Finite Group Databasebeta

← C2×#10591438 #11865599

Subgroups — C2×#10591438 #11865599

Order 1152.

1269 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10591438C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5163—31nomaximal
10C2×#5075—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×#67—21no—
14C22×C3×D12C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#940—22no—
19C3×#940C2214yes—
20C2×C3×#214—24no—
21C2×C3×#214C2214yescomplemented
22C2×C3×C4×Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×Dic32—21no—
26Dic3×Dic6—22no—
27Dic3×Dic6C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yescomplemented
30#63659C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63563C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×#127—31no—
35C2×Q8×Dic3—31no—
36C22×#215—31no—
37C2×#940D311yescharacteristic
38C22×#214—31no—
39C22×#214D311yescharacteristic, complemented
40C2×C4×Dic6—31no—
41C2×#832—31no—
42C2×#832—31no—
43C2×#832—31no—
44C2×#832—61no—
45#5163—38no—
46C2×#821—31no—
47C2×Dic3⋊C8—31no—
48#5075—38no—
49C2×C4⋊(C3⋊C8)—31no—
50C24×C32—21no—
51C23×C3×D3—21no—
52C2×C32×D4—22no—
53C2×C32×D4—21no—
54C2×C32×D4—22no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×C3×#67—24no—
59C2×C3×#67—24no—
60C2×C3×#67—44no—
61C2×C3×#67—44no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×D12—22no—
66C2×C3×D12—22no—
67C2×C3×D12—21no—
68C2×C3×D12C2312yes—
69C2×C3×Dic6—21no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6D414yescomplemented
72C2×C3×Dic6C2312yes—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×#214—28no—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82Dic3⋊Dic3—24no—
83Dic32—24no—
84#3715—28no—
85C2×#460—91noSylow
86C22×C3×Q8—31no—
87C22×C3×D4—21no—
88C22×C3×D4—31no—
89C22×C3×D4—61no—
90C22×C3×D4—61no—
91C22×C3×D4C2×D311yescharacteristic
92C22×C3×D4C2×D311yescharacteristic
93C22×#67—21no—
94C22×#67—21no—
95C22×D12C2×D311yescharacteristic
96C22×Dic6C2×D311yescharacteristic
97C2×C3×SD16—34no—
98C2×C3×SD16—64no—
99C22×C3×C8—31no—
100C3×#127—34no—
101C3×#127—62no—
102C2×C3×C42—31no—
103Q8×Dic3—34no—
104Q8×Dic3—62no—
105C2×#215—34no—
106C2×#215—64no—
107#940—22no—
108#940C2×D314yes—
109C2×#214—24no—
110C2×#214—34no—
111C2×#214—64no—
112C2×#214C2×D314yescomplemented
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3—61no—
117C2×Dic3⋊C4—61no—
118C2×C4×Dic3—61no—
119C2×C4×Dic3—61no—
120C2×C4×Dic3C2×D311yescharacteristic
121C22×C3⋊C8—31no—
122C22×C3⋊C8—31no—
123C22×C3⋊C8—61no—
124C22×C3⋊C8C2×D311yescharacteristic
125C4×Dic6—34no—
126C4×Dic6—62no—
127#832—34no—
128#832—34no—
129#832—34no—
130#832—64no—
131#821—34no—
132Dic3⋊C8—34no—
133C4⋊(C3⋊C8)—34no—
134C23×C32—22no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32C2×D411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C32×D4—22no—
144C32×D4—22no—
145C32×D4—42no—
146C2×C32×C4C2×D411yescharacteristic
147C2×C32×C4C2×D412yes—
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—42no—
152C3×#67—48no—
153C3×#67—48no—
154C2×C3×Dic3—24no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3SD1614yescomplemented
158C2×C3×Dic3C2×D412yes—
159C2×C3×Dic3C2×D412yes—
160C3×D12—22no—
161C3×D12—22no—
162C3×D12—42no—
163C3×Dic6—24no—
164C3×Dic6—22no—
165C3×Dic6C2×D414yescomplemented
166C3⋊(C3⋊C8)—22no—
167C3×C3⋊C8—22no—
168C22×SD16—31no—
169C22×SD16—91no—
170C2×#127—31no—
171C2×C4×Q8—91no—
172#460—98no—
173C2×C4⋊C8—91no—
174C2×#102—91no—
175C2×#102—91no—
176C24×C3—21no—
177C24×C3—21no—
178C24×C3—41no—
179C24×C3—61no—
180C23×D3—21no—
181C2×C3×Q8—34no—
182C2×C3×Q8—32no—
183C2×C3×Q8—62no—
184C2×C3×Q8—61no—
185C2×C3×D4—24no—
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—22no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—32no—
194C2×C3×D4—42no—
195C2×C3×D4—41no—
196C2×C3×D4—64no—
197C2×C3×D4—64no—
198C2×C3×D4—61no—
199C2×C3×D4—62no—
200C2×C3×D4—62no—
201C2×C3×D4—124no—
202C2×C3×D4—124no—
203C2×C3×D4C22×D312yes—
204C2×C3×D4C22×D312yes—
205C22×C3×C4—21no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—61no—
209C22×C3×C4C22×D311yescharacteristic
210C22×C3×C4C22×D311yescharacteristic
211C2×#67—24no—
212C2×#67—24no—
213C2×#67—44no—
214C2×#67—44no—
215C22×Dic3—21no—
216C22×Dic3—61no—
217C22×Dic3—61no—
218C22×Dic3—121no—
219C22×Dic3#6711yescharacteristic
220C22×Dic3#6711yescharacteristic
221C2×D12—22no—
222C2×D12—22no—
223C2×D12—21no—
224C2×D12C22×D312yes—
225C2×Dic6—21no—
226C2×Dic6—22no—
227C2×Dic6#6714yescomplemented
228C2×Dic6C22×D312yes—
229C3×SD16—68no—
230C2×C3×C8—32no—
231C2×C3×C8—62no—
232C3×C42—32no—
233C3×C42—32no—
234#215—68no—
235#214—28no—
236#214—68no—
237C4⋊Dic3—32no—
238C4⋊Dic3—32no—
239C4⋊Dic3—62no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—64no—
243C4⋊Dic3—121no—
244Dic3⋊C4—64no—
245C4×Dic3—64no—
246C4×Dic3—64no—
247C4×Dic3#6712yes—
248C4×Dic3C22×D312yes—
249C2×C3⋊C8—22no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—62no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—122no—
256C2×C3⋊C8C22×D312yes—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32—84no—
261C22×C32#12112yes—
262C22×C32C2×SD1612yes—
263C22×C32AGL(1,ℤ/8)12yes—
264C22×C32C22×D411yescharacteristic
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—84no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—42no—
273C3×Dic3—24no—
274C3×Dic3—22no—
275C3×Dic3C2×SD1614yescomplemented
276C22×Q8—31no—
277C22×D4—31no—
278C22×D4—61no—
279C22×D4—61no—
280C22×D4D3211yescharacteristic
281C2×SD16—34no—
282C2×SD16—64no—
283C2×SD16—94no—
284C2×SD16—184no—
285C22×C8—31no—
286C22×C8—91no—
287#127—34no—
288#127—62no—
289C4×Q8—94no—
290C4×Q8—182no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—181no—
293C2×C42—31no—
294C2×C42—181no—
295C4⋊C8—94no—
296#102—94no—
297#102—94no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—42no—
302C23×C3—44no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—62no—
310C23×C3—82no—
311C23×C3—82no—
312C23×C3—122no—
313C23×C3—122no—
314C23×C3—122no—
315C23×C3D3×D411yescharacteristic
316C23×C3C2×#6711yescharacteristic
317C22×D3—22no—
318C22×D3—42no—
319C22×D3—42no—
320C22×D3—42no—
321C3×Q8—34no—
322C3×Q8—64no—
323C3×Q8—62no—
324C3×D4—24no—
325C3×D4—22no—
326C3×D4—22no—
327C3×D4—22no—
328C3×D4—22no—
329C3×D4—42no—
330C3×D4—44no—
331C3×D4—42no—
332C3×D4—42no—
333C3×D4—62no—
334C3×D4—62no—
335C3×D4—128no—
336C3×D4—128no—
337C3×D4—122no—
338C2×C3×C4—21no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—21no—
342C2×C3×C4—34no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—62no—
346C2×C3×C4—64no—
347C2×C3×C4—62no—
348C2×C3×C4D3×D412yes—
349C2×C3×C4D3×D411yescharacteristic
350C2×C3×C4#23712yes—
351C2×C3×C4#23712yes—
352C2×C3×C4C2×#6711yescharacteristic
353C2×C3×C4C2×#6712yes—
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356#67—48no—
357#67—48no—
358C2×Dic3—22no—
359C2×Dic3—24no—
360C2×Dic3—22no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—122no—
364C2×Dic3—122no—
365C2×Dic3—122no—
366C2×Dic3—242no—
367C2×Dic3#21414yescomplemented
368C2×Dic3C2×#6712yes—
369C2×Dic3C2×#6712yes—
370D12—22no—
371D12—22no—
372D12—42no—
373Dic6—24no—
374Dic6—22no—
375Dic6C2×#6714yescomplemented
376C3×C8—62no—
377C3⋊C8—22no—
378C3⋊C8—62no—
379C3⋊C8—62no—
380C3⋊C8—122no—
381C2×C32—82no—
382C2×C32#46014yescomplemented
383C2×C32C2×#12111yescharacteristic
384C2×C32C22×SD1611yescharacteristic
385C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
386C3×D3—82no—
387C24—21no—
388C24—61no—
389C2×Q8—32no—
390C2×Q8—34no—
391C2×Q8—62no—
392C2×Q8—61no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—32no—
397C2×D4—64no—
398C2×D4—64no—
399C2×D4—62no—
400C2×D4—62no—
401C2×D4—61no—
402C2×D4—124no—
403C2×D4—124no—
404C2×D4C2×D3212yes—
405C22×C4—31no—
406C22×C4—31no—
407C22×C4—61no—
408C22×C4—181no—
409C22×C4C2×D3211yescharacteristic
410SD16—68no—
411SD16—188no—
412C2×C8—32no—
413C2×C8—62no—
414C2×C8—92no—
415C2×C8—182no—
416C4⋊C4—92no—
417C4⋊C4—184no—
418C4⋊C4—181no—
419C42—32no—
420C42—32no—
421C42—184no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—44no—
427C22×C3—42no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—82no—
434C22×C3—82no—
435C22×C3—88no—
436C22×C3—84no—
437C22×C3—84no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—244no—
442C22×C3D3×SD1612yes—
443C22×C3#91412yes—
444C22×C3#93212yes—
445C22×C3C2×#21412yes—
446C22×C3#93812yes—
447C22×C3#93912yes—
448C22×C3C2×D3×D411yescharacteristic
449C22×C3C22×#6711yescharacteristic
450C2×D3—42no—
451C2×D3—42no—
452C2×D3—42no—
453C2×D3—84no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—34no—
458C3×C4—62no—
459C3×C4—64no—
460C3×C4#93812yes—
461C3×C4#93912yes—
462C3×C4C2×D3×D411yescharacteristic
463C3×C4C2×#23711yescharacteristic
464C3×C4C2×#23711yescharacteristic
465C3×C4C22×#6711yescharacteristic
466Dic3—22no—
467Dic3—24no—
468Dic3—122no—
469Dic3—122no—
470Dic3—242no—
471Dic3C2×#21414yescomplemented
472C32C2×#46011yescharacteristic, complemented, Sylow
473C23—22no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—62no—
478C23—122no—
479C23—122no—
480C23—122no—
481C23D3×#6711yescharacteristic
482Q8—34no—
483Q8—62no—
484Q8—64no—
485D4—22no—
486D4—22no—
487D4—42no—
488D4—62no—
489D4—62no—
490D4—128no—
491D4—128no—
492D4—122no—
493C2×C4—32no—
494C2×C4—34no—
495C2×C4—32no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—64no—
499C2×C4—182no—
500C2×C4—362no—
501C2×C4#380512yes—
502C2×C4D3×#6712yes—
503C2×C4D3×#6711yescharacteristic
504C2×C4C22×D3211yescharacteristic
505C8—62no—
506C8—182no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—24no—
511C2×C3—84no—
512C2×C3—82no—
513C2×C3—82no—
514C2×C3—242no—
515C2×C3#507514yescomplemented
516C2×C3#516314yescomplemented
517C2×C3C2×D3×SD1611yescharacteristic
518C2×C3C2×#91411yescharacteristic
519C2×C3C2×#93211yescharacteristic
520C2×C3C22×#21411yescharacteristic
521C2×C3C2×#93811yescharacteristic
522C2×C3C2×#93911yescharacteristic
523D3—82no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—84no—
528C22—122no—
529C22—122no—
530C22—122no—
531C22—244no—
532C22D3×#21412yes—
533C22#6393412yes—
534C22#6397012yes—
535C22C2×D3×#6711yescharacteristic
536C4—34no—
537C4—62no—
538C4—64no—
539C4—362no—
540C4#6397012yes—
541C4C2×#380511yescharacteristic
542C4C2×D3×#6711yescharacteristic
543C3—21no—
544C3C2×#507511yescharacteristic, complemented
545C3C2×#516311yescharacteristic, complemented
546C2—82no—
547C2—242no—
548C2#1059143814yesdirect product factor
549C2C2×D3×#21411yescharacteristic
550C2C2×#6393411yescharacteristic
551C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32C2×#460
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C2×Dic3×Dic6C2semidirect
4. C22×#3715C2semidirect
5. C2×#63659C2semidirect
6. #10591438C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63563C2semidirect
21. C2×C3×#214C22semidirect
27. Dic3×Dic6C22semidirect
29. C2×#3715C22semidirect
30. #63659C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63563C22semidirect
39. C22×#214D3semidirect
71. C2×C3×Dic6D4semidirect
112. C2×#214C2×D3semidirect
157. C2×C3×Dic3SD16semidirect
165. C3×Dic6C2×D4semidirect
227. C2×Dic6#67semidirect
275. C3×Dic3C2×SD16semidirect
367. C2×Dic3#214semidirect
375. Dic6C2×#67semidirect
382. C2×C32#460semidirect
471. Dic3C2×#214semidirect
472. C32C2×#460semidirect
515. C2×C3#5075semidirect
516. C2×C3#5163semidirect
544. C3C2×#5075semidirect
545. C3C2×#5163semidirect
548. C2#10591438direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9402
C22×C3×#2142
C2×Dic3×Dic62
C22×#37152
C2×#636592
#105914382
C2×Dic3⋊(C3⋊C8)2
C2×#635632
C2×#51633
C2×#50753