Finite Group Databasebeta

← #11787749

Subgroups — #11787749

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic
2#10594990C211yesmaximal, characteristic, complemented
3#10591320C211yesmaximal, characteristic, complemented
4C2×#63570C211yesmaximal, characteristic, complemented
5#10591096C211yesmaximal, characteristic, complemented
6C3×#4555C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#69005—31nomaximal
9#68776—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64117—22no—
14#64117C414yescomplemented
15C2×#3745—21no—
16C2×#3744—21no—
17C3×#926C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C2×#3722—22no—
22#63952—22no—
23#63900—21no—
24#63894—21no—
25#63849—21no—
26#63844—21no—
27#63570—22no—
28#63564—21no—
29#63564—21no—
30C2×#908—31no—
31C2×#908—31no—
32C2×#908—61no—
33#5523—31no—
34#5504—31no—
35C2×#825—31no—
36#5131—31no—
37#5001—31no—
38#4988—31no—
39#4939—31no—
40C2×#805—31no—
41C3×#343—31no—
42C3×#339—31no—
43#4555D311yescharacteristic, complemented
44#4554D311yescharacteristic, complemented
45C23×C3⋊D3—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48#3828—21no—
49#3828—21no—
50#3828C2×C412yes—
51#3828D412yes—
52C2×C4⋊(C3⋊D3)—21no—
53C2×C4⋊(C3⋊D3)—21no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2×C412yescomplemented
58C2×C4⋊(C3⋊D3)D411yescharacteristic
59C2×C4×C3⋊D3—21no—
60C2×#634D411yescharacteristic
61C22×C3×Dic3—21no—
62C22×C3×Dic3D412yes—
63C2×#624—22no—
64C32×M16—21no—
65C32×M16C2×C412yescomplemented
66C2×C32×C8—21no—
67#3745—24no—
68#3744—24no—
69C3×#217—21no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3D411yescharacteristic
73C3×C4⋊Dic3D411yescharacteristic
74C3×C4×Dic3—21no—
75C3×C4×Dic3—21no—
76C3×C4×Dic3—21no—
77C3×#208—21no—
78C3×#208—21no—
79C2×C3×C3⋊C8—21no—
80#3724—22no—
81#3722—22no—
82#3722—44no—
83Dic32—22no—
84#1883—91noSylow
85C2×#235—31no—
86C2×#235—31no—
87C2×#235—61no—
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C2×C3×M16—21no—
92C2×C3×M16—31no—
93C2×C3×M16C2×D311yescharacteristic
94C2×C3×M16C2×D311yescharacteristic
95C3×#117—31no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C42—31no—
98C4×#67—62no—
99C2×(C2×D3)⋊C4—62no—
100C2×(C2×D3)⋊C4—62no—
101#926C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4×Dic3C2×D311yescharacteristic
104C2×#208C2×D311yescharacteristic
105#908—34no—
106#908—34no—
107#908—64no—
108#908—62no—
109#908—62no—
110#908—64no—
111C2×D24—61no—
112C2×D24—61no—
113C2×D24—62no—
114C2×#204—61no—
115C2×#204—61no—
116C2×#204—62no—
117#893—61no—
118#892—61no—
119#892—61no—
120D3×C4⋊C4—61no—
121D3×C4⋊C4—61no—
122#887—61no—
123#67⋊C4—62no—
124C4×D12—61no—
125C4×Dic6—61no—
126#825—62no—
127#821—61no—
128#821—61no—
129#809—61no—
130#809—61no—
131#805—62no—
132C23×C32C2×D411yescharacteristic
133C22×C3⋊D3—21no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—41no—
136C22×C3⋊D3—41no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C2×C32×C4C22×C411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4#4111yescharacteristic
144C2×C32×C4#4111yescharacteristic
145#638—22no—
146#638—22no—
147C2×C3⋊Dic3—21no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—21no—
151C4⋊(C3⋊D3)—41no—
152C4⋊(C3⋊D3)—41no—
153C4⋊(C3⋊D3)C22⋊C412yescomplemented
154C4×C3⋊D3—22no—
155C4×C3⋊D3—22no—
156#634—21no—
157#634C22⋊C412yescomplemented
158C2×C3×Dic3—22no—
159C2×C3×Dic3—21no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—21no—
162C2×C3×Dic3—41no—
163C2×C3×Dic3—41no—
164C2×C3×Dic3—42no—
165#624—82no—
166C32×C8—22no—
167C3×C3⋊C8—41no—
168C2×AGL(1,ℤ/8)—91no—
169#520—91no—
170C2×#104—91no—
171#418—91no—
172#390—91no—
173#343—31no—
174#339—31no—
175C23×D3—61no—
176C23×D3—61no—
177C23×D3—121no—
178C22×C3×C4—21no—
179C22×C3×C4—32no—
180C22×C3×C4—61no—
181C22×C3×C4C22×D311yescharacteristic
182C22×C3×C4C22×D311yescharacteristic
183C2×#67—61no—
184C2×#67—61no—
185C2×#67—121no—
186C22×Dic3—21no—
187C22×Dic3D1212yes—
188#235—32no—
189#235—32no—
190#235—32no—
191#235—32no—
192#235—62no—
193#235—62no—
194#235—61no—
195#235—61no—
196#235—61no—
197#235—61no—
198#235—121no—
199#235—121no—
200C2×D12—31no—
201C2×D12—31no—
202C2×D12—32no—
203C2×D12—32no—
204C2×D12—61no—
205C2×D12—62no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12—61no—
210C2×D12—61no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—61no—
215C2×D12—61no—
216C2×D12—61no—
217C2×D12—61no—
218C2×D12—121no—
219C2×D12—121no—
220C2×D12—121no—
221C2×C4×D3—61no—
222C2×C4×D3—61no—
223C2×C4×D3—62no—
224C2×C4×D3—62no—
225C2×C4×D3—121no—
226C2×Dic6—31no—
227C2×Dic6—31no—
228C2×Dic6—61no—
229C3×M16—22no—
230C3×M16—21no—
231C3×M16—21no—
232C3×M16—22no—
233C3×M16—61no—
234C3×M16—61no—
235C3×M16C4×D312yescomplemented
236C3×M16C4×D312yescomplemented
237C2×C3×C8—22no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—61no—
241C3×C4⋊C4—31no—
242C3×C4⋊C4—31no—
243C3×C4⋊C4—61no—
244C3×C4⋊C4—61no—
245C3×C22⋊C4—61no—
246C3×C42—61no—
247C3×C42—61no—
248C3×C42—61no—
249#217—21no—
250(C2×D3)⋊C4—62no—
251(C2×D3)⋊C4—62no—
252(C2×D3)⋊C4—124no—
253(C2×D3)⋊C4—124no—
254C4⋊Dic3—21no—
255C4⋊Dic3—21no—
256C4⋊Dic3D1211yescharacteristic
257C4⋊Dic3D1211yescharacteristic
258Dic3⋊C4—62no—
259Dic3⋊C4—62no—
260C4×Dic3—21no—
261C4×Dic3—21no—
262C4×Dic3—21no—
263C4×Dic3—62no—
264C4×Dic3—62no—
265#208—21no—
266#208—21no—
267C2×C3⋊C8—21no—
268D24—64no—
269D24—64no—
270D24—68no—
271#204—64no—
272#204—64no—
273#204—68no—
274C22×C32—21no—
275C22×C32—21no—
276C22×C32C4×D411yescharacteristic
277C22×C32#12011yescharacteristic
278C22×C32#12111yescharacteristic
279C2×C3⋊D3—22no—
280C2×C3⋊D3—42no—
281C2×C3⋊D3—41no—
282C2×C3⋊D3—41no—
283C2×C3⋊D3—44no—
284C2×C3⋊D3—82no—
285C2×C3⋊D3—81no—
286C2×C3⋊D3—81no—
287C32×C4C2×C22⋊C411yescharacteristic
288C32×C4C4×D411yescharacteristic
289C32×C4#12111yescharacteristic
290C32×C4#12311yescharacteristic
291C3⋊Dic3—22no—
292C3×Dic3—42no—
293C3×Dic3—41no—
294C3×Dic3—42no—
295C3×Dic3—41no—
296C2×#41—91no—
297C22×D4—91no—
298AGL(1,ℤ/8)—94no—
299AGL(1,ℤ/8)—182no—
300C2×SD16—181no—
301C2×D8—181no—
302C2×M16—31no—
303C2×M16D3211yescharacteristic
304C4×Q8—181no—
305C4×D4—181no—
306C4×D4—182no—
307#117—31no—
308#117—181no—
309C2×C4⋊C4—31no—
310C2×C4⋊C4—181no—
311C2×C22⋊C4—182no—
312C2×C42—31no—
313#104—182no—
314#102—181no—
315#102—181no—
316C23×C3—21no—
317C23×C3C2×D1211yescharacteristic
318C23×C3D3×D411yescharacteristic
319C22×D3—61no—
320C22×D3—61no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—121no—
324C22×D3—122no—
325C22×D3—122no—
326C22×D3—122no—
327C22×D3—122no—
328C22×D3—122no—
329C22×D3—122no—
330C22×D3—122no—
331C22×D3—121no—
332C22×D3—121no—
333C22×D3—121no—
334C22×D3—121no—
335C22×D3—242no—
336C22×D3—242no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—21no—
340C2×C3×C4—21no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—62no—
344C2×C3×C4—61no—
345C2×C3×C4—62no—
346C2×C3×C4—61no—
347C2×C3×C4—121no—
348C2×C3×C4—121no—
349C2×C3×C4—122no—
350C2×C3×C4C2×C4×D311yescharacteristic
351C2×C3×C4C2×C4×D311yescharacteristic
352C2×C3×C4C2×D1211yescharacteristic
353C2×C3×C4#23511yescharacteristic
354C2×C3×C4#23511yescharacteristic
355C2×C3×C4D3×D411yescharacteristic
356C2×C3×C4D3×D411yescharacteristic
357C2×C3×C4D3×D411yescharacteristic
358C2×C3×C4D3×D411yescharacteristic
359C2×C3×C4D3×D411yescharacteristic
360C2×C3×C4#23911yescharacteristic
361C2×C3×C4#23911yescharacteristic
362#67—62no—
363#67—62no—
364#67—62no—
365#67—62no—
366#67—122no—
367#67—122no—
368C2×Dic3—22no—
369C2×Dic3—21no—
370C2×Dic3—21no—
371C2×Dic3—22no—
372C2×Dic3—41no—
373C2×Dic3—41no—
374C2×Dic3—42no—
375C2×Dic3—61no—
376C2×Dic3—61no—
377C2×Dic3—121no—
378D12—32no—
379D12—32no—
380D12—62no—
381D12—64no—
382D12—62no—
383D12—62no—
384D12—62no—
385D12—62no—
386D12—61no—
387D12—61no—
388D12—122no—
389D12—121no—
390D12—122no—
391D12—122no—
392D12—121no—
393D12—121no—
394D12—121no—
395D12—121no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—62no—
399C4×D3—62no—
400C4×D3—122no—
401C4×D3—122no—
402C4×D3—242no—
403C4×D3—242no—
404Dic6—32no—
405Dic6—32no—
406Dic6—62no—
407Dic6—61no—
408Dic6—61no—
409Dic6—121no—
410C3×C8—24no—
411C3×C8—22no—
412C3×C8—22no—
413C3×C8—121no—
414C3⋊C8—41no—
415C2×C32—21no—
416C2×C32—21no—
417C2×C32#38611yescharacteristic
418C2×C32#45311yescharacteristic
419C2×C32#45411yescharacteristic
420C3⋊D3—42no—
421C3⋊D3—82no—
422C24—181no—
423#41—92no—
424#41—92no—
425#41—181no—
426#41—181no—
427C2×Q8—91no—
428C2×D4—92no—
429C2×D4—91no—
430C2×D4—181no—
431C2×D4—181no—
432C2×D4—181no—
433C2×D4—181no—
434C2×D4—181no—
435C2×D4—181no—
436C22×C4—32no—
437C22×C4—61no—
438C22×C4—182no—
439C22×C4—181no—
440C22×C4C2×D3211yescharacteristic
441SD16—184no—
442D8—184no—
443M16—21no—
444M16—61no—
445M16—61no—
446M16#62412yescomplemented
447C2×C8—21no—
448C2×C8—61no—
449C4⋊C4—31no—
450C4⋊C4—31no—
451C4⋊C4—61no—
452C4⋊C4—61no—
453C4⋊C4—182no—
454C22⋊C4—61no—
455C22⋊C4—182no—
456C22⋊C4—364no—
457C42—61no—
458C42—61no—
459C42—61no—
460C42—182no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3C4×D1211yescharacteristic
471C22×C3#88211yescharacteristic
472C22×C3#88211yescharacteristic
473C22×C3#88411yescharacteristic
474C22×C3#89311yescharacteristic
475C22×C3#89511yescharacteristic
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—122no—
479C2×D3—121no—
480C2×D3—121no—
481C2×D3—121no—
482C2×D3—121no—
483C2×D3—124no—
484C2×D3—124no—
485C2×D3—124no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—241no—
489C2×D3—241no—
490C2×D3—244no—
491C2×D3—242no—
492C2×D3—242no—
493C2×D3—242no—
494C2×D3—242no—
495C2×D3—244no—
496C2×D3—241no—
497C2×D3—241no—
498C2×D3—241no—
499C2×D3—241no—
500C3×C4—21no—
501C3×C4—21no—
502C3×C4—21no—
503C3×C4—21no—
504C3×C4—122no—
505C3×C4—121no—
506C3×C4—121no—
507C3×C4—122no—
508C3×C4C4×D1211yescharacteristic
509C3×C4D3×C22⋊C411yescharacteristic
510C3×C4D3×C22⋊C411yescharacteristic
511C3×C4#88411yescharacteristic
512C3×C4#89311yescharacteristic
513C3×C4#89411yescharacteristic
514C3×C4#89411yescharacteristic
515C3×C4#89511yescharacteristic
516Dic3—42no—
517Dic3—42no—
518Dic3—41no—
519Dic3—41no—
520Dic3—62no—
521Dic3—62no—
522Dic3—122no—
523C32#188311yescharacteristic, complemented, Sylow
524C23—181no—
525C23—182no—
526C23—362no—
527C23—362no—
528C23—361no—
529C23—361no—
530C23D3×D1211yescharacteristic
531Q8—92no—
532Q8—181no—
533D4—92no—
534D4—182no—
535D4—182no—
536D4—182no—
537D4—181no—
538D4—182no—
539D4—361no—
540D4—361no—
541C2×C4—62no—
542C2×C4—61no—
543C2×C4—61no—
544C2×C4—62no—
545C2×C4—121no—
546C2×C4—121no—
547C2×C4—122no—
548C2×C4—181no—
549C2×C4—182no—
550C2×C4—182no—
551C2×C4—722no—
552C2×C4#379911yescharacteristic
553C2×C4#379911yescharacteristic
554C2×C4D3×D1211yescharacteristic
555C2×C4C2×#62411yescharacteristic
556C2×C4#381111yescharacteristic
557C2×C4#381111yescharacteristic
558C8—22no—
559C8—121no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—41no—
568C2×C3—41no—
569C2×C3#466511yescharacteristic
570C2×C3#466511yescharacteristic
571C2×C3#474711yescharacteristic
572C2×C3#475311yescharacteristic
573C2×C3#482211yescharacteristic
574C2×C3#482711yescharacteristic
575D3—122no—
576D3—122no—
577D3—242no—
578D3—244no—
579D3—242no—
580D3—242no—
581C22—21no—
582C22—21no—
583C22—182no—
584C22—364no—
585C22—361no—
586C22—361no—
587C22—362no—
588C22—722no—
589C22—721no—
590C22—721no—
591C22#6389411yescharacteristic
592C22#6391011yescharacteristic
593C22#6392311yescharacteristic
594C4—122no—
595C4—122no—
596C4—121no—
597C4—121no—
598C4—182no—
599C4#6389411yescharacteristic
600C4#6389711yescharacteristic
601C4#6391011yescharacteristic
602C4#6397411yescharacteristic
603C3—21no—
604C3#6877611yescharacteristic, complemented
605C3#6900511yescharacteristic, complemented
606C2—21no—
607C2—21no—
608C2—362no—
609C2—722no—
610C2#1059101511yescharacteristic
611C2#1059102211yescharacteristic
612C2#1059138011yescharacteristic
subgroupG/H
centerC22#63923
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#120
prime radicalC2×#64117C2
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. #10594990C2semidirect
3. #10591320C2semidirect
4. C2×#63570C2semidirect
5. #10591096C2semidirect
6. C3×#4555C2semidirect
7. C3×#4554C2semidirect
14. #64117C4semidirect
43. #4555D3semidirect
44. #4554D3semidirect
57. C2×C4⋊(C3⋊D3)C2×C4semidirect
65. C32×M16C2×C4semidirect
153. C4⋊(C3⋊D3)C22⋊C4semidirect
157. #634C22⋊C4semidirect
235. C3×M16C4×D3semidirect
236. C3×M16C4×D3semidirect
446. M16#624semidirect
523. C32#1883semidirect
604. C3#68776semidirect
605. C3#69005semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
#105949902
#105913202
C2×#635702
#105910962
C3×#45552
C3×#45542
#690053
#687763