no—
427C2—41no—
428C2—41no—
429C2—41no—
430C2#1126011yescharacteristic
431C2#1127911yescharacteristic
432C2#1129011yescharacteristic
subgroupG/H
center, socleC22#1442
commutatorC23×C4C22×C4
Frattini, cosocleC24×C4C23
prime radicalC25#41
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22 ◁ C24×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
27. #1280C4semidirect

Maximal subgroups

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

subgroupindex
#219412
#81072
C2×#12982
#79832
C2×#12892
#79252
#79152