Finite Group Databasebeta

← #11787745

Subgroups — #11787745

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
1C3×#5504C211yesmaximal, characteristic, complemented
2C2×#63823C211yesmaximal, characteristic
3C3×#4988C211yesmaximal, characteristic, complemented
4C2×#63569C211yesmaximal, characteristic, complemented
5#10591085C211yesmaximal, characteristic, complemented
6#10589396C211yesmaximal, characteristic, complemented
7#10589161C211yesmaximal, characteristic, complemented
8#71667—31nomaximal
9#69663—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×C4⋊C4C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×C4×#67—22no—
16C2×C3×(C2×D3)⋊C4—22no—
17C3×#926C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C3×#893—21no—
20C3×#892—21no—
21C3×D3×C4⋊C4—21no—
22C3×#887—21no—
23C2×#3715—21no—
24#63823—22no—
25#63823C414yescomplemented
26C2×#3713—21no—
27#63569—22no—
28#63562—21no—
29#63562—21no—
30C3×#520—31no—
31C2×#949—31no—
32C2×#932—31no—
33#5504D311yescharacteristic, complemented
34C3×#390—31no—
35C2×#837—31no—
36#5215—31no—
37#5001—31no—
38#4988D311yescharacteristic, complemented
39C2×#805—31no—
40#4532—31no—
41#4530—31no—
42#4530—31no—
43#4530—61no—
44#4523—31no—
45C23×C3×D3—21no—
46C22×C32×C4D412yes—
47C22×C32×C4C2311yescharacteristic
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×C4×D3—22no—
63C2×C3×Dic6D411yescharacteristic
64C32×C4⋊C4—21no—
65C32×C4⋊C4—21no—
66#3748—21no—
67#3748—21no—
68#3748—21no—
69#3748C2×C412yescomplemented
70C2×C3⋊(C3⋊C8)—21no—
71C2×C3⋊(C3⋊C8)—21no—
72C3×#217—21no—
73C3×(C2×D3)⋊C4—22no—
74C3×(C2×D3)⋊C4—44no—
75C3×C4⋊Dic3D411yescharacteristic
76C3×C4⋊Dic3D411yescharacteristic
77C3×Dic3⋊C4—22no—
78C3×C4×Dic3—22no—
79C3×C4×Dic3—21no—
80C3×C4×Dic3—21no—
81C3×C4×Dic3—21no—
82#3715—24no—
83#3713—24no—
84#1883—91noSylow
85C2×C3×#41—31no—
86C22×C3×D4—31no—
87C2×#235C2×D311yescharacteristic
88C22×D12C2×D311yescharacteristic
89C3×C4×Q8—61no—
90C3×C4×D4—61no—
91C3×C4×D4—62no—
92C3×#117—31no—
93C3×#117—61no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4—61no—
96C2×C3×C4⋊C4C2×D311yescharacteristic
97C2×C3×C4⋊C4C2×D311yescharacteristic
98C2×C3×C22⋊C4—62no—
99C2×C3×C42—31no—
100#949—34no—
101#949—62no—
102C2×#215—61no—
103C2×#214—61no—
104#932—34no—
105#932—62no—
106C2×#213—61no—
107C2×#213—61no—
108C4×#67—22no—
109C2×(C2×D3)⋊C4—22no—
110#926C2×D311yescharacteristic
111C2×C4×Dic3C2×D311yescharacteristic
112C2×#208—31no—
113C2×#208—31no—
114C2×#208—31no—
115C2×#208—31no—
116C2×#208—61no—
117C2×#208—61no—
118#893—21no—
119#892—21no—
120D3×C4⋊C4—21no—
121#887—21no—
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×C4—22no—
136C2×C32×C4—42no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4111yescharacteristic
142C2×C32×C4#4111yescharacteristic
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×C4×D3—82no—
160C3×Dic6—21no—
161C3×Dic6C22⋊C412yescomplemented
162C3⋊(C3⋊C8)—22no—
163C3⋊(C3⋊C8)—41no—
164C2×AGL(1,ℤ/8)—91no—
165#520—31no—
166C2×#104—91no—
167#418—91no—
168#390—31no—
169#343—91no—
170#339—91no—
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—22no—
187C22×C3×C4—21no—
188C22×C3×C4—62no—
189C22×C3×C4—61no—
190C22×C3×C4—61no—
191C22×C3×C4#6712yes—
192C22×C3×C4#6712yes—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—21no—
196C22×Dic3—21no—
197#235—21no—
198#235—21no—
199#235C4×D312yes—
200#235D1212yes—
201C2×D12—21no—
202C2×D12—21no—
203C2×D12—21no—
204C2×D12—21no—
205C2×D12—21no—
206C2×D12C4×D312yescomplemented
207C2×D12#6711yescharacteristic
208C2×C4×D3—21no—
209C2×C4×D3—22no—
210C2×Dic6#6711yescharacteristic
211C3×C4⋊C4—21no—
212C3×C4⋊C4—21no—
213C3×C4⋊C4—21no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—31no—
216C3×C4⋊C4—31no—
217C3×C4⋊C4—41no—
218C3×C4⋊C4—41no—
219C3×C4⋊C4—62no—
220C3×C22⋊C4—62no—
221C3×C22⋊C4—61no—
222C3×C22⋊C4—124no—
223C3×C42—62no—
224C3×C42—61no—
225C3×C42—61no—
226C3×C42—61no—
227#217—21no—
228#215—64no—
229#214—64no—
230#213—64no—
231#213—64no—
232(C2×D3)⋊C4—22no—
233(C2×D3)⋊C4—44no—
234C4⋊Dic3#6711yescharacteristic
235C4⋊Dic3#6711yescharacteristic
236Dic3⋊C4—22no—
237C4×Dic3—22no—
238C4×Dic3—21no—
239C4×Dic3—21no—
240C4×Dic3—21no—
241#208—32no—
242#208—32no—
243#208—62no—
244#208—61no—
245#208—61no—
246#208—62no—
247#208—61no—
248#208—61no—
249#208—61no—
250#208—61no—
251#208—121no—
252#208—121no—
253C2×C3⋊C8—61no—
254C2×C3⋊C8—61no—
255C2×C3⋊C8—61no—
256C2×C3⋊C8—61no—
257C2×C3⋊C8—121no—
258C2×C3⋊C8—121no—
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×C4—42no—
273C32×C4C2×C22⋊C411yescharacteristic
274C32×C4C4×D411yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12311yescharacteristic
277C3×Dic3—22no—
278C3×Dic3—42no—
279C3×Dic3—41no—
280C3×Dic3—41no—
281C2×#41—31no—
282C22×D4—31no—
283AGL(1,ℤ/8)—94no—
284AGL(1,ℤ/8)—182no—
285C2×SD16—181no—
286C2×D8—181no—
287C2×M16—91no—
288C2×M16—91no—
289C4×Q8—61no—
290C4×D4—61no—
291C4×D4—62no—
292#117—31no—
293#117—61no—
294C2×C4⋊C4—61no—
295C2×C4⋊C4D3211yescharacteristic
296C2×C22⋊C4—62no—
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×C3C2×#6711yescharacteristic
309C23×C3C2×#6711yescharacteristic
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—61no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—121no—
325C3×D4—121no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—42no—
337C2×C3×C4—61no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4—82no—
344C2×C3×C4—121no—
345C2×C3×C4—121no—
346C2×C3×C4—242no—
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C2×C4×D311yescharacteristic
349C2×C3×C4C2×D1211yescharacteristic
350C2×C3×C4#23511yescharacteristic
351C2×C3×C4#23511yescharacteristic
352C2×C3×C4#23511yescharacteristic
353C2×C3×C4D3×D411yescharacteristic
354C2×C3×C4D3×D411yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4#23711yescharacteristic
357C2×C3×C4C2×#6711yescharacteristic
358C2×C3×C4C2×#6711yescharacteristic
359#67—22no—
360#67—22no—
361C2×Dic3—21no—
362C2×Dic3—22no—
363C2×Dic3—21no—
364C2×Dic3—21no—
365C2×Dic3—41no—
366C2×Dic3—41no—
367D12—22no—
368D12—22no—
369D12—21no—
370D12—41no—
371D12—41no—
372D12(C2×D3)⋊C412yescomplemented
373C4×D3—22no—
374C4×D3—22no—
375C4×D3—82no—
376Dic6—21no—
377Dic6(C2×D3)⋊C412yescomplemented
378C3⋊C8—62no—
379C3⋊C8—62no—
380C3⋊C8—122no—
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—62no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4#62512yes—
409C22×C4C2×D3211yescharacteristic
410SD16—184no—
411D8—184no—
412M16—92no—
413M16—181no—
414M16—181no—
415M16—181no—
416C2×C8—181no—
417C2×C8—181no—
418C4⋊C4—21no—
419C4⋊C4—21no—
420C4⋊C4—31no—
421C4⋊C4—31no—
422C4⋊C4—62no—
423C22⋊C4—62no—
424C22⋊C4—61no—
425C22⋊C4—124no—
426C42—62no—
427C42—61no—
428C42—61no—
429C42—61no—
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×C3C4×#6711yescharacteristic
448C22×C3C4×#6711yescharacteristic
449C22×C3#93011yescharacteristic
450C22×C3#93711yescharacteristic
451C22×C3#93811yescharacteristic
452C22×C3#95311yescharacteristic
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—42no—
466C3×C4—42no—
467C3×C4—62no—
468C3×C4—82no—
469C3×C4—122no—
470C3×C4—121no—
471C3×C4—121no—
472C3×C4D3×C22⋊C411yescharacteristic
473C3×C4#67⋊C411yescharacteristic
474C3×C4#88311yescharacteristic
475C3×C4#88411yescharacteristic
476C3×C4C2×(C2×D3)⋊C411yescharacteristic
477C3×C4C4×#6711yescharacteristic
478C3×C4#92911yescharacteristic
479C3×C4#93011yescharacteristic
480Dic3—22no—
481Dic3—42no—
482Dic3—41no—
483Dic3—41no—
484C32#188311yescharacteristic, complemented, Sylow
485C23—61no—
486C23—62no—
487C23—122no—
488C23—122no—
489C23—121no—
490C23—121no—
491C23C2×#62511yescharacteristic
492Q8—32no—
493Q8—61no—
494D4—32no—
495D4—62no—
496D4—62no—
497D4—62no—
498D4—61no—
499D4—62no—
500D4—121no—
501D4—121no—
502C2×C4—22no—
503C2×C4—42no—
504C2×C4—61no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—121no—
511C2×C4—121no—
512C2×C4—242no—
513C2×C4#379511yescharacteristic
514C2×C4#379811yescharacteristic
515C2×C4C4×D3211yescharacteristic
516C2×C4D3×D1211yescharacteristic
517C2×C4D3×#6711yescharacteristic
518C2×C4D3×#6711yescharacteristic
519C8—182no—
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#495611yescharacteristic
533C2×C3#506211yescharacteristic
534C2×C3#507711yescharacteristic
535C2×C3#521311yescharacteristic
536C2×C3#524111yescharacteristic
537C2×C3#524511yescharacteristic
538D3—42no—
539D3—82no—
540C22—21no—
541C22—21no—
542C22—62no—
543C22—124no—
544C22—121no—
545C22—121no—
546C22—122no—
547C22—242no—
548C22—241no—
549C22—241no—
550C22C4×#62511yescharacteristic
551C22#6390811yescharacteristic
552C22#6397611yescharacteristic
553C4—42no—
554C4—62no—
555C4—122no—
556C4—121no—
557C4—121no—
558C4#6387911yescharacteristic
559C4#6390511yescharacteristic
560C4#6390611yescharacteristic
561C4D3×(C2×D3)⋊C411yescharacteristic
562C3—21no—
563C3#6966311yescharacteristic, complemented
564C3#7166711yescharacteristic, complemented
565C2—21no—
566C2—21no—
567C2—122no—
568C2—242no—
569C2#1059138111yescharacteristic
570C2#1059150911yescharacteristic
571C2#1059164511yescharacteristic
subgroupG/H
centerC22#63976
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#120
prime radicalC2×#63823C2
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1883
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#5504C2semidirect
3. C3×#4988C2semidirect
4. C2×#63569C2semidirect
5. #10591085C2semidirect
6. #10589396C2semidirect
7. #10589161C2semidirect
25. #63823C4semidirect
33. #5504D3semidirect
38. #4988D3semidirect
59. C2×C3×D12C2×C4semidirect
69. #3748C2×C4semidirect
156. C3×D12C22⋊C4semidirect
161. C3×Dic6C22⋊C4semidirect
206. C2×D12C4×D3semidirect
372. D12(C2×D3)⋊C4semidirect
377. Dic6(C2×D3)⋊C4semidirect
484. C32#1883semidirect
563. C3#69663semidirect
564. C3#71667semidirect

Maximal subgroups

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

subgroupindex
C3×#55042
C2×#638232
C3×#49882
C2×#635692
#105910852
#105893962
#105891612
#716673
#696633