Finite Group Databasebeta

← #11787748

Subgroups — #11787748

Order 1152.

795 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic
2#10594986C211yesmaximal, characteristic, complemented
3#10591323C211yesmaximal, characteristic, complemented
4C2×#63568C211yesmaximal, characteristic, complemented
5#10591086C211yesmaximal, characteristic, complemented
6#10589421C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#72088—31nomaximal
9#69005—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#908—22no—
18C3×#908C414yescomplemented
19C2×C3×D24—21no—
20C2×C3×#204—21no—
21Dic3×#67—22no—
22C2×(C2×D3)⋊Dic3—22no—
23#63898—21no—
24D3×C4⋊Dic3—21no—
25#63843—21no—
26#63841—21no—
27#63568—22no—
28#63563—21no—
29#63563—21no—
30C2×C3×AGL(1,ℤ/8)—31no—
31#5827—31no—
32C2×#908D311yescharacteristic
33#5504—31no—
34C2×#837—31no—
35#5221—31no—
36#5215—31no—
37C2×#825—31no—
38#5131—31no—
39#4988—31no—
40C3×#343—31no—
41#4555—31no—
42#4555—31no—
43#4555—61no—
44#4554D311yescharacteristic, complemented
45C23×C3×D3—21no—
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C2×C3×#67—21no—
49C22×C3×Dic3D412yes—
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—
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×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×M16—31no—
95C2×C3×M16C2×D311yescharacteristic
96C2×C3×M16C2×D311yescharacteristic
97C2×C3×C4⋊C4—31no—
98C2×#217—62no—
99Q8×Dic3—61no—
100D4×Dic3—61no—
101D4×Dic3—62no—
102C4×#67—62no—
103C2×(C2×D3)⋊C4—62no—
104#926—31no—
105#926—31no—
106#926—61no—
107#926—61no—
108C2×C4⋊Dic3—61no—
109C2×C4⋊Dic3C2×D311yescharacteristic
110C2×C4×Dic3—31no—
111C2×C4×Dic3—31no—
112C2×C4×Dic3—61no—
113C2×#208C2×D311yescharacteristic
114#908—22no—
115#908Dic314yescomplemented
116C2×D24—21no—
117C2×#204—21no—
118#893—61no—
119#892—61no—
120D3×C4⋊C4—61no—
121#887—61no—
122#837—62no—
123#832—61no—
124#832—61no—
125#825—62no—
126#821—61no—
127#821—61no—
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—21no—
143C2×C3⋊Dic3—21no—
144C2×C3⋊Dic3—41no—
145C2×C3⋊Dic3—41no—
146C3×#67—22no—
147C3×#67—22no—
148C2×C3×Dic3—21no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—42no—
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—31no—
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—21no—
187C22×C3×C4—32no—
188C22×C3×C4—61no—
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C2×#67—21no—
192C22×Dic3—62no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C22×Dic3—121no—
196C22×Dic3D1212yes—
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×M16—61no—
218C3×M16—61no—
219C3×M16C4×D312yescomplemented
220C3×M16C2×Dic312yescomplemented
221C2×C3×C8—21no—
222C2×C3×C8—21no—
223C2×C3×C8—41no—
224C2×C3×C8—61no—
225C3×C4⋊C4—61no—
226C3×C4⋊C4—61no—
227#217—62no—
228#217—61no—
229#217—61no—
230#217—121no—
231#217—124no—
232(C2×D3)⋊C4—62no—
233(C2×D3)⋊C4—124no—
234C4⋊Dic3—21no—
235C4⋊Dic3—21no—
236C4⋊Dic3—31no—
237C4⋊Dic3—31no—
238C4⋊Dic3—31no—
239C4⋊Dic3—31no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—62no—
243Dic3⋊C4—62no—
244C4×Dic3—62no—
245C4×Dic3—62no—
246C4×Dic3—61no—
247C4×Dic3—61no—
248C4×Dic3—62no—
249C4×Dic3—61no—
250C4×Dic3—61no—
251C4×Dic3—61no—
252C4×Dic3—61no—
253C4×Dic3—121no—
254C4×Dic3—121no—
255#208—21no—
256#208—21no—
257C2×C3⋊C8—21no—
258D24—24no—
259#204—24no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32C4×D411yescharacteristic
263C22×C32#12011yescharacteristic
264C22×C32#12111yescharacteristic
265C2×C3×D3—22no—
266C2×C3×D3—41no—
267C2×C3×D3—41no—
268C2×C3×D3—44no—
269C2×C3×D3—42no—
270C2×C3×D3—82no—
271C2×C3×D3—81no—
272C2×C3×D3—81no—
273C32×C4C2×C22⋊C411yescharacteristic
274C32×C4C4×D411yescharacteristic
275C32×C4#12111yescharacteristic
276C32×C4#12311yescharacteristic
277C3⋊Dic3—42no—
278C3⋊Dic3—41no—
279C3⋊Dic3—41no—
280C3×Dic3—22no—
281C3×Dic3—42no—
282C2×#41—31no—
283C22×D4—31no—
284AGL(1,ℤ/8)—34no—
285AGL(1,ℤ/8)—62no—
286C2×SD16—61no—
287C2×D8—61no—
288C2×M16—31no—
289C2×M16D3211yescharacteristic
290C4×Q8—181no—
291C4×D4—181no—
292C4×D4—182no—
293#117—91no—
294#117—181no—
295C2×C4⋊C4—31no—
296C2×C4⋊C4—181no—
297C2×C22⋊C4—182no—
298C2×C42—91no—
299#104—182no—
300#102—181no—
301#102—181no—
302C23×C3—21no—
303C23×C3—61no—
304C23×C3—62no—
305C23×C3—122no—
306C23×C3—122no—
307C23×C3—121no—
308C23×C3—121no—
309C23×C3C2×D1211yescharacteristic
310C23×C3D3×D411yescharacteristic
311C22×D3—21no—
312C22×D3—22no—
313C22×D3—42no—
314C22×D3—42no—
315C22×D3—41no—
316C22×D3—41no—
317C3×Q8—32no—
318C3×Q8—61no—
319C3×D4—32no—
320C3×D4—62no—
321C3×D4—62no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—61no—
325C3×D4—121no—
326C3×D4—121no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—61no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—122no—
338C2×C3×C4C2×C4×D311yescharacteristic
339C2×C3×C4#23511yescharacteristic
340C2×C3×C4D3×D411yescharacteristic
341C2×C3×C4D3×D411yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23711yescharacteristic
345C2×C3×C4#23711yescharacteristic
346C2×C3×C4#23911yescharacteristic
347C2×C3×C4C22×Dic311yescharacteristic
348C2×C3×C4C2×#6711yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350#67—22no—
351#67—22no—
352C2×Dic3—21no—
353C2×Dic3—22no—
354C2×Dic3—42no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—122no—
362C2×Dic3—121no—
363C2×Dic3—121no—
364C2×Dic3—122no—
365C2×Dic3—121no—
366C2×Dic3—121no—
367C2×Dic3—122no—
368C2×Dic3—121no—
369C2×Dic3—121no—
370C2×Dic3—242no—
371D12—22no—
372D12—21no—
373D12—22no—
374D12—41no—
375D12—41no—
376D12#21712yescomplemented
377C4×D3—22no—
378C4×D3—22no—
379C4×D3—242no—
380Dic6—21no—
381Dic6#21712yescomplemented
382C3×C8—22no—
383C3×C8—22no—
384C3×C8—42no—
385C3×C8—121no—
386C3⋊C8—41no—
387C2×C32—21no—
388C2×C32—21no—
389C2×C32#38611yescharacteristic
390C2×C32#45311yescharacteristic
391C2×C32#45411yescharacteristic
392C3×D3—42no—
393C3×D3—82no—
394C24—61no—
395#41—32no—
396#41—32no—
397#41—61no—
398#41—61no—
399C2×Q8—31no—
400C2×D4—32no—
401C2×D4—31no—
402C2×D4—61no—
403C2×D4—61no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—61no—
407C2×D4—61no—
408C22×C4—32no—
409C22×C4—61no—
410C22×C4—182no—
411C22×C4—181no—
412C22×C4C2×D3211yescharacteristic
413SD16—64no—
414D8—64no—
415M16—21no—
416M16—61no—
417M16—61no—
418M16D3×Dic312yescomplemented
419C2×C8—21no—
420C2×C8—61no—
421C4⋊C4—61no—
422C4⋊C4—61no—
423C4⋊C4—91no—
424C4⋊C4—91no—
425C4⋊C4—182no—
426C22⋊C4—182no—
427C22⋊C4—181no—
428C22⋊C4—364no—
429C42—182no—
430C42—181no—
431C42—181no—
432C42—181no—
433C22×C3—21no—
434C22×C3—21no—
435C22×C3—21no—
436C22×C3—21no—
437C22×C3—21no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3—62no—
443C22×C3—124no—
444C22×C3—121no—
445C22×C3—121no—
446C22×C3—122no—
447C22×C3—242no—
448C22×C3—241no—
449C22×C3—241no—
450C22×C3C4×D1211yescharacteristic
451C22×C3#88211yescharacteristic
452C22×C3#89511yescharacteristic
453C22×C3D4×Dic311yescharacteristic
454C22×C3#93711yescharacteristic
455C22×C3#93911yescharacteristic
456C2×D3—22no—
457C2×D3—41no—
458C2×D3—41no—
459C2×D3—44no—
460C2×D3—42no—
461C2×D3—82no—
462C2×D3—81no—
463C2×D3—81no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—62no—
469C3×C4—122no—
470C3×C4D3×C22⋊C411yescharacteristic
471C3×C4#88411yescharacteristic
472C3×C4#89311yescharacteristic
473C3×C4#89411yescharacteristic
474C3×C4D4×Dic311yescharacteristic
475C3×C4#93511yescharacteristic
476C3×C4#93911yescharacteristic
477C3×C4C2×#21711yescharacteristic
478Dic3—22no—
479Dic3—42no—
480Dic3—122no—
481Dic3—122no—
482Dic3—124no—
483Dic3—121no—
484Dic3—121no—
485Dic3—121no—
486Dic3—121no—
487Dic3—241no—
488Dic3—241no—
489C32#188311yescharacteristic, complemented, Sylow
490C23—61no—
491C23—62no—
492C23—122no—
493C23—122no—
494C23—121no—
495C23—121no—
496C23D3×D1211yescharacteristic
497Q8—32no—
498Q8—61no—
499D4—32no—
500D4—62no—
501D4—62no—
502D4—61no—
503D4—62no—
504D4—62no—
505D4—121no—
506D4—121no—
507C2×C4—61no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—122no—
512C2×C4—182no—
513C2×C4—181no—
514C2×C4—181no—
515C2×C4—361no—
516C2×C4—361no—
517C2×C4—722no—
518C2×C4#379511yescharacteristic
519C2×C4#379611yescharacteristic
520C2×C4#380211yescharacteristic
521C2×C4C2×D3×Dic311yescharacteristic
522C2×C4D3×#6711yescharacteristic
523C2×C4D3×#6711yescharacteristic
524C8—22no—
525C8—121no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—41no—
534C2×C3—41no—
535C2×C3—122no—
536C2×C3—242no—
537C2×C3#466511yescharacteristic
538C2×C3#474711yescharacteristic
539C2×C3#475311yescharacteristic
540C2×C3#519811yescharacteristic
541C2×C3#520111yescharacteristic
542C2×C3#522011yescharacteristic
543D3—42no—
544D3—82no—
545C22—21no—
546C22—21no—
547C22—62no—
548C22—124no—
549C22—121no—
550C22—121no—
551C22—122no—
552C22—242no—
553C22—241no—
554C22—241no—
555C22#6388611yescharacteristic
556C22Dic3×D1211yescharacteristic
557C22#6392211yescharacteristic
558C4—62no—
559C4—122no—
560C4—362no—
561C4—361no—
562C4—361no—
563C4#6388411yescharacteristic
564C4#6388511yescharacteristic
565C4#6389811yescharacteristic
566C4D3×#21711yescharacteristic
567C3—21no—
568C3#6900511yescharacteristic, complemented
569C3#7208811yescharacteristic, complemented
570C2—21no—
571C2—21no—
572C2—122no—
573C2—242no—
574C2#1059101411yescharacteristic
575C2#1059102011yescharacteristic
576C2#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. #10594986C2semidirect
3. #10591323C2semidirect
4. C2×#63568C2semidirect
5. #10591086C2semidirect
6. #10589421C2semidirect
7. C3×#4554C2semidirect
18. C3×#908C4semidirect
44. #4554D3semidirect
59. C2×C3×D12C2×C4semidirect
65. C32×M16C2×C4semidirect
115. #908Dic3semidirect
156. C3×D12C22⋊C4semidirect
160. C3×Dic6C22⋊C4semidirect
206. C2×D12C2×Dic3semidirect
219. C3×M16C4×D3semidirect
220. C3×M16C2×Dic3semidirect
376. D12#217semidirect
381. Dic6#217semidirect
418. M16D3×Dic3semidirect
489. C32#1883semidirect
568. C3#69005semidirect
569. 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
#105949862
#105913232
C2×#635682
#105910862
#105894212
C3×#45542
#720883
#690053