Finite Group Databasebeta

← #11787750

Subgroups — #11787750

Order 1152.

789 conjugacy classes of subgroups.

The subgroup lattice has 573 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2#10594992C211yesmaximal, characteristic, complemented
3#10591318C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic, complemented
5#10591085C211yesmaximal, characteristic, complemented
6#10589420C211yesmaximal, characteristic, complemented
7C3×#4555C211yesmaximal, characteristic, complemented
8#72088—31nomaximal
9#68776—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C3×#908—22no—
18C3×#908C414yescomplemented
19C2×C3×D24—21no—
20C2×C3×#204—21no—
21#67⋊Dic3—22no—
22C2×(C2×D3)⋊Dic3—22no—
23Dic3×D12—21no—
24D3×C4⋊Dic3—21no—
25Dic3×Dic6—21no—
26#63841—21no—
27#63569—22no—
28#63562—21no—
29#63562—21no—
30C2×C3×AGL(1,ℤ/8)—31no—
31#5827—31no—
32C2×#908D311yescharacteristic
33#5523—31no—
34C2×#837—31no—
35#5221—31no—
36#5215—31no—
37#5001—31no—
38#4939—31no—
39C2×#805—31no—
40C3×#339—31no—
41#4555D311yescharacteristic, complemented
42#4554—31no—
43#4554—31no—
44#4554—61no—
45C23×C3×D3—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3D412yes—
48C2×C3×#67—21no—
49C22×C3×Dic3—21no—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235C2×C412yes—
53C3×#235D412yes—
54C2×C3×D12—21no—
55C2×C3×D12—21no—
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12C2×C412yescomplemented
60C2×C3×D12D411yescharacteristic
61C2×C3×C4×D3—21no—
62C2×C3×Dic6D411yescharacteristic
63C2×D3×Dic3—22no—
64C32×M16—21no—
65C32×M16C2×C412yescomplemented
66C2×C32×C8—21no—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)—21no—
69#3748—21no—
70#3748—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C3×#217—21no—
73C3×C4⋊Dic3D411yescharacteristic
74C3×C4⋊Dic3D411yescharacteristic
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×C4×Dic3—21no—
78C3×D24—24no—
79C3×#204—24no—
80Dic3⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82(C2×D3)⋊Dic3—44no—
83Dic32—22no—
84#1883—91noSylow
85C2×C3×#41—31no—
86C22×C3×D4—31no—
87C2×#235C2×D311yescharacteristic
88C22×D12C2×D311yescharacteristic
89C3×AGL(1,ℤ/8)—34no—
90C3×AGL(1,ℤ/8)—62no—
91C2×C3×SD16—61no—
92C2×C3×D8—61no—
93C2×C3×M16—21no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C3×#117—31no—
97C2×C3×C42—31no—
98C2×#217—62no—
99Q8×Dic3—61no—
100D4×Dic3—61no—
101D4×Dic3—62no—
102C2×(C2×D3)⋊C4—62no—
103#926—61no—
104#926C2×D311yescharacteristic
105C2×C4⋊Dic3—31no—
106C2×C4⋊Dic3—31no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3—61no—
109C2×C4×Dic3C2×D311yescharacteristic
110C2×#208—31no—
111C2×#208—31no—
112C2×#208—61no—
113#908—22no—
114#908Dic314yescomplemented
115C2×D24—21no—
116C2×#204—21no—
117#892—61no—
118D3×C4⋊C4—61no—
119#67⋊C4—62no—
120C4×D12—61no—
121C4×Dic6—61no—
122#837—62no—
123#832—61no—
124#832—61no—
125#809—61no—
126#809—61no—
127#805—62no—
128C23×C32C2×D411yescharacteristic
129C22×C3×D3—21no—
130C22×C3×D3—22no—
131C22×C3×D3—42no—
132C22×C3×D3—42no—
133C22×C3×D3—41no—
134C22×C3×D3—41no—
135C2×C32×C4C22×C411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140C2×C32×C4#4111yescharacteristic
141C2×C3⋊Dic3—22no—
142C2×C3⋊Dic3—42no—
143C3×#67—22no—
144C3×#67—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—21no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—41no—
150C2×C3×Dic3—41no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—21no—
154C3×D12—41no—
155C3×D12—41no—
156C3×D12C22⋊C412yescomplemented
157C3×C4×D3—22no—
158C3×C4×D3—22no—
159C3×Dic6—21no—
160C3×Dic6C22⋊C412yescomplemented
161D3×Dic3—82no—
162C32×C8—22no—
163C3⋊(C3⋊C8)—41no—
164C2×AGL(1,ℤ/8)—31no—
165#520—91no—
166C2×#104—91no—
167#418—91no—
168#390—91no—
169#343—91no—
170#339—31no—
171C24×C3—61no—
172C23×D3—21no—
173C3×#41—32no—
174C3×#41—32no—
175C3×#41—61no—
176C3×#41—61no—
177C2×C3×Q8—31no—
178C2×C3×D4—32no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C2×C3×D4—61no—
182C2×C3×D4—61no—
183C2×C3×D4—61no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—61no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—21no—
192C22×Dic3—21no—
193C22×Dic3—32no—
194C22×Dic3—32no—
195C22×Dic3—62no—
196C22×Dic3—62no—
197#235—21no—
198#235—21no—
199#235C2×Dic312yes—
200#235#6712yes—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12C2×Dic312yescomplemented
207C2×D12#6711yescharacteristic
208C2×C4×D3—21no—
209C2×C4×D3—62no—
210C2×Dic6#6711yescharacteristic
211C3×SD16—64no—
212C3×D8—64no—
213C3×M16—21no—
214C3×M16—21no—
215C3×M16—22no—
216C3×M16—41no—
217C3×M16C4×D312yescomplemented
218C3×M16C2×Dic312yescomplemented
219C2×C3×C8—21no—
220C2×C3×C8—21no—
221C2×C3×C8—41no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—31no—
224C3×C22⋊C4—61no—
225C3×C42—61no—
226C3×C42—61no—
227C3×C42—61no—
228#217—21no—
229#217—62no—
230#217—124no—
231(C2×D3)⋊C4—62no—
232(C2×D3)⋊C4—124no—
233C4⋊Dic3—62no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—61no—
238C4⋊Dic3—121no—
239C4⋊Dic3—121no—
240C4⋊Dic3D1211yescharacteristic
241C4⋊Dic3D1211yescharacteristic
242Dic3⋊C4—62no—
243C4×Dic3—21no—
244C4×Dic3—21no—
245C4×Dic3—21no—
246C4×Dic3—62no—
247C4×Dic3—62no—
248#208—62no—
249#208—61no—
250#208—61no—
251#208—61no—
252#208—61no—
253#208—121no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—121no—
257D24—24no—
258#204—24no—
259C22×C32—21no—
260C22×C32—21no—
261C22×C32C4×D411yescharacteristic
262C22×C32#12011yescharacteristic
263C22×C32#12111yescharacteristic
264C2×C3×D3—22no—
265C2×C3×D3—41no—
266C2×C3×D3—41no—
267C2×C3×D3—44no—
268C2×C3×D3—42no—
269C2×C3×D3—82no—
270C2×C3×D3—81no—
271C2×C3×D3—81no—
272C32×C4C2×C22⋊C411yescharacteristic
273C32×C4C4×D411yescharacteristic
274C32×C4#12111yescharacteristic
275C32×C4#12311yescharacteristic
276C3⋊Dic3—42no—
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3—41no—
280C3×Dic3—41no—
281C2×#41—31no—
282C22×D4—31no—
283AGL(1,ℤ/8)—34no—
284AGL(1,ℤ/8)—62no—
285C2×SD16—61no—
286C2×D8—61no—
287C2×M16—91no—
288C2×M16D3211yescharacteristic
289C4×Q8—181no—
290C4×D4—181no—
291C4×D4—182no—
292#117—31no—
293#117—181no—
294C2×C4⋊C4—91no—
295C2×C4⋊C4—181no—
296C2×C22⋊C4—182no—
297C2×C42—31no—
298#104—182no—
299#102—181no—
300#102—181no—
301C23×C3—21no—
302C23×C3—61no—
303C23×C3—62no—
304C23×C3—122no—
305C23×C3—122no—
306C23×C3—121no—
307C23×C3—121no—
308C23×C3D3×D411yescharacteristic
309C23×C3D3×D411yescharacteristic
310C22×D3—21no—
311C22×D3—22no—
312C22×D3—42no—
313C22×D3—42no—
314C22×D3—41no—
315C22×D3—41no—
316C3×Q8—32no—
317C3×Q8—61no—
318C3×D4—32no—
319C3×D4—62no—
320C3×D4—62no—
321C3×D4—62no—
322C3×D4—62no—
323C3×D4—61no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—61no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—61no—
337C2×C3×C4—61no—
338C2×C3×C4—121no—
339C2×C3×C4—121no—
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4C2×D1211yescharacteristic
342C2×C3×C4#23511yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4#23711yescharacteristic
347C2×C3×C4#23711yescharacteristic
348C2×C3×C4#23911yescharacteristic
349C2×C3×C4C22×Dic311yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352#67—22no—
353#67—22no—
354C2×Dic3—21no—
355C2×Dic3—22no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—41no—
359C2×Dic3—41no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—242no—
366C2×Dic3—242no—
367D12—22no—
368D12—21no—
369D12—22no—
370D12—41no—
371D12—41no—
372D12#21712yescomplemented
373C4×D3—22no—
374C4×D3—22no—
375C4×D3—242no—
376Dic6—21no—
377Dic6#21712yescomplemented
378C3×C8—22no—
379C3×C8—22no—
380C3×C8—42no—
381C3⋊C8—122no—
382C3⋊C8—121no—
383C3⋊C8—121no—
384C2×C32—21no—
385C2×C32—21no—
386C2×C32#38611yescharacteristic
387C2×C32#45311yescharacteristic
388C2×C32#45411yescharacteristic
389C3×D3—42no—
390C3×D3—82no—
391C24—61no—
392#41—32no—
393#41—32no—
394#41—61no—
395#41—61no—
396C2×Q8—31no—
397C2×D4—32no—
398C2×D4—31no—
399C2×D4—61no—
400C2×D4—61no—
401C2×D4—61no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—92no—
408C22×C4—182no—
409C22×C4C2×D3211yescharacteristic
410SD16—64no—
411D8—64no—
412M16—21no—
413M16—181no—
414M16—181no—
415M16D3×Dic312yescomplemented
416C2×C8—21no—
417C2×C8—181no—
418C4⋊C4—31no—
419C4⋊C4—31no—
420C4⋊C4—182no—
421C4⋊C4—181no—
422C4⋊C4—181no—
423C22⋊C4—61no—
424C22⋊C4—182no—
425C22⋊C4—364no—
426C42—61no—
427C42—61no—
428C42—61no—
429C42—182no—
430C22×C3—21no—
431C22×C3—21no—
432C22×C3—21no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—62no—
440C22×C3—124no—
441C22×C3—121no—
442C22×C3—121no—
443C22×C3—122no—
444C22×C3—242no—
445C22×C3—241no—
446C22×C3—241no—
447C22×C3#88211yescharacteristic
448C22×C3#88411yescharacteristic
449C22×C3#89311yescharacteristic
450C22×C3D4×Dic311yescharacteristic
451C22×C3#93711yescharacteristic
452C22×C3#93911yescharacteristic
453C2×D3—22no—
454C2×D3—41no—
455C2×D3—41no—
456C2×D3—44no—
457C2×D3—42no—
458C2×D3—82no—
459C2×D3—81no—
460C2×D3—81no—
461C3×C4—21no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—62no—
466C3×C4—122no—
467C3×C4—121no—
468C3×C4—121no—
469C3×C4C4×D1211yescharacteristic
470C3×C4D3×C22⋊C411yescharacteristic
471C3×C4#89411yescharacteristic
472C3×C4#89511yescharacteristic
473C3×C4D4×Dic311yescharacteristic
474C3×C4#93511yescharacteristic
475C3×C4#93911yescharacteristic
476C3×C4C2×#21711yescharacteristic
477Dic3—22no—
478Dic3—42no—
479Dic3—41no—
480Dic3—41no—
481Dic3—122no—
482Dic3—122no—
483Dic3—242no—
484C32#188311yescharacteristic, complemented, Sylow
485C23—61no—
486C23—62no—
487C23—122no—
488C23—122no—
489C23—121no—
490C23—121no—
491C23#380211yescharacteristic
492Q8—32no—
493Q8—61no—
494D4—32no—
495D4—62no—
496D4—62no—
497D4—61no—
498D4—62no—
499D4—62no—
500D4—121no—
501D4—121no—
502C2×C4—61no—
503C2×C4—62no—
504C2×C4—62no—
505C2×C4—62no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—121no—
509C2×C4—121no—
510C2×C4—182no—
511C2×C4—362no—
512C2×C4—722no—
513C2×C4#379511yescharacteristic
514C2×C4#379611yescharacteristic
515C2×C4D3×D1211yescharacteristic
516C2×C4C2×D3×Dic311yescharacteristic
517C2×C4D3×#6711yescharacteristic
518C2×C4D3×#6711yescharacteristic
519C8—22no—
520C8—361no—
521C2×C3—21no—
522C2×C3—21no—
523C2×C3—21no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—41no—
529C2×C3—41no—
530C2×C3—122no—
531C2×C3—242no—
532C2×C3#466511yescharacteristic
533C2×C3#482211yescharacteristic
534C2×C3#482711yescharacteristic
535C2×C3#519811yescharacteristic
536C2×C3#520111yescharacteristic
537C2×C3#522011yescharacteristic
538D3—42no—
539D3—82no—
540C22—21no—
541C22—21no—
542C22—62no—
543C22—124no—
544C22—121no—
545C22—121no—
546C22—122no—
547C22—242no—
548C22—241no—
549C22—241no—
550C22#6388511yescharacteristic
551C22#6389811yescharacteristic
552C22#6392211yescharacteristic
553C4—62no—
554C4—122no—
555C4—121no—
556C4—121no—
557C4—362no—
558C4#6388411yescharacteristic
559C4#6388611yescharacteristic
560C4Dic3×D1211yescharacteristic
561C4D3×#21711yescharacteristic
562C3—21no—
563C3#6877611yescharacteristic, complemented
564C3#7208811yescharacteristic, complemented
565C2—21no—
566C2—21no—
567C2—122no—
568C2—242no—
569C2#1059101311yescharacteristic
570C2#1059101911yescharacteristic
571C2#1059137611yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×C3×#908C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1883
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10594992C2semidirect
3. #10591318C2semidirect
4. C2×#63569C2semidirect
5. #10591085C2semidirect
6. #10589420C2semidirect
7. C3×#4555C2semidirect
18. C3×#908C4semidirect
41. #4555D3semidirect
59. C2×C3×D12C2×C4semidirect
65. C32×M16C2×C4semidirect
114. #908Dic3semidirect
156. C3×D12C22⋊C4semidirect
160. C3×Dic6C22⋊C4semidirect
206. C2×D12C2×Dic3semidirect
217. C3×M16C4×D3semidirect
218. C3×M16C2×Dic3semidirect
372. D12#217semidirect
377. Dic6#217semidirect
415. M16D3×Dic3semidirect
484. C32#1883semidirect
563. C3#68776semidirect
564. C3#72088semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
#105949922
#105913182
C2×#635692
#105910852
#105894202
C3×#45552
#720883
#687763