Finite Group Databasebeta

← #120778

Subgroups — #120778

Order 512.

520 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20764C211yesmaximal, characteristic
2#10853C211yesmaximal, characteristic
3#8045C211yesmaximal, characteristic
4#8043C211yesmaximal, characteristic
5C2×#1296C211yesmaximal, characteristic
6C2×#1283C211yesmaximal, characteristic
7#7893C211yesmaximal, characteristic
8C2×#431C2211yescharacteristic
9C2×#423C2211yescharacteristic
10C22×C4⋊C8C2211yescharacteristic
11C22×C4⋊C8C2211yescharacteristic
12C2×C4×M16C2211yescharacteristic
13#2285C2211yescharacteristic
14C2×#384C2211yescharacteristic
15#1836—22no—
16#1834—21no—
17#1834—21no—
18C2×#341—21no—
19C2×#341—21no—
20#1736—21no—
21#1736—21no—
22#1296—22no—
23#1296—22no—
24#1296—21no—
25#1296—21no—
26#1283C414yescomplemented
27#1279—22no—
28C22×M16—21no—
29C22×M16D411yescharacteristic
30C22×M16D411yescharacteristic
31C23×C8—21no—
32C23×C8—21no—
33C2×#117—21no—
34C22×C4⋊C4—21no—
35C22×C4⋊C4—21no—
36C22×C4⋊C4—21no—
37C22×C42C2311yescharacteristic
38#431—21no—
39#431—21no—
40#431—21no—
41#431C2×C412yes—
42#423—21no—
43#423—21no—
44#423—21no—
45#423Q812yes—
46C2×C4⋊C8—21no—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C4⋊C8—21no—
50C2×C4⋊C8—21no—
51C2×C4⋊C8—21no—
52C2×C4⋊C8—21no—
53C2×C4⋊C8—21no—
54C2×C4⋊C8—21no—
55C2×C4⋊C8—21no—
56C2×C4⋊C8—21no—
57C2×C4⋊C8—21no—
58C2×C4⋊C8—21no—
59C2×C4⋊C8C2×C412yes—
60C2×C4⋊C8D412yes—
61C2×C22⋊C8—21no—
62C4×M16—21no—
63C4×M16—21no—
64C4×M16C2×C412yes—
65C4×M16Q812yes—
66C2×#97—21no—
67C2×C4×C8—21no—
68C2×C4×C8—21no—
69#384—21no—
70#384—21no—
71#384—21no—
72#384D411yescharacteristic
73#384D411yescharacteristic
74#384D412yes—
75#382—21no—
76#380—21no—
77#380—21no—
78C4×C4⋊C4—21no—
79C4×C4⋊C4—21no—
80#341—42no—
81#341—42no—
82#340—22no—
83#340—22no—
84#340—22no—
85#340—22no—
86C23×C4—41no—
87C23×C4C2×D411yescharacteristic
88C23×C4#4111yescharacteristic
89C23×C4#4111yescharacteristic
90C2×M16—21no—
91C2×M16—21no—
92C2×M16—21no—
93C2×M16—21no—
94C2×M16—21no—
95C2×M16—21no—
96C2×M16—21no—
97C2×M16—21no—
98C2×M16—21no—
99C2×M16—21no—
100C2×M16—22no—
101C2×M16—41no—
102C2×M16—41no—
103C2×M16—41no—
104C2×M16—41no—
105C2×M16—41no—
106C2×M16C4⋊C412yes—
107C2×M16C4⋊C412yes—
108C22×C8—21no—
109C22×C8—21no—
110C22×C8—22no—
111C22×C8—22no—
112C22×C8—41no—
113C22×C8—41no—
114C22×C8—41no—
115C22×C8—41no—
116C22×C8—41no—
117C22×C8—41no—
118C22×C8—41no—
119C22×C8—41no—
120C22×C8—41no—
121C22×C8—41no—
122C22×C8—81no—
123C22×C8—81no—
124#117—41no—
125#117—41no—
126#117—41no—
127#117—41no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—21no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—21no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—21no—
136C2×C4⋊C4—21no—
137C2×C4⋊C4—41no—
138C2×C4⋊C4—41no—
139C2×C4⋊C4—41no—
140C2×C4⋊C4—41no—
141C2×C4⋊C4—41no—
142C2×C4⋊C4—41no—
143C2×C4⋊C4—41no—
144C2×C4⋊C4—82no—
145C2×C4⋊C4—81no—
146C2×C4⋊C4—81no—
147C2×C22⋊C4—41no—
148C2×C42—41no—
149C2×C42C22×C411yescharacteristic
150C2×C42C2×D411yescharacteristic
151C2×C42C2×D411yescharacteristic
152C2×C42C2×D411yescharacteristic
153C2×C42C2×Q811yescharacteristic
154C2×C42C2×Q811yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C2×C42#4111yescharacteristic
159C2×C42#4111yescharacteristic
160C2×C42#4111yescharacteristic
161C4⋊C8—22no—
162C4⋊C8—22no—
163C4⋊C8—22no—
164C4⋊C8—22no—
165C4⋊C8—22no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8—41no—
169C4⋊C8—41no—
170C4⋊C8—41no—
171C4⋊C8—41no—
172C4⋊C8—41no—
173C4⋊C8—41no—
174C4⋊C8—41no—
175C22⋊C8—22no—
176C22⋊C8—41no—
177#97—22no—
178#97—22no—
179C4×C8—22no—
180C4×C8—22no—
181C4×C8—22no—
182C4×C8—41no—
183#95—41no—
184#95—41no—
185C24#12411yescharacteristic
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4—21no—
190C22×C4—41no—
191C22×C4—41no—
192C22×C4—41no—
193C22×C4—41no—
194C22×C4—42no—
195C22×C4—82no—
196C22×C4—82no—
197C22×C4—81no—
198C22×C4—81no—
199C22×C4C2×C4⋊C411yescharacteristic
200C22×C4#11711yescharacteristic
201C22×C4#11711yescharacteristic
202C22×C4#12011yescharacteristic
203C22×C4#12111yescharacteristic
204C22×C4#12111yescharacteristic
205C22×C4#12111yescharacteristic
206C22×C4C22⋊Q811yescharacteristic
207C22×C4#12311yescharacteristic
208C22×C4#12311yescharacteristic
209C22×C4#12311yescharacteristic
210C22×C4#12411yescharacteristic
211C22×C4#12511yescharacteristic
212C22×C4#12511yescharacteristic
213C22×C4#12511yescharacteristic
214C22×C4#12511yescharacteristic
215C22×C4#12611yescharacteristic
216C22×C4#12611yescharacteristic
217C22×C4#13511yescharacteristic
218C22×C4#13511yescharacteristic
219C22×C4#13511yescharacteristic
220C22×C4#13511yescharacteristic
221C22×C4AGL(1,ℤ/8)11yescharacteristic
222C22×C4AGL(1,ℤ/8)11yescharacteristic
223C22×C4#13711yescharacteristic
224C22×C4#13711yescharacteristic
225M16—22no—
226M16—22no—
227M16—22no—
228M16—22no—
229M16—41no—
230M16—41no—
231M16—41no—
232M16—41no—
233M16—42no—
234M16—42no—
235M16—81no—
236M16—81no—
237C2×C8—22no—
238C2×C8—22no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—42no—
244C2×C8—42no—
245C2×C8—42no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—81no—
250C2×C8—81no—
251C2×C8—82no—
252C2×C8—81no—
253C2×C8—81no—
254C2×C8—81no—
255C2×C8—81no—
256C2×C8—81no—
257C2×C8—81no—
258C2×C8—81no—
259C2×C8—81no—
260C2×C8—82no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—81no—
272C4⋊C4—81no—
273C4⋊C4—82no—
274C4⋊C4—82no—
275C4⋊C4—82no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C42—81no—
283C42—81no—
284C42C4×D411yescharacteristic
285C42C4×D411yescharacteristic
286C42C4×D411yescharacteristic
287C42C4×Q811yescharacteristic
288C42C22⋊Q811yescharacteristic
289C42C22⋊Q811yescharacteristic
290C42C22⋊Q811yescharacteristic
291C42C22⋊Q811yescharacteristic
292C42#12311yescharacteristic
293C42#12311yescharacteristic
294C42#12411yescharacteristic
295C42#12411yescharacteristic
296C42#12511yescharacteristic
297C42#12611yescharacteristic
298C42#12611yescharacteristic
299C42C4⋊Q811yescharacteristic
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23#38211yescharacteristic
305C23#39411yescharacteristic
306C23#40011yescharacteristic
307C23#48811yescharacteristic
308C23#48811yescharacteristic
309C23#48911yescharacteristic
310C23#48911yescharacteristic
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—82no—
330C2×C4—81no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—82no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—82no—
338C2×C4—162no—
339C2×C4—162no—
340C2×C4#38511yescharacteristic
341C2×C4#38711yescharacteristic
342C2×C4#38711yescharacteristic
343C2×C4#38811yescharacteristic
344C2×C4#38811yescharacteristic
345C2×C4#38911yescharacteristic
346C2×C4#39311yescharacteristic
347C2×C4#39711yescharacteristic
348C2×C4#39811yescharacteristic
349C2×C4#39811yescharacteristic
350C2×C4#40011yescharacteristic
351C2×C4#40011yescharacteristic
352C2×C4#42711yescharacteristic
353C2×C4#42711yescharacteristic
354C2×C4#42811yescharacteristic
355C2×C4#42811yescharacteristic
356C2×C4#44911yescharacteristic
357C2×C4#44911yescharacteristic
358C2×C4#45211yescharacteristic
359C2×C4#45211yescharacteristic
360C2×C4#46311yescharacteristic
361C2×C4#46311yescharacteristic
362C2×C4#46411yescharacteristic
363C2×C4#46411yescharacteristic
364C2×C4#47111yescharacteristic
365C2×C4#47111yescharacteristic
366C2×C4#47211yescharacteristic
367C2×C4#47311yescharacteristic
368C2×C4#47811yescharacteristic
369C2×C4#47811yescharacteristic
370C2×C4#47911yescharacteristic
371C2×C4#47911yescharacteristic
372C2×C4#48211yescharacteristic
373C2×C4#48211yescharacteristic
374C2×C4#48511yescharacteristic
375C2×C4#48511yescharacteristic
376C2×C4#48811yescharacteristic
377C2×C4#48811yescharacteristic
378C2×C4#49011yescharacteristic
379C2×C4#49111yescharacteristic
380C8—42no—
381C8—42no—
382C8—82no—
383C8—82no—
384C8—82no—
385C8—82no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22#144211yescharacteristic
399C22#183511yescharacteristic
400C22#183611yescharacteristic
401C22#204211yescharacteristic
402C22#204211yescharacteristic
403C22#204811yescharacteristic
404C22#204911yescharacteristic
405C22#205111yescharacteristic
406C22#205211yescharacteristic
407C22#210111yescharacteristic
408C22#210111yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—21no—
414C4—21no—
415C4—161no—
416C4—161no—
417C4—162no—
418C4#185411yescharacteristic
419C4#185411yescharacteristic
420C4#193011yescharacteristic
421C4#193111yescharacteristic
422C4#194911yescharacteristic
423C4#194911yescharacteristic
424C4#202511yescharacteristic
425C4#202611yescharacteristic
426C4#207311yescharacteristic
427C4#207411yescharacteristic
428C4#208911yescharacteristic
429C4#209011yescharacteristic
430C2—21no—
431C2—21no—
432C2—21no—
433C2—21no—
434C2#1055111yescharacteristic
435C2#1055211yescharacteristic
436C2#1055311yescharacteristic
437C2#1055411yescharacteristic
438C2#1126811yescharacteristic
439C2#1127411yescharacteristic
440C2#1129011yescharacteristic
subgroupG/H
center, socleC23#394
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#124
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C22×C42 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
26. #1283C4semidirect

Maximal subgroups

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

subgroupindex
#207642
#108532
#80452
#80432
C2×#12962
C2×#12832
#78932