Finite Group Databasebeta

← #416266

Subgroups — #416266

Order 512.

901 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21177C211yesmaximal, characteristic
2#21177C211yesmaximal, characteristic
3#20769C211yesmaximal, characteristic
4C2×#1801C211yesmaximal, characteristic
5C2×#1801C211yesmaximal, characteristic
6C2×C4×#101C211yesmaximal, characteristic
7#11312C212yesmaximal
8#11252C212yesmaximal
9#11140C212yesmaximal
10#11140C212yesmaximal
11C4⋊#338C211yesmaximal, characteristic
12C22×C4×Q8C2211yescharacteristic
13C2×#430C2212yes—
14C2×#430C2212yes—
15C2×#423C2211yescharacteristic
16C2×#423C2211yescharacteristic
17C2×#423C2211yescharacteristic
18C2×#423C2211yescharacteristic
19C22×#101C2211yescharacteristic
20C22×#101C2211yescharacteristic
21C22×#101C2212yes—
22C22×#101C2212yes—
23C2×C4×M16C2211yescharacteristic
24C2×C4×M16C2211yescharacteristic
25#1950—22no—
26#1950—22no—
27#1950—22no—
28#1950—22no—
29#1838—22no—
30#1837—22no—
31#1801—22no—
32#1801—22no—
33#1801—22no—
34#1801—22no—
35C4×#101—22no—
36C4×#101—22no—
37C2×#343C2211yescharacteristic
38C2×#343C2212yes—
39C2×#343C2212yes—
40C2×#343C2211yescharacteristic
41#1738C2212yes—
42#1738C2212yes—
43#1738C2212yes—
44#1738C2212yes—
45C2×#338C2212yes—
46C2×#338C2212yes—
47C23×Q8C2311yescharacteristic
48C22×M16C2312yes—
49C22×M16C2312yes—
50C22×M16C2311yescharacteristic
51C22×M16C2311yescharacteristic
52C22×M16C2312yes—
53C22×M16C2312yes—
54C22×M16C2311yescharacteristic
55C22×M16C2311yescharacteristic
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×Q8—21no—
68C22×C4⋊C4Q812yes—
69C22×C4⋊C4C2311yescharacteristic
70C22×C42Q812yes—
71C22×C42C2311yescharacteristic
72#430—24no—
73#430—42no—
74#430—42no—
75#430—42no—
76C2×#108—24no—
77C2×#108—24no—
78#423—21no—
79#423—21no—
80#423—21no—
81#423—21no—
82#423—21no—
83#423—21no—
84#423—21no—
85#423—21no—
86#423—21no—
87#423—21no—
88#423—21no—
89#423—21no—
90#423D412yes—
91#423D412yes—
92#423D412yes—
93#423D412yes—
94C2×C4⋊C8—21no—
95C2×C4⋊C8—21no—
96C2×C4⋊C8—21no—
97C2×C4⋊C8—21no—
98C2×C4⋊C8—21no—
99C2×C4⋊C8—21no—
100C2×C4⋊C8—21no—
101C2×C4⋊C8—21no—
102C2×#101—22no—
103C2×#101—22no—
104C2×#101—22no—
105C2×#101—22no—
106C2×#101—22no—
107C2×#101—22no—
108C2×#101—24no—
109C2×#101—24no—
110C2×#101—24no—
111C2×#101—24no—
112C2×#101—42no—
113C2×#101—42no—
114C4×M16—21no—
115C4×M16—21no—
116C4×M16—21no—
117C4×M16—21no—
118C4×M16—21no—
119C4×M16—21no—
120C4×M16D412yes—
121C4×M16D412yes—
122C2×#97—21no—
123C2×#97—21no—
124C2×C4×C8—21no—
125C2×C4×C8—21no—
126#343—24no—
127#343—24no—
128#343—22no—
129#343—22no—
130#341—24no—
131#341—24no—
132#341—24no—
133#341—24no—
134#338—24no—
135#338—42no—
136C22×Q8—21no—
137C22×Q8—21no—
138C22×Q8—21no—
139C22×Q8—21no—
140C22×Q8—21no—
141C22×Q8—21no—
142C22×Q8—21no—
143C22×Q8—21no—
144C22×Q8—21no—
145C22×Q8—21no—
146C22×Q8—21no—
147C22×Q8—21no—
148C22×Q8#4112yes—
149C22×Q8#4112yes—
150C23×C4C2×Q812yes—
151C23×C4C2×Q812yes—
152C23×C4C2×Q811yescharacteristic
153C23×C4C2×Q811yescharacteristic
154C23×C4C2411yescharacteristic
155C2×M16—21no—
156C2×M16—21no—
157C2×M16—22no—
158C2×M16—22no—
159C2×M16—21no—
160C2×M16—21no—
161C2×M16—21no—
162C2×M16—21no—
163C2×M16—21no—
164C2×M16—21no—
165C2×M16—22no—
166C2×M16—21no—
167C2×M16—21no—
168C2×M16—21no—
169C2×M16—22no—
170C2×M16—21no—
171C2×M16—21no—
172C2×M16—21no—
173C2×M16—22no—
174C2×M16—22no—
175C2×M16—22no—
176C2×M16—22no—
177C2×M16—22no—
178C2×M16—21no—
179C2×M16—21no—
180C2×M16—21no—
181C2×M16—21no—
182C2×M16—21no—
183C2×M16—22no—
184C2×M16—21no—
185C2×M16—22no—
186C2×M16—22no—
187C2×M16—22no—
188C2×M16—22no—
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16C2×D412yes—
198C2×M16C2×D414yes—
199C2×M16C2×D414yes—
200C2×M16C2×D412yes—
201C2×M16#4112yes—
202C2×M16#4112yes—
203C22×C8—21no—
204C22×C8—21no—
205C22×C8—22no—
206C22×C8—22no—
207C22×C8—21no—
208C22×C8—21no—
209C22×C8—22no—
210C22×C8—22no—
211C4×Q8—41no—
212C4×Q8—41no—
213C4×Q8—41no—
214C4×Q8—41no—
215C4×Q8—41no—
216C4×Q8—41no—
217C4×Q8—41no—
218C4×Q8—41no—
219C4×Q8—41no—
220C4×Q8—41no—
221C4×Q8—41no—
222C4×Q8—41no—
223C4×Q8—41no—
224C4×Q8—41no—
225C4×Q8—41no—
226C4×Q8—41no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—22no—
229C2×C4⋊C4—22no—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C42—22no—
240C2×C42—22no—
241C2×C42—22no—
242C2×C42—22no—
243C2×C42—22no—
244C2×C42—22no—
245C2×C42C2×D411yescharacteristic
246C2×C42C2×D411yescharacteristic
247C2×C42C2×D411yescharacteristic
248C2×C42C2×D411yescharacteristic
249C2×C42C2×D411yescharacteristic
250C2×C42C2×D411yescharacteristic
251C2×C42#4111yescharacteristic
252C2×C42#4111yescharacteristic
253C2×C42#4111yescharacteristic
254C2×C42#4111yescharacteristic
255C2×C42#4111yescharacteristic
256C2×C42#4111yescharacteristic
257#108—48no—
258#108—48no—
259C4⋊C8—22no—
260C4⋊C8—22no—
261C4⋊C8—22no—
262C4⋊C8—22no—
263C4⋊C8—22no—
264C4⋊C8—22no—
265C4⋊C8—22no—
266C4⋊C8—22no—
267C4⋊C8—41no—
268C4⋊C8—41no—
269C4⋊C8—41no—
270C4⋊C8—41no—
271C4⋊C8—41no—
272C4⋊C8—41no—
273C4⋊C8—41no—
274C4⋊C8—41no—
275#101—28no—
276#101—28no—
277#101—48no—
278#101—48no—
279#97—22no—
280#97—22no—
281#97—41no—
282#97—41no—
283C4×C8—22no—
284C4×C8—22no—
285C4×C8—41no—
286C4×C8—41no—
287C24C22×Q811yescharacteristic
288C2×Q8—22no—
289C2×Q8—22no—
290C2×Q8—22no—
291C2×Q8—22no—
292C2×Q8—22no—
293C2×Q8—22no—
294C2×Q8—22no—
295C2×Q8—22no—
296C2×Q8—22no—
297C2×Q8—22no—
298C2×Q8—22no—
299C2×Q8—22no—
300C2×Q8—41no—
301C2×Q8—41no—
302C2×Q8—41no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—41no—
310C2×Q8—41no—
311C2×Q8—41no—
312C2×Q8—41no—
313C2×Q8—41no—
314C2×Q8—41no—
315C2×Q8—41no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—42no—
326C22×C4—81no—
327C22×C4—82no—
328C22×C4C22⋊Q811yescharacteristic
329C22×C4C22⋊Q811yescharacteristic
330C22×C4C22⋊Q811yescharacteristic
331C22×C4C22⋊Q811yescharacteristic
332C22×C4C22⋊Q811yescharacteristic
333C22×C4C22⋊Q811yescharacteristic
334C22×C4C22⋊Q811yescharacteristic
335C22×C4C22⋊Q811yescharacteristic
336C22×C4C22⋊Q811yescharacteristic
337C22×C4C22⋊Q811yescharacteristic
338C22×C4C22⋊Q811yescharacteristic
339C22×C4C22⋊Q811yescharacteristic
340C22×C4#12514yes—
341C22×C4C22×D411yescharacteristic
342C22×C4C22×D411yescharacteristic
343C22×C4C22×D411yescharacteristic
344C22×C4C2×#4111yescharacteristic
345C22×C4C2×#4111yescharacteristic
346C22×C4C2×#4111yescharacteristic
347C22×C4C2×#4111yescharacteristic
348C22×C4C2×#4111yescharacteristic
349C22×C4C2×#4111yescharacteristic
350C22×C4C2×#4111yescharacteristic
351C22×C4H(5,𝔽2)11yescharacteristic
352C22×C4H(5,𝔽2)11yescharacteristic
353C22×C42−1+411yescharacteristic
354C22×C42−1+411yescharacteristic
355M16—22no—
356M16—22no—
357M16—22no—
358M16—22no—
359M16—22no—
360M16—22no—
361M16—24no—
362M16—24no—
363M16—22no—
364M16—24no—
365M16—24no—
366M16—22no—
367M16—42no—
368M16—41no—
369M16—41no—
370M16—42no—
371M16—41no—
372M16—41no—
373M16—41no—
374M16—41no—
375M16—42no—
376M16—42no—
377M16—41no—
378M16—41no—
379M16—42no—
380M16—42no—
381M16—42no—
382M16—42no—
383M16—42no—
384M16—42no—
385M16—42no—
386M16—42no—
387C2×C8—22no—
388C2×C8—22no—
389C2×C8—24no—
390C2×C8—24no—
391C2×C8—22no—
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—42no—
396C2×C8—42no—
397C2×C8—42no—
398C2×C8—41no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—42no—
402C2×C8—41no—
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—42no—
406C2×C8—42no—
407C2×C8—42no—
408C2×C8—42no—
409C2×C8—42no—
410C2×C8—42no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—42no—
416C4⋊C4—42no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C42—42no—
420C42—42no—
421C42—42no—
422C42—42no—
423C42#12111yescharacteristic
424C42#12111yescharacteristic
425C42#12111yescharacteristic
426C42#12111yescharacteristic
427C42#12111yescharacteristic
428C42#12111yescharacteristic
429C42#12111yescharacteristic
430C42#12111yescharacteristic
431C42#12111yescharacteristic
432C42#12111yescharacteristic
433C42#12111yescharacteristic
434C42#12111yescharacteristic
435C42#12611yescharacteristic
436C42#12611yescharacteristic
437C42#12611yescharacteristic
438C42#12611yescharacteristic
439C23—41no—
440C23—41no—
441C23C2×C22⋊Q811yescharacteristic
442C23C2×C22⋊Q811yescharacteristic
443C23C2×C22⋊Q811yescharacteristic
444C23C2×#12511yescharacteristic
445C23#53311yescharacteristic
446C23#54411yescharacteristic
447C23#54411yescharacteristic
448Q8—42no—
449Q8—42no—
450Q8—42no—
451Q8—42no—
452Q8—42no—
453Q8—42no—
454Q8—42no—
455Q8—42no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—22no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—42no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4#39611yescharacteristic
480C2×C4#39611yescharacteristic
481C2×C4#39611yescharacteristic
482C2×C4#39611yescharacteristic
483C2×C4#39611yescharacteristic
484C2×C4#39611yescharacteristic
485C2×C4#39611yescharacteristic
486C2×C4#39611yescharacteristic
487C2×C4C2×#12111yescharacteristic
488C2×C4C2×#12111yescharacteristic
489C2×C4C2×#12111yescharacteristic
490C2×C4#52511yescharacteristic
491C2×C4#52511yescharacteristic
492C2×C4C2×#12611yescharacteristic
493C2×C4#52911yescharacteristic
494C2×C4#52911yescharacteristic
495C2×C4#53511yescharacteristic
496C2×C4#53611yescharacteristic
497C2×C4#54211yescharacteristic
498C2×C4#54211yescharacteristic
499C2×C4#54611yescharacteristic
500C2×C4#54611yescharacteristic
501C2×C4#54611yescharacteristic
502C2×C4#54711yescharacteristic
503C2×C4#54811yescharacteristic
504C2×C4#54811yescharacteristic
505C2×C4#54811yescharacteristic
506C2×C4#55011yescharacteristic
507C2×C4#55211yescharacteristic
508C2×C4#55211yescharacteristic
509C2×C4#55211yescharacteristic
510C2×C4#55311yescharacteristic
511C2×C4#55311yescharacteristic
512C2×C4#55311yescharacteristic
513C2×C4#55511yescharacteristic
514C2×C4#55611yescharacteristic
515C8—42no—
516C8—42no—
517C8—44no—
518C8—44no—
519C8—42no—
520C8—42no—
521C8—82no—
522C8—82no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22C2×#39611yescharacteristic
534C22#243911yescharacteristic
535C22#244111yescharacteristic
536C22#244211yescharacteristic
537C22#244211yescharacteristic
538C22#262811yescharacteristic
539C22#285111yescharacteristic
540C4—21no—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—44no—
548C4—82no—
549C4#207012yes—
550C4#241411yescharacteristic
551C4#241511yescharacteristic
552C4#242611yescharacteristic
553C4#242711yescharacteristic
554C4#249411yescharacteristic
555C4#249511yescharacteristic
556C4#253511yescharacteristic
557C4#253611yescharacteristic
558C2—21no—
559C2—21no—
560C2—21no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2#1522011yescharacteristic
565C2C2×#207011yescharacteristic
566C2#2362211yescharacteristic
subgroupG/H
center, socleC22C2×#396
commutator, Frattini, cosocleC23×C4C24
prime radicalC24C22×Q8
LCSG ▷ C23×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C42 ◁ 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
#211772
#207692
C2×#18012
C2×C4×#1012
#113122
#112522
#111402
C4⋊#3382