Finite Group Databasebeta

← #11788625

Subgroups — #11788625

Order 1152.

745 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63830C211yesmaximal, characteristic
2C2×#63817C211yesmaximal, characteristic, complemented
3#10592832C211yesmaximal, characteristic, complemented
4C2×C3×#823C211yesmaximal, characteristic, complemented
5C2×#63563C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70088—31nomaximal
9#68948—31nomaximal
10C2×#3828C2211yescharacteristic
11C22×C3×D12C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63830—22no—
18#63830C414yescomplemented
19C2×#3716—21no—
20C2×#3714—21no—
21C2×#3712—21no—
22#63817—22no—
23#63817—22no—
24C2×#3710—21no—
25#63648—21no—
26#63643—21no—
27C3×#823—22no—
28#63563—21no—
29#63563—21no—
30C2×#932—31no—
31C2×#908—31no—
32C2×#907—31no—
33C2×#901—31no—
34C2×C3×#100—31no—
35C2×#832—31no—
36#5133—31no—
37#5133—31no—
38#5133—61no—
39C2×#823D311yescharacteristic, complemented
40C2×#821—31no—
41C3×#341—31no—
42#4558D311yescharacteristic, complemented
43#4554—31no—
44#4554—31no—
45C23×C3×D3—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—21no—
48C22×C3⋊Dic3—21no—
49#3828—21no—
50#3828—21no—
51#3828C2×C412yes—
52#3828D412yes—
53C2×C4⋊(C3⋊D3)D411yescharacteristic
54C2×C4×C3⋊D3—21no—
55C2×#634D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—21no—
59C2×C3×D12—21no—
60C2×C3×D12—21no—
61C2×C3×D12C2×C412yes—
62C32×M16—21no—
63C32×M16—21no—
64C2×C32×C8—21no—
65C4⋊(C3⋊Dic3)—21no—
66C4⋊(C3⋊Dic3)—21no—
67C3×#208—21no—
68C3×#208—21no—
69C3×#208C2×C412yes—
70C3×#208D412yes—
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8D411yescharacteristic
76C2×C3×C3⋊C8D411yescharacteristic
77#3716—24no—
78#3714—24no—
79#3712—24no—
80#3710—24no—
81#1907—91noSylow
82C22×C3×D4—31no—
83C2×#235—31no—
84C2×#235—31no—
85C2×#235—61no—
86C22×D12C2×D311yescharacteristic
87C2×C3×M16—21no—
88C2×C3×M16—31no—
89C2×C3×M16—31no—
90C2×C3×M16C2×D311yescharacteristic
91C2×C3×M16C2×D311yescharacteristic
92C22×C3×C8—31no—
93C2×#214—61no—
94#932—34no—
95#932—62no—
96C2×#213—61no—
97C2×C4⋊Dic3—31no—
98C2×C4⋊Dic3—31no—
99C2×C4⋊Dic3—61no—
100C2×#208C2×D311yescharacteristic
101C2×#208C2×D311yescharacteristic
102C22×C3⋊C8C2×D311yescharacteristic
103#908—34no—
104#908—62no—
105#907—62no—
106#907—62no—
107C2×D24—61no—
108C2×#204—61no—
109#901—62no—
110#901—62no—
111C2×ΓL(1,𝔽25)—61no—
112C2×ΓL(1,𝔽25)—61no—
113C2×D3×C8—61no—
114C2×D3×C8—61no—
115C3×#100—62no—
116#832—61no—
117#832—61no—
118#823—22no—
119#821—61no—
120#821—61no—
121#821—62no—
122#821—61no—
123#821—61no—
124#816—61no—
125#816—61no—
126#816—62no—
127C23×C32#4111yescharacteristic
128C22×C3⋊D3—21no—
129C22×C3×D3—22no—
130C22×C3×D3—41no—
131C22×C3×D3—41no—
132C22×C3×D3—81no—
133C22×C3×D3—81no—
134C2×C32×C4C22×C411yescharacteristic
135C2×C32×C4C2×D411yescharacteristic
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4#4111yescharacteristic
140#638—22no—
141#638—22no—
142C2×C3⋊Dic3—21no—
143C2×C3⋊Dic3—41no—
144C2×C3⋊Dic3—81no—
145C4⋊(C3⋊D3)—21no—
146C4⋊(C3⋊D3)C22⋊C412yes—
147C4×C3⋊D3—22no—
148C4×C3⋊D3—22no—
149#634—21no—
150#634C22⋊C412yes—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12—41no—
154C3×D12—41no—
155C32×C8—41no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—21no—
158C3×C3⋊C8—22no—
159C3×C3⋊C8—21no—
160C2×AGL(1,ℤ/8)—91no—
161C2×#131—91no—
162#417—91no—
163C2×#102—91no—
164C2×#100—31no—
165#343—91no—
166#341—31no—
167C24×C3—61no—
168C23×D3—21no—
169C2×C3×D4—32no—
170C2×C3×D4—61no—
171C2×C3×D4—61no—
172C2×C3×D4—61no—
173C2×C3×D4—61no—
174C2×C3×D4—61no—
175C22×C3×C4—21no—
176C22×C3×C4C22×D311yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C2×#67—61no—
179C2×#67—61no—
180C2×#67—121no—
181C22×Dic3—61no—
182C22×Dic3—61no—
183C22×Dic3—121no—
184#235—32no—
185#235—32no—
186#235—32no—
187#235—32no—
188#235—62no—
189#235—62no—
190#235—61no—
191#235—61no—
192#235—61no—
193#235—61no—
194#235—121no—
195#235—121no—
196C2×D12—21no—
197C2×D12—21no—
198C2×D12—21no—
199C2×D12—21no—
200C2×D12—21no—
201C2×D12—31no—
202C2×D12—31no—
203C2×D12—61no—
204C2×D12C4×D312yes—
205C2×C4×D3—61no—
206C2×C4×D3—61no—
207C2×C4×D3—121no—
208C2×Dic6—31no—
209C2×Dic6—31no—
210C2×Dic6—61no—
211C3×M16—21no—
212C3×M16—21no—
213C3×M16—21no—
214C3×M16—21no—
215C3×M16—32no—
216C3×M16—32no—
217C3×M16—41no—
218C3×M16—41no—
219C3×M16—61no—
220C3×M16—61no—
221C2×C3×C8—22no—
222C2×C3×C8—21no—
223C2×C3×C8—21no—
224C2×C3×C8—31no—
225C2×C3×C8—31no—
226C2×C3×C8—61no—
227C2×C3×C8—61no—
228C2×C3×C8—61no—
229C2×C3×C8—61no—
230#214—64no—
231#213—64no—
232C4⋊Dic3—62no—
233C4⋊Dic3—61no—
234C4⋊Dic3—61no—
235C4⋊Dic3—61no—
236C4⋊Dic3—61no—
237C4⋊Dic3—121no—
238#208—21no—
239#208—21no—
240#208C4×D312yes—
241#208#6712yes—
242C2×C3⋊C8—21no—
243C2×C3⋊C8—21no—
244C2×C3⋊C8—21no—
245C2×C3⋊C8—21no—
246C2×C3⋊C8D1211yescharacteristic
247C2×C3⋊C8D1211yescharacteristic
248D24—64no—
249#204—64no—
250ΓL(1,𝔽25)—64no—
251ΓL(1,𝔽25)—64no—
252D3×C8—64no—
253D3×C8—64no—
254C22×C32—21no—
255C22×C32—21no—
256C22×C32C4×D411yescharacteristic
257C22×C32#12111yescharacteristic
258C22×C32#12311yescharacteristic
259C2×C3⋊D3—22no—
260C2×C3⋊D3—41no—
261C2×C3⋊D3—41no—
262C2×C3×D3—42no—
263C2×C3×D3—82no—
264C2×C3×D3—81no—
265C2×C3×D3—81no—
266C2×C3×D3—82no—
267C32×C4C2×C22⋊C411yescharacteristic
268C32×C4C4×D411yescharacteristic
269C32×C4#12011yescharacteristic
270C32×C4#12111yescharacteristic
271C3⋊Dic3—22no—
272C3⋊Dic3—81no—
273C2×#41—91no—
274C22×D4—31no—
275AGL(1,ℤ/8)—94no—
276AGL(1,ℤ/8)—182no—
277C2×SD16—181no—
278C2×D8—181no—
279#131—182no—
280#131—182no—
281C2×M16—31no—
282C2×M16—31no—
283C2×M16—181no—
284C2×M16D3211yescharacteristic
285C22×C8—31no—
286C22×C8—181no—
287C2×C4⋊C4—91no—
288#103—181no—
289#102—181no—
290#102—181no—
291#102—181no—
292#100—62no—
293C23×C3—21no—
294C23×C3—62no—
295C23×C3—121no—
296C23×C3—121no—
297C23×C3—241no—
298C23×C3—241no—
299C23×C3#23511yescharacteristic
300C23×C3#23911yescharacteristic
301C22×D3—22no—
302C22×D3—41no—
303C22×D3—41no—
304C22×D3—61no—
305C22×D3—61no—
306C22×D3—81no—
307C22×D3—81no—
308C22×D3—121no—
309C3×D4—62no—
310C3×D4—62no—
311C3×D4—121no—
312C3×D4—121no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4C2×C4×D311yescharacteristic
321C2×C3×C4C2×D1211yescharacteristic
322C2×C3×C4#23511yescharacteristic
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4D3×D411yescharacteristic
325C2×C3×C4D3×D411yescharacteristic
326C2×C3×C4D3×D411yescharacteristic
327C2×C3×C4D3×D411yescharacteristic
328C2×C3×C4D3×D411yescharacteristic
329C2×C3×C4#23711yescharacteristic
330C2×C3×C4C2×#6711yescharacteristic
331#67—62no—
332#67—62no—
333#67—62no—
334#67—62no—
335#67—122no—
336#67—122no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—121no—
340C2×Dic3—122no—
341C2×Dic3—121no—
342C2×Dic3—121no—
343C2×Dic3—242no—
344C2×Dic3—241no—
345C2×Dic3—241no—
346D12—22no—
347D12—22no—
348D12—32no—
349D12—32no—
350D12—41no—
351D12—41no—
352D12—62no—
353D12—61no—
354D12—61no—
355D12—121no—
356C4×D3—62no—
357C4×D3—62no—
358C4×D3—62no—
359C4×D3—62no—
360C4×D3—122no—
361C4×D3—122no—
362Dic6—32no—
363Dic6—32no—
364Dic6—62no—
365Dic6—61no—
366Dic6—61no—
367Dic6—121no—
368C3×C8—42no—
369C3×C8—41no—
370C3×C8—41no—
371C3×C8—62no—
372C3×C8—62no—
373C3×C8—61no—
374C3×C8—61no—
375C3⋊C8—22no—
376C3⋊C8—21no—
377C3⋊C8—21no—
378C3⋊C8—22no—
379C2×C32—21no—
380C2×C32—21no—
381C2×C32#38611yescharacteristic
382C2×C32#47111yescharacteristic
383C2×C32#47211yescharacteristic
384C3⋊D3—42no—
385C3×D3—82no—
386C24—61no—
387#41—92no—
388#41—92no—
389#41—181no—
390#41—181no—
391C2×Q8—91no—
392C2×D4—32no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—91no—
399C2×D4—181no—
400C22×C4—181no—
401C22×C4—181no—
402C22×C4C2×D3211yescharacteristic
403SD16—184no—
404D8—184no—
405M16—21no—
406M16—21no—
407M16—32no—
408M16—32no—
409M16—61no—
410M16—61no—
411M16—184no—
412C2×C8—21no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8—61no—
416C2×C8—61no—
417C2×C8—61no—
418C2×C8—61no—
419C2×C8—184no—
420C4⋊C4—181no—
421C4⋊C4—181no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—21no—
429C22×C3—41no—
430C22×C3—41no—
431C22×C3—122no—
432C22×C3—242no—
433C22×C3—242no—
434C22×C3—241no—
435C22×C3—241no—
436C22×C3#88311yescharacteristic
437C22×C3#88411yescharacteristic
438C22×C3#89311yescharacteristic
439C22×C3#89411yescharacteristic
440C22×C3#89511yescharacteristic
441C22×C3C4×#6711yescharacteristic
442C2×D3—42no—
443C2×D3—62no—
444C2×D3—62no—
445C2×D3—82no—
446C2×D3—81no—
447C2×D3—81no—
448C2×D3—82no—
449C2×D3—122no—
450C2×D3—121no—
451C2×D3—121no—
452C2×D3—121no—
453C2×D3—121no—
454C2×D3—241no—
455C2×D3—241no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—21no—
459C3×C4—21no—
460C3×C4C4×D1211yescharacteristic
461C3×C4D3×C22⋊C411yescharacteristic
462C3×C4D3×C22⋊C411yescharacteristic
463C3×C4#67⋊C411yescharacteristic
464C3×C4#88211yescharacteristic
465C3×C4#88411yescharacteristic
466C3×C4#93711yescharacteristic
467C3×C4#93811yescharacteristic
468Dic3—62no—
469Dic3—62no—
470Dic3—122no—
471Dic3—242no—
472Dic3—241no—
473Dic3—241no—
474C32#190711yescharacteristic, complemented, Sylow
475C23—62no—
476C23—121no—
477C23—121no—
478C23—181no—
479C23—241no—
480C23—241no—
481C23#379911yescharacteristic
482Q8—92no—
483Q8—181no—
484D4—62no—
485D4—62no—
486D4—92no—
487D4—121no—
488D4—121no—
489D4—182no—
490D4—182no—
491D4—181no—
492C2×C4—181no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4—361no—
496C2×C4—721no—
497C2×C4C4×D3211yescharacteristic
498C2×C4D3×D1211yescharacteristic
499C2×C4#380211yescharacteristic
500C2×C4#380411yescharacteristic
501C2×C4D3×#6711yescharacteristic
502C2×C4#381111yescharacteristic
503C8—41no—
504C8—62no—
505C8—61no—
506C8—61no—
507C8—62no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—41no—
516C2×C3—41no—
517C2×C3—242no—
518C2×C3#466511yescharacteristic
519C2×C3#474811yescharacteristic
520C2×C3#474911yescharacteristic
521C2×C3#489711yescharacteristic
522C2×C3#489811yescharacteristic
523C2×C3#495611yescharacteristic
524D3—82no—
525D3—122no—
526D3—122no—
527D3—242no—
528C22—21no—
529C22—21no—
530C22—122no—
531C22—182no—
532C22—242no—
533C22—242no—
534C22—241no—
535C22—241no—
536C22—361no—
537C22—361no—
538C22#6385411yescharacteristic
539C22#6390411yescharacteristic
540C22#6391011yescharacteristic
541C4—182no—
542C4—721no—
543C4#6388011yescharacteristic
544C4#6392111yescharacteristic
545C4#6392211yescharacteristic
546C4#6395811yescharacteristic
547C3—21no—
548C3#6894811yescharacteristic, complemented
549C3#7008811yescharacteristic, complemented
550C2—21no—
551C2—21no—
552C2—242no—
553C2—362no—
554C2#1059098711yescharacteristic
555C2#1059098911yescharacteristic
556C2#1059127511yescharacteristic
subgroupG/H
centerC22#63910
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×#63830C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1907
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. C2×#63817C2semidirect
3. #10592832C2semidirect
4. C2×C3×#823C2semidirect
5. C2×#63563C2semidirect
6. C3×#4558C2semidirect
7. #10589168C2semidirect
18. #63830C4semidirect
39. C2×#823D3semidirect
42. #4558D3semidirect
474. C32#1907semidirect
548. C3#68948semidirect
549. C3#70088semidirect

Maximal subgroups

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

subgroupindex
C2×#638302
C2×#638172
#105928322
C2×C3×#8232
C2×#635632
C3×#45582
#105891682
#700883
#689483