Finite Group Databasebeta

← #11860714

Subgroups — #11860714

Order 1152.

1476 conjugacy classes of subgroups.

The subgroup lattice has 549 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×C3⋊D3C211yesmaximal, characteristic
2#10596043C211yesmaximal, characteristic, complemented
3#10596016C211yesmaximal, characteristic
4C32×C4×SD16C211yesmaximal, characteristic, complemented
5SD16×C3⋊Dic3C211yesmaximal, characteristic, complemented
6#10592725C211yesmaximal, characteristic, complemented
7#10592717C211yesmaximal, characteristic, complemented
8#10592559C211yesmaximal, characteristic, complemented
9#10592551C211yesmaximal, characteristic, complemented
10#10592516C211yesmaximal, characteristic, complemented
11#10592501C211yesmaximal, characteristic, complemented
12#10592469C211yesmaximal, characteristic
13#10592456C211yesmaximal, characteristic, complemented
14C4×#3744C211yesmaximal, characteristic, complemented
15#10592388C211yesmaximal, characteristic, complemented
16#79649—34nomaximal
17C2×Q8×C3⋊D3C2211yescharacteristic
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×C32×SD16C2211yescharacteristic
20C32×C4×Q8C2211yescharacteristic, complemented
21C32×C4×D4C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3755C2211yescharacteristic
24D4×C3⋊Dic3C2211yescharacteristic
25C2×#3754C2211yescharacteristic
26C4×#638—21no—
27C2×#3752—21no—
28SD16×C3⋊D3C418yescomplemented
29C2×#3744C2211yescharacteristic
30C2×#3743C2211yescharacteristic
31C2×C8×C3⋊D3C2211yescharacteristic
32#64102C2211yescharacteristic
33#64101—21no—
34#64101C2211yescharacteristic
35#64101C2211yescharacteristic
36#64096—21no—
37#64096C2211yescharacteristic, complemented
38#64090—21no—
39C22⋊C4×C3⋊D3—21no—
40C4×C4⋊(C3⋊D3)C2211yescharacteristic
41#64081—21no—
42#64081C2211yescharacteristic
43C4×#634—21no—
44C4×#634C2211yescharacteristic, complemented
45C32×#106C2211yescharacteristic, complemented
46C32×#103C2211yescharacteristic, complemented
47C32×#102C2211yescharacteristic
48C32×C4×C8C2211yescharacteristic, complemented
49#63662C2211yescharacteristic, complemented
50#63659C2211yescharacteristic
51#63648C2211yescharacteristic
52#63644C2211yescharacteristic, complemented
53#63643C2211yescharacteristic, complemented
54#63642C2211yescharacteristic, complemented
55C8×C3⋊Dic3C2211yescharacteristic, complemented
56#63637C2211yescharacteristic, complemented
57#63636C2211yescharacteristic
58#63634C2211yescharacteristic, complemented
59#63634C2211yescharacteristic, complemented
60#63630C2211yescharacteristic, complemented
61C2×D3×SD16—34no—
62#5572—34no—
63#5545—34no—
64C3×C4×SD16D314yescomplemented
65Dic3×SD16—34no—
66#5026—34no—
67#5018—34no—
68#4860—34no—
69#4852—34no—
70#4817—34no—
71#4802—34no—
72#4770—34no—
73#4757—34no—
74C4×#204—34no—
75#4689—34no—
76C23×C3⋊D3—21no—
77C2×C32×Q8C2311yescharacteristic
78C2×C32×D4C2311yescharacteristic
79C22×C32×C4—21no—
80C2×#638—21no—
81C22×C3⋊Dic3—21no—
82Q8×C3⋊D3—22no—
83Q8×C3⋊D3C2×C414yescomplemented
84D4×C3⋊D3—22no—
85D4×C3⋊D3C2×C414yes—
86C2×C4⋊(C3⋊D3)C2311yescharacteristic
87C2×C4×C3⋊D3—21no—
88C2×C4×C3⋊D3—21no—
89C2×C4×C3⋊D3—21no—
90C2×C4×C3⋊D3C2311yescharacteristic
91C2×#634—21no—
92C2×#634C2311yescharacteristic
93C32×SD16C2×C414yescomplemented
94C2×C32×C8C2311yescharacteristic
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4—21no—
97C32×C4⋊C4C2311yescharacteristic
98C32×C4⋊C4C2311yescharacteristic
99C32×C22⋊C4—21no—
100C32×C42—21no—
101C32×C42C2311yescharacteristic
102#3757—21no—
103#3755C2×C414yescomplemented
104#3754C2×C414yescomplemented
105#3752—21no—
106#3752—21no—
107#3752—21no—
108#3752—21no—
109#3752D411yescharacteristic
110#3752D411yescharacteristic
111C4⋊(C3⋊Dic3)—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3750—21no—
116#3750D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3—21no—
119C4×C3⋊Dic3—21no—
120C4×C3⋊Dic3—21no—
121C4×C3⋊Dic3—21no—
122C4×C3⋊Dic3—21no—
123C4×C3⋊Dic3C2311yescharacteristic
124C2×C3⋊(C3⋊C8)C2311yescharacteristic
125C2×C3⋊(C3⋊C8)C2311yescharacteristic
126#3744C2×C414yescomplemented
127#3743—22no—
128C8×C3⋊D3C2×C414yescomplemented
129#2949—91noSylow
130C2×D3×Q8—34no—
131C2×D3×D4—34no—
132C2×C3×SD16C2×D314yes—
133C3×C4×Q8C2×D314yescomplemented
134C3×C4×D4C2×D314yes—
135Q8×Dic3—34no—
136C2×#215—34no—
137D4×Dic3—34no—
138C2×#214—34no—
139C4×#67—64no—
140C2×(C2×D3)⋊C4—64no—
141D3×SD16—332no—
142C2×#204—34no—
143C2×ΓL(1,𝔽25)—34no—
144C2×D3×C8—34no—
145#893—34no—
146#892—34no—
147#892—34no—
148#892—64no—
149#887—34no—
150#887—64no—
151#67⋊C4—64no—
152D3×C22⋊C4—64no—
153C4×D12—34no—
154#872—34no—
155#872—64no—
156C4×Dic6—34no—
157C4×Dic6—64no—
158C3×#106C2×D314yescomplemented
159C3×#103C2×D314yescomplemented
160C3×#102C2×D314yes—
161C3×C4×C8C2×D314yescomplemented
162#835—34no—
163#832—34no—
164#821—34no—
165#817—34no—
166#816—34no—
167#815—34no—
168C8×Dic3—34no—
169#810—34no—
170#809—34no—
171#807—34no—
172#807—34no—
173#803—34no—
174C23×C32—21no—
175C22×C3⋊D3—21no—
176C22×C3⋊D3—24no—
177C22×C3⋊D3—81no—
178C22×C3⋊D3—81no—
179C22×C3⋊D3C2×D411yescharacteristic
180C32×Q8—21no—
181C32×Q8C22×C412yes—
182C32×D4—21no—
183C32×D4C22×C412yes—
184C2×C32×C4—21no—
185C2×C32×C4—21no—
186C2×C32×C4—21no—
187C2×C32×C4—81no—
188C2×C32×C4C2×D411yescharacteristic
189C2×C32×C4C2×D411yescharacteristic
190C2×C32×C4C2411yescharacteristic
191#638—24no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—81no—
196C2×C3⋊Dic3C2×D411yescharacteristic
197C2×C3⋊Dic3C2×D411yescharacteristic
198C2×C3⋊Dic3C2×D411yescharacteristic
199C4⋊(C3⋊D3)—21no—
200C4⋊(C3⋊D3)C22×C412yes—
201C4×C3⋊D3—24no—
202C4×C3⋊D3—81no—
203C4×C3⋊D3—81no—
204C4×C3⋊D3C22×C412yes—
205C4×C3⋊D3#4112yes—
206#634—21no—
207#634—24no—
208#634C22×C412yes—
209C32×C8—21no—
210C32×C8C22×C412yes—
211C3⋊(C3⋊C8)—21no—
212C3⋊(C3⋊C8)C22×C412yes—
213C22×SD16—91no—
214#519—91no—
215#518—91no—
216#440—91no—
217#440—91no—
218#440—91no—
219#440—91no—
220C4×SD16—91no—
221C4×SD16—91no—
222C4×SD16—91no—
223C4×SD16C3⋊D311yescharacteristic, complemented
224#427—91no—
225#419—91no—
226#418—91no—
227#405—91no—
228C23×D3—64no—
229C2×C3×Q8C22×D314yes—
230C2×C3×D4C22×D314yes—
231C22×C3×C4—24no—
232C2×#67—64no—
233C22×Dic3—64no—
234D3×Q8—316no—
235D3×Q8—68no—
236D3×D4—316no—
237D3×D4—68no—
238C2×D12—34no—
239C2×C4×D3—34no—
240C2×C4×D3—64no—
241C2×C4×D3—64no—
242C2×C4×D3—64no—
243C2×Dic6—34no—
244C2×Dic6—64no—
245C3×SD16C4×D3116yescomplemented
246C2×C3×C8C22×D314yes—
247C2×C3×C8C22×D314yes—
248C3×C4⋊C4—24no—
249C3×C4⋊C4C22×D314yes—
250C3×C4⋊C4C22×D314yes—
251C3×C22⋊C4—24no—
252C3×C42—24no—
253C3×C42C22×D314yes—
254#217—64no—
255#215—316no—
256#214—316no—
257(C2×D3)⋊C4—34no—
258(C2×D3)⋊C4—34no—
259(C2×D3)⋊C4—64no—
260(C2×D3)⋊C4—64no—
261(C2×D3)⋊C4—64no—
262(C2×D3)⋊C4—64no—
263C4⋊Dic3—34no—
264C4⋊Dic3—34no—
265C4⋊Dic3—64no—
266Dic3⋊C4—34no—
267Dic3⋊C4—34no—
268Dic3⋊C4—64no—
269Dic3⋊C4—64no—
270C4×Dic3—34no—
271C4×Dic3—64no—
272C4×Dic3—64no—
273C4×Dic3—64no—
274C4×Dic3—64no—
275C4×Dic3—64no—
276C2×C3⋊C8—34no—
277C2×C3⋊C8—34no—
278#204—316no—
279ΓL(1,𝔽25)—68no—
280D3×C8—316no—
281C22×C32—22no—
282C22×C32—41no—
283C22×C32—41no—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—21no—
286C2×C3⋊D3—21no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—41no—
289C2×C3⋊D3—41no—
290C2×C3⋊D3—84no—
291C2×C3⋊D3C4×D412yes—
292C32×C4—22no—
293C32×C4—21no—
294C32×C4—21no—
295C32×C4—41no—
296C32×C4—41no—
297C32×C4C23×C411yescharacteristic
298C32×C4C2×#4111yescharacteristic
299C3⋊Dic3—22no—
300C3⋊Dic3—21no—
301C3⋊Dic3—21no—
302C3⋊Dic3—41no—
303C3⋊Dic3—41no—
304C3⋊Dic3C4×D412yes—
305C22×Q8—91no—
306C22×D4—91no—
307C2×SD16—91no—
308C2×SD16—91no—
309C2×SD16—98no—
310C2×SD16—91no—
311C2×SD16C2×C3⋊D311yescharacteristic
312C2×M16—91no—
313C22×C8—91no—
314C4×Q8—91no—
315C4×Q8—91no—
316C4×Q8—91no—
317C4×Q8—181no—
318C4×Q8—181no—
319C4×Q8C2×C3⋊D311yescharacteristic, complemented
320C4×D4—91no—
321C4×D4—91no—
322C4×D4—91no—
323C4×D4—181no—
324C4×D4—181no—
325C4×D4C2×C3⋊D311yescharacteristic
326#117—91no—
327#117—91no—
328#117—91no—
329#117—181no—
330#117—181no—
331C2×C22⋊C4—181no—
332C2×C22⋊C4—181no—
333#107—91no—
334#107—91no—
335#106—91no—
336#106C2×C3⋊D311yescharacteristic, complemented
337#103—91no—
338#103—91no—
339#103—91no—
340#103C2×C3⋊D311yescharacteristic, complemented
341#102—91no—
342#102—91no—
343#102—91no—
344#102C2×C3⋊D311yescharacteristic
345#97—91no—
346#97—91no—
347C4×C8—91no—
348C4×C8C2×C3⋊D311yescharacteristic, complemented
349C23×C3—24no—
350C22×D3—34no—
351C22×D3—616no—
352C22×D3—64no—
353C22×D3—244no—
354C22×D3—244no—
355C3×Q8—24no—
356C3×Q8C2×C4×D318yes—
357C3×D4—24no—
358C3×D4C2×C4×D318yes—
359C2×C3×C4—24no—
360C2×C3×C4—24no—
361C2×C3×C4—24no—
362C2×C3×C4—84no—
363C2×C3×C4D3×D414yes—
364C2×C3×C4D3×D414yes—
365C2×C3×C4C23×D314yes—
366#67—616no—
367C2×Dic3—34no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—244no—
374D12—38no—
375D12—64no—
376C4×D3—38no—
377C4×D3—38no—
378C4×D3—616no—
379C4×D3—244no—
380C4×D3—244no—
381Dic6—38no—
382Dic6—616no—
383Dic6—64no—
384C3×C8—24no—
385C3×C8C2×C4×D318yes—
386C3⋊C8—38no—
387C3⋊C8—64no—
388C2×C32—42no—
389C2×C32C2×C4×D411yescharacteristic
390C2×C32#57711yescharacteristic
391C2×C32#57711yescharacteristic
392C3⋊D3—22no—
393C3⋊D3—42no—
394C24—181no—
395C2×Q8—94no—
396C2×Q8—91no—
397C2×Q8—181no—
398C2×Q8—182no—
399C2×Q8C22×C3⋊D311yescharacteristic
400C2×D4—94no—
401C2×D4—91no—
402C2×D4—182no—
403C2×D4—181no—
404C2×D4C22×C3⋊D311yescharacteristic
405C22×C4—21no—
406C22×C4—91no—
407C22×C4—181no—
408C22×C4—181no—
409C22×C4—181no—
410C22×C4—181no—
411SD16—94no—
412SD16—94no—
413SD16—94no—
414SD16C4×C3⋊D314yescomplemented
415M16—182no—
416C2×C8—91no—
417C2×C8—94no—
418C2×C8—91no—
419C2×C8C22×C3⋊D311yescharacteristic
420C2×C8C22×C3⋊D311yescharacteristic
421C4⋊C4—21no—
422C4⋊C4—91no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—91no—
426C4⋊C4—181no—
427C4⋊C4—181no—
428C4⋊C4—181no—
429C4⋊C4C22×C3⋊D311yescharacteristic
430C4⋊C4C22×C3⋊D311yescharacteristic
431C22⋊C4—21no—
432C22⋊C4—91no—
433C22⋊C4—91no—
434C22⋊C4—181no—
435C22⋊C4—181no—
436C22⋊C4—181no—
437C22⋊C4—181no—
438C22⋊C4—181no—
439C42—21no—
440C42—91no—
441C42—181no—
442C42—181no—
443C42—181no—
444C42—181no—
445C42—181no—
446C42C22×C3⋊D311yescharacteristic
447C22×C3—28no—
448C22×C3—44no—
449C22×C3—44no—
450C22×C3C2×D3×D414yes—
451C2×D3—38no—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—68no—
455C2×D3—124no—
456C2×D3—124no—
457C2×D3—2416no—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4—28no—
461C3×C4—44no—
462C3×C4—44no—
463C3×C4C22×C4×D314yes—
464C3×C4D3×#4114yes—
465Dic3—38no—
466Dic3—64no—
467Dic3—64no—
468Dic3—68no—
469Dic3—124no—
470Dic3—124no—
471C32#294911yescharacteristic, complemented, Sylow
472C23—21no—
473C23—91no—
474C23—184no—
475C23—181no—
476C23—721no—
477C23—721no—
478Q8—21no—
479Q8—92no—
480Q8—184no—
481Q8—181no—
482Q8C2×C4×C3⋊D312yes—
483D4—21no—
484D4—92no—
485D4—184no—
486D4—181no—
487D4C2×C4×C3⋊D312yes—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—81no—
492C2×C4—91no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—91no—
496C2×C4—91no—
497C2×C4—184no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—721no—
502C2×C4—721no—
503C2×C4—721no—
504C2×C4D4×C3⋊D311yescharacteristic
505C2×C4D4×C3⋊D311yescharacteristic
506C2×C4C23×C3⋊D311yescharacteristic
507C8—21no—
508C8—92no—
509C8—181no—
510C8C2×C4×C3⋊D312yes—
511C2×C3—48no—
512C2×C3C4×D3×D414yes—
513C2×C3#576214yes—
514C2×C3#577014yes—
515D3—68no—
516D3—128no—
517C22—22no—
518C22—41no—
519C22—41no—
520C22—92no—
521C22—181no—
522C22—181no—
523C22—182no—
524C22—361no—
525C22—361no—
526C22—724no—
527C22C2×D4×C3⋊D311yescharacteristic
528C4—21no—
529C4—21no—
530C4—22no—
531C4—41no—
532C4—41no—
533C4—92no—
534C4—181no—
535C4—181no—
536C4—182no—
537C4—361no—
538C4—361no—
539C4C22×C4×C3⋊D311yescharacteristic
540C4#41×C3⋊D311yescharacteristic
541C3#7964914yescomplemented
542C2—42no—
543C2—182no—
544C2—362no—
545C2C4×D4×C3⋊D311yescharacteristic
546C2#1059623311yescharacteristic
547C2#1059624111yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC32×C4×SD16C2
socleC22×C32C22×D4
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C32×C4C24
hypercenterC4×SD16C3⋊D3
hypocenterC32#2949
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #10596043C2semidirect
4. C32×C4×SD16C2semidirect
5. SD16×C3⋊Dic3C2semidirect
6. #10592725C2semidirect
7. #10592717C2semidirect
8. #10592559C2semidirect
9. #10592551C2semidirect
10. #10592516C2semidirect
11. #10592501C2semidirect
13. #10592456C2semidirect
14. C4×#3744C2semidirect
15. #10592388C2semidirect
20. C32×C4×Q8C22semidirect
22. Q8×C3⋊Dic3C22semidirect
28. SD16×C3⋊D3C4semidirect
37. #64096C22semidirect
44. C4×#634C22semidirect
45. C32×#106C22semidirect
46. C32×#103C22semidirect
48. C32×C4×C8C22semidirect
49. #63662C22semidirect
52. #63644C22semidirect
53. #63643C22semidirect
54. #63642C22semidirect
55. C8×C3⋊Dic3C22semidirect
56. #63637C22semidirect
58. #63634C22semidirect
59. #63634C22semidirect
60. #63630C22semidirect
64. C3×C4×SD16D3semidirect
83. Q8×C3⋊D3C2×C4semidirect
93. C32×SD16C2×C4semidirect
103. #3755C2×C4semidirect
104. #3754C2×C4semidirect
126. #3744C2×C4semidirect
128. C8×C3⋊D3C2×C4semidirect
133. C3×C4×Q8C2×D3semidirect
158. C3×#106C2×D3semidirect
159. C3×#103C2×D3semidirect
161. C3×C4×C8C2×D3semidirect
223. C4×SD16C3⋊D3semidirect
245. C3×SD16C4×D3semidirect
319. C4×Q8C2×C3⋊D3semidirect
336. #106C2×C3⋊D3semidirect
340. #103C2×C3⋊D3semidirect
348. C4×C8C2×C3⋊D3semidirect
414. SD16C4×C3⋊D3semidirect
471. C32#2949semidirect
541. C3#79649semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C3⋊D32
#105960432
#105960162
C32×C4×SD162
SD16×C3⋊Dic32
#105927252
#105927172
#105925592
#105925512
#105925162
#105925012
#105924692
#105924562
C4×#37442
#105923882
#796493