Finite Group Databasebeta

← #120973

Subgroups — #120973

Order 512.

584 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14164C211yesmaximal, characteristic
2#10851C211yesmaximal, characteristic
3C2×#1300C211yesmaximal, characteristic
4#8022C211yesmaximal, characteristic
5#8018C211yesmaximal, characteristic
6C2×#1288C211yesmaximal, characteristic
7C2×#1285C211yesmaximal, characteristic
8C2×#432C2211yescharacteristic
9C2×#432C2211yescharacteristic
10C2×C4×M16C2211yescharacteristic
11#2285C2211yescharacteristic
12C2×#383C2211yescharacteristic
13C2×C4×C4⋊C4C2211yescharacteristic
14C2×#376C2211yescharacteristic
15C2×#339—21no—
16C2×#339—21no—
17#1444—21no—
18#1442—21no—
19#1436—21no—
20#1436—21no—
21#1436—21no—
22#1436—21no—
23#1300—22no—
24#1294—21no—
25#1294—21no—
26#1294—21no—
27#1294—21no—
28#1288C414yescomplemented
29#1285—22no—
30C22×M16—21no—
31C2×#117—21no—
32C22×C4⋊C4—21no—
33C22×C4⋊C4—21no—
34C22×C4⋊C4—21no—
35C22×C42—21no—
36C22×C42D411yescharacteristic
37C22×C42D411yescharacteristic
38C22×C42C2311yescharacteristic
39#432—21no—
40#432—21no—
41#432—21no—
42#432—21no—
43#432—21no—
44#432—21no—
45#432C2×C412yes—
46#432D412yes—
47C2×C4⋊C8—21no—
48C2×C4⋊C8—21no—
49C2×C22⋊C8—21no—
50C2×C22⋊C8—21no—
51C4×M16—21no—
52C4×M16—21no—
53C4×M16—21no—
54C4×M16C2×C412yes—
55C2×#97—21no—
56C2×#97—21no—
57C2×#97—21no—
58C2×C4×C8—21no—
59#384Q811yescharacteristic
60#384Q811yescharacteristic
61#383—21no—
62#383—21no—
63#383C2×C412yes—
64#383Q812yes—
65#382—21no—
66#380—21no—
67#380—21no—
68C4×C4⋊C4—21no—
69C4×C4⋊C4—21no—
70C4×C4⋊C4—21no—
71C4×C4⋊C4—21no—
72C4×C4⋊C4—21no—
73C4×C4⋊C4—21no—
74#376—21no—
75#376—21no—
76#376—21no—
77#376—21no—
78C2×#95—21no—
79C2×#95—21no—
80C2×#95—21no—
81C2×#95—21no—
82C2×#95—21no—
83C2×#95—21no—
84C2×#95—21no—
85C2×#95—21no—
86C2×#95—21no—
87C2×#95—21no—
88C2×#95D411yescharacteristic
89C2×#95D411yescharacteristic
90C2×#95D411yescharacteristic
91C2×#95D411yescharacteristic
92#339—42no—
93#339—42no—
94C23×C4—21no—
95C23×C4—21no—
96C23×C4—21no—
97C23×C4—21no—
98C23×C4—21no—
99C23×C4—21no—
100C23×C4C2×D411yescharacteristic
101C23×C4C2×D411yescharacteristic
102C23×C4C2×D411yescharacteristic
103C2×M16—22no—
104C2×M16—22no—
105C2×M16—22no—
106C2×M16—41no—
107C2×M16—41no—
108C2×M16—41no—
109C22×C8—41no—
110C22×C8—41no—
111C22×C8—41no—
112#117—41no—
113#117—41no—
114#117—41no—
115#117—41no—
116C2×C4⋊C4—21no—
117C2×C4⋊C4—21no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—21no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—42no—
123C2×C4⋊C4—42no—
124C2×C4⋊C4—41no—
125C2×C4⋊C4—41no—
126C2×C4⋊C4—42no—
127C2×C4⋊C4—42no—
128C2×C4⋊C4—42no—
129C2×C4⋊C4—42no—
130C2×C4⋊C4—81no—
131C2×C4⋊C4—81no—
132C2×C22⋊C4—41no—
133C2×C42—21no—
134C2×C42—21no—
135C2×C42—21no—
136C2×C42—21no—
137C2×C42—42no—
138C2×C42—42no—
139C2×C42—41no—
140C2×C42—41no—
141C2×C42—41no—
142C2×C42—41no—
143C2×C42—41no—
144C2×C42—41no—
145C2×C42—41no—
146C2×C42C22×C411yescharacteristic
147C2×C42C2×D411yescharacteristic
148C2×C42C2×Q811yescharacteristic
149C2×C42C2×Q811yescharacteristic
150C2×C42#4111yescharacteristic
151C2×C42#4111yescharacteristic
152C2×C42#4111yescharacteristic
153C2×C42#4111yescharacteristic
154C2×C42#4111yescharacteristic
155C2×C42#4111yescharacteristic
156C2×C42#4111yescharacteristic
157C2×C42#4111yescharacteristic
158C4⋊C8—22no—
159C4⋊C8—22no—
160C4⋊C8—41no—
161C4⋊C8—41no—
162C22⋊C8—22no—
163C22⋊C8—22no—
164C22⋊C8—41no—
165C22⋊C8—41no—
166#97—22no—
167#97—22no—
168#97—22no—
169#97—41no—
170#97—41no—
171#97—41no—
172C4×C8—22no—
173C4×C8—41no—
174#95—22no—
175#95—22no—
176#95—22no—
177#95—22no—
178#95—21no—
179#95—21no—
180#95—21no—
181#95—21no—
182#95—21no—
183#95—21no—
184#95—42no—
185#95—42no—
186#95—42no—
187#95—42no—
188#95—41no—
189#95—41no—
190#95—41no—
191#95—41no—
192#95—41no—
193#95—41no—
194#95—81no—
195#95—81no—
196#95C4⋊C412yes—
197#95C4⋊C412yes—
198C24#12011yescharacteristic
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—41no—
227C22×C4—41no—
228C22×C4—41no—
229C22×C4—41no—
230C22×C4—41no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4C2×C4⋊C411yescharacteristic
252C22×C4C4×D411yescharacteristic
253C22×C4C4×D411yescharacteristic
254C22×C4#12111yescharacteristic
255C22×C4#12111yescharacteristic
256C22×C4#12111yescharacteristic
257C22×C4C22⋊Q811yescharacteristic
258C22×C4C22⋊Q811yescharacteristic
259C22×C4C22⋊Q811yescharacteristic
260C22×C4C22⋊Q811yescharacteristic
261C22×C4C22⋊Q811yescharacteristic
262C22×C4#12311yescharacteristic
263C22×C4#12311yescharacteristic
264C22×C4#12311yescharacteristic
265C22×C4#12411yescharacteristic
266C22×C4#12411yescharacteristic
267C22×C4#12411yescharacteristic
268C22×C4#12411yescharacteristic
269M16—24no—
270M16—42no—
271M16—42no—
272M16—42no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—42no—
278C2×C8—81no—
279C2×C8—81no—
280C2×C8—81no—
281C2×C8—81no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—44no—
287C4⋊C4—44no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C4⋊C4—81no—
292C4⋊C4—84no—
293C4⋊C4—84no—
294C22⋊C4—81no—
295C22⋊C4—81no—
296C42—42no—
297C42—42no—
298C42—44no—
299C42—44no—
300C42—81no—
301C42—81no—
302C42—81no—
303C42—81no—
304C42#11711yescharacteristic
305C42#11711yescharacteristic
306C42C4×D411yescharacteristic
307C42C4×Q811yescharacteristic
308C42#12311yescharacteristic
309C42#12311yescharacteristic
310C42#12511yescharacteristic
311C42#12511yescharacteristic
312C42#12511yescharacteristic
313C42#12511yescharacteristic
314C42#12511yescharacteristic
315C42#12611yescharacteristic
316C42#12611yescharacteristic
317C42#12611yescharacteristic
318C42#12611yescharacteristic
319C42C4⋊Q811yescharacteristic
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23#38511yescharacteristic
325C23#39311yescharacteristic
326C23#39411yescharacteristic
327C23#45311yescharacteristic
328C23#45411yescharacteristic
329C23#45511yescharacteristic
330C23#45611yescharacteristic
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—42no—
360C2×C4—42no—
361C2×C4—42no—
362C2×C4—42no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—42no—
372C2×C4—42no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—81no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4—81no—
385C2×C4—81no—
386C2×C4—81no—
387C2×C4—81no—
388C2×C4—81no—
389C2×C4—81no—
390C2×C4—81no—
391C2×C4—81no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—81no—
399C2×C4—81no—
400C2×C4—81no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4#38211yescharacteristic
408C2×C4#38711yescharacteristic
409C2×C4#38711yescharacteristic
410C2×C4#38811yescharacteristic
411C2×C4#38811yescharacteristic
412C2×C4#38911yescharacteristic
413C2×C4#39711yescharacteristic
414C2×C4#39811yescharacteristic
415C2×C4#39811yescharacteristic
416C2×C4#40011yescharacteristic
417C2×C4#40011yescharacteristic
418C2×C4#40011yescharacteristic
419C8—44no—
420C8—82no—
421C8—82no—
422C22—21no—
423C22—21no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22#144211yescharacteristic
435C22#185911yescharacteristic
436C22#186011yescharacteristic
437C22#202711yescharacteristic
438C22#202811yescharacteristic
439C22#203111yescharacteristic
440C22#203111yescharacteristic
441C22#203111yescharacteristic
442C22#203111yescharacteristic
443C22#203711yescharacteristic
444C22#203811yescharacteristic
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—21no—
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—82no—
458C4—82no—
459C4—82no—
460C4—82no—
461C4—82no—
462C4—82no—
463C4—161no—
464C4—161no—
465C2—21no—
466C2—21no—
467C2—21no—
468C2—21no—
469C2#1037811yescharacteristic
470C2#1037911yescharacteristic
471C2#1038011yescharacteristic
472C2#1038111yescharacteristic
473C2#1126311yescharacteristic
474C2#1127611yescharacteristic
475C2#1128211yescharacteristic
subgroupG/H
center, socleC23#393
commutatorC2×C42C22×C4
Frattini, cosocleC22×C42C23
prime radicalC24#120
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
28. #1288C4semidirect

Maximal subgroups

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

subgroupindex
#141642
#108512
C2×#13002
#80222
#80182
C2×#12882
C2×#12852