Finite Group Databasebeta

← #370638

Subgroups — #370638

Order 512.

1006 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#2571C211yesmaximal, characteristic
2#21146C211yesmaximal, characteristic
3C4⋊C4×M16C211yesmaximal, characteristic
4#11355C212yesmaximal
5#11204C212yesmaximal
6#10913C212yesmaximal
7#10858C212yesmaximal
8#10857C211yesmaximal, characteristic
9#10857C211yesmaximal, characteristic
10#10847C211yesmaximal, characteristic
11C4×#343C211yesmaximal, characteristic
12C2×#423C2211yescharacteristic
13C2×#423C2212yes—
14C2×#423C2211yescharacteristic
15C2×C4×M16C2211yescharacteristic
16C2×C4×M16C2212yes—
17C2×C4×M16C2211yescharacteristic
18#2571—21no—
19#2571—21no—
20#2571—22no—
21#2571—21no—
22#2571—21no—
23#2571—22no—
24C2×#400C414yes—
25C2×#389C412yes—
26C2×#389C2212yes—
27C2×#384C2211yescharacteristic
28C2×#382C412yes—
29C2×#382C2212yes—
30C2×C4×C4⋊C4C2211yescharacteristic
31C2×C4×C4⋊C4C2211yescharacteristic
32#1940—22no—
33#1939—21no—
34#1939—21no—
35#1771—22no—
36#1770—21no—
37C8×C4⋊C4—21no—
38C2×#343C2211yescharacteristic
39C2×#343C2212yes—
40C2×#343C2212yes—
41C2×#343C2211yescharacteristic
42C2×#343C2211yescharacteristic
43C2×#343C2211yescharacteristic
44C2×#343C2212yes—
45C2×#343C2212yes—
46C2×#343C2212yes—
47C2×#343C2212yes—
48#1728C2212yes—
49#1728C2212yes—
50C22×M16C2312yes—
51C22×M16C2312yes—
52C22×M16C2311yescharacteristic
53C22×M16C2311yescharacteristic
54C22×M16C2311yescharacteristic
55C22×M16C2311yescharacteristic
56C22×C4⋊C4C2×C412yes—
57C22×C4⋊C4C2×C412yes—
58C22×C4⋊C4C2×C414yes—
59C22×C4⋊C4C2×C411yescharacteristic
60C22×C4⋊C4C2×C411yescharacteristic
61C22×C4⋊C4C2311yescharacteristic
62C22×C4⋊C4C2311yescharacteristic
63C22×C4⋊C4C2312yes—
64C22×C42C2×C412yes—
65C22×C42C2312yes—
66C22×C42C2311yescharacteristic
67#423—22no—
68#423—24no—
69#423—22no—
70#423—22no—
71#423—42no—
72#423Q814yes—
73C2×C4⋊C8—21no—
74C2×C4⋊C8—21no—
75C2×C4⋊C8—21no—
76C2×C4⋊C8—22no—
77C2×C4⋊C8—22no—
78C2×C4⋊C8—21no—
79C4×M16—22no—
80C4×M16—24no—
81C4×M16—22no—
82C4×M16—22no—
83C4×M16—42no—
84C4×M16Q814yes—
85C2×#97—21no—
86C2×#97—21no—
87C2×#97—22no—
88C2×C4×C8—21no—
89C2×C4×C8—21no—
90C2×C4×C8—22no—
91#400—24no—
92#400—24no—
93#400—24no—
94#400—24no—
95#389—22no—
96#389—22no—
97#389—24no—
98#389—22no—
99#389—22no—
100#389—22no—
101#389—22no—
102#384—21no—
103#384—21no—
104#384—21no—
105#384—21no—
106#382—22no—
107#382—22no—
108#382—24no—
109#382—22no—
110#382—22no—
111#382—22no—
112#382—22no—
113C4×C4⋊C4—21no—
114C4×C4⋊C4—21no—
115C4×C4⋊C4—21no—
116C4×C4⋊C4—21no—
117C4×C4⋊C4D411yescharacteristic
118C4×C4⋊C4D411yescharacteristic
119C4×C4⋊C4D412yes—
120C4×C4⋊C4D411yescharacteristic
121C4×C4⋊C4D411yescharacteristic
122C4×C4⋊C4D412yes—
123C2×#95C2×C412yes—
124C2×#95C2×C414yes—
125C2×#95C2×C414yes—
126C2×#95C2×C414yes—
127C2×#95C2×C412yes—
128#343—22no—
129#343—24no—
130#343—22no—
131#343—22no—
132#343—22no—
133#343—24no—
134#343—42no—
135#343—42no—
136#343—42no—
137#343—42no—
138#336—22no—
139#336—22no—
140#336—22no—
141#336—22no—
142C23×C4C22×C411yescharacteristic
143C23×C4C22×C414yes—
144C23×C4C22×C412yes—
145C23×C4C22×C412yes—
146C23×C4C22×C412yes—
147C23×C4C22×C412yes—
148C23×C4C22×C411yescharacteristic
149C23×C4C2411yescharacteristic
150C2×M16—21no—
151C2×M16—21no—
152C2×M16—21no—
153C2×M16—21no—
154C2×M16—22no—
155C2×M16—21no—
156C2×M16—21no—
157C2×M16—21no—
158C2×M16—21no—
159C2×M16—21no—
160C2×M16—21no—
161C2×M16—22no—
162C2×M16—21no—
163C2×M16—21no—
164C2×M16—21no—
165C2×M16—21no—
166C2×M16—22no—
167C2×M16—21no—
168C2×M16—21no—
169C2×M16—22no—
170C2×M16—22no—
171C2×M16—21no—
172C2×M16—21no—
173C2×M16—22no—
174C2×M16—22no—
175C2×M16—22no—
176C2×M16—22no—
177C2×M16—22no—
178C2×M16—22no—
179C2×M16C2×Q812yes—
180C2×M16C2×Q814yes—
181C2×M16C2×Q812yes—
182C2×M16#4112yes—
183C2×M16#4112yes—
184C2×M16#4112yes—
185C2×M16#4112yes—
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—21no—
189C22×C8—22no—
190C22×C8—21no—
191C22×C8—22no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—22no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—21no—
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—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—42no—
217C2×C4⋊C4—42no—
218C2×C4⋊C4—44no—
219C2×C4⋊C4—82no—
220C2×C4⋊C4—84no—
221C2×C4⋊C4C22⋊C411yescharacteristic
222C2×C4⋊C4C22⋊C411yescharacteristic
223C2×C4⋊C4C22⋊C411yescharacteristic
224C2×C4⋊C4C22⋊C411yescharacteristic
225C2×C4⋊C4C22⋊C412yes—
226C2×C4⋊C4C22⋊C412yes—
227C2×C42—22no—
228C2×C42—22no—
229C2×C42—22no—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42—22no—
233C2×C42—44no—
234C2×C42C2×D412yes—
235C2×C42C2×D412yes—
236C2×C42C2×D412yes—
237C2×C42C2×D412yes—
238C2×C42C2×D411yescharacteristic
239C2×C42C2×D411yescharacteristic
240C2×C42C2×D411yescharacteristic
241C2×C42C2×D411yescharacteristic
242C2×C42C2×Q812yes—
243C2×C42C2×Q812yes—
244C2×C42#4112yes—
245C2×C42#4112yes—
246C4⋊C8—24no—
247C4⋊C8—24no—
248C4⋊C8—44no—
249C4⋊C8—44no—
250C4⋊C8—42no—
251C4⋊C8—42no—
252#97—24no—
253#97—44no—
254#97—42no—
255C4×C8—24no—
256C4×C8—44no—
257C4×C8—42no—
258#95—22no—
259#95—22no—
260#95—24no—
261#95—24no—
262#95—24no—
263#95—24no—
264#95—24no—
265#95—24no—
266#95C22⋊C412yes—
267#95C22⋊C412yes—
268#95C22⋊C412yes—
269#95C22⋊C412yes—
270C24C23×C411yescharacteristic
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—24no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—24no—
285C22×C4—22no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4—42no—
289C22×C4—42no—
290C22×C4—42no—
291C22×C4—42no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—44no—
295C22×C4—44no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4C2×C22⋊C412yes—
299C22×C4C2×C22⋊C412yes—
300C22×C4C2×C22⋊C412yes—
301C22×C4C2×C22⋊C412yes—
302C22×C4C2×C22⋊C411yescharacteristic
303C22×C4C2×C22⋊C411yescharacteristic
304C22×C4C2×C22⋊C411yescharacteristic
305C22×C4C2×C22⋊C411yescharacteristic
306C22×C4C4×Q812yes—
307C22×C4C4×Q812yes—
308C22×C4C4×Q812yes—
309C22×C4C4×Q812yes—
310C22×C4C22×D411yescharacteristic
311C22×C4C22×D411yescharacteristic
312C22×C4C22×Q811yescharacteristic
313C22×C4C22×Q811yescharacteristic
314C22×C4C2×#4111yescharacteristic
315C22×C4C2×#4111yescharacteristic
316C22×C4C2×#4111yescharacteristic
317C22×C4C2×#4111yescharacteristic
318C22×C4C2×#4111yescharacteristic
319C22×C4C2×#4111yescharacteristic
320C22×C4H(5,𝔽2)11yescharacteristic
321C22×C4H(5,𝔽2)11yescharacteristic
322C22×C42−1+411yescharacteristic
323C22×C42−1+411yescharacteristic
324M16—22no—
325M16—22no—
326M16—22no—
327M16—22no—
328M16—22no—
329M16—22no—
330M16—22no—
331M16—22no—
332M16—22no—
333M16—24no—
334M16—24no—
335M16—42no—
336M16—42no—
337M16—41no—
338M16—41no—
339M16—41no—
340M16—41no—
341M16—41no—
342M16—41no—
343M16—42no—
344M16—42no—
345M16—42no—
346M16—42no—
347M16#12514yes—
348C2×C8—22no—
349C2×C8—22no—
350C2×C8—22no—
351C2×C8—22no—
352C2×C8—24no—
353C2×C8—22no—
354C2×C8—22no—
355C2×C8—41no—
356C2×C8—41no—
357C2×C8—42no—
358C2×C8—41no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—42no—
362C2×C8—41no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—42no—
366C4⋊C4—22no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—42no—
371C4⋊C4—42no—
372C4⋊C4—44no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—42no—
379C4⋊C4—41no—
380C4⋊C4—42no—
381C4⋊C4—41no—
382C4⋊C4—42no—
383C4⋊C4—41no—
384C4⋊C4—42no—
385C4⋊C4—44no—
386C4⋊C4—82no—
387C4⋊C4—82no—
388C4⋊C4—84no—
389C4⋊C4—84no—
390C42—22no—
391C42—22no—
392C42—22no—
393C42—22no—
394C42—22no—
395C42—22no—
396C42—22no—
397C42—22no—
398C42—44no—
399C42—44no—
400C42C22⋊Q812yes—
401C42C22⋊Q812yes—
402C42C22⋊Q812yes—
403C42C22⋊Q812yes—
404C42#12412yes—
405C42#12412yes—
406C42C4⋊Q812yes—
407C42C4⋊Q812yes—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23C22×C22⋊C411yescharacteristic
413C23C2×C4×Q811yescharacteristic
414C23C2×C4×Q811yescharacteristic
415C23C4×#4111yescharacteristic
416C23C4×#4111yescharacteristic
417C23#52011yescharacteristic
418C23#52011yescharacteristic
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—24no—
426C2×C4—24no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—22no—
430C2×C4—22no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—44no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—44no—
447C2×C4—44no—
448C2×C4—42no—
449C2×C4—42no—
450C2×C4—82no—
451C2×C4—82no—
452C2×C4—82no—
453C2×C4—82no—
454C2×C4—82no—
455C2×C4—82no—
456C2×C4—84no—
457C2×C4—84no—
458C2×C4—82no—
459C2×C4—82no—
460C2×C4#39112yes—
461C2×C4#39112yes—
462C2×C4#39112yes—
463C2×C4#39112yes—
464C2×C4#41312yes—
465C2×C4#41312yes—
466C2×C4C2×C22⋊Q811yescharacteristic
467C2×C4C2×C22⋊Q811yescharacteristic
468C2×C4C2×#12411yescharacteristic
469C2×C4C2×#12511yescharacteristic
470C2×C4#52911yescharacteristic
471C2×C4#52911yescharacteristic
472C2×C4C2×C4⋊Q811yescharacteristic
473C2×C4#53311yescharacteristic
474C2×C4#54011yescharacteristic
475C2×C4#54111yescharacteristic
476C2×C4#54411yescharacteristic
477C2×C4#54411yescharacteristic
478C2×C4#54611yescharacteristic
479C2×C4#54611yescharacteristic
480C2×C4#54711yescharacteristic
481C2×C4#54711yescharacteristic
482C2×C4#54811yescharacteristic
483C2×C4#54811yescharacteristic
484C2×C4#55011yescharacteristic
485C2×C4#55011yescharacteristic
486C2×C4#55211yescharacteristic
487C2×C4#55211yescharacteristic
488C2×C4#55311yescharacteristic
489C2×C4#55311yescharacteristic
490C2×C4#55411yescharacteristic
491C2×C4#55411yescharacteristic
492C2×C4#55711yescharacteristic
493C2×C4#55711yescharacteristic
494C8—24no—
495C8—42no—
496C8—44no—
497C8—42no—
498C8—42no—
499C8—82no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22C2×#39111yescharacteristic
513C22C4×#12511yescharacteristic
514C22#233011yescharacteristic
515C22#233911yescharacteristic
516C22#234111yescharacteristic
517C22#237011yescharacteristic
518C22#237011yescharacteristic
519C22C2×#41311yescharacteristic
520C22C2×#41311yescharacteristic
521C22#288811yescharacteristic
522C22#288911yescharacteristic
523C4—22no—
524C4—22no—
525C4—22no—
526C4—42no—
527C4—42no—
528C4—42no—
529C4—42no—
530C4—82no—
531C4—84no—
532C4—82no—
533C4#199814yes—
534C4#244111yescharacteristic
535C4#244211yescharacteristic
536C4#245311yescharacteristic
537C4#245411yescharacteristic
538C4#248911yescharacteristic
539C4#249011yescharacteristic
540C4#255011yescharacteristic
541C4#255211yescharacteristic
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2#1405411yescharacteristic
547C2C2×#199811yescharacteristic
548C2#2133811yescharacteristic
549C2#2248311yescharacteristic
550C2#2248411yescharacteristic
551C2#2253711yescharacteristic
552C2#2253911yescharacteristic
subgroupG/H
center, socleC23C22×C22⋊C4
commutator, prime radicalC24C23×C4
Frattini, cosocleC23×C4C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×C4×C4⋊C4 ◁ 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×#25712
#211462
C4⋊C4×M162
#113552
#112042
#109132
#108582
#108572
#108472
C4×#3432