Finite Group Databasebeta

← C2×#10591431 #11865544

Subgroups — C2×#10591431 #11865544

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#936C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic
3C2×Dic3×D12C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10591431C218yesmaximal, direct product factor
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C2×#63566C211yesmaximal, characteristic, complemented
9C2×#5153—31nomaximal
10C2×#5057—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×D3×Dic3—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×#217—21no—
18C2×C3×#217—21no—
19C3×#936—22no—
20C3×#936C2214yescomplemented
21C2×C3×#213—24no—
22C2×C3×#213C2214yes—
23C2×C3×C4×Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26Dic3×D12—22no—
27Dic3×D12C2214yescomplemented
28C2×#3715—24no—
29C2×#3715C2214yescomplemented
30#63659C2214yescomplemented
31Dic3⋊(C3⋊C8)C2214yescomplemented
32#63566C2214yescomplemented
33C22×C3×D8—31no—
34C2×C3×#124—31no—
35C22×#215—31no—
36C2×#936D311yescharacteristic, complemented
37C2×D4×Dic3—31no—
38C22×#214—31no—
39C22×#213D311yescharacteristic
40C2×C4×D12—31no—
41C2×#835—31no—
42C2×#832—31no—
43C2×#832—31no—
44C2×#832—61no—
45#5153—38no—
46C2×#816—31no—
47C2×Dic3⋊C8—31no—
48#5057—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—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12D414yes—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×D3×Dic3—24no—
70C2×D3×Dic3—44no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#217—24no—
76C3×#217—24no—
77C3×#213—28no—
78C3×C4×Dic3D412yes—
79C3×C4×Dic3C2312yes—
80C2×C3×C3⋊C8—22no—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83#3715—28no—
84C2×#463—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—21no—
87C22×C3×D4—31no—
88C22×C3×D4C2×D311yescharacteristic
89C22×C3×D4C2×D311yescharacteristic
90C23×Dic3—61no—
91C22×D12C2×D311yescharacteristic
92C22×C4×D3—61no—
93C22×Dic6C2×D311yescharacteristic
94C2×C3×D8—34no—
95C2×C3×D8—64no—
96C22×C3×C8—31no—
97C3×#124—34no—
98C3×#124—62no—
99C2×C3×C22⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—31no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217—61no—
105C2×#215—34no—
106C2×#215—64no—
107#936—22no—
108#936C2×D314yescomplemented
109D4×Dic3—34no—
110D4×Dic3—62no—
111C2×#214—34no—
112C2×#214—64no—
113C2×#213—24no—
114C2×#213C2×D314yes—
115C2×(C2×D3)⋊C4—61no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—61no—
119C2×C4×Dic3C2×D311yescharacteristic
120C22×C3⋊C8—31no—
121C22×C3⋊C8—31no—
122C22×C3⋊C8—61no—
123C22×C3⋊C8C2×D311yescharacteristic
124C4×D12—34no—
125C4×D12—62no—
126#835—34no—
127#832—34no—
128#832—34no—
129#832—64no—
130#816—34no—
131Dic3⋊C8—34no—
132C4⋊(C3⋊C8)—34no—
133C23×C32—22no—
134C23×C32—42no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32C2×D411yescharacteristic
138C22×C3×D3—24no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C32×D4—22no—
143C32×D4—22no—
144C32×D4—42no—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2×D412yes—
147C2×C32×C4#4112yes—
148C2×C32×C4C2411yescharacteristic
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—42no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3C2×D412yes—
156C2×C3×Dic3C2×D412yes—
157C3×D12—24no—
158C3×D12—22no—
159C3×D12C2×D414yes—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163D3×Dic3—48no—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8—22no—
166C22×SD16—91no—
167C22×D8—31no—
168C2×#124—31no—
169C2×C4×D4—91no—
170#463—98no—
171C2×C4⋊C8—91no—
172C2×#103—91no—
173C2×#102—91no—
174C24×C3—21no—
175C24×C3—21no—
176C24×C3—41no—
177C24×C3—61no—
178C23×D3—21no—
179C2×C3×Q8—32no—
180C2×C3×Q8—61no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C2×C3×D4—24no—
184C2×C3×D4—22no—
185C2×C3×D4—21no—
186C2×C3×D4—22no—
187C2×C3×D4—22no—
188C2×C3×D4—22no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—34no—
192C2×C3×D4—32no—
193C2×C3×D4—42no—
194C2×C3×D4—41no—
195C2×C3×D4—62no—
196C2×C3×D4—61no—
197C2×C3×D4C22×D312yes—
198C2×C3×D4C22×D312yes—
199C22×C3×C4—21no—
200C22×C3×C4—31no—
201C22×C3×C4—31no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—21no—
206C22×Dic3—61no—
207C22×Dic3—61no—
208C22×Dic3—64no—
209C22×Dic3—121no—
210C22×Dic3—124no—
211C22×Dic3#6711yescharacteristic
212C22×Dic3#6711yescharacteristic
213C2×D12—21no—
214C2×D12—22no—
215C2×D12#6714yes—
216C2×D12C22×D312yes—
217C2×C4×D3—64no—
218C2×C4×D3—124no—
219C2×Dic6—22no—
220C2×Dic6—22no—
221C2×Dic6—21no—
222C2×Dic6C22×D312yes—
223C3×D8—68no—
224C2×C3×C8—32no—
225C2×C3×C8—62no—
226C3×C22⋊C4—64no—
227C3×C22⋊C4—64no—
228C3×C42—32no—
229C3×C42—32no—
230#217—24no—
231#217—24no—
232#217—64no—
233#215—68no—
234#214—68no—
235#213—28no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—32no—
238C4⋊Dic3—32no—
239C4⋊Dic3—62no—
240C4⋊Dic3—61no—
241C4⋊Dic3—61no—
242C4⋊Dic3—121no—
243C4×Dic3#6712yes—
244C4×Dic3C22×D312yes—
245C2×C3⋊C8—22no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—32no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8—62no—
251C2×C3⋊C8—122no—
252C2×C3⋊C8C22×D312yes—
253C22×C32—42no—
254C22×C32—42no—
255C22×C32—42no—
256C22×C32—84no—
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—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×D4—31no—
274C22×D4D3211yescharacteristic
275C23×C4—181no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×D8—34no—
279C2×D8—64no—
280C22×C8—31no—
281C22×C8—91no—
282#124—34no—
283#124—62no—
284C4×D4—94no—
285C4×D4—182no—
286C2×C4⋊C4—91no—
287C2×C22⋊C4—61no—
288C2×C22⋊C4—61no—
289C2×C22⋊C4—181no—
290C2×C42—31no—
291C4⋊C8—94no—
292#103—94no—
293#102—94no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—21no—
297C23×C3—42no—
298C23×C3—44no—
299C23×C3—42no—
300C23×C3—42no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—42no—
304C23×C3—42no—
305C23×C3—64no—
306C23×C3—62no—
307C23×C3—82no—
308C23×C3—82no—
309C23×C3—122no—
310C23×C3—122no—
311C23×C3D3×D411yescharacteristic
312C23×C3C2×#6711yescharacteristic
313C22×D3—24no—
314C22×D3—22no—
315C22×D3—42no—
316C22×D3—42no—
317C3×Q8—62no—
318C3×Q8—62no—
319C3×Q8—122no—
320C3×D4—24no—
321C3×D4—22no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—34no—
326C3×D4—42no—
327C3×D4—44no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—64no—
331C3×D4—62no—
332C2×C3×C4—21no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—21no—
336C2×C3×C4—32no—
337C2×C3×C4—32no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—122no—
342C2×C3×C4D3×D412yes—
343C2×C3×C4D3×D411yescharacteristic
344C2×C3×C4#23712yes—
345C2×C3×C4#23712yes—
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C2×#6712yes—
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—42no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—122no—
357C2×Dic3—128no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—242no—
361C2×Dic3C2×#6712yes—
362C2×Dic3C2×#6712yes—
363D12—24no—
364D12—22no—
365D12C2×#6714yes—
366C4×D3—128no—
367Dic6—22no—
368Dic6—22no—
369Dic6—42no—
370C3×C8—62no—
371C3⋊C8—22no—
372C3⋊C8—62no—
373C3⋊C8—62no—
374C3⋊C8—122no—
375C2×C32—82no—
376C2×C32#46314yescomplemented
377C2×C32C2×#12111yescharacteristic
378C2×C32C2×#13511yescharacteristic
379C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
380C3×D3—44no—
381C24—21no—
382C24—61no—
383C2×Q8—32no—
384C2×Q8—61no—
385C2×Q8—62no—
386C2×Q8—62no—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—21no—
390C2×D4—32no—
391C2×D4—34no—
392C2×D4—62no—
393C2×D4—61no—
394C2×D4C2×D3212yes—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—61no—
398C22×C4—184no—
399C22×C4—181no—
400C22×C4—364no—
401C22×C4C2×D3211yescharacteristic
402SD16—188no—
403D8—68no—
404C2×C8—32no—
405C2×C8—62no—
406C2×C8—92no—
407C2×C8—182no—
408C4⋊C4—92no—
409C4⋊C4—181no—
410C22⋊C4—64no—
411C22⋊C4—64no—
412C22⋊C4—184no—
413C42—32no—
414C42—32no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—44no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3—64no—
427C22×C3—82no—
428C22×C3—82no—
429C22×C3—88no—
430C22×C3—84no—
431C22×C3—84no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—128no—
435C22×C3#91112yes—
436C22×C3#91212yes—
437C22×C3#93812yes—
438C22×C3#93912yes—
439C22×C3#94912yes—
440C22×C3#95012yes—
441C22×C3C2×D3×D411yescharacteristic
442C22×C3C22×#6711yescharacteristic
443C2×D3—24no—
444C2×D3—48no—
445C2×D3—42no—
446C2×D3—42no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—62no—
451C3×C4—62no—
452C3×C4—122no—
453C3×C4#93812yes—
454C3×C4#93912yes—
455C3×C4C2×D3×D411yescharacteristic
456C3×C4C2×#23711yescharacteristic
457C3×C4C2×#23711yescharacteristic
458C3×C4C22×#6711yescharacteristic
459Dic3—22no—
460Dic3—22no—
461Dic3—42no—
462Dic3—122no—
463Dic3—122no—
464Dic3—242no—
465C32C2×#46311yescharacteristic, complemented, Sylow
466C23—22no—
467C23—42no—
468C23—42no—
469C23—42no—
470C23—62no—
471C23—64no—
472C23—122no—
473C23—122no—
474C23D3×#6711yescharacteristic
475Q8—62no—
476Q8—62no—
477Q8—122no—
478D4—22no—
479D4—22no—
480D4—34no—
481D4—42no—
482D4—62no—
483D4—64no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—122no—
490C2×C4—182no—
491C2×C4—368no—
492C2×C4—362no—
493C2×C4#380512yes—
494C2×C4D3×#6712yes—
495C2×C4D3×#6711yescharacteristic
496C2×C4C22×D3211yescharacteristic
497C8—62no—
498C8—182no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—24no—
503C2×C3—84no—
504C2×C3—82no—
505C2×C3—82no—
506C2×C3—124no—
507C2×C3#505714yescomplemented
508C2×C3#515314yescomplemented
509C2×C3C2×#91111yescharacteristic
510C2×C3C2×#91211yescharacteristic
511C2×C3C2×#93811yescharacteristic
512C2×C3C2×#93911yescharacteristic
513C2×C3C2×#94911yescharacteristic
514C2×C3C2×#95011yescharacteristic
515D3—44no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—64no—
520C22—84no—
521C22—122no—
522C22—122no—
523C22—128no—
524C22#6392512yes—
525C22#6393312yes—
526C22#6397012yes—
527C22C2×D3×#6711yescharacteristic
528C4—62no—
529C4—62no—
530C4—122no—
531C4—362no—
532C4#6397012yes—
533C4C2×#380511yescharacteristic
534C4C2×D3×#6711yescharacteristic
535C3—21no—
536C3C2×#505711yescharacteristic, complemented
537C3C2×#515311yescharacteristic, complemented
538C2—82no—
539C2—124no—
540C2#1059143114yesdirect product factor
541C2C2×#6392511yescharacteristic
542C2C2×#6393311yescharacteristic
543C2C2×#6397011yescharacteristic
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. C2×C3×#936C2semidirect
3. C2×Dic3×D12C2semidirect
4. C22×#3715C2semidirect
5. C2×#63659C2semidirect
6. #10591431C2direct (N × H)
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. C2×#63566C2semidirect
20. C3×#936C22semidirect
27. Dic3×D12C22semidirect
29. C2×#3715C22semidirect
30. #63659C22semidirect
31. Dic3⋊(C3⋊C8)C22semidirect
32. #63566C22semidirect
36. C2×#936D3semidirect
108. #936C2×D3semidirect
376. C2×C32#463semidirect
465. C32C2×#463semidirect
507. C2×C3#5057semidirect
508. C2×C3#5153semidirect
536. C3C2×#5057semidirect
537. C3C2×#5153semidirect
540. C2#10591431direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9362
C22×C3×#2132
C2×Dic3×D122
C22×#37152
C2×#636592
#105914312
C2×Dic3⋊(C3⋊C8)2
C2×#635662
C2×#51533
C2×#50573