Finite Group Databasebeta

← #11787699

Subgroups — #11787699

Order 1152.

723 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic
3#10591221C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic
5#10591100C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#72100—31nomaximal
9#69004—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#909—22no—
18C3×#909C414yescomplemented
19C2×C3×Dic12—21no—
20C2×C3×#204—21no—
21Dic3×#67—22no—
22#63898—21no—
23D3×C4⋊Dic3—21no—
24#63843—21no—
25#63841—21no—
26#63579—22no—
27#63568—22no—
28#63566—21no—
29#63566—21no—
30C2×C3×#137—31no—
31#5827—31no—
32C2×#909D311yescharacteristic
33#5504—31no—
34C2×#837—31no—
35#5229—31no—
36#5225—31no—
37C2×#825—31no—
38#5120—31no—
39#4973—31no—
40C3×#343—31no—
41#4555—31no—
42#4555—31no—
43#4555—61no—
44#4554D311yescharacteristic, complemented
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D412yes—
50C3×#235—21no—
51C3×#235—21no—
52C3×#235C2×C412yes—
53C3×#235D412yes—
54C2×C3×D12D411yescharacteristic
55C2×C3×C4×D3—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6—21no—
59C2×C3×Dic6—21no—
60C2×C3×Dic6—21no—
61C2×C3×Dic6C2×C412yescomplemented
62C2×C3×Dic6D411yescharacteristic
63C2×D3×Dic3—22no—
64C32×M16—21no—
65C32×M16C2×C412yescomplemented
66C2×C32×C8—21no—
67#3757—21no—
68C4⋊(C3⋊Dic3)D411yescharacteristic
69C4⋊(C3⋊Dic3)D411yescharacteristic
70C4×C3⋊Dic3—21no—
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3—21no—
73C3×C4⋊Dic3—21no—
74C3×C4⋊Dic3—21no—
75C3×#208—21no—
76C3×#208—21no—
77C2×C3×C3⋊C8—21no—
78C3×Dic12—24no—
79C3×#204—24no—
80Dic3⋊Dic3—22no—
81(C2×D3)⋊Dic3—22no—
82Dic32—22no—
83#1882—91noSylow
84C2×C3×#41—31no—
85C22×C3×Q8—31no—
86C2×#235C2×D311yescharacteristic
87C22×Dic6C2×D311yescharacteristic
88C3×#137—34no—
89C3×#137—62no—
90C2×C3×Q16—61no—
91C2×C3×SD16—61no—
92C2×C3×M16—21no—
93C2×C3×M16—31no—
94C2×C3×M16C2×D311yescharacteristic
95C2×C3×M16C2×D311yescharacteristic
96C2×C3×C4⋊C4—31no—
97Q8×Dic3—61no—
98D4×Dic3—61no—
99D4×Dic3—62no—
100C4×#67—62no—
101#926—31no—
102#926—31no—
103#926—61no—
104#926—61no—
105C2×C4⋊Dic3—61no—
106C2×C4⋊Dic3C2×D311yescharacteristic
107C2×C4×Dic3—31no—
108C2×C4×Dic3—31no—
109C2×C4×Dic3—61no—
110C2×#208C2×D311yescharacteristic
111#909—22no—
112#909Dic314yescomplemented
113C2×Dic12—21no—
114C2×#204—21no—
115#893—61no—
116#892—61no—
117D3×C4⋊C4—61no—
118#887—61no—
119#837—62no—
120#835—61no—
121#835—61no—
122C3⋊#95—62no—
123C3⋊#95—62no—
124#825—62no—
125#816—61no—
126#816—61no—
127C23×C32C2×D411yescharacteristic
128C22×C3×D3—21no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2×D411yescharacteristic
133C2×C32×C4#4111yescharacteristic
134C2×C32×C4#4111yescharacteristic
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C2×C3⋊Dic3—41no—
139C2×C3⋊Dic3—41no—
140C3×#67—22no—
141C3×#67—22no—
142C2×C3×Dic3—21no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—22no—
145C2×C3×Dic3—41no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—42no—
148C3×D12—21no—
149C3×D12C22⋊C412yes—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×Dic6—21no—
153C3×Dic6—22no—
154C3×Dic6—22no—
155C3×Dic6—41no—
156C3×Dic6—41no—
157C3×Dic6C22⋊C412yes—
158D3×Dic3—82no—
159C32×C8—22no—
160C3×C3⋊C8—41no—
161C2×#137—31no—
162#520—91no—
163C2×#104—91no—
164#419—91no—
165#391—91no—
166#343—31no—
167#339—91no—
168C3×#41—32no—
169C3×#41—32no—
170C3×#41—61no—
171C3×#41—61no—
172C2×C3×Q8—32no—
173C2×C3×Q8—31no—
174C2×C3×Q8—61no—
175C2×C3×Q8—61no—
176C2×C3×Q8—61no—
177C2×C3×Q8—61no—
178C2×C3×Q8—61no—
179C2×C3×D4—31no—
180C2×C3×D4—61no—
181C22×C3×C4—21no—
182C22×C3×C4—32no—
183C22×C3×C4—61no—
184C22×C3×C4—61no—
185C22×C3×C4C22×D311yescharacteristic
186C22×C3×C4C22×D311yescharacteristic
187C2×#67—21no—
188C22×Dic3—21no—
189C22×Dic3—62no—
190C22×Dic3—61no—
191C22×Dic3—61no—
192C22×Dic3—121no—
193C22×Dic3D1212yes—
194#235—21no—
195#235—21no—
196#235C2×Dic312yes—
197#235#6712yes—
198C2×D12#6711yescharacteristic
199C2×C4×D3—21no—
200C2×C4×D3—62no—
201C2×Dic6—21no—
202C2×Dic6—21no—
203C2×Dic6—21no—
204C2×Dic6—21no—
205C2×Dic6—21no—
206C2×Dic6C2×Dic312yescomplemented
207C2×Dic6#6711yescharacteristic
208C3×Q16—64no—
209C3×SD16—64no—
210C3×M16—21no—
211C3×M16—21no—
212C3×M16—22no—
213C3×M16—41no—
214C3×M16—61no—
215C3×M16—61no—
216C3×M16C4×D312yescomplemented
217C3×M16C2×Dic312yescomplemented
218C2×C3×C8—21no—
219C2×C3×C8—21no—
220C2×C3×C8—41no—
221C2×C3×C8—61no—
222C3×C4⋊C4—61no—
223C3×C4⋊C4—61no—
224#217—62no—
225#217—61no—
226#217—61no—
227#217—121no—
228(C2×D3)⋊C4—62no—
229C4⋊Dic3—21no—
230C4⋊Dic3—21no—
231C4⋊Dic3—31no—
232C4⋊Dic3—31no—
233C4⋊Dic3—31no—
234C4⋊Dic3—31no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—62no—
238Dic3⋊C4—62no—
239C4×Dic3—62no—
240C4×Dic3—62no—
241C4×Dic3—61no—
242C4×Dic3—61no—
243C4×Dic3—62no—
244C4×Dic3—61no—
245C4×Dic3—61no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—121no—
249C4×Dic3—121no—
250#208—21no—
251#208—21no—
252C2×C3⋊C8—21no—
253Dic12—24no—
254#204—24no—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32C4×D411yescharacteristic
258C22×C32#12011yescharacteristic
259C22×C32#12111yescharacteristic
260C2×C3×D3—22no—
261C2×C3×D3—41no—
262C2×C3×D3—41no—
263C32×C4C2×C22⋊C411yescharacteristic
264C32×C4C4×D411yescharacteristic
265C32×C4#12111yescharacteristic
266C32×C4#12311yescharacteristic
267C3⋊Dic3—42no—
268C3⋊Dic3—41no—
269C3⋊Dic3—41no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C3×Dic3—42no—
273C2×#41—31no—
274C22×Q8—31no—
275#137—34no—
276#137—62no—
277C2×Q16—61no—
278C2×SD16—61no—
279C2×M16—31no—
280C2×M16D3211yescharacteristic
281C4×Q8—181no—
282C4×D4—181no—
283C4×D4—182no—
284#117—91no—
285#117—181no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—181no—
288C2×C42—91no—
289#104—182no—
290#103—181no—
291#103—181no—
292#95—182no—
293C23×C3—21no—
294C23×C3—61no—
295C23×C3C2×D1211yescharacteristic
296C23×C3D3×D411yescharacteristic
297C22×D3—21no—
298C3×Q8—32no—
299C3×Q8—61no—
300C3×Q8—62no—
301C3×Q8—62no—
302C3×Q8—121no—
303C3×Q8—121no—
304C3×D4—32no—
305C3×D4—62no—
306C3×D4—62no—
307C3×D4—61no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—61no—
315C2×C3×C4—62no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—62no—
319C2×C3×C4—121no—
320C2×C3×C4—121no—
321C2×C3×C4—122no—
322C2×C3×C4C2×C4×D311yescharacteristic
323C2×C3×C4#23511yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4#23711yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4#23911yescharacteristic
331C2×C3×C4C22×Dic311yescharacteristic
332C2×C3×C4C2×#6711yescharacteristic
333C2×C3×C4C2×#6711yescharacteristic
334#67—22no—
335#67—22no—
336C2×Dic3—21no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—41no—
340C2×Dic3—41no—
341C2×Dic3—42no—
342C2×Dic3—62no—
343C2×Dic3—62no—
344C2×Dic3—61no—
345C2×Dic3—61no—
346C2×Dic3—61no—
347C2×Dic3—61no—
348C2×Dic3—122no—
349C2×Dic3—121no—
350C2×Dic3—121no—
351C2×Dic3—122no—
352C2×Dic3—121no—
353C2×Dic3—121no—
354C2×Dic3—122no—
355C2×Dic3—121no—
356C2×Dic3—121no—
357C2×Dic3—242no—
358D12—21no—
359D12#21712yes—
360C4×D3—22no—
361C4×D3—22no—
362C4×D3—242no—
363Dic6—21no—
364Dic6—22no—
365Dic6—22no—
366Dic6—41no—
367Dic6—41no—
368Dic6#21712yes—
369C3×C8—22no—
370C3×C8—22no—
371C3×C8—42no—
372C3×C8—121no—
373C3⋊C8—41no—
374C2×C32—21no—
375C2×C32—21no—
376C2×C32#38611yescharacteristic
377C2×C32#45511yescharacteristic
378C2×C32#45611yescharacteristic
379C3×D3—42no—
380#41—32no—
381#41—32no—
382#41—61no—
383#41—61no—
384C2×Q8—32no—
385C2×Q8—31no—
386C2×Q8—61no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×Q8—61no—
391C2×D4—31no—
392C2×D4—61no—
393C22×C4—32no—
394C22×C4—61no—
395C22×C4—61no—
396C22×C4—182no—
397C22×C4—181no—
398C22×C4C2×D3211yescharacteristic
399Q16—64no—
400SD16—64no—
401M16—21no—
402M16—61no—
403M16—61no—
404M16D3×Dic312yescomplemented
405C2×C8—21no—
406C2×C8—61no—
407C4⋊C4—61no—
408C4⋊C4—61no—
409C4⋊C4—91no—
410C4⋊C4—91no—
411C4⋊C4—182no—
412C22⋊C4—182no—
413C22⋊C4—181no—
414C42—182no—
415C42—181no—
416C42—181no—
417C42—181no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—41no—
426C22×C3—41no—
427C22×C3—62no—
428C22×C3—121no—
429C22×C3—121no—
430C22×C3C4×D1211yescharacteristic
431C22×C3#88211yescharacteristic
432C22×C3#89511yescharacteristic
433C22×C3D4×Dic311yescharacteristic
434C22×C3#93711yescharacteristic
435C22×C3#93911yescharacteristic
436C2×D3—22no—
437C2×D3—41no—
438C2×D3—41no—
439C3×C4—21no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—62no—
444C3×C4—122no—
445C3×C4—122no—
446C3×C4D3×C22⋊C411yescharacteristic
447C3×C4#88411yescharacteristic
448C3×C4#89311yescharacteristic
449C3×C4#89411yescharacteristic
450C3×C4D4×Dic311yescharacteristic
451C3×C4#93511yescharacteristic
452C3×C4#93911yescharacteristic
453C3×C4C2×#21711yescharacteristic
454Dic3—22no—
455Dic3—42no—
456Dic3—42no—
457Dic3—122no—
458Dic3—122no—
459Dic3—124no—
460Dic3—121no—
461Dic3—121no—
462Dic3—121no—
463Dic3—121no—
464Dic3—241no—
465Dic3—241no—
466C32#188211yescharacteristic, complemented, Sylow
467C23—61no—
468C23D3×D1211yescharacteristic
469Q8—32no—
470Q8—61no—
471Q8—62no—
472Q8—62no—
473Q8—121no—
474Q8—121no—
475D4—32no—
476D4—62no—
477D4—62no—
478D4—61no—
479C2×C4—61no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—62no—
484C2×C4—121no—
485C2×C4—121no—
486C2×C4—122no—
487C2×C4—182no—
488C2×C4—181no—
489C2×C4—181no—
490C2×C4—361no—
491C2×C4—361no—
492C2×C4—722no—
493C2×C4#379511yescharacteristic
494C2×C4#379611yescharacteristic
495C2×C4#380211yescharacteristic
496C2×C4C2×D3×Dic311yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C2×C4D3×#6711yescharacteristic
499C8—22no—
500C8—121no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—41no—
509C2×C3—41no—
510C2×C3—122no—
511C2×C3#466511yescharacteristic
512C2×C3#474611yescharacteristic
513C2×C3#475211yescharacteristic
514C2×C3#520211yescharacteristic
515C2×C3#520511yescharacteristic
516C2×C3#522011yescharacteristic
517D3—42no—
518C22—21no—
519C22—21no—
520C22—62no—
521C22—121no—
522C22—121no—
523C22#6388611yescharacteristic
524C22Dic3×D1211yescharacteristic
525C22#6392211yescharacteristic
526C4—62no—
527C4—122no—
528C4—122no—
529C4—362no—
530C4—361no—
531C4—361no—
532C4#6388411yescharacteristic
533C4#6388511yescharacteristic
534C4#6389811yescharacteristic
535C4D3×#21711yescharacteristic
536C3—21no—
537C3#6900411yescharacteristic, complemented
538C3#7210011yescharacteristic, complemented
539C2—21no—
540C2—21no—
541C2—122no—
542C2#1059101211yescharacteristic
543C2#1059101811yescharacteristic
544C2#1059137611yescharacteristic
subgroupG/H
centerC22#63922
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1882
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
3. #10591221C2semidirect
5. #10591100C2semidirect
6. #10589421C2semidirect
7. C3×#4554C2semidirect
18. C3×#909C4semidirect
44. #4554D3semidirect
61. C2×C3×Dic6C2×C4semidirect
65. C32×M16C2×C4semidirect
112. #909Dic3semidirect
206. C2×Dic6C2×Dic3semidirect
216. C3×M16C4×D3semidirect
217. C3×M16C2×Dic3semidirect
404. M16D3×Dic3semidirect
466. C32#1882semidirect
537. C3#69004semidirect
538. C3#72100semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
#105949862
#105912212
C2×#635682
#105911002
#105894212
C3×#45542
#721003
#690043