Finite Group Databasebeta

← #11788633

Subgroups — #11788633

Order 1152.

757 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#932C211yesmaximal, characteristic
2C2×#63814C211yesmaximal, characteristic, complemented
3C2×#63660C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591087C211yesmaximal, characteristic, complemented
6#10589167C211yesmaximal, characteristic, complemented
7#10589166C211yesmaximal, characteristic, complemented
8#72091—31nomaximal
9#70218—31nomaximal
10C22×C32×D4C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C2×C3×#214—21no—
15C3×#932—22no—
16C3×#932C414yescomplemented
17C2×C3×#213—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C2×#3711—21no—
22#63814—22no—
23#63814—22no—
24C2×D3×C3⋊C8—21no—
25#63660—22no—
26C3×#832—21no—
27C3×#832—21no—
28#63565—21no—
29#63562—21no—
30C2×C3×AGL(1,ℤ/8)—31no—
31C2×#948—31no—
32C2×#932D311yescharacteristic
33C2×#901—31no—
34C2×C3×#102—31no—
35#5232—31no—
36C2×#833—31no—
37C2×#833—31no—
38C2×#833—61no—
39C2×#832D311yescharacteristic, complemented
40#4966—31no—
41#4558—31no—
42#4554—31no—
43#4552—31no—
44#4530—31no—
45C24×C32—21no—
46C2×C32×D4—21no—
47C2×C32×D4—21no—
48C2×C32×D4—21no—
49C2×C32×D4—21no—
50C2×C32×D4—21no—
51C2×C32×D4C2×C412yes—
52C22×C32×C4C2311yescharacteristic
53C2×C3×#67—21no—
54C22×C3×Dic3—21no—
55C3×#235—21no—
56C3×#235—21no—
57C3×#235C2×C412yes—
58C3×#235D412yes—
59C2×C3×D12D411yescharacteristic
60C2×C3×C4×D3—21no—
61C2×C3×Dic6D411yescharacteristic
62#3748—21no—
63#3748—21no—
64#3748—21no—
65#3748D412yes—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)—21no—
68C3×#214—24no—
69C3×#213—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×#208—21no—
73C3×#208C2×C412yes—
74C2×C3×C3⋊C8—21no—
75C2×C3×C3⋊C8—21no—
76C2×C3×C3⋊C8—21no—
77C2×C3×C3⋊C8D411yescharacteristic
78C2×C3×C3⋊C8D411yescharacteristic
79#3711—24no—
80D3×C3⋊C8—24no—
81#1907—91noSylow
82C2×C3×#41—31no—
83C22×C3×D4—21no—
84C22×C3×D4C2×D311yescharacteristic
85C22×C3×D4C2×D311yescharacteristic
86C2×#235C2×D311yescharacteristic
87C3×AGL(1,ℤ/8)—34no—
88C3×AGL(1,ℤ/8)—62no—
89C2×C3×SD16—61no—
90C2×C3×D8—61no—
91C2×C3×M16—31no—
92C22×C3×C8—31no—
93C2×C3×C4⋊C4—31no—
94#948—62no—
95#948—62no—
96C2×#214—21no—
97#932—22no—
98#932Dic314yescomplemented
99C2×#213—21no—
100C2×C4⋊Dic3C2×D311yescharacteristic
101C2×#208—31no—
102C2×#208—31no—
103C2×#208—31no—
104C2×#208—31no—
105C2×#208—61no—
106C2×#208—61no—
107C2×#208—61no—
108C2×#208C2×D311yescharacteristic
109C22×C3⋊C8—61no—
110C22×C3⋊C8C2×D311yescharacteristic
111#901—62no—
112#901—62no—
113C2×ΓL(1,𝔽25)—61no—
114C2×D3×C8—61no—
115C3×#102—61no—
116C3×#102—61no—
117#835—61no—
118#833—62no—
119#833—62no—
120#833—64no—
121#832—21no—
122#832—21no—
123#832—61no—
124#810—61no—
125#809—61no—
126C23×C32—22no—
127C23×C32—41no—
128C23×C32—41no—
129C23×C32—81no—
130C23×C32—81no—
131C23×C32#4111yescharacteristic
132C22×C3×D3—21no—
133C32×D4—22no—
134C32×D4—22no—
135C32×D4—41no—
136C32×D4—41no—
137C2×C32×C4C22×C411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D411yescharacteristic
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4C2×D411yescharacteristic
142C2×C32×C4#4111yescharacteristic
143C3×#67—22no—
144C3×#67—22no—
145C2×C3×Dic3—21no—
146C2×C3×Dic3—41no—
147C2×C3×Dic3—81no—
148C3×D12—21no—
149C3×D12C22⋊C412yes—
150C3×C4×D3—22no—
151C3×C4×D3—22no—
152C3×Dic6—21no—
153C3×Dic6C22⋊C412yes—
154C3⋊(C3⋊C8)—22no—
155C3⋊(C3⋊C8)—41no—
156C3×C3⋊C8—22no—
157C3×C3⋊C8—21no—
158C3×C3⋊C8—21no—
159C2×AGL(1,ℤ/8)—31no—
160C2×#131—91no—
161#417—91no—
162C2×#102—31no—
163C2×#100—91no—
164#343—91no—
165#341—91no—
166C24×C3—22no—
167C24×C3—21no—
168C24×C3—21no—
169C3×#41—32no—
170C3×#41—32no—
171C3×#41—61no—
172C3×#41—61no—
173C2×C3×Q8—31no—
174C2×C3×D4—22no—
175C2×C3×D4—21no—
176C2×C3×D4—21no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—21no—
180C2×C3×D4—21no—
181C2×C3×D4—21no—
182C2×C3×D4—21no—
183C2×C3×D4—21no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—31no—
187C2×C3×D4—41no—
188C2×C3×D4—41no—
189C2×C3×D4—41no—
190C2×C3×D4—41no—
191C2×C3×D4—61no—
192C2×C3×D4C4×D312yes—
193C2×C3×D4C2×Dic312yes—
194C22×C3×C4—21no—
195C22×C3×C4—61no—
196C22×C3×C4—61no—
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C2×#67—21no—
200C22×Dic3—21no—
201#235—21no—
202#235—21no—
203#235C2×Dic312yes—
204#235#6712yes—
205C2×D12#6711yescharacteristic
206C2×C4×D3—21no—
207C2×Dic6#6711yescharacteristic
208C3×SD16—64no—
209C3×D8—64no—
210C3×M16—32no—
211C3×M16—61no—
212C2×C3×C8—31no—
213C2×C3×C8—31no—
214C2×C3×C8—61no—
215C2×C3×C8—61no—
216C2×C3×C8—61no—
217C3×C4⋊C4—61no—
218C3×C4⋊C4—61no—
219#214—24no—
220#213—24no—
221C4⋊Dic3—21no—
222C4⋊Dic3—21no—
223#208—21no—
224#208—32no—
225#208—32no—
226#208—62no—
227#208—64no—
228#208—61no—
229#208—61no—
230#208—62no—
231#208—61no—
232#208—61no—
233#208—61no—
234#208—61no—
235#208—121no—
236#208—121no—
237#208C2×Dic312yes—
238C2×C3⋊C8—21no—
239C2×C3⋊C8—21no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—64no—
242C2×C3⋊C8—61no—
243C2×C3⋊C8—61no—
244C2×C3⋊C8—61no—
245C2×C3⋊C8—61no—
246C2×C3⋊C8—121no—
247C2×C3⋊C8—121no—
248C2×C3⋊C8#6711yescharacteristic
249C2×C3⋊C8#6711yescharacteristic
250ΓL(1,𝔽25)—64no—
251D3×C8—64no—
252C22×C32—21no—
253C22×C32—21no—
254C22×C32—42no—
255C22×C32—82no—
256C22×C32—82no—
257C22×C32—81no—
258C22×C32—81no—
259C22×C32C4×D411yescharacteristic
260C22×C32#12111yescharacteristic
261C22×C32#12311yescharacteristic
262C2×C3×D3—22no—
263C2×C3×D3—41no—
264C2×C3×D3—41no—
265C32×C4C2×C22⋊C411yescharacteristic
266C32×C4C4×D411yescharacteristic
267C32×C4#12011yescharacteristic
268C32×C4#12111yescharacteristic
269C3×Dic3—22no—
270C3×Dic3—81no—
271C2×#41—31no—
272C22×D4D3211yescharacteristic
273AGL(1,ℤ/8)—34no—
274AGL(1,ℤ/8)—62no—
275C2×SD16—61no—
276C2×D8—61no—
277#131—182no—
278#131—182no—
279C2×M16—31no—
280C2×M16—91no—
281C2×M16—91no—
282C2×M16—181no—
283C22×C8—31no—
284C22×C8—181no—
285C2×C4⋊C4—31no—
286#103—181no—
287#102—61no—
288#102—61no—
289#102—181no—
290#100—182no—
291C23×C3—24no—
292C23×C3—22no—
293C23×C3—22no—
294C23×C3—21no—
295C23×C3—42no—
296C23×C3—42no—
297C23×C3—41no—
298C23×C3—41no—
299C23×C3—41no—
300C23×C3—41no—
301C23×C3—61no—
302C23×C3—81no—
303C23×C3—81no—
304C23×C3—81no—
305C23×C3—81no—
306C23×C3—82no—
307C23×C3—82no—
308C23×C3#23711yescharacteristic
309C23×C3#23711yescharacteristic
310C22×D3—21no—
311C3×Q8—32no—
312C3×Q8—61no—
313C3×D4—22no—
314C3×D4—22no—
315C3×D4—22no—
316C3×D4—22no—
317C3×D4—32no—
318C3×D4—42no—
319C3×D4—42no—
320C3×D4—42no—
321C3×D4—42no—
322C3×D4—41no—
323C3×D4—41no—
324C3×D4—41no—
325C3×D4—41no—
326C3×D4—62no—
327C3×D4—62no—
328C3×D4—61no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—61no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—121no—
339C2×C3×C4—241no—
340C2×C3×C4C2×C4×D311yescharacteristic
341C2×C3×C4#23511yescharacteristic
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4D3×D411yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4#23711yescharacteristic
348C2×C3×C4C22×Dic311yescharacteristic
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C2×#6711yescharacteristic
351C2×C3×C4C2×#6711yescharacteristic
352#67—22no—
353#67—22no—
354C2×Dic3—21no—
355C2×Dic3—41no—
356C2×Dic3—81no—
357D12—21no—
358D12#21712yes—
359C4×D3—22no—
360C4×D3—22no—
361Dic6—21no—
362Dic6#21712yes—
363C3×C8—62no—
364C3×C8—61no—
365C3×C8—61no—
366C3⋊C8—21no—
367C3⋊C8—21no—
368C3⋊C8—22no—
369C3⋊C8—62no—
370C3⋊C8—62no—
371C3⋊C8—122no—
372C3⋊C8—122no—
373C3⋊C8—121no—
374C3⋊C8—121no—
375C2×C32—21no—
376C2×C32—21no—
377C2×C32—82no—
378C2×C32#38611yescharacteristic
379C2×C32#47111yescharacteristic
380C2×C32#47211yescharacteristic
381C3×D3—42no—
382C24—21no—
383#41—32no—
384#41—32no—
385#41—61no—
386#41—61no—
387C2×Q8—31no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—31no—
394C2×D4—61no—
395C2×D4D3×Dic312yes—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4C2×D3211yescharacteristic
399SD16—64no—
400D8—64no—
401M16—32no—
402M16—61no—
403M16—92no—
404M16—184no—
405M16—181no—
406M16—181no—
407M16—181no—
408C2×C8—31no—
409C2×C8—31no—
410C2×C8—61no—
411C2×C8—61no—
412C2×C8—61no—
413C2×C8—184no—
414C2×C8—181no—
415C2×C8—181no—
416C4⋊C4—61no—
417C4⋊C4—61no—
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—44no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—62no—
431C22×C3—82no—
432C22×C3—82no—
433C22×C3—82no—
434C22×C3—82no—
435C22×C3—82no—
436C22×C3—82no—
437C22×C3—84no—
438C22×C3—84no—
439C22×C3—81no—
440C22×C3—81no—
441C22×C3—81no—
442C22×C3—81no—
443C22×C3—121no—
444C22×C3—121no—
445C22×C3#67⋊C411yescharacteristic
446C22×C3#88311yescharacteristic
447C22×C3D4×Dic311yescharacteristic
448C22×C3#93511yescharacteristic
449C22×C3#93811yescharacteristic
450C22×C3#93911yescharacteristic
451C2×D3—22no—
452C2×D3—41no—
453C2×D3—41no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—21no—
457C3×C4—21no—
458C3×C4—62no—
459C3×C4—241no—
460C3×C4D3×C22⋊C411yescharacteristic
461C3×C4#88411yescharacteristic
462C3×C4C4×#6711yescharacteristic
463C3×C4D4×Dic311yescharacteristic
464C3×C4#93711yescharacteristic
465C3×C4#93711yescharacteristic
466C3×C4#93911yescharacteristic
467C3×C4C2×#21711yescharacteristic
468Dic3—22no—
469Dic3—81no—
470C32#190711yescharacteristic, complemented, Sylow
471C23—22no—
472C23—41no—
473C23—41no—
474C23—61no—
475C23—81no—
476C23—81no—
477C23#380511yescharacteristic
478Q8—32no—
479Q8—61no—
480D4—22no—
481D4—22no—
482D4—32no—
483D4—41no—
484D4—41no—
485D4—62no—
486D4—62no—
487D4—61no—
488C2×C4—61no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—121no—
492C2×C4—241no—
493C2×C4C2×D3×Dic311yescharacteristic
494C2×C4#380411yescharacteristic
495C2×C4D3×#6711yescharacteristic
496C2×C4D3×#6711yescharacteristic
497C2×C4D3×#6711yescharacteristic
498C2×C4#381111yescharacteristic
499C8—62no—
500C8—61no—
501C8—61no—
502C8—182no—
503C8—361no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—41no—
512C2×C3—41no—
513C2×C3—84no—
514C2×C3—82no—
515C2×C3—82no—
516C2×C3—122no—
517C2×C3#495611yescharacteristic
518C2×C3#516011yescharacteristic
519C2×C3#517711yescharacteristic
520C2×C3#519911yescharacteristic
521C2×C3#520011yescharacteristic
522C2×C3#522011yescharacteristic
523D3—42no—
524C22—21no—
525C22—21no—
526C22—42no—
527C22—62no—
528C22—82no—
529C22—82no—
530C22—81no—
531C22—81no—
532C22—121no—
533C22—121no—
534C22#6396911yescharacteristic
535C22#6397011yescharacteristic
536C22#67⋊Dic311yescharacteristic
537C4—62no—
538C4—241no—
539C4D3×#21711yescharacteristic
540C4#6397111yescharacteristic
541C4Dic3×#6711yescharacteristic
542C4#6398311yescharacteristic
543C3—21no—
544C3#7021811yescharacteristic, complemented
545C3#7209111yescharacteristic, complemented
546C2—21no—
547C2—21no—
548C2—82no—
549C2—122no—
550C2#1059150511yescharacteristic
551C2#1059150611yescharacteristic
552C2#1059172111yescharacteristic
subgroupG/H
centerC22#63970
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×D4C22
socleC22×C32#121
prime radicalC2×C3×#932C2
cosocleC22×C32×C4C23
hypercenterC22×D4D32
hypocenterC32#1907
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#63814C2semidirect
3. C2×#63660C2semidirect
4. C2×C3×#832C2semidirect
5. #10591087C2semidirect
6. #10589167C2semidirect
7. #10589166C2semidirect
16. C3×#932C4semidirect
39. C2×#832D3semidirect
98. #932Dic3semidirect
470. C32#1907semidirect
544. C3#70218semidirect
545. C3#72091semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9322
C2×#638142
C2×#636602
C2×C3×#8322
#105910872
#105891672
#105891662
#720913
#702183