Finite Group Databasebeta

← #482445

Subgroups — #482445

Order 512.

927 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#34952C211yesmaximal, characteristic
2#20728C211yesmaximal, characteristic
3#17366C211yesmaximal, characteristic
4#11905C214yesmaximal, complemented
5#11816C214yesmaximal, complemented
6#11791C212yesmaximal, complemented
7#11790C212yesmaximal, complemented
8C2×C4×#41C2211yescharacteristic
9C22×C4×Q8C411yescharacteristic
10#2920—21no—
11#2920—21no—
12#2582—21no—
13#2581C2212yes—
14#2580C412yes—
15#2579—21no—
16#2579—21no—
17#2538—21no—
18#2487C411yescharacteristic
19#2487C2211yescharacteristic
20#2409C411yescharacteristic
21#2409C2211yescharacteristic
22#2396C412yes—
23#2396C2212yes—
24C4×C22⋊Q8—21no—
25C4×C22⋊Q8—21no—
26#2297—21no—
27#2296—21no—
28#2285C411yescharacteristic
29#1822C2212yes—
30#1801C2212yes—
31#1800—21no—
32#1785—21no—
33C4×#101—21no—
34C4×#100C2212yes—
35#1465—21no—
36#1465C2212yes—
37#1464—21no—
38#1464C2212yes—
39#1461C2212yes—
40#1460—21no—
41#1354C2218yes—
42#1353C2218yes—
43C22×#41D411yescharacteristic
44C23×Q8C2×C411yescharacteristic
45C2×C22⋊Q8—21no—
46C2×C22⋊Q8—21no—
47C4×#41—41no—
48C4×#41—41no—
49C4×#41—41no—
50C4×#41—41no—
51C2×C4×Q8—21no—
52C2×C4×Q8—21no—
53C2×C4×Q8—41no—
54C2×C4×Q8—41no—
55C2×C4×Q8—41no—
56C2×C4×Q8—41no—
57C2×C4×Q8C2×C412yes—
58C2×C4×Q8C2×C412yes—
59C2×C4×Q8D411yescharacteristic
60C2×C4×Q8C2311yescharacteristic
61C2×C4×D4C2×C411yescharacteristic
62C2×C4×D4C2×C411yescharacteristic
63C2×C4×D4D411yescharacteristic
64C2×C4×D4D411yescharacteristic
65C2×C4×D4D411yescharacteristic
66C2×C4×D4C2311yescharacteristic
67C2×#117—21no—
68C2×#117C2×C411yescharacteristic
69C2×#117D411yescharacteristic
70C2×#117C2311yescharacteristic
71C22×C4⋊C4—21no—
72C22×C4⋊C4C2×C411yescharacteristic
73C22×C42—21no—
74C22×C42C2×C411yescharacteristic
75C22×C42D411yescharacteristic
76C22×C42D411yescharacteristic
77#432—22no—
78#432—41no—
79#432—41no—
80#432—41no—
81#431—22no—
82#431—41no—
83#431—41no—
84#431—41no—
85#423—22no—
86#423—41no—
87C2×#101—22no—
88C2×#100—22no—
89#407—22no—
90#407—22no—
91C4×M16—22no—
92C4×M16—41no—
93#400C2×C412yes—
94#400C2312yes—
95#399C2×C412yes—
96#399C2×C412yes—
97#398—22no—
98#398—22no—
99#396—22no—
100#396—22no—
101#395C2×C412yes—
102#395C2312yes—
103#393C2×C412yes—
104#393C2×C412yes—
105#391—22no—
106#391—21no—
107#391—21no—
108#390—22no—
109#389—22no—
110#389—22no—
111#389—21no—
112#389—21no—
113#387—22no—
114#387—22no—
115#386—21no—
116#386—21no—
117#386—21no—
118#386—21no—
119#385—22no—
120#385—22no—
121#385—21no—
122#385—21no—
123#385—21no—
124#385—21no—
125#384—21no—
126#382C2×C412yes—
127#380—21no—
128#380—21no—
129#380—21no—
130#380C2×C411yescharacteristic
131#380C2×C411yescharacteristic
132C4×C4⋊C4—22no—
133C4×C4⋊C4—21no—
134C4×C4⋊C4—22no—
135C4×C4⋊C4C2×C412yes—
136C4×C22⋊C4—22no—
137C4×C22⋊C4—22no—
138#343—22no—
139#343C2314yes—
140#324—22no—
141#324C2314yes—
142#323—22no—
143#323—22no—
144C2×#41—24no—
145C2×#41—41no—
146C2×#41—41no—
147C2×#41—42no—
148C22×Q8—21no—
149C22×Q8—41no—
150C22×Q8—41no—
151C22×Q8—44no—
152C22×Q8C22×C412yes—
153C22×Q8C2×D411yescharacteristic
154C22×D4C22⋊C411yescharacteristic
155C22×D4C22⋊C411yescharacteristic
156C22×D4C2×D411yescharacteristic
157C23×C4—21no—
158C23×C4—21no—
159C23×C4C22⋊C411yescharacteristic
160C23×C4C22⋊C411yescharacteristic
161C23×C4C22⋊C411yescharacteristic
162C23×C4C22⋊C411yescharacteristic
163C23×C4C22⋊C411yescharacteristic
164C23×C4C22⋊C411yescharacteristic
165C23×C4C22×C411yescharacteristic
166C23×C4C2×D411yescharacteristic
167C23×C4C2×D411yescharacteristic
168C2×M16—24no—
169C2×M16—42no—
170C22⋊Q8—44no—
171C22⋊Q8—44no—
172C4×Q8—41no—
173C4×Q8—41no—
174C4×Q8—41no—
175C4×Q8—41no—
176C4×Q8—42no—
177C4×Q8—42no—
178C4×Q8—42no—
179C4×Q8—42no—
180C4×Q8—42no—
181C4×Q8—42no—
182C4×Q8—41no—
183C4×Q8—41no—
184C4×Q8—41no—
185C4×Q8—41no—
186C4×D4—41no—
187C4×D4—41no—
188C4×D4—41no—
189C4×D4—41no—
190C4×D4—41no—
191C4×D4—41no—
192C4×D4—41no—
193C4×D4—41no—
194C4×D4—41no—
195C4×D4—41no—
196C4×D4—41no—
197C4×D4—41no—
198#117—41no—
199#117—41no—
200#117—41no—
201#117—41no—
202#117—41no—
203#117—41no—
204#117—44no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—22no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—22no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4—22no—
215C2×C4⋊C4—22no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4—42no—
218C2×C4⋊C4—41no—
219C2×C4⋊C4—41no—
220C2×C4⋊C4C22⋊C411yescharacteristic
221C2×C4⋊C4C22⋊C411yescharacteristic
222C2×C4⋊C4C22×C412yes—
223C2×C4⋊C4C22×C411yescharacteristic
224C2×C4⋊C4C2×D411yescharacteristic
225C2×C4⋊C4C2×D411yescharacteristic
226C2×C4⋊C4C2411yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—22no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4C22⋊C411yescharacteristic
234C2×C22⋊C4C22⋊C411yescharacteristic
235C2×C22⋊C4C22×C411yescharacteristic
236C2×C22⋊C4C22×C411yescharacteristic
237C2×C22⋊C4C2×D411yescharacteristic
238C2×C22⋊C4C2×D411yescharacteristic
239C2×C42—21no—
240C2×C42—21no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42—21no—
244C2×C42—21no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—21no—
248C2×C42—21no—
249C2×C42—21no—
250C2×C42—21no—
251C2×C42—22no—
252C2×C42—22no—
253C2×C42—22no—
254C2×C42—42no—
255C2×C42—42no—
256C2×C42C22⋊C411yescharacteristic
257C2×C42C22⋊C411yescharacteristic
258C2×C42C22⋊C411yescharacteristic
259C2×C42C22⋊C411yescharacteristic
260C2×C42C22×C411yescharacteristic
261C2×C42C22×C411yescharacteristic
262C2×C42C2×D411yescharacteristic
263C2×C42C2×D411yescharacteristic
264C2×C42C2×D411yescharacteristic
265C2×C42C2×D411yescharacteristic
266C4⋊C8—42no—
267C4⋊C8—42no—
268C4⋊C8—42no—
269C4⋊C8—42no—
270#101—44no—
271#100—44no—
272C22⋊C8—24no—
273C22⋊C8—42no—
274C22⋊C8—42no—
275C22⋊C8—42no—
276#97—42no—
277#97—42no—
278C4×C8—42no—
279C4×C8—42no—
280#95—22no—
281#95—22no—
282#95—22no—
283#95—22no—
284#95—22no—
285#95—22no—
286#95—22no—
287#95—22no—
288#95—22no—
289#95C22×C412yes—
290#95C22×C412yes—
291C24C2×C22⋊C411yescharacteristic
292C24C2×C22⋊C411yescharacteristic
293C24C2×C22⋊C411yescharacteristic
294#41—48no—
295#41—48no—
296C2×Q8—24no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—44no—
300C2×Q8—42no—
301C2×Q8—42no—
302C2×Q8—44no—
303C2×Q8—48no—
304C2×Q8—44no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8#13714yes—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—41no—
344C22×C4—41no—
345C22×C4—44no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—81no—
352C22×C4—81no—
353C22×C4—82no—
354C22×C4—81no—
355C22×C4C2×C22⋊C411yescharacteristic
356C22×C4C2×C22⋊C411yescharacteristic
357C22×C4C2×C22⋊C411yescharacteristic
358C22×C4C2×C22⋊C411yescharacteristic
359C22×C4C2×C22⋊C411yescharacteristic
360C22×C4C2×C22⋊C411yescharacteristic
361C22×C4C2×C22⋊C411yescharacteristic
362C22×C4C2×C22⋊C411yescharacteristic
363C22×C4C2×C22⋊C411yescharacteristic
364C22×C4C23×C411yescharacteristic
365C22×C4C22×D411yescharacteristic
366C22×C4C22×D411yescharacteristic
367M16—44no—
368M16—44no—
369M16—84no—
370C2×C8—44no—
371C2×C8—44no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—42no—
379C4⋊C4—44no—
380C4⋊C4—44no—
381C4⋊C4—42no—
382C4⋊C4—42no—
383C4⋊C4—44no—
384C4⋊C4—44no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—41no—
388C4⋊C4—41no—
389C4⋊C4—82no—
390C4⋊C4—82no—
391C4⋊C4—82no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4—41no—
397C22⋊C4—41no—
398C22⋊C4—44no—
399C22⋊C4—44no—
400C22⋊C4—42no—
401C22⋊C4—42no—
402C22⋊C4—82no—
403C22⋊C4—82no—
404C42—21no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42—21no—
409C42—21no—
410C42—21no—
411C42—21no—
412C42—21no—
413C42—21no—
414C42—21no—
415C42—21no—
416C42—21no—
417C42—21no—
418C42—21no—
419C42—21no—
420C42—21no—
421C42—21no—
422C42—44no—
423C42—44no—
424C42—42no—
425C42—42no—
426C42#9911yescharacteristic
427C42#9911yescharacteristic
428C42#9911yescharacteristic
429C42#9911yescharacteristic
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—41no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23#42112yes—
445C23C22×C22⋊C411yescharacteristic
446Q8—44no—
447Q8—44no—
448Q8—44no—
449Q8—44no—
450Q8—44no—
451D4—44no—
452D4—44no—
453D4—44no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—22no—
465C2×C4—24no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—42no—
480C2×C4—42no—
481C2×C4—48no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—81no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—84no—
508C2×C4C2×#9911yescharacteristic
509C2×C4C2×#9911yescharacteristic
510C2×C4C2×#9911yescharacteristic
511C2×C4C2×#9911yescharacteristic
512C2×C4C2×#9911yescharacteristic
513C2×C4C2×#9911yescharacteristic
514C2×C4#41912yes—
515C2×C4#41912yes—
516C2×C4C2×#13712yes—
517C8—84no—
518C8—84no—
519C22—21no—
520C22—21no—
521C22—22no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—81no—
535C22—81no—
536C22C22×#9911yescharacteristic
537C22C2×#41911yescharacteristic
538C22C2×#42111yescharacteristic
539C4—21no—
540C4—21no—
541C4—21no—
542C4—22no—
543C4—21no—
544C4—21no—
545C4—22no—
546C4—22no—
547C4—41no—
548C4—44no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—82no—
555C4—82no—
556C4—82no—
557C4#212012yes—
558C2—21no—
559C2—21no—
560C2—42no—
561C2—81no—
562C2—81no—
563C2#1757811yescharacteristic
564C2C2×#212011yescharacteristic
565C2#3336911yescharacteristic
subgroupG/H
center, socleC22C22×#99
commutatorC22×C4C23×C4
Frattini, cosocleC2×C4⋊C4C24
prime radicalC22×#41D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×#41 ◁ G
LECSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
4. #11905C2semidirect
5. #11816C2semidirect
6. #11791C2semidirect
7. #11790C2semidirect

Maximal subgroups

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

subgroupindex
#349522
#207282
#173662
#119052
#118162
#117912
#117902