Finite Group Databasebeta

← #483297

Subgroups — #483297

Order 512.

686 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62474C211yesmaximal, characteristic
2#33504C211yesmaximal, characteristic, complemented
3#17836C211yesmaximal, characteristic, complemented
4#11985C211yesmaximal, characteristic, complemented
5#11982C211yesmaximal, characteristic, complemented
6#11981C211yesmaximal, characteristic, complemented
7#11976C211yesmaximal, characteristic, complemented
8#11974C211yesmaximal, characteristic, complemented
9#11973C211yesmaximal, characteristic, complemented
10#11952C211yesmaximal, characteristic, complemented
11#11951C211yesmaximal, characteristic, complemented
12#11947C211yesmaximal, characteristic, complemented
13#11942C211yesmaximal, characteristic, complemented
14#11939C211yesmaximal, characteristic, complemented
15C2×#1364C211yesmaximal, characteristic, complemented
16#3511—21no—
17#3380—21no—
18#3380C412yes—
19#3341—21no—
20#3341C412yes—
21#3339—21no—
22#3339—21no—
23#3339C412yes—
24#3339C412yes—
25#3228—21no—
26#3228—21no—
27#3227—21no—
28#3169C2211yescharacteristic
29#3169C2211yescharacteristic
30#3169C2211yescharacteristic
31#3160C2211yescharacteristic
32#3160C2211yescharacteristic
33C2×#500C2211yescharacteristic
34#2990—21no—
35C8×#41C2211yescharacteristic
36#2183—21no—
37#2168—21no—
38#2168—21no—
39D4×C16—21no—
40#2163C2211yescharacteristic
41#2163C2211yescharacteristic
42#2162C2211yescharacteristic
43#2150C2211yescharacteristic
44C2×C4⋊C16C2211yescharacteristic
45C2×C4⋊C16C2211yescharacteristic
46#1574—21no—
47#1573—21no—
48#1573—21no—
49#1568C2211yescharacteristic
50#1568C2211yescharacteristic
51#1567C2211yescharacteristic
52#1564C2211yescharacteristic
53C2×#335C2211yescharacteristic
54C2×#335C2211yescharacteristic
55#1365C2211yescharacteristic
56#1365C2211yescharacteristic
57#1365C2211yescharacteristic
58#1365C2211yescharacteristic
59#1364C2211yescharacteristic
60#1364C2211yescharacteristic
61#1364C2211yescharacteristic
62#1364C2211yescharacteristic
63#1364C2211yescharacteristic
64#1364C2211yescharacteristic
65#1364C2211yescharacteristic
66#1364C2211yescharacteristic
67#1361C2211yescharacteristic
68#1361C2211yescharacteristic
69#1361C2211yescharacteristic
70#1361C2211yescharacteristic
71#556—41no—
72#555—22no—
73#554—22no—
74#553—22no—
75#553—22no—
76#548—41no—
77#548—41no—
78#547—41no—
79#542—41no—
80#542—41no—
81#537—41no—
82#533—21no—
83#533—21no—
84#532—21no—
85#532—21no—
86#532—21no—
87C2×C4⋊Q8—21no—
88#520—41no—
89C4×#41D411yescharacteristic
90C2×M32—21no—
91C22×C16—21no—
92C22×C16—21no—
93#500—21no—
94#500—21no—
95#500C2×C412yes—
96#500C2311yescharacteristic
97#500C2311yescharacteristic
98#500C2311yescharacteristic
99#499—21no—
100#499—21no—
101#499C2×C412yes—
102#499C2×C412yes—
103#498—21no—
104#498—21no—
105#493C2311yescharacteristic
106#486—21no—
107#486—21no—
108#486—21no—
109#482—22no—
110#482—22no—
111#482—22no—
112#482—22no—
113#481—22no—
114#481—22no—
115#478—22no—
116#478—22no—
117#478—22no—
118#478—22no—
119#476—22no—
120#476—22no—
121#466—21no—
122#466—21no—
123#466—21no—
124#466C2×C412yes—
125#466C2×C412yes—
126#466C2×C412yes—
127#446—41no—
128C8×Q8C2×C411yescharacteristic
129C8×Q8D411yescharacteristic
130C4×D8—21no—
131C4×D8—21no—
132C4×D8—21no—
133C4×D8C2×C412yes—
134C4×D8C2×C412yes—
135C4×D8C2×C412yes—
136#435—41no—
137#435—41no—
138C8×D4—41no—
139C8×D4C2×C411yescharacteristic
140C8×D4C2×C411yescharacteristic
141C8×D4C2×C411yescharacteristic
142C8×D4D411yescharacteristic
143C8×D4D411yescharacteristic
144C8×D4D411yescharacteristic
145#432—21no—
146#432—21no—
147#431—21no—
148#431D411yescharacteristic
149#431D411yescharacteristic
150#431D411yescharacteristic
151#427—21no—
152#427—21no—
153#427C2×C412yes—
154#427C2×C412yes—
155C2×#107—21no—
156C2×#107C2×C412yes—
157#423—21no—
158C2×C4⋊C8—21no—
159C2×C4⋊C8—21no—
160C2×C4×C8C2311yescharacteristic
161C2×C4×C8C2311yescharacteristic
162C2×C4×C8C2311yescharacteristic
163C4⋊C16—21no—
164C4⋊C16—21no—
165C4⋊C16—21no—
166C4⋊C16C2311yescharacteristic
167C4⋊C16C2311yescharacteristic
168C4⋊C16C2311yescharacteristic
169C4⋊C16C2311yescharacteristic
170C22⋊C16—21no—
171C22⋊C16—21no—
172C22⋊C16—21no—
173#346—21no—
174#346—21no—
175C4×C16—21no—
176#335—21no—
177#335—21no—
178#335—21no—
179#335C2311yescharacteristic
180#335C2311yescharacteristic
181#335C2311yescharacteristic
182#335C2311yescharacteristic
183#334—21no—
184#334—21no—
185#334—21no—
186C2×#41—41no—
187C2×#41—41no—
188C2×#41—41no—
189C2×#41SD1611yescharacteristic
190C22×Q8—41no—
191C2×D8—21no—
192C2×D8C22×C412yes—
193C2×M16—41no—
194C22×C8—41no—
195C22×C8—41no—
196C22×C8C22×C411yescharacteristic
197C22×C8C22×C411yescharacteristic
198C22×C8C22×C411yescharacteristic
199C22×C8C2×D411yescharacteristic
200C22×C8C2×D411yescharacteristic
201C22×C8C2×D411yescharacteristic
202C4⋊Q8—22no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205C4⋊Q8—21no—
206C4⋊Q8—41no—
207C4⋊Q8—41no—
208#127—21no—
209#126—42no—
210#126—42no—
211#125—22no—
212#125—22no—
213#124—42no—
214#124—42no—
215#124—41no—
216#124—41no—
217#124—41no—
218#123—42no—
219#123—42no—
220C22⋊Q8—42no—
221C22⋊Q8—41no—
222C22⋊Q8—41no—
223C22⋊Q8—41no—
224C22⋊Q8—41no—
225C22⋊Q8—42no—
226C22⋊Q8—42no—
227#121—22no—
228#121—22no—
229#121—22no—
230#121—42no—
231#121—42no—
232#121—42no—
233#121—41no—
234#121—41no—
235#121—41no—
236C4×Q8—41no—
237C4×Q8—41no—
238C4×Q8—41no—
239C4×Q8—41no—
240C4×Q8C22⋊C411yescharacteristic
241C4×Q8D811yescharacteristic
242C4×D4—22no—
243C4×D4—22no—
244C4×D4—22no—
245C4×D4—42no—
246C4×D4—42no—
247C4×D4—41no—
248C4×D4—41no—
249C4×D4—41no—
250C4×D4C22⋊C411yescharacteristic
251C4×D4C22⋊C411yescharacteristic
252C4×D4C22⋊C411yescharacteristic
253C4×D4D811yescharacteristic
254C4×D4D811yescharacteristic
255C4×D4D811yescharacteristic
256#117—22no—
257#117—22no—
258#117—42no—
259#117SD1611yescharacteristic
260#117SD1611yescharacteristic
261#117SD1611yescharacteristic
262C2×C4⋊C4—22no—
263C2×C4⋊C4—41no—
264C2×C4⋊C4—42no—
265C2×C42C2×D411yescharacteristic
266C2×C42C2×D411yescharacteristic
267C2×C42C2×D411yescharacteristic
268M32—81no—
269C2×C16—21no—
270C2×C16—21no—
271C2×C16—21no—
272C2×C16—21no—
273C2×C16—81no—
274C2×C16—81no—
275#107—22no—
276#107—22no—
277#107—21no—
278#107—21no—
279#107—21no—
280#107C22×C412yes—
281#107C22×C412yes—
282#107C22×C412yes—
283#106—22no—
284#106—22no—
285#106—22no—
286#106—22no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8—21no—
290C4⋊C8—21no—
291C4⋊C8—41no—
292C4⋊C8—41no—
293C4⋊C8—41no—
294C4⋊C8C22⋊C411yescharacteristic
295C4⋊C8C22⋊C411yescharacteristic
296C4⋊C8C22⋊C411yescharacteristic
297C4⋊C8C22⋊C411yescharacteristic
298C4⋊C8C22⋊C411yescharacteristic
299C4⋊C8C22⋊C411yescharacteristic
300#102—22no—
301#102—22no—
302#102—22no—
303#102—22no—
304#102—22no—
305#102—22no—
306C22⋊C8—41no—
307C22⋊C8—41no—
308C22⋊C8—41no—
309C22⋊C8C22⋊C411yescharacteristic
310C22⋊C8C22⋊C411yescharacteristic
311C22⋊C8C22⋊C411yescharacteristic
312C22⋊C8C22⋊C411yescharacteristic
313C22⋊C8C22⋊C411yescharacteristic
314C22⋊C8C22⋊C411yescharacteristic
315#97—41no—
316#97—41no—
317C4×C8—41no—
318C4×C8C22×C411yescharacteristic
319C4×C8C22×C411yescharacteristic
320C4×C8C22×C411yescharacteristic
321C4×C8C2×D411yescharacteristic
322C4×C8C2×D411yescharacteristic
323C4×C8C2×D411yescharacteristic
324C4×C8C2×D411yescharacteristic
325C4×C8C2×D411yescharacteristic
326C4×C8C2×D411yescharacteristic
327C4×C8C2411yescharacteristic
328#41—42no—
329#41—84no—
330#41—161no—
331#41—161no—
332#41—161no—
333#41—161no—
334C2×Q8—41no—
335C2×Q8—41no—
336C2×Q8—41no—
337C2×Q8—42no—
338C2×Q8—161no—
339C2×Q8—161no—
340C2×Q8#10211yescharacteristic
341C2×D4—22no—
342C2×D4—42no—
343C2×D4—42no—
344C2×D4—42no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4#10211yescharacteristic
348C2×D4#10211yescharacteristic
349C2×D4#10211yescharacteristic
350C22×C4—42no—
351C22×C4—42no—
352C22×C4—42no—
353C22×C4—42no—
354C22×C4C2×C22⋊C411yescharacteristic
355C22×C4C2×C22⋊C411yescharacteristic
356C22×C4C2×C22⋊C411yescharacteristic
357C22×C4C2×D811yescharacteristic
358C22×C4C2×D811yescharacteristic
359C22×C4C2×D811yescharacteristic
360C22×C4C2×SD1611yescharacteristic
361C22×C4C2×SD1611yescharacteristic
362C22×C4C2×SD1611yescharacteristic
363D8—42no—
364D8—41no—
365D8—41no—
366M16—161no—
367C2×C8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C2×C8—161no—
381C2×C8—161no—
382C2×C8C2×C22⋊C411yescharacteristic
383C2×C8C2×C22⋊C411yescharacteristic
384C2×C8C2×C22⋊C411yescharacteristic
385C2×C8C2×C22⋊C411yescharacteristic
386C2×C8C2×C22⋊C411yescharacteristic
387C2×C8C2×C22⋊C411yescharacteristic
388C2×C8C23×C411yescharacteristic
389C2×C8C22×D411yescharacteristic
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—42no—
397C4⋊C4—42no—
398C4⋊C4—42no—
399C4⋊C4—42no—
400C4⋊C4—42no—
401C4⋊C4—42no—
402C4⋊C4#10211yescharacteristic
403C4⋊C4#10211yescharacteristic
404C4⋊C4#10211yescharacteristic
405C4⋊C4#10211yescharacteristic
406C4⋊C4#10211yescharacteristic
407C4⋊C4#10211yescharacteristic
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—42no—
411C22⋊C4—42no—
412C22⋊C4—42no—
413C22⋊C4—42no—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C22⋊C4#10211yescharacteristic
417C22⋊C4#10211yescharacteristic
418C22⋊C4#10211yescharacteristic
419C22⋊C4#10211yescharacteristic
420C22⋊C4#10211yescharacteristic
421C22⋊C4#10211yescharacteristic
422C42—42no—
423C42—42no—
424C42C2×C22⋊C411yescharacteristic
425C42C2×C22⋊C411yescharacteristic
426C42C2×C22⋊C411yescharacteristic
427C42C2×D811yescharacteristic
428C42C2×D811yescharacteristic
429C42C2×D811yescharacteristic
430C42C2×SD1611yescharacteristic
431C42C2×SD1611yescharacteristic
432C42C2×SD1611yescharacteristic
433C42C22×D411yescharacteristic
434C16—41no—
435C16—41no—
436C16—41no—
437C16—41no—
438C23—42no—
439C23C2×#10211yescharacteristic
440C23C2×#10211yescharacteristic
441C23C2×#10211yescharacteristic
442Q8—41no—
443Q8—82no—
444Q8—81no—
445Q8—81no—
446Q8—81no—
447Q8—81no—
448Q8—162no—
449D4—22no—
450D4—22no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—82no—
455D4—84no—
456D4—81no—
457D4—81no—
458D4—162no—
459D4—162no—
460C2×C4—22no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—84no—
479C2×C4—162no—
480C2×C4—162no—
481C2×C4—162no—
482C2×C4C2×#10211yescharacteristic
483C2×C4C2×#10211yescharacteristic
484C2×C4C2×#10211yescharacteristic
485C2×C4C2×#10211yescharacteristic
486C2×C4C2×#10211yescharacteristic
487C2×C4C2×#10211yescharacteristic
488C2×C4C2×#10211yescharacteristic
489C2×C4C2×#10211yescharacteristic
490C2×C4C2×#10211yescharacteristic
491C2×C4C22×C22⋊C411yescharacteristic
492C2×C4C22×D811yescharacteristic
493C2×C4C22×SD1611yescharacteristic
494C8—21no—
495C8—21no—
496C8—21no—
497C8—21no—
498C8—21no—
499C8—21no—
500C8—21no—
501C8—81no—
502C8—81no—
503C8—81no—
504C8—81no—
505C8#57711yescharacteristic
506C8#57811yescharacteristic
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—82no—
516C22—82no—
517C22—82no—
518C22#214812yes—
519C22C22×#10211yescharacteristic
520C4—21no—
521C4—21no—
522C4—21no—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—82no—
531C4—82no—
532C4—82no—
533C4#288911yescharacteristic
534C4#289811yescharacteristic
535C4#341511yescharacteristic
536C4#341611yescharacteristic
537C2—22no—
538C2—41no—
539C2—41no—
540C2—162no—
541C2#1772111yescharacteristic
542C2#3338111yescharacteristic
543C2C2×#214811yescharacteristic
subgroupG/H
center, socleC22C22×#102
commutatorC2×C8C23×C4
Frattini, cosocleC4×C8C24
prime radical#62474C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C4×#41 ◁ C8×#41 ◁ G
LECSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #33504C2semidirect
3. #17836C2semidirect
4. #11985C2semidirect
5. #11982C2semidirect
6. #11981C2semidirect
7. #11976C2semidirect
8. #11974C2semidirect
9. #11973C2semidirect
10. #11952C2semidirect
11. #11951C2semidirect
12. #11947C2semidirect
13. #11942C2semidirect
14. #11939C2semidirect
15. C2×#1364C2semidirect

Maximal subgroups

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

subgroupindex
#624742
#335042
#178362
#119852
#119822
#119812
#119762
#119742
#119732
#119522
#119512
#119472
#119422
#119392
C2×#13642