Finite Group Databasebeta

← #111849

Subgroups — #111849

Order 512.

982 conjugacy classes of subgroups.

The subgroup lattice has 595 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3078C211yesmaximal, characteristic
2#21385C211yesmaximal, characteristic
3C2×#1518C211yesmaximal, characteristic
4C2×#1479C211yesmaximal, characteristic
5#13942C211yesmaximal, characteristic
6C2×#1286C211yesmaximal, characteristic
7#7901C211yesmaximal, characteristic
8C2×#533C2211yescharacteristic
9C22×C4×Q8C2211yescharacteristic
10#3078—22no—
11#3078—22no—
12#3078—22no—
13#3078C414yescomplemented
14C2×#479—22no—
15C2×#477—21no—
16C2×#475—21no—
17C2×#431C2211yescharacteristic
18C2×#431C2211yescharacteristic
19C2×#428—21no—
20C2×#423C2211yescharacteristic
21C2×#419—21no—
22C2×#391—21no—
23C2×#382C2211yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25#1987—21no—
26#1981—21no—
27#1872—22no—
28C4×#103—22no—
29#1518—22no—
30#1518—22no—
31C2×#328—22no—
32#1479—22no—
33#1479—22no—
34C2×Q8⋊C8—22no—
35#1441—22no—
36C4⋊#95—21no—
37#1434—22no—
38#1286—22no—
39#1279—22no—
40C23×Q8D411yescharacteristic
41C22×M16—21no—
42#533—21no—
43#533—21no—
44#533—21no—
45#533—21no—
46#533—21no—
47#533—21no—
48#533C2×C412yes—
49#533D412yes—
50C2×C4⋊Q8D411yescharacteristic
51C2×C4⋊Q8D411yescharacteristic
52C2×#125—21no—
53C2×C22⋊Q8—21no—
54C2×C22⋊Q8—21no—
55C2×C4×Q8—21no—
56C2×C4×Q8—21no—
57C2×C4×Q8—21no—
58C2×C4×Q8—21no—
59C2×C4×Q8—21no—
60C2×C4×Q8—21no—
61C2×C4×Q8—21no—
62C2×C4×Q8—21no—
63C2×C4×Q8—21no—
64C2×C4×Q8—21no—
65C2×C4×Q8—21no—
66C2×C4×Q8—21no—
67C2×C4×Q8C2×C412yes—
68C2×C4×Q8D412yes—
69C2×#117—21no—
70C22×C4⋊C4—21no—
71C22×C4⋊C4—21no—
72C22×C4⋊C4D411yescharacteristic
73C22×C4⋊C4D412yes—
74C22×C42—21no—
75C22×C42—21no—
76C22×C42C2311yescharacteristic
77#479—28no—
78#479—28no—
79#477—24no—
80#477—24no—
81#475—24no—
82#475—24no—
83#431—21no—
84#431—21no—
85#431—21no—
86#431—21no—
87#431—21no—
88#431—21no—
89#431—21no—
90#431D412yes—
91#428—24no—
92#428—24no—
93C2×#107—22no—
94C2×#106—22no—
95#423—21no—
96#423—21no—
97#423C2×C412yes—
98#423D412yes—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×C4⋊C8D412yes—
103#419—24no—
104#419—24no—
105C2×#103—22no—
106C2×#103—22no—
107C2×#103—24no—
108C2×C22⋊C8—21no—
109C2×C22⋊C8—21no—
110C2×C4×C8—21no—
111C2×C4×C8D412yes—
112#391—42no—
113#391—42no—
114#382—21no—
115#382—21no—
116#382—21no—
117#382—21no—
118C4×C4⋊C4—21no—
119C4×C4⋊C4—21no—
120C4×C4⋊C4—21no—
121C4×C4⋊C4—21no—
122C2×#95—24no—
123C2×#95—24no—
124C2×#95—21no—
125C2×#95—21no—
126C2×#95D412yes—
127#340—24no—
128#328—28no—
129Q8⋊C8—28no—
130C22×Q8—21no—
131C22×Q8—21no—
132C22×Q8—21no—
133C22×Q8—21no—
134C22×Q8—21no—
135C22×Q8—21no—
136C22×Q8—21no—
137C22×Q8—21no—
138C22×Q8—21no—
139C22×Q8—21no—
140C22×Q8—21no—
141C22×Q8—21no—
142C22×Q8—21no—
143C22×Q8C22⋊C412yes—
144C22×Q8SD1612yes—
145C22×Q8Q1612yes—
146C23×C4—21no—
147C23×C4—21no—
148C23×C4—22no—
149C23×C4—22no—
150C23×C4C2×D411yescharacteristic
151C23×C4C2×D411yescharacteristic
152C23×C4C2×D411yescharacteristic
153C2×M16—22no—
154C2×M16—22no—
155C2×M16—41no—
156C2×M16—41no—
157C2×M16—41no—
158C2×M16—41no—
159C22×C8—22no—
160C22×C8—22no—
161C22×C8—41no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—21no—
167C4⋊Q8—21no—
168C4⋊Q8C22⋊C412yes—
169C4⋊Q8C22⋊C412yes—
170#125—22no—
171#125—22no—
172#125—41no—
173#125—41no—
174C22⋊Q8—22no—
175C22⋊Q8—22no—
176C22⋊Q8—22no—
177C22⋊Q8—22no—
178C22⋊Q8—41no—
179C22⋊Q8—41no—
180C22⋊Q8—41no—
181C22⋊Q8—41no—
182C4×Q8—22no—
183C4×Q8—22no—
184C4×Q8—22no—
185C4×Q8—22no—
186C4×Q8—22no—
187C4×Q8—22no—
188C4×Q8—22no—
189C4×Q8—22no—
190C4×Q8—22no—
191C4×Q8—22no—
192C4×Q8—22no—
193C4×Q8—22no—
194C4×Q8—41no—
195C4×Q8—41no—
196C4×Q8—41no—
197C4×Q8—41no—
198C4×Q8—41no—
199C4×Q8—41no—
200C4×Q8—41no—
201C4×Q8—41no—
202C4×Q8—41no—
203C4×Q8—41no—
204C4×Q8—41no—
205C4×Q8—41no—
206#117—22no—
207#117—22no—
208#117—41no—
209#117—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—22no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—22no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—22no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—44no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—41no—
226C2×C4⋊C4—41no—
227C2×C4⋊C4—41no—
228C2×C4⋊C4—41no—
229C2×C4⋊C4—41no—
230C2×C4⋊C4—41no—
231C2×C4⋊C4—41no—
232C2×C4⋊C4—41no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4—41no—
235C2×C4⋊C4—41no—
236C2×C4⋊C4C22⋊C412yes—
237C2×C22⋊C4—41no—
238C2×C42—22no—
239C2×C42—22no—
240C2×C42—41no—
241C2×C42—41no—
242C2×C42—41no—
243C2×C42—41no—
244C2×C42—41no—
245C2×C42—41no—
246C2×C42—41no—
247C2×C42—41no—
248C2×C42—41no—
249C2×C42—41no—
250C2×C42—41no—
251C2×C42C22×C411yescharacteristic
252C2×C42C2×D411yescharacteristic
253C2×C42C2×D411yescharacteristic
254C2×C42C2×D411yescharacteristic
255C2×C42C2×D411yescharacteristic
256C2×C42C2×D411yescharacteristic
257C2×C42C2×D411yescharacteristic
258C2×C42C2×D411yescharacteristic
259C2×C42#4111yescharacteristic
260C2×C42#4111yescharacteristic
261C2×C42#4111yescharacteristic
262C2×C42#4111yescharacteristic
263#107—28no—
264#106—28no—
265C4⋊C8—22no—
266C4⋊C8—22no—
267C4⋊C8—22no—
268C4⋊C8—22no—
269C4⋊C8—41no—
270C4⋊C8—41no—
271C4⋊C8—41no—
272C4⋊C8C22⋊C414yes—
273#103—28no—
274#103—28no—
275#103—48no—
276C22⋊C8—22no—
277C22⋊C8—41no—
278C22⋊C8—41no—
279C22⋊C8—41no—
280C4×C8—22no—
281C4×C8—22no—
282C4×C8—22no—
283C4×C8—41no—
284#95—22no—
285#95—22no—
286#95—48no—
287#95—48no—
288#95—41no—
289#95—41no—
290#95—41no—
291#95—41no—
292C24#12011yescharacteristic
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8—22no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—22no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—22no—
308C2×Q8—22no—
309C2×Q8—22no—
310C2×Q8—44no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C2×Q8—41no—
317C2×Q8—41no—
318C2×Q8—41no—
319C2×Q8—41no—
320C2×Q8—41no—
321C2×Q8—41no—
322C2×Q8—41no—
323C2×Q8—41no—
324C2×Q8—41no—
325C2×Q8—82no—
326C2×Q8#10314yescomplemented
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—24no—
331C22×C4—22no—
332C22×C4—42no—
333C22×C4—42no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—44no—
339C22×C4—42no—
340C22×C4—42no—
341C22×C4—42no—
342C22×C4—41no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—44no—
350C22×C4—44no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C2×C22⋊C411yescharacteristic
355C22×C4C4×D411yescharacteristic
356C22×C4C4×D411yescharacteristic
357C22×C4#12011yescharacteristic
358C22×C4#12011yescharacteristic
359C22×C4#12011yescharacteristic
360C22×C4#12011yescharacteristic
361C22×C4#12111yescharacteristic
362C22×C4#12111yescharacteristic
363C22×C4#12111yescharacteristic
364C22×C4#12111yescharacteristic
365C22×C4#12111yescharacteristic
366C22×C4#12111yescharacteristic
367C22×C4#12111yescharacteristic
368C22×C4#12111yescharacteristic
369C22×C4#12311yescharacteristic
370C22×C4#12711yescharacteristic
371C22×C4#12711yescharacteristic
372C22×C4C2×SD1611yescharacteristic
373C22×C4C2×Q1611yescharacteristic
374C22×C4#13511yescharacteristic
375C22×C4#13511yescharacteristic
376C22×C4AGL(1,ℤ/8)11yescharacteristic
377C22×C4#13711yescharacteristic
378C22×C4#13711yescharacteristic
379C22×C4#13711yescharacteristic
380M16—42no—
381M16—42no—
382M16—42no—
383M16—42no—
384C2×C8—24no—
385C2×C8—42no—
386C2×C8—42no—
387C2×C8—44no—
388C2×C8—42no—
389C2×C8—42no—
390C2×C8—82no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—22no—
396C4⋊C4—22no—
397C4⋊C4—22no—
398C4⋊C4—22no—
399C4⋊C4—42no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—42no—
405C4⋊C4—42no—
406C4⋊C4—41no—
407C4⋊C4—42no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—42no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—42no—
415C4⋊C4—81no—
416C4⋊C4—81no—
417C4⋊C4—81no—
418C4⋊C4—81no—
419C22⋊C4—42no—
420C22⋊C4—42no—
421C42—42no—
422C42—42no—
423C42—42no—
424C42—42no—
425C42—42no—
426C42—42no—
427C42—81no—
428C42—81no—
429C42—81no—
430C42—81no—
431C42C2×C22⋊C411yescharacteristic
432C42C2×C22⋊C411yescharacteristic
433C42C4×D411yescharacteristic
434C42C4×D411yescharacteristic
435C42#12011yescharacteristic
436C42#12011yescharacteristic
437C42#12011yescharacteristic
438C42#12111yescharacteristic
439C42#12111yescharacteristic
440C42#12111yescharacteristic
441C42#12111yescharacteristic
442C42#12311yescharacteristic
443C42#12311yescharacteristic
444C42#12311yescharacteristic
445C42#12411yescharacteristic
446C42#12411yescharacteristic
447C23—22no—
448C23—22no—
449C23#38611yescharacteristic
450C23#39211yescharacteristic
451C23#39211yescharacteristic
452C23#45011yescharacteristic
453C23#45111yescharacteristic
454C23#45211yescharacteristic
455C23#45211yescharacteristic
456Q8—24no—
457Q8—24no—
458Q8—44no—
459Q8—42no—
460Q8—42no—
461Q8—42no—
462Q8—42no—
463Q8—42no—
464Q8—42no—
465Q8—82no—
466Q8—82no—
467Q8—82no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—42no—
487C2×C4—44no—
488C2×C4—44no—
489C2×C4—44no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—44no—
494C2×C4—82no—
495C2×C4—82no—
496C2×C4—82no—
497C2×C4—82no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—84no—
503C2×C4—84no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4#37911yescharacteristic
508C2×C4#38611yescharacteristic
509C2×C4#38611yescharacteristic
510C2×C4#38611yescharacteristic
511C2×C4#39011yescharacteristic
512C2×C4#39011yescharacteristic
513C2×C4#39211yescharacteristic
514C2×C4#39211yescharacteristic
515C2×C4#39411yescharacteristic
516C2×C4#39411yescharacteristic
517C2×C4#39411yescharacteristic
518C2×C4#39411yescharacteristic
519C2×C4C2×#10311yescharacteristic
520C2×C4#41611yescharacteristic
521C2×C4#41711yescharacteristic
522C2×C4#41911yescharacteristic
523C2×C4#44811yescharacteristic
524C2×C4#44811yescharacteristic
525C2×C4#44911yescharacteristic
526C2×C4#44911yescharacteristic
527C2×C4#45111yescharacteristic
528C2×C4#45111yescharacteristic
529C2×C4#45211yescharacteristic
530C2×C4#45211yescharacteristic
531C2×C4#46511yescharacteristic
532C2×C4#46511yescharacteristic
533C2×C4#46711yescharacteristic
534C2×C4#46711yescharacteristic
535C2×C4#46811yescharacteristic
536C2×C4#46811yescharacteristic
537C2×C4#47011yescharacteristic
538C2×C4#47011yescharacteristic
539C2×C4#48311yescharacteristic
540C2×C4#48411yescharacteristic
541C2×C4#48511yescharacteristic
542C2×C4#48511yescharacteristic
543C8—44no—
544C8—82no—
545C8—82no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22#143811yescharacteristic
555C22#187211yescharacteristic
556C22#187311yescharacteristic
557C22#200011yescharacteristic
558C22#200011yescharacteristic
559C22#200111yescharacteristic
560C22#200111yescharacteristic
561C22#200912yes—
562C22#201012yes—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—21no—
569C4—21no—
570C4—21no—
571C4—44no—
572C4—84no—
573C4—82no—
574C4—82no—
575C4—82no—
576C4—162no—
577C4#178711yescharacteristic
578C4#178811yescharacteristic
579C4#189211yescharacteristic
580C4#189411yescharacteristic
581C4#203511yescharacteristic
582C4#203511yescharacteristic
583C4#203611yescharacteristic
584C4#203611yescharacteristic
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2#1000112yes—
590C2#1000312yes—
591C2#1097011yescharacteristic
592C2#1103111yescharacteristic
593C2#1104111yescharacteristic
subgroupG/H
center, socleC23#392
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
13. #3078C4semidirect
326. C2×Q8#103semidirect

Maximal subgroups

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

subgroupindex
C2×#30782
#213852
C2×#15182
C2×#14792
#139422
C2×#12862
#79012