Finite Group Databasebeta

← #411151

Subgroups — #411151

Order 512.

1196 conjugacy classes of subgroups.

The subgroup lattice has 611 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2100C211yesmaximal, characteristic
2C2×#2043C211yesmaximal, characteristic
3#14714C211yesmaximal, characteristic
4C4×#389C211yesmaximal, characteristic
5#11371C211yesmaximal, characteristic
6#11190C212yesmaximal
7#11067C212yesmaximal
8#11010C211yesmaximal, characteristic
9#10932C212yesmaximal
10#10932C212yesmaximal
11#10795C211yesmaximal, characteristic
12C22×C4⋊Q8C2211yescharacteristic
13C22×#103C2212yes—
14C22×#103C2212yes—
15C22×#103C2212yes—
16C22×#103C2212yes—
17C2×#391C2212yes—
18C2×#391C2212yes—
19C2×#389C2211yescharacteristic
20C2×#389C2211yescharacteristic
21C2×#384C2211yescharacteristic
22C2×C4×C4⋊C4—21no—
23C2×C4×C4⋊C4C2211yescharacteristic
24C2×C4×C4⋊C4C2211yescharacteristic
25C2×C43C2211yescharacteristic
26#2100—24no—
27#2043—24no—
28C2×#340C2212yes—
29C2×#340C2212yes—
30C2×#340C2212yes—
31C2×#340C2212yes—
32C2×#336C2211yescharacteristic
33C2×#336C2211yescharacteristic
34C2×#336C2212yes—
35C2×#336C2212yes—
36#1436—21no—
37#1436—21no—
38C4⋊#95—21no—
39C4⋊#95—21no—
40C4⋊#95—21no—
41C4⋊#95—21no—
42C4⋊#95C2211yescharacteristic
43C4⋊#95C2211yescharacteristic
44C4×#95—21no—
45C23×Q8C2312yes—
46C23×C8C2312yes—
47C23×C8C2312yes—
48C2×C4⋊Q8—24no—
49C2×C4⋊Q8—22no—
50C2×C4⋊Q8—22no—
51C2×C4⋊Q8—42no—
52C22×C4⋊C4—21no—
53C22×C4⋊C4—21no—
54C22×C4⋊C4—21no—
55C22×C4⋊C4—21no—
56C22×C4⋊C4—21no—
57C22×C4⋊C4—21no—
58C22×C4⋊C4C2312yes—
59C22×C4⋊C4C2311yescharacteristic
60C22×C4⋊C4C2311yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C42—21no—
64C22×C42—21no—
65C22×C42D411yescharacteristic
66C22×C42D411yescharacteristic
67C22×C42D411yescharacteristic
68C22×C42D411yescharacteristic
69C22×C42C2311yescharacteristic
70C22×C42C2311yescharacteristic
71C22×C42C2311yescharacteristic
72C2×#103—24no—
73C2×#103—24no—
74C2×#103—24no—
75C2×#103—24no—
76C2×#103—24no—
77C2×#103—24no—
78C2×#103—24no—
79C2×#103—24no—
80C2×#103—42no—
81C2×#103—42no—
82C2×#103—42no—
83C2×#103—42no—
84#391—24no—
85#391—24no—
86#391—42no—
87#391—42no—
88#389—22no—
89#389—22no—
90#389—22no—
91#389D414yes—
92#384—22no—
93#384—22no—
94C4×C4⋊C4—22no—
95C4×C4⋊C4—22no—
96C4×C4⋊C4—42no—
97C4×C4⋊C4—44no—
98C2×#95—21no—
99C2×#95—21no—
100C2×#95—21no—
101C2×#95—21no—
102C2×#95—21no—
103C2×#95—22no—
104C2×#95—22no—
105C2×#95—22no—
106C2×#95—22no—
107C2×#95—21no—
108C2×#95—21no—
109C2×#95—21no—
110C43—42no—
111#340—24no—
112#340—24no—
113#340—42no—
114#340—42no—
115#336—22no—
116#336—22no—
117#336—24no—
118#336—42no—
119C22×Q8—22no—
120C22×Q8—22no—
121C22×Q8—22no—
122C22×Q8—22no—
123C22×Q8—22no—
124C22×Q8—22no—
125C22×Q8—22no—
126C22×Q8—22no—
127C22×Q8—22no—
128C22×Q8—22no—
129C22×Q8—22no—
130C22×Q8—22no—
131C22×Q8—22no—
132C22×Q8#4114yes—
133C23×C4—21no—
134C23×C4—22no—
135C23×C4—21no—
136C23×C4—21no—
137C23×C4—21no—
138C23×C4—22no—
139C23×C4C2×D411yescharacteristic
140C23×C4C2×D411yescharacteristic
141C23×C4C2×D411yescharacteristic
142C23×C4C2×D411yescharacteristic
143C23×C4C2×D411yescharacteristic
144C23×C4C2×D411yescharacteristic
145C23×C4C2411yescharacteristic
146C22×C8—22no—
147C22×C8—22no—
148C22×C8—22no—
149C22×C8—22no—
150C22×C8—22no—
151C22×C8—22no—
152C22×C8—22no—
153C22×C8—22no—
154C22×C8—22no—
155C22×C8—22no—
156C22×C8—22no—
157C22×C8—22no—
158C22×C8—22no—
159C22×C8—22no—
160C4⋊Q8—48no—
161C4⋊Q8—48no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—22no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—24no—
172C2×C4⋊C4—24no—
173C2×C4⋊C4—24no—
174C2×C4⋊C4—24no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—22no—
179C2×C4⋊C4—22no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—22no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—42no—
185C2×C4⋊C4—42no—
186C2×C4⋊C4—42no—
187C2×C4⋊C4—42no—
188C2×C4⋊C4—42no—
189C2×C4⋊C4—42no—
190C2×C4⋊C4—42no—
191C2×C4⋊C4—42no—
192C2×C4⋊C4—42no—
193C2×C4⋊C4—42no—
194C2×C4⋊C4—42no—
195C2×C4⋊C4—42no—
196C2×C4⋊C4—42no—
197C2×C4⋊C4—42no—
198C2×C4⋊C4C2×D412yes—
199C2×C4⋊C4C2×D412yes—
200C2×C4⋊C4#4112yes—
201C2×C4⋊C4#4112yes—
202C2×C4⋊C4#4112yes—
203C2×C4⋊C4#4112yes—
204C2×C42—22no—
205C2×C42—21no—
206C2×C42—21no—
207C2×C42—22no—
208C2×C42—22no—
209C2×C42—24no—
210C2×C42—22no—
211C2×C42—22no—
212C2×C42—21no—
213C2×C42—21no—
214C2×C42—22no—
215C2×C42—22no—
216C2×C42—41no—
217C2×C42—41no—
218C2×C42—41no—
219C2×C42—41no—
220C2×C42—41no—
221C2×C42—41no—
222C2×C42—41no—
223C2×C42—41no—
224C2×C42—42no—
225C2×C42—42no—
226C2×C42—42no—
227C2×C42—42no—
228C2×C42—42no—
229C2×C42SD1614yes—
230C2×C42Q1614yes—
231C2×C42C2×D412yes—
232C2×C42#4112yes—
233C2×C42#4114yes—
234#103—48no—
235#103—48no—
236#103—48no—
237#103—48no—
238#95—24no—
239#95—24no—
240#95—24no—
241#95—42no—
242#95—42no—
243#95—44no—
244#95—44no—
245#95—44no—
246#95—44no—
247#95—42no—
248#95—42no—
249#95—42no—
250C24C22×D411yescharacteristic
251C2×Q8—24no—
252C2×Q8—24no—
253C2×Q8—24no—
254C2×Q8—24no—
255C2×Q8—24no—
256C2×Q8—24no—
257C2×Q8—42no—
258C2×Q8—42no—
259C2×Q8—42no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—42no—
263C2×Q8—42no—
264C2×Q8—42no—
265C2×Q8—42no—
266C2×Q8—42no—
267C2×Q8—42no—
268C2×Q8—42no—
269C2×Q8—42no—
270C2×Q8—42no—
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—42no—
275C2×Q8—42no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×Q8—42no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—22no—
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—22no—
295C22×C4—22no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—21no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—24no—
316C22×C4—41no—
317C22×C4—41no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4—42no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—42no—
324C22×C4—42no—
325C22×C4—42no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—42no—
329C22×C4—42no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—41no—
338C22×C4—41no—
339C22×C4—41no—
340C22×C4—41no—
341C22×C4—41no—
342C22×C4—41no—
343C22×C4—41no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—42no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4#12112yes—
352C22×C4#12112yes—
353C22×C4#12412yes—
354C22×C4#12412yes—
355C22×C4C2×SD1612yes—
356C22×C4C2×SD1612yes—
357C22×C4C2×SD1612yes—
358C22×C4C2×Q1612yes—
359C22×C4C2×Q1612yes—
360C22×C4C2×Q1612yes—
361C22×C4#13712yes—
362C22×C4#13712yes—
363C22×C4C22×D411yescharacteristic
364C22×C4C2×#4111yescharacteristic
365C22×C4C2×#4111yescharacteristic
366C22×C4C2×#4111yescharacteristic
367C22×C4C2×#4112yes—
368C22×C4C2×#4112yes—
369C22×C4C2×#4111yescharacteristic
370C22×C4C2×#4111yescharacteristic
371C22×C4H(5,𝔽2)12yes—
372C22×C4H(5,𝔽2)12yes—
373C2×C8—42no—
374C2×C8—42no—
375C2×C8—42no—
376C2×C8—42no—
377C2×C8—42no—
378C2×C8—42no—
379C2×C8—42no—
380C2×C8—42no—
381C2×C8—42no—
382C2×C8—42no—
383C2×C8—42no—
384C2×C8—42no—
385C2×C8—42no—
386C2×C8—42no—
387C4⋊C4—22no—
388C4⋊C4—22no—
389C4⋊C4—22no—
390C4⋊C4—24no—
391C4⋊C4—24no—
392C4⋊C4—24no—
393C4⋊C4—48no—
394C4⋊C4—48no—
395C4⋊C4—48no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4—48no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—84no—
405C4⋊C4—84no—
406C4⋊C4#12414yes—
407C42—24no—
408C42—24no—
409C42—24no—
410C42—24no—
411C42—44no—
412C42—44no—
413C42—48no—
414C42—44no—
415C42—44no—
416C42—42no—
417C42—42no—
418C42—84no—
419C23C2×#12111yescharacteristic
420C23#52511yescharacteristic
421C23#52511yescharacteristic
422C23#52511yescharacteristic
423C23C2×#12411yescharacteristic
424C23#53411yescharacteristic
425C23#53511yescharacteristic
426C23C22×SD1611yescharacteristic
427C23C22×Q1611yescharacteristic
428C23C2×#13711yescharacteristic
429C23C2×#13711yescharacteristic
430C23#57511yescharacteristic
431C23#57511yescharacteristic
432C23#57511yescharacteristic
433C23#57511yescharacteristic
434Q8—44no—
435Q8—44no—
436Q8—44no—
437Q8—44no—
438Q8—82no—
439Q8—82no—
440Q8—82no—
441Q8—82no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—42no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—44no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—44no—
500C2×C4—82no—
501C2×C4—81no—
502C2×C4—81no—
503C2×C4—82no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—82no—
507C2×C4—81no—
508C2×C4—81no—
509C2×C4—81no—
510C2×C4—81no—
511C2×C4—81no—
512C2×C4—81no—
513C2×C4—81no—
514C2×C4—81no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—82no—
523C2×C4#46114yes—
524C2×C4#46214yes—
525C2×C4#48714yes—
526C2×C4C2×#12411yescharacteristic
527C2×C4#52911yescharacteristic
528C2×C4#52912yes—
529C2×C4#52912yes—
530C2×C4#52911yescharacteristic
531C2×C4#53211yescharacteristic
532C2×C4#53812yes—
533C2×C4#54012yes—
534C2×C4#54612yes—
535C2×C4#55012yes—
536C2×C4#55112yes—
537C2×C4#55112yes—
538C2×C4#55312yes—
539C2×C4#55312yes—
540C2×C4#55312yes—
541C2×C4#55912yes—
542C8—82no—
543C8—82no—
544C22#239811yescharacteristic
545C22#253411yescharacteristic
546C22#254811yescharacteristic
547C22#259111yescharacteristic
548C22#259811yescharacteristic
549C22#263511yescharacteristic
550C22#285011yescharacteristic
551C22C2×#46111yescharacteristic
552C22C2×#46211yescharacteristic
553C22#304011yescharacteristic
554C22#304011yescharacteristic
555C22#310111yescharacteristic
556C22#310111yescharacteristic
557C22#310311yescharacteristic
558C22#310411yescharacteristic
559C22#310411yescharacteristic
560C22#310411yescharacteristic
561C22#311611yescharacteristic
562C22#311611yescharacteristic
563C22#311611yescharacteristic
564C22#311611yescharacteristic
565C22#311711yescharacteristic
566C22#311711yescharacteristic
567C22C2×#48711yescharacteristic
568C22#313511yescharacteristic
569C22#313911yescharacteristic
570C22#314211yescharacteristic
571C22#318711yescharacteristic
572C22#318911yescharacteristic
573C22#319611yescharacteristic
574C22#319611yescharacteristic
575C22#320611yescharacteristic
576C22#320911yescharacteristic
577C22#321911yescharacteristic
578C22#321911yescharacteristic
579C4—24no—
580C4—24no—
581C4—24no—
582C4—44no—
583C4—42no—
584C4—42no—
585C4—42no—
586C4—84no—
587C4—82no—
588C4—82no—
589C4—82no—
590C4—162no—
591C4#249012yes—
592C4#251612yes—
593C4#255412yes—
594C4#259512yes—
595C2#1510711yescharacteristic
596C2#2381611yescharacteristic
597C2#2382511yescharacteristic
598C2#2811511yescharacteristic
599C2#2812111yescharacteristic
600C2#2874811yescharacteristic
601C2#2875711yescharacteristic
602C2#2932911yescharacteristic
603C2#2933811yescharacteristic
604C2#2936811yescharacteristic
605C2#2937011yescharacteristic
606C2#3010611yescharacteristic
607C2#3010911yescharacteristic
608C2#3302611yescharacteristic
609C2#3302711yescharacteristic
subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC23×C4C24
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C43 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

Maximal subgroups

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

subgroupindex
C2×#21002
C2×#20432
#147142
C4×#3892
#113712
#111902
#110672
#110102
#109322
#107952