Finite Group Databasebeta

← C2×#10591568 #11865552

Subgroups — C2×#10591568 #11865552

Order 1152.

1277 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3755C211yesmaximal, characteristic, complemented
2C2×C3×#947C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591568C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5057—31nomaximal
10C2×#4819—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×#624—21no—
15C2×#3755—24no—
16C2×#3755C2214yescomplemented
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#947—22no—
19C3×#947C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×(C2×D3)⋊C4—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×#3722—21no—
26#63894—22no—
27#63894C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yes—
30C3×#835C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63562C2214yescomplemented
33C2×C3×#124—31no—
34C2×#947D311yescharacteristic, complemented
35C22×#215—31no—
36C22×#215—31no—
37C22×#215—61no—
38C22×#213—31no—
39C22×D24—31no—
40C2×#893—31no—
41C2×C4×D12—31no—
42C2×C3×#103—31no—
43C2×#835D311yescharacteristic, complemented
44C2×#832—31no—
45C2×Dic3⋊C8—31no—
46#5057—38no—
47C2×#809—31no—
48C2×C4⋊(C3⋊C8)—31no—
49#4819—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—22no—
54C2×C32×Q8—22no—
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)D414yes—
61C2×C4⋊(C3⋊D3)C2312yes—
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×#624—24no—
70C2×#624—44no—
71#3755—28no—
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)C2312yes—
74C3×(C2×D3)⋊C4—24no—
75C3×(C2×D3)⋊C4—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#3714—28no—
84C2×#463—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C22×D12—31no—
90C22×D12—31no—
91C22×D12—61no—
92C22×D12C2×D311yescharacteristic
93C22×C4×D3—61no—
94C22×C4×D3—61no—
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—
102#947—22no—
103#947C2×D314yescomplemented
104C2×#215—34no—
105C2×#215—34no—
106C2×#215—64no—
107C2×#215—64no—
108C2×#215—64no—
109C2×#215—68no—
110C2×#213—34no—
111C2×#213—64no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
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×D24—34no—
123C2×D24—64no—
124#893—34no—
125#893—62no—
126C4×D12—34no—
127C4×D12—62no—
128C3×#103—34no—
129#835C2×D314yescomplemented
130#832—34no—
131Dic3⋊C8—34no—
132#809—34no—
133C4⋊(C3⋊C8)—34no—
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—24no—
136C22×C3⋊D3—22no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C32×Q8—22no—
144C32×Q8—22no—
145C32×Q8—42no—
146C2×C32×C4—22no—
147C2×C32×C4—42no—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D411yescharacteristic
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C4⋊(C3⋊D3)—24no—
153C4⋊(C3⋊D3)—22no—
154C4⋊(C3⋊D3)C2×D414yes—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—42no—
159C2×C3×Dic3C2×D412yes—
160C2×C3×Dic3C2×D412yes—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—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—31no—
174C2×#102—91no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—61no—
178C23×D3—61no—
179C23×D3—121no—
180C2×C3×Q8—21no—
181C2×C3×Q8—21no—
182C2×C3×Q8—24no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—22no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×Q8—41no—
189C2×C3×Q8—42no—
190C2×C3×Q8C22×D312yes—
191C2×C3×Q8C22×D312yes—
192C2×C3×D4—32no—
193C2×C3×D4—62no—
194C2×C3×D4—62no—
195C2×C3×D4—61no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—31no—
200C22×C3×C4—31no—
201C22×C3×C4—41no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—21no—
206C22×Dic3#6711yescharacteristic
207C22×Dic3#6711yescharacteristic
208C2×D12—22no—
209C2×D12—22no—
210C2×D12—21no—
211C2×D12—34no—
212C2×D12—34no—
213C2×D12—32no—
214C2×D12—32no—
215C2×D12—64no—
216C2×D12—62no—
217C2×D12—62no—
218C2×D12—61no—
219C2×D12—62no—
220C2×D12—61no—
221C2×D12—122no—
222C2×D12—121no—
223C2×D12C22×D312yes—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—124no—
227C2×C4×D3—124no—
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#215—68no—
237#215—68no—
238#215—616no—
239#213—68no—
240(C2×D3)⋊C4—24no—
241(C2×D3)⋊C4—24no—
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—
256D24—68no—
257C22×C32#12112yes—
258C22×C32#13512yes—
259C22×C32AGL(1,ℤ/8)12yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—24no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3⋊D3—48no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—84no—
269C32×C4—42no—
270C32×C4#12112yes—
271C32×C4C22×D411yescharacteristic
272C32×C4C2×#4111yescharacteristic
273C3×Dic3—22no—
274C3×Dic3—22no—
275C3×Dic3—42no—
276C22×Q8D3211yescharacteristic
277C22×D4—31no—
278C22×D4—91no—
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—34no—
297#102—94no—
298C23×C3—21no—
299C23×C3—62no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—22no—
306C22×D3—42no—
307C22×D3—42no—
308C22×D3—42no—
309C22×D3—64no—
310C22×D3—64no—
311C22×D3—62no—
312C22×D3—62no—
313C22×D3—122no—
314C22×D3—124no—
315C22×D3—122no—
316C22×D3—122no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—242no—
320C22×D3—242no—
321C3×Q8—24no—
322C3×Q8—22no—
323C3×Q8—22no—
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—42no—
327C3×Q8—44no—
328C3×Q8—42no—
329C3×Q8—42no—
330C3×D4—62no—
331C3×D4—62no—
332C3×D4—122no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—22no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—42no—
342C2×C3×C4—44no—
343C2×C3×C4—42no—
344C2×C3×C4—42no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
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—42no—
361C2×Dic3C2×#6712yes—
362C2×Dic3C2×#6712yes—
363D12—22no—
364D12—22no—
365D12—34no—
366D12—34no—
367D12—42no—
368D12—64no—
369D12—64no—
370D12—64no—
371D12—62no—
372D12—62no—
373D12—122no—
374D12—124no—
375C4×D3—128no—
376C4×D3—128no—
377C3×C8—62no—
378C3⋊C8—22no—
379C3⋊C8—64no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C2×C32#46314yescomplemented
383C2×C32C2×#12111yescharacteristic
384C2×C32C2×#13511yescharacteristic
385C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
386C3⋊D3—44no—
387C3×D3—82no—
388C24—61no—
389C24—181no—
390C2×Q8—21no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8C2×D3212yes—
394C2×D4—32no—
395C2×D4—62no—
396C2×D4—61no—
397C2×D4—62no—
398C2×D4—92no—
399C2×D4—94no—
400C2×D4—182no—
401C2×D4—181no—
402C22×C4—21no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—61no—
406C22×C4—184no—
407C22×C4—364no—
408C22×C4C2×D3211yescharacteristic
409SD16—188no—
410D8—188no—
411C2×C8—32no—
412C2×C8—62no—
413C2×C8—92no—
414C2×C8—182no—
415C4⋊C4—32no—
416C4⋊C4—61no—
417C22⋊C4—64no—
418C22⋊C4—64no—
419C22⋊C4—184no—
420C42—32no—
421C42—32no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—122no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—244no—
430C22×C3#88412yes—
431C22×C3#91412yes—
432C22×C3#91912yes—
433C22×C3#93812yes—
434C22×C3#94912yes—
435C22×C3#95012yes—
436C22×C3C2×D3×D411yescharacteristic
437C22×C3C22×#6711yescharacteristic
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—64no—
442C2×D3—64no—
443C2×D3—84no—
444C2×D3—124no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—128no—
450C2×D3—128no—
451C2×D3—242no—
452C2×D3—248no—
453C2×D3—242no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—44no—
458C3×C4—42no—
459C3×C4—42no—
460C3×C4—62no—
461C3×C4—62no—
462C3×C4—122no—
463C3×C4#88412yes—
464C3×C4#93812yes—
465C3×C4C2×#23511yescharacteristic
466C3×C4C2×D3×D411yescharacteristic
467C3×C4C2×D3×D411yescharacteristic
468C3×C4C2×#23711yescharacteristic
469Dic3—22no—
470Dic3—22no—
471Dic3—42no—
472C32C2×#46311yescharacteristic, complemented, Sylow
473C23—62no—
474C23—122no—
475C23—122no—
476C23—122no—
477C23—182no—
478C23—184no—
479C23—362no—
480C23—362no—
481C23D3×#6711yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—42no—
485D4—62no—
486D4—62no—
487D4—94no—
488D4—122no—
489D4—182no—
490D4—184no—
491C2×C4—22no—
492C2×C4—32no—
493C2×C4—32no—
494C2×C4—42no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—122no—
499C2×C4—368no—
500C2×C4#380412yes—
501C2×C4D3×#6711yescharacteristic
502C2×C4#381112yes—
503C2×C4C22×D3211yescharacteristic
504C8—62no—
505C8—182no—
506C2×C3—21no—
507C2×C3—24no—
508C2×C3—21no—
509C2×C3—21no—
510C2×C3—242no—
511C2×C3#481914yescomplemented
512C2×C3#505714yescomplemented
513C2×C3C2×#88411yescharacteristic
514C2×C3C2×#91411yescharacteristic
515C2×C3C2×#91911yescharacteristic
516C2×C3C2×#93811yescharacteristic
517C2×C3C2×#94911yescharacteristic
518C2×C3C2×#95011yescharacteristic
519D3—82no—
520D3—124no—
521D3—124no—
522D3—244no—
523C22—122no—
524C22—122no—
525C22—122no—
526C22—184no—
527C22—244no—
528C22—362no—
529C22—368no—
530C22—362no—
531C22#6393912yes—
532C22#6394912yes—
533C22#6395812yes—
534C22C2×D3×#6711yescharacteristic
535C4—42no—
536C4—62no—
537C4—62no—
538C4—122no—
539C4#6395812yes—
540C4C2×#380411yescharacteristic
541C4C2×#381111yescharacteristic
542C3—21no—
543C3C2×#481911yescharacteristic, complemented
544C3C2×#505711yescharacteristic, complemented
545C2—242no—
546C2—364no—
547C2#1059156814yesdirect product factor
548C2C2×#6393911yescharacteristic
549C2C2×#6394911yescharacteristic
550C2C2×#6395811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC22×Q8D32
hypocenterC32C2×#463
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3755C2semidirect
2. C2×C3×#947C2semidirect
3. C2×#63894C2semidirect
5. C2×C3×#835C2semidirect
6. #10591568C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63562C2semidirect
16. C2×#3755C22semidirect
19. C3×#947C22semidirect
27. #63894C22semidirect
30. C3×#835C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63562C22semidirect
34. C2×#947D3semidirect
43. C2×#835D3semidirect
103. #947C2×D3semidirect
129. #835C2×D3semidirect
382. C2×C32#463semidirect
472. C32C2×#463semidirect
511. C2×C3#4819semidirect
512. C2×C3#5057semidirect
543. C3C2×#4819semidirect
544. C3C2×#5057semidirect
547. C2#10591568direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37552
C2×C3×#9472
C2×#638942
C22×#37142
C2×C3×#8352
#105915682
C2×Dic3⋊(C3⋊C8)2
C2×#635622
C2×#50573
C2×#48193