Finite Group Databasebeta

← #483300

Subgroups — #483300

Order 512.

658 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#62473C211yesmaximal, characteristic
2#33504C211yesmaximal, characteristic
3#17836C211yesmaximal, characteristic
4#11987C211yesmaximal, characteristic, complemented
5#11984C211yesmaximal, characteristic, complemented
6#11983C211yesmaximal, characteristic, complemented
7#11976C211yesmaximal, characteristic, complemented
8#11975C211yesmaximal, characteristic, complemented
9#11973C211yesmaximal, characteristic, complemented
10#11954C211yesmaximal, characteristic, complemented
11#11953C211yesmaximal, characteristic, complemented
12#11949C211yesmaximal, characteristic, complemented
13#11942C211yesmaximal, characteristic, complemented
14#11939C211yesmaximal, characteristic, complemented
15C2×#1365C211yesmaximal, characteristic, complemented
16#3509—21no—
17#3383—21no—
18#3383C412yes—
19#3342—21no—
20#3342C412yes—
21#3336—21no—
22#3336—21no—
23#3336C412yes—
24#3336C412yes—
25#3231—21no—
26#3231—21no—
27#3229—21no—
28#3170C2211yescharacteristic
29#3170C2211yescharacteristic
30#3170C2211yescharacteristic
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#1365C2211yescharacteristic
60#1365C2211yescharacteristic
61#1365C2211yescharacteristic
62#1365C2211yescharacteristic
63#1364C2211yescharacteristic
64#1364C2211yescharacteristic
65#1364C2211yescharacteristic
66#1364C2211yescharacteristic
67#1362C2211yescharacteristic
68#1362C2211yescharacteristic
69#1362C2211yescharacteristic
70#1362C2211yescharacteristic
71#557—22no—
72#557—41no—
73#556—22no—
74#556—41no—
75#552—22no—
76#552—22no—
77#552—41no—
78#552—41no—
79#541—41no—
80#541—41no—
81#536—41no—
82#533—21no—
83#533—21no—
84#533—21no—
85#533—21no—
86#533—21no—
87C2×C4⋊Q8—21no—
88#519—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#494C2311yescharacteristic
106#487—21no—
107#487—21no—
108#487—21no—
109#485—22no—
110#485—22no—
111#485—22no—
112#485—22no—
113#483—22no—
114#483—22no—
115#479—22no—
116#479—22no—
117#479—22no—
118#479—22no—
119#475—22no—
120#475—22no—
121#467—21no—
122#467—21no—
123#467—21no—
124#467C2×C412yes—
125#467C2×C412yes—
126#467C2×C412yes—
127#446—41no—
128C8×Q8C2×C411yescharacteristic
129C8×Q8D411yescharacteristic
130C4×Q16—21no—
131C4×Q16—21no—
132C4×Q16—21no—
133C4×Q16C2×C412yes—
134C4×Q16C2×C412yes—
135C4×Q16C2×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×#41SD1611yescharacteristic
187C22×Q8—41no—
188C2×Q16—21no—
189C2×Q16C22×C412yes—
190C2×M16—41no—
191C22×C8—41no—
192C22×C8—41no—
193C22×C8C22×C411yescharacteristic
194C22×C8C22×C411yescharacteristic
195C22×C8C22×C411yescharacteristic
196C22×C8C2×D411yescharacteristic
197C22×C8C2×D411yescharacteristic
198C22×C8C2×D411yescharacteristic
199C4⋊Q8—22no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8—21no—
204C4⋊Q8—42no—
205C4⋊Q8—41no—
206C4⋊Q8—41no—
207#126—42no—
208#126—42no—
209#126—42no—
210#126—42no—
211#125—22no—
212#125—22no—
213#125—42no—
214#125—42no—
215#125—42no—
216#125—42no—
217#125—41no—
218#125—41no—
219#125—41no—
220#124—42no—
221#123—42no—
222#123—42no—
223C22⋊Q8—22no—
224C22⋊Q8—22no—
225C22⋊Q8—22no—
226C22⋊Q8—41no—
227C22⋊Q8—41no—
228C22⋊Q8—41no—
229C22⋊Q8—41no—
230C22⋊Q8—41no—
231C22⋊Q8—41no—
232C22⋊Q8—41no—
233C4×Q8—22no—
234C4×Q8—22no—
235C4×Q8—22no—
236C4×Q8—42no—
237C4×Q8—42no—
238C4×Q8—41no—
239C4×Q8—41no—
240C4×Q8—41no—
241C4×Q8—41no—
242C4×Q8—41no—
243C4×Q8—41no—
244C4×Q8—41no—
245C4×Q8C22⋊C411yescharacteristic
246C4×Q8D811yescharacteristic
247C4×D4C22⋊C411yescharacteristic
248C4×D4C22⋊C411yescharacteristic
249C4×D4C22⋊C411yescharacteristic
250C4×D4D811yescharacteristic
251C4×D4D811yescharacteristic
252C4×D4D811yescharacteristic
253#117—22no—
254#117—22no—
255#117—41no—
256#117—41no—
257#117—41no—
258#117—42no—
259#117—42no—
260#117SD1611yescharacteristic
261#117SD1611yescharacteristic
262#117SD1611yescharacteristic
263C2×C4⋊C4—22no—
264C2×C4⋊C4—41no—
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#103—22no—
301#103—22no—
302#103—22no—
303#103—22no—
304#103—22no—
305#103—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—
329C2×Q8—22no—
330C2×Q8—41no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8—42no—
334C2×Q8—84no—
335C2×Q8#10211yescharacteristic
336C2×D4#10211yescharacteristic
337C2×D4#10211yescharacteristic
338C2×D4#10211yescharacteristic
339C22×C4—42no—
340C22×C4C2×C22⋊C411yescharacteristic
341C22×C4C2×C22⋊C411yescharacteristic
342C22×C4C2×C22⋊C411yescharacteristic
343C22×C4C2×D811yescharacteristic
344C22×C4C2×D811yescharacteristic
345C22×C4C2×D811yescharacteristic
346C22×C4C2×SD1611yescharacteristic
347C22×C4C2×SD1611yescharacteristic
348C22×C4C2×SD1611yescharacteristic
349Q16—42no—
350Q16—41no—
351Q16—41no—
352M16—161no—
353C2×C8—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—41no—
360C2×C8—41no—
361C2×C8—41no—
362C2×C8—41no—
363C2×C8—41no—
364C2×C8—41no—
365C2×C8—41no—
366C2×C8—161no—
367C2×C8—161no—
368C2×C8C2×C22⋊C411yescharacteristic
369C2×C8C2×C22⋊C411yescharacteristic
370C2×C8C2×C22⋊C411yescharacteristic
371C2×C8C2×C22⋊C411yescharacteristic
372C2×C8C2×C22⋊C411yescharacteristic
373C2×C8C2×C22⋊C411yescharacteristic
374C2×C8C23×C411yescharacteristic
375C2×C8C22×D411yescharacteristic
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—42no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4—42no—
389C4⋊C4—42no—
390C4⋊C4—42no—
391C4⋊C4—42no—
392C4⋊C4—42no—
393C4⋊C4—42no—
394C4⋊C4—42no—
395C4⋊C4—42no—
396C4⋊C4#10211yescharacteristic
397C4⋊C4#10211yescharacteristic
398C4⋊C4#10211yescharacteristic
399C4⋊C4#10211yescharacteristic
400C4⋊C4#10211yescharacteristic
401C4⋊C4#10211yescharacteristic
402C22⋊C4—42no—
403C22⋊C4—42no—
404C22⋊C4—42no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C22⋊C4#10211yescharacteristic
408C22⋊C4#10211yescharacteristic
409C22⋊C4#10211yescharacteristic
410C22⋊C4#10211yescharacteristic
411C22⋊C4#10211yescharacteristic
412C22⋊C4#10211yescharacteristic
413C42—42no—
414C42—42no—
415C42—42no—
416C42—42no—
417C42—42no—
418C42C2×C22⋊C411yescharacteristic
419C42C2×C22⋊C411yescharacteristic
420C42C2×C22⋊C411yescharacteristic
421C42C2×D811yescharacteristic
422C42C2×D811yescharacteristic
423C42C2×D811yescharacteristic
424C42C2×SD1611yescharacteristic
425C42C2×SD1611yescharacteristic
426C42C2×SD1611yescharacteristic
427C42C22×D411yescharacteristic
428C16—41no—
429C16—41no—
430C16—41no—
431C16—41no—
432C23C2×#10211yescharacteristic
433C23C2×#10211yescharacteristic
434C23C2×#10211yescharacteristic
435Q8—41no—
436Q8—42no—
437Q8—42no—
438Q8—82no—
439Q8—82no—
440Q8—84no—
441Q8—81no—
442Q8—81no—
443D4—22no—
444D4—22no—
445D4—41no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—84no—
466C2×C4C2×#10211yescharacteristic
467C2×C4C2×#10211yescharacteristic
468C2×C4C2×#10211yescharacteristic
469C2×C4C2×#10211yescharacteristic
470C2×C4C2×#10211yescharacteristic
471C2×C4C2×#10211yescharacteristic
472C2×C4C2×#10211yescharacteristic
473C2×C4C2×#10211yescharacteristic
474C2×C4C2×#10211yescharacteristic
475C2×C4C22×C22⋊C411yescharacteristic
476C2×C4C22×D811yescharacteristic
477C2×C4C22×SD1611yescharacteristic
478C8—21no—
479C8—21no—
480C8—21no—
481C8—21no—
482C8—21no—
483C8—21no—
484C8—21no—
485C8—81no—
486C8—81no—
487C8—81no—
488C8—81no—
489C8#57711yescharacteristic
490C8#57811yescharacteristic
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22#214812yes—
500C22C22×#10211yescharacteristic
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—21no—
506C4—21no—
507C4—21no—
508C4—21no—
509C4—21no—
510C4—21no—
511C4—82no—
512C4—82no—
513C4—82no—
514C4—82no—
515C4#288911yescharacteristic
516C4#289811yescharacteristic
517C4#341611yescharacteristic
518C4#341711yescharacteristic
519C2—22no—
520C2—41no—
521C2—41no—
522C2#1772111yescharacteristic
523C2#3338211yescharacteristic
524C2C2×#214811yescharacteristic
subgroupG/H
center, socleC22C22×#102
commutatorC2×C8C23×C4
Frattini, cosocleC4×C8C24
prime radicalC2×#41SD16
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
4. #11987C2semidirect
5. #11984C2semidirect
6. #11983C2semidirect
7. #11976C2semidirect
8. #11975C2semidirect
9. #11973C2semidirect
10. #11954C2semidirect
11. #11953C2semidirect
12. #11949C2semidirect
13. #11942C2semidirect
14. #11939C2semidirect
15. C2×#1365C2semidirect

Maximal subgroups

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

subgroupindex
#624732
#335042
#178362
#119872
#119842
#119832
#119762
#119752
#119732
#119542
#119532
#119492
#119422
#119392
C2×#13652