Finite Group Databasebeta

← C2×#10591432 #11865543

Subgroups — C2×#10591432 #11865543

Order 1152.

1297 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
1C22×#3753C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591432C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63565C211yesmaximal, characteristic, complemented
9C2×#5057—31nomaximal
10C2×#4787—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#624—21no—
15C2×#3753—24no—
16C2×#3753C2214yes—
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—21no—
19C2×C3×#217—21no—
20C3×#936—22no—
21C3×#936C2214yescomplemented
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—21no—
26#63894—22no—
27#63894C2214yescomplemented
28C2×#3717—24no—
29C2×#3717C2214yescomplemented
30C3×#832C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63565C2214yescomplemented
33C2×C3×#124—31no—
34C22×#215—31no—
35C2×#936D311yescharacteristic, complemented
36C22×#213—31no—
37C22×#213—31no—
38C22×#213—61no—
39C22×#204—31no—
40C2×#893—31no—
41C2×C4×D12—31no—
42C2×C3×#102—31no—
43C2×#835—31no—
44C2×#832D311yescharacteristic, complemented
45C2×Dic3⋊C8—31no—
46#5057—38no—
47C2×#810—31no—
48C2×C4⋊(C3⋊C8)—31no—
49#4787—38no—
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
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)D414yes—
60C2×C4⋊(C3⋊D3)C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C22×C3×Dic3D411yescharacteristic
64C22×C3×Dic3D411yescharacteristic
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×#624—24no—
70C2×#624—44no—
71#3753—28no—
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)C2312yes—
74C3×#217—24no—
75C3×#217—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82#3722—24no—
83#3717—28no—
84C2×#463—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C22×D12—31no—
90C22×D12—31no—
91C22×D12—61no—
92C22×C4×D3—61no—
93C22×C4×D3—61no—
94C22×Dic6C2×D311yescharacteristic
95C22×C3×C8—31no—
96C3×#124—34no—
97C3×#124—62no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C22⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—31no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#215—34no—
105C2×#215—64no—
106#936—22no—
107#936C2×D314yescomplemented
108C2×#213—34no—
109C2×#213—34no—
110C2×#213—64no—
111C2×#213—64no—
112C2×#213—64no—
113C2×#213—68no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—61no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×C4×Dic3C2×D311yescharacteristic
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—61no—
121C22×C3⋊C8C2×D311yescharacteristic
122C2×#204—34no—
123C2×#204—64no—
124#893—34no—
125#893—62no—
126C4×D12—34no—
127C4×D12—62no—
128C3×#102—34no—
129#835—34no—
130#832C2×D314yescomplemented
131Dic3⋊C8—34no—
132#810—34no—
133C4⋊(C3⋊C8)—34no—
134C23×C32—22no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32C2×D411yescharacteristic
139C22×C3⋊D3—24no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—42no—
142C22×C3⋊D3—42no—
143C32×D4—22no—
144C32×D4—22no—
145C32×D4—42no—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150C4⋊(C3⋊D3)—24no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)C2×D414yes—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—42no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C2×D412yes—
160C2×C3×Dic3C2×D412yes—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164#624—48no—
165C3⋊(C3⋊C8)—22no—
166C3×C3⋊C8—22no—
167C22×SD16—91no—
168C22×D8—91no—
169C2×#124—31no—
170C2×C4×D4—91no—
171#463—98no—
172C2×C4⋊C8—91no—
173C2×#103—91no—
174C2×#102—31no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—41no—
178C23×D3—61no—
179C23×D3—61no—
180C23×D3—121no—
181C2×C3×Q8—32no—
182C2×C3×Q8—61no—
183C2×C3×Q8—62no—
184C2×C3×Q8—62no—
185C2×C3×D4—24no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—42no—
194C2×C3×D4—41no—
195C2×C3×D4C22×D312yes—
196C2×C3×D4C22×D312yes—
197C22×C3×C4—21no—
198C22×C3×C4—31no—
199C22×C3×C4—31no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—21no—
205C22×Dic3—21no—
206C22×Dic3#6711yescharacteristic
207C22×Dic3#6711yescharacteristic
208C2×D12—34no—
209C2×D12—34no—
210C2×D12—32no—
211C2×D12—32no—
212C2×D12—64no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—61no—
216C2×D12—62no—
217C2×D12—61no—
218C2×D12—122no—
219C2×D12—121no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—124no—
223C2×C4×D3—124no—
224C2×Dic6—22no—
225C2×Dic6—22no—
226C2×Dic6—21no—
227C2×Dic6C22×D312yes—
228C2×C3×C8—32no—
229C2×C3×C8—62no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—61no—
232C3×C22⋊C4—64no—
233C3×C22⋊C4—64no—
234C3×C42—32no—
235C3×C42—32no—
236#217—24no—
237#217—24no—
238#215—68no—
239#213—68no—
240#213—68no—
241#213—616no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244C4⋊Dic3—21no—
245C4⋊Dic3C22×D312yes—
246C4×Dic3#6712yes—
247C4×Dic3C22×D312yes—
248C2×C3⋊C8—22no—
249C2×C3⋊C8—32no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—62no—
252C2×C3⋊C8—64no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8C22×D312yes—
256#204—68no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32—84no—
261C22×C32#12112yes—
262C22×C32#13512yes—
263C22×C32AGL(1,ℤ/8)12yes—
264C22×C32C22×D411yescharacteristic
265C2×C3⋊D3—24no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—48no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3×Dic3—22no—
273C3×Dic3—22no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C22×Q8—31no—
277C22×D4—91no—
278C22×D4D3211yescharacteristic
279C23×C4—181no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—94no—
283C2×D8—184no—
284C22×C8—31no—
285C22×C8—91no—
286#124—34no—
287#124—62no—
288C4×D4—94no—
289C4×D4—182no—
290C2×C4⋊C4—31no—
291C2×C22⋊C4—61no—
292C2×C22⋊C4—61no—
293C2×C22⋊C4—181no—
294C2×C42—31no—
295C4⋊C8—94no—
296#103—94no—
297#102—34no—
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—82no—
310C23×C3—82no—
311C23×C3D3×D411yescharacteristic
312C23×C3C2×#6711yescharacteristic
313C22×D3—64no—
314C22×D3—64no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—122no—
318C22×D3—124no—
319C22×D3—122no—
320C22×D3—122no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—242no—
324C22×D3—242no—
325C3×Q8—62no—
326C3×Q8—62no—
327C3×Q8—122no—
328C3×D4—24no—
329C3×D4—22no—
330C3×D4—22no—
331C3×D4—22no—
332C3×D4—22no—
333C3×D4—42no—
334C3×D4—44no—
335C3×D4—42no—
336C3×D4—42no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—32no—
342C2×C3×C4—32no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—122no—
348C2×C3×C4—122no—
349C2×C3×C4#23512yes—
350C2×C3×C4D3×D411yescharacteristic
351C2×C3×C4D3×D412yes—
352C2×C3×C4D3×D412yes—
353C2×C3×C4#23712yes—
354C2×C3×C4C2×#6711yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D311yescharacteristic
357C2×Dic3—22no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—42no—
362C2×Dic3—42no—
363C2×Dic3C2×#6712yes—
364C2×Dic3C2×#6712yes—
365D12—34no—
366D12—34no—
367D12—64no—
368D12—64no—
369D12—64no—
370D12—62no—
371D12—62no—
372D12—122no—
373D12—124no—
374C4×D3—128no—
375C4×D3—128no—
376Dic6—22no—
377Dic6—22no—
378Dic6—42no—
379C3×C8—62no—
380C3⋊C8—22no—
381C3⋊C8—64no—
382C3⋊C8—62no—
383C3⋊C8—62no—
384C2×C32—82no—
385C2×C32#46314yescomplemented
386C2×C32C2×#12111yescharacteristic
387C2×C32C2×#13511yescharacteristic
388C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
389C3⋊D3—44no—
390C24—21no—
391C24—181no—
392C2×Q8—32no—
393C2×Q8—61no—
394C2×Q8—62no—
395C2×Q8—62no—
396C2×D4—22no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—92no—
400C2×D4—94no—
401C2×D4—182no—
402C2×D4—181no—
403C2×D4C2×D3212yes—
404C22×C4—31no—
405C22×C4—31no—
406C22×C4—61no—
407C22×C4—61no—
408C22×C4—184no—
409C22×C4—364no—
410C22×C4C2×D3211yescharacteristic
411SD16—188no—
412D8—188no—
413C2×C8—32no—
414C2×C8—62no—
415C2×C8—92no—
416C2×C8—182no—
417C4⋊C4—32no—
418C4⋊C4—61no—
419C22⋊C4—64no—
420C22⋊C4—64no—
421C22⋊C4—184no—
422C42—32no—
423C42—32no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—44no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—82no—
436C22×C3—82no—
437C22×C3—88no—
438C22×C3—84no—
439C22×C3—84no—
440C22×C3#88412yes—
441C22×C3#91112yes—
442C22×C3#91612yes—
443C22×C3#93812yes—
444C22×C3#94912yes—
445C22×C3#95012yes—
446C22×C3C2×D3×D411yescharacteristic
447C22×C3C22×#6711yescharacteristic
448C2×D3—64no—
449C2×D3—64no—
450C2×D3—124no—
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—128no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—128no—
457C2×D3—242no—
458C2×D3—242no—
459C2×D3—248no—
460C3×C4—21no—
461C3×C4—21no—
462C3×C4—22no—
463C3×C4—62no—
464C3×C4—62no—
465C3×C4—122no—
466C3×C4—122no—
467C3×C4#88412yes—
468C3×C4#93812yes—
469C3×C4C2×#23511yescharacteristic
470C3×C4C2×D3×D411yescharacteristic
471C3×C4C2×D3×D411yescharacteristic
472C3×C4C2×#23711yescharacteristic
473Dic3—22no—
474Dic3—22no—
475Dic3—42no—
476Dic3—42no—
477C32C2×#46311yescharacteristic, complemented, Sylow
478C23—22no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—182no—
483C23—184no—
484C23—362no—
485C23—362no—
486C23D3×#6711yescharacteristic
487Q8—62no—
488Q8—62no—
489Q8—122no—
490D4—22no—
491D4—22no—
492D4—42no—
493D4—94no—
494D4—182no—
495D4—184no—
496C2×C4—32no—
497C2×C4—32no—
498C2×C4—62no—
499C2×C4—62no—
500C2×C4—62no—
501C2×C4—62no—
502C2×C4—122no—
503C2×C4—122no—
504C2×C4—368no—
505C2×C4#380412yes—
506C2×C4D3×#6711yescharacteristic
507C2×C4#381112yes—
508C2×C4C22×D3211yescharacteristic
509C8—62no—
510C8—182no—
511C2×C3—21no—
512C2×C3—21no—
513C2×C3—21no—
514C2×C3—24no—
515C2×C3—84no—
516C2×C3—82no—
517C2×C3—82no—
518C2×C3#478714yescomplemented
519C2×C3#505714yescomplemented
520C2×C3C2×#88411yescharacteristic
521C2×C3C2×#91111yescharacteristic
522C2×C3C2×#91611yescharacteristic
523C2×C3C2×#93811yescharacteristic
524C2×C3C2×#94911yescharacteristic
525C2×C3C2×#95011yescharacteristic
526D3—124no—
527D3—124no—
528D3—244no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—84no—
533C22—184no—
534C22—362no—
535C22—362no—
536C22—368no—
537C22#6392512yes—
538C22#6393512yes—
539C22#6395812yes—
540C22C2×D3×#6711yescharacteristic
541C4—62no—
542C4—62no—
543C4—122no—
544C4—122no—
545C4#6395812yes—
546C4C2×#380411yescharacteristic
547C4C2×#381111yescharacteristic
548C3—21no—
549C3C2×#478711yescharacteristic, complemented
550C3C2×#505711yescharacteristic, complemented
551C2—82no—
552C2—364no—
553C2#1059143214yesdirect product factor
554C2C2×#6392511yescharacteristic
555C2C2×#6393511yescharacteristic
556C2C2×#6395811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×#3753C2
hypercenterC22×D4D32
hypocenterC32C2×#463
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. C2×C3×#936C2semidirect
3. C2×#63894C2semidirect
4. C22×#3717C2semidirect
5. C2×C3×#832C2semidirect
6. #10591432C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63565C2semidirect
21. C3×#936C22semidirect
27. #63894C22semidirect
29. C2×#3717C22semidirect
30. C3×#832C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63565C22semidirect
35. C2×#936D3semidirect
44. C2×#832D3semidirect
107. #936C2×D3semidirect
130. #832C2×D3semidirect
385. C2×C32#463semidirect
477. C32C2×#463semidirect
518. C2×C3#4787semidirect
519. C2×C3#5057semidirect
549. C3C2×#4787semidirect
550. C3C2×#5057semidirect
553. C2#10591432direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37532
C2×C3×#9362
C2×#638942
C22×#37172
C2×C3×#8322
#105914322
C2×Dic3⋊(C3⋊C8)2
C2×#635652
C2×#50573
C2×#47873