Finite Group Databasebeta

← C2×#10591468 #11865550

Subgroups — C2×#10591468 #11865550

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×#3754C211yesmaximal, characteristic, complemented
2C2×C3×D4×Dic3C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic
4C2×#63860C211yesmaximal, characteristic, complemented
5#10591468C218yesmaximal, direct product factor
6C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5153—31nomaximal
10C2×#5016—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C23×C3×Dic3—21no—
14C22×C3×D12C2211yescharacteristic
15C2×#3754—24no—
16C2×#3754C2214yescomplemented
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—21no—
19C3×D4×Dic3—22no—
20C3×D4×Dic3C2214yescomplemented
21C2×C3×#213—24no—
22C2×C3×#213C2214yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×(C2×D3)⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63860—22no—
29#63860C2214yescomplemented
30Dic3⋊(C3⋊C8)C2214yescomplemented
31#63567C2214yescomplemented
32#63562C2214yescomplemented
33C22×C3×D8—31no—
34C2×C3×C4×D4—31no—
35C2×#936—31no—
36C2×D4×Dic3D311yescharacteristic, complemented
37C22×#214—31no—
38C22×#214—31no—
39C22×#214—61no—
40C22×#213D311yescharacteristic
41C2×#875—31no—
42C2×#832—31no—
43#5153—38no—
44C2×#816—31no—
45C2×Dic3⋊C8—31no—
46#5016—38no—
47C2×#810—31no—
48C2×#809—31no—
49C2×C4⋊(C3⋊C8)—31no—
50C24×C32—21no—
51C23×C3×D3—21no—
52C2×C32×D4—21no—
53C2×C32×D4—22no—
54C2×C32×D4D414yes—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634—21no—
61C2×#634C2312yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—24no—
64C22×C3×Dic3—44no—
65C22×C3×Dic3D411yescharacteristic
66C22×C3×Dic3D411yescharacteristic
67C2×C3×D12—22no—
68C2×C3×D12—22no—
69C2×C3×D12—21no—
70C2×C3×D12C2312yes—
71#3754—28no—
72C2×C3⋊(C3⋊C8)—22no—
73C2×C3⋊(C3⋊C8)C2312yes—
74C3×#217—24no—
75C3×#213—28no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83(C2×D3)⋊Dic3—24no—
84C2×#463—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—31no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C23×C3×C4—61no—
90C23×Dic3—21no—
91C22×D12C2×D311yescharacteristic
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C2×C3×D8—34no—
96C2×C3×D8—64no—
97C22×C3×C8—31no—
98C3×C4×D4—34no—
99C3×C4×D4—62no—
100C2×C3×C4⋊C4—31no—
101C2×C3×C22⋊C4—61no—
102C2×C3×C42—31no—
103C2×#217—21no—
104C2×#217—61no—
105C2×#217—61no—
106#936—34no—
107#936—62no—
108D4×Dic3—22no—
109D4×Dic3C2×D314yescomplemented
110C2×#214—34no—
111C2×#214—34no—
112C2×#214—64no—
113C2×#214—68no—
114C2×#214—64no—
115C2×#214—64no—
116C2×#213—24no—
117C2×#213C2×D314yes—
118C2×(C2×D3)⋊C4—61no—
119C2×(C2×D3)⋊C4—61no—
120C2×C4⋊Dic3C2×D311yescharacteristic
121C2×C4×Dic3C2×D311yescharacteristic
122C22×C3⋊C8—31no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—61no—
125C22×C3⋊C8C2×D311yescharacteristic
126#875—34no—
127#875—62no—
128#832—34no—
129#816—34no—
130Dic3⋊C8—34no—
131#810—34no—
132#809—34no—
133C4⋊(C3⋊C8)—34no—
134C23×C32—24no—
135C23×C32—22no—
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—24no—
144C32×D4—22no—
145C32×D4C2×D414yes—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
150C2×C3⋊Dic3—22no—
151C2×C3⋊Dic3—42no—
152#634—22no—
153#634—22no—
154#634—42no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—48no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3C2×D412yes—
161C2×C3×Dic3C2×D412yes—
162C3×D12—22no—
163C3×D12—22no—
164C3×D12—42no—
165C3⋊(C3⋊C8)—22no—
166C3×C3⋊C8—22no—
167C22×SD16—91no—
168C22×D8—31no—
169C2×#124—91no—
170C2×C4×D4—31no—
171#463—98no—
172C2×C4⋊C8—91no—
173C2×#103—91no—
174C2×#102—91no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—41no—
178C24×C3—61no—
179C23×D3—21no—
180C2×C3×D4—22no—
181C2×C3×D4—21no—
182C2×C3×D4—22no—
183C2×C3×D4—21no—
184C2×C3×D4—24no—
185C2×C3×D4—22no—
186C2×C3×D4—32no—
187C2×C3×D4—42no—
188C2×C3×D4—41no—
189C2×C3×D4—62no—
190C2×C3×D4—62no—
191C2×C3×D4—61no—
192C2×C3×D4D1214yes—
193C2×C3×D4#6714yes—
194C2×C3×D4C22×D312yes—
195C2×C3×D4C22×D312yes—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—64no—
200C22×C3×C4—61no—
201C22×C3×C4—124no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C22×Dic3—21no—
205C22×Dic3—24no—
206C22×Dic3—44no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—121no—
210C22×Dic3#6711yescharacteristic
211C22×Dic3#6711yescharacteristic
212C2×D12—22no—
213C2×D12—22no—
214C2×D12—21no—
215C2×D12C22×D312yes—
216C2×Dic6—32no—
217C2×Dic6—32no—
218C2×Dic6—62no—
219C2×Dic6—64no—
220C2×Dic6—62no—
221C2×Dic6—62no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—61no—
225C2×Dic6—61no—
226C2×Dic6—121no—
227C2×Dic6—122no—
228C3×D8—68no—
229C2×C3×C8—32no—
230C2×C3×C8—62no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—61no—
233C3×C22⋊C4—64no—
234C3×C42—32no—
235C3×C42—32no—
236#217—24no—
237#217—64no—
238#217—64no—
239#214—616no—
240#214—68no—
241#214—68no—
242#213—28no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3—21no—
246C4⋊Dic3C22×D312yes—
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—64no—
254C2×C3⋊C8—62no—
255C2×C3⋊C8—62no—
256C2×C3⋊C8C22×D312yes—
257C22×C32—24no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32—48no—
261C22×C32#12112yes—
262C22×C32#13512yes—
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—22no—
274C3×Dic3—22no—
275C3×Dic3—42no—
276C22×Q8—91no—
277C22×D4—31no—
278C22×D4D3211yescharacteristic
279C23×C4—61no—
280C2×SD16—94no—
281C2×SD16—184no—
282C2×D8—34no—
283C2×D8—64no—
284C22×C8—31no—
285C22×C8—91no—
286#124—94no—
287#124—182no—
288C4×D4—34no—
289C4×D4—62no—
290C2×C4⋊C4—31no—
291C2×C22⋊C4—61no—
292C2×C22⋊C4—181no—
293C2×C22⋊C4—181no—
294C2×C42—31no—
295C4⋊C8—94no—
296#103—94no—
297#102—94no—
298C23×C3—24no—
299C23×C3—24no—
300C23×C3—22no—
301C23×C3—22no—
302C23×C3—21no—
303C23×C3—42no—
304C23×C3—44no—
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×D4—24no—
322C3×D4—24no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—24no—
326C3×D4—42no—
327C3×D4—44no—
328C3×D4—62no—
329C3×D4—62no—
330C3×D4—122no—
331C3×D4C2×D1214yes—
332C3×D4C2×#6714yes—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—32no—
338C2×C3×C4—32no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—128no—
343C2×C3×C4—122no—
344C2×C3×C4C2×D1212yes—
345C2×C3×C4#23512yes—
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4#23712yes—
348C2×C3×C4C2×#6712yes—
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—48no—
356C2×Dic3—42no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—122no—
360C2×Dic3—124no—
361C2×Dic3—122no—
362C2×Dic3—122no—
363C2×Dic3C2×#6712yes—
364C2×Dic3C2×#6712yes—
365D12—22no—
366D12—22no—
367D12—42no—
368Dic6—64no—
369Dic6—62no—
370Dic6—62no—
371Dic6—62no—
372Dic6—62no—
373Dic6—122no—
374Dic6—124no—
375Dic6—122no—
376Dic6—122no—
377C3×C8—62no—
378C3⋊C8—22no—
379C3⋊C8—64no—
380C3⋊C8—62no—
381C3⋊C8—62no—
382C2×C32—44no—
383C2×C32#46314yescomplemented
384C2×C32C2×#12111yescharacteristic
385C2×C32C2×#13511yescharacteristic
386C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
387C3×D3—82no—
388C24—21no—
389C24—61no—
390C2×Q8—92no—
391C2×Q8—181no—
392C2×Q8—182no—
393C2×Q8—182no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—32no—
397C2×D4—62no—
398C2×D4—62no—
399C2×D4—61no—
400C2×D4#62614yes—
401C2×D4C2×D3212yes—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—64no—
405C22×C4—61no—
406C22×C4—124no—
407C22×C4—181no—
408C22×C4C2×D3211yescharacteristic
409SD16—188no—
410D8—68no—
411C2×C8—32no—
412C2×C8—62no—
413C2×C8—92no—
414C2×C8—182no—
415C4⋊C4—32no—
416C4⋊C4—61no—
417C22⋊C4—64no—
418C22⋊C4—184no—
419C22⋊C4—184no—
420C42—32no—
421C42—32no—
422C22×C3—24no—
423C22×C3—24no—
424C22×C3—21no—
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—44no—
429C22×C3—48no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—48no—
433C22×C3—42no—
434C22×C3—42no—
435C22×C3—82no—
436C22×C3—82no—
437C22×C3—88no—
438C22×C3—122no—
439C22×C3—122no—
440C22×C3—122no—
441C22×C3—244no—
442C22×C3#91112yes—
443C22×C3#91212yes—
444C22×C3#93012yes—
445C22×C3#93212yes—
446C22×C3#93912yes—
447C22×C3#95012yes—
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—62no—
458C3×C4—62no—
459C3×C4—122no—
460C3×C4#93012yes—
461C3×C4#93912yes—
462C3×C4C22×D1211yescharacteristic
463C3×C4C2×#23511yescharacteristic
464C3×C4C2×#23711yescharacteristic
465C3×C4C22×#6711yescharacteristic
466Dic3—22no—
467Dic3—22no—
468Dic3—42no—
469Dic3—124no—
470Dic3—122no—
471Dic3—122no—
472C32C2×#46311yescharacteristic, complemented, Sylow
473C23—22no—
474C23—24no—
475C23—42no—
476C23—42no—
477C23—62no—
478C23—122no—
479C23—122no—
480C23—122no—
481C23D3×#6711yescharacteristic
482Q8—182no—
483Q8—182no—
484Q8—362no—
485D4—22no—
486D4—24no—
487D4—62no—
488D4—62no—
489D4—122no—
490D4C2×#62614yes—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—128no—
497C2×C4—122no—
498C2×C4—182no—
499C2×C4—362no—
500C2×C4#380412yes—
501C2×C4C2×#62612yes—
502C2×C4D3×#6711yescharacteristic
503C2×C4C22×D3211yescharacteristic
504C8—62no—
505C8—182no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—24no—
510C2×C3—44no—
511C2×C3—44no—
512C2×C3—84no—
513C2×C3—242no—
514C2×C3#501614yescomplemented
515C2×C3#515314yescomplemented
516C2×C3C2×#91111yescharacteristic
517C2×C3C2×#91211yescharacteristic
518C2×C3C2×#93011yescharacteristic
519C2×C3C2×#93211yescharacteristic
520C2×C3C2×#93911yescharacteristic
521C2×C3C2×#95011yescharacteristic
522D3—82no—
523C22—24no—
524C22—42no—
525C22—42no—
526C22—48no—
527C22—122no—
528C22—122no—
529C22—122no—
530C22—244no—
531C22#6393212yes—
532C22#6393312yes—
533C22#6397812yes—
534C22C2×D3×#6711yescharacteristic
535C4—62no—
536C4—62no—
537C4—122no—
538C4—362no—
539C4#6397812yes—
540C4C2×#380411yescharacteristic
541C4C22×#62611yescharacteristic
542C3—21no—
543C3C2×#501611yescharacteristic, complemented
544C3C2×#515311yescharacteristic, complemented
545C2—44no—
546C2—242no—
547C2#1059146814yesdirect product factor
548C2C2×#6393211yescharacteristic
549C2C2×#6393311yescharacteristic
550C2C2×#6397811yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
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
1. C22×#3754C2semidirect
2. C2×C3×D4×Dic3C2semidirect
4. C2×#63860C2semidirect
5. #10591468C2direct (N × H)
6. C2×Dic3⋊(C3⋊C8)C2semidirect
7. C2×#63567C2semidirect
8. C2×#63562C2semidirect
16. C2×#3754C22semidirect
20. C3×D4×Dic3C22semidirect
29. #63860C22semidirect
30. Dic3⋊(C3⋊C8)C22semidirect
31. #63567C22semidirect
32. #63562C22semidirect
36. C2×D4×Dic3D3semidirect
109. D4×Dic3C2×D3semidirect
383. C2×C32#463semidirect
472. C32C2×#463semidirect
514. C2×C3#5016semidirect
515. C2×C3#5153semidirect
543. C3C2×#5016semidirect
544. C3C2×#5153semidirect
547. C2#10591468direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37542
C2×C3×D4×Dic32
C22×C3×#2132
C2×#638602
#105914682
C2×Dic3⋊(C3⋊C8)2
C2×#635672
C2×#635622
C2×#51533
C2×#50163