Finite Group Databasebeta

← C2×#10591476 #11865549

Subgroups — C2×#10591476 #11865549

Order 1152.

1341 conjugacy classes of subgroups.

The subgroup lattice has 559 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C22×C3×#213C211yesmaximal, characteristic
4C2×#63863C211yesmaximal, characteristic, complemented
5#10591476C218yesmaximal, direct product factor
6C2×#63572C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5165—31nomaximal
10C2×#5153—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C23×C3⋊Dic3—21no—
13C22×C3×D12C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C2×#3757—21no—
16D4×C3⋊Dic3—22no—
17D4×C3⋊Dic3C2214yescomplemented
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#214—24no—
21C2×C3×#214C2214yescomplemented
22C2×C3×#213—24no—
23C2×C3×#213C2214yes—
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×(C2×D3)⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63863—22no—
29#63863C2214yescomplemented
30#63572C2214yescomplemented
31#63566C2214yescomplemented
32#63563C2214yescomplemented
33C22×C3×SD16—31no—
34C22×C3×D8—31no—
35C2×#947—31no—
36C2×#936—31no—
37C2×D4×Dic3—31no—
38C2×D4×Dic3—31no—
39C2×D4×Dic3—61no—
40C22×#214D311yescharacteristic, complemented
41C22×#213D311yescharacteristic
42C2×#835—31no—
43C2×#832—31no—
44#5165—38no—
45#5153—38no—
46C2×#821—31no—
47C2×#816—31no—
48C2×Dic3⋊C8—31no—
49C2×Dic3⋊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—
58C22×C3⋊Dic3—24no—
59C22×C3⋊Dic3—44no—
60C22×C3⋊Dic3D411yescharacteristic
61C22×C3⋊Dic3D411yescharacteristic
62C22×C3×Dic3—21no—
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12C2312yes—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71#3757—24no—
72C4⋊(C3⋊Dic3)—21no—
73C4⋊(C3⋊Dic3)C2312yes—
74C4×C3⋊Dic3D412yes—
75C4×C3⋊Dic3C2312yes—
76C3×#214—28no—
77C3×#213—28no—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83(C2×D3)⋊Dic3—24no—
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—
91C23×Dic3—61no—
92C23×Dic3—62no—
93C22×D12C2×D311yescharacteristic
94C22×Dic6C2×D311yescharacteristic
95C2×C3×SD16—34no—
96C2×C3×SD16—64no—
97C2×C3×D8—34no—
98C2×C3×D8—64no—
99C22×C3×C8—31no—
100C22×C3×C8—31no—
101C2×#217—61no—
102C2×#217—61no—
103C2×#217—61no—
104C2×#217—61no—
105C2×#217—62no—
106#947—34no—
107#947—62no—
108#936—34no—
109#936—62no—
110D4×Dic3—34no—
111D4×Dic3—34no—
112D4×Dic3—64no—
113D4×Dic3—62no—
114D4×Dic3—62no—
115D4×Dic3—64no—
116C2×#214—24no—
117C2×#214C2×D314yescomplemented
118C2×#213—24no—
119C2×#213C2×D314yes—
120C2×(C2×D3)⋊C4—61no—
121C2×(C2×D3)⋊C4—61no—
122C2×C4⋊Dic3—31no—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—61no—
125C2×C4×Dic3—31no—
126C2×C4×Dic3—31no—
127C2×C4×Dic3—61no—
128C22×C3⋊C8C2×D311yescharacteristic
129C22×C3⋊C8C2×D311yescharacteristic
130#835—34no—
131#832—34no—
132#821—34no—
133#816—34no—
134Dic3⋊C8—34no—
135Dic3⋊C8—34no—
136C23×C32—24no—
137C23×C32—22no—
138C23×C32—42no—
139C23×C32—42no—
140C23×C32C2×D411yescharacteristic
141C22×C3×D3—22no—
142C22×C3×D3—42no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C32×D4—24no—
146C32×D4—22no—
147C32×D4C2×D414yes—
148C2×C32×C4C2×D411yescharacteristic
149C2×C32×C4C2×D412yes—
150C2×C32×C4#4112yes—
151C2×C32×C4C2411yescharacteristic
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3—48no—
156C2×C3⋊Dic3—42no—
157C2×C3⋊Dic3C2×D412yes—
158C2×C3⋊Dic3C2×D412yes—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—42no—
161C3×D12—22no—
162C3×D12—22no—
163C3×D12—42no—
164C3×Dic6—22no—
165C3×Dic6—22no—
166C3×Dic6—42no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C22×SD16—31no—
170C22×D8—31no—
171C2×#124—91no—
172C2×C4×D4—91no—
173#463—98no—
174C2×C4⋊C8—91no—
175C2×#103—91no—
176C2×#102—91no—
177C24×C3—22no—
178C24×C3—21no—
179C24×C3—21no—
180C24×C3—61no—
181C23×D3—21no—
182C2×C3×Q8—32no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×Q8—62no—
186C2×C3×D4—22no—
187C2×C3×D4—24no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—22no—
192C2×C3×D4—24no—
193C2×C3×D4—22no—
194C2×C3×D4—32no—
195C2×C3×D4—61no—
196C2×C3×D4—62no—
197C2×C3×D4—62no—
198C2×C3×D4#6714yes—
199C2×C3×D4#6714yes—
200C2×C3×D4C22×D312yes—
201C2×C3×D4C22×D312yes—
202C22×C3×C4—21no—
203C22×C3×C4—61no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C22×Dic3—21no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—31no—
210C22×Dic3—31no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—64no—
214C22×Dic3—64no—
215C22×Dic3—62no—
216C22×Dic3—68no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—128no—
220C22×Dic3—124no—
221C22×Dic3—124no—
222C2×D12—22no—
223C2×D12—22no—
224C2×D12—21no—
225C2×D12C22×D312yes—
226C2×Dic6—22no—
227C2×Dic6—22no—
228C2×Dic6—21no—
229C2×Dic6C22×D312yes—
230C3×SD16—68no—
231C3×D8—68no—
232C2×C3×C8—32no—
233C2×C3×C8—32no—
234C2×C3×C8—62no—
235C2×C3×C8—62no—
236#217—64no—
237#217—64no—
238#217—64no—
239#217—64no—
240#217—68no—
241#214—28no—
242#213—28no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245C4⋊Dic3—32no—
246C4⋊Dic3—32no—
247C4⋊Dic3—62no—
248C4⋊Dic3—62no—
249C4⋊Dic3—61no—
250C4⋊Dic3—61no—
251C4×Dic3—32no—
252C4×Dic3—32no—
253C4×Dic3—32no—
254C4×Dic3—32no—
255C4×Dic3—62no—
256C4×Dic3—62no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8—22no—
259C2×C3⋊C8C22×D312yes—
260C2×C3⋊C8C22×D312yes—
261C22×C32—24no—
262C22×C32—42no—
263C22×C32—42no—
264C22×C32—48no—
265C22×C32#12112yes—
266C22×C32#13512yes—
267C22×C32AGL(1,ℤ/8)12yes—
268C22×C32C22×D411yescharacteristic
269C2×C3×D3—42no—
270C2×C3×D3—42no—
271C2×C3×D3—42no—
272C2×C3×D3—84no—
273C32×C4#12112yes—
274C32×C4C22×D411yescharacteristic
275C32×C4C2×#4111yescharacteristic
276C3⋊Dic3—22no—
277C3⋊Dic3—22no—
278C3⋊Dic3—42no—
279C3×Dic3—42no—
280C22×Q8—31no—
281C22×D4—31no—
282C22×D4D3211yescharacteristic
283C23×C4—181no—
284C2×SD16—34no—
285C2×SD16—64no—
286C2×D8—34no—
287C2×D8—64no—
288C22×C8—31no—
289C22×C8—31no—
290#124—94no—
291#124—182no—
292C4×D4—94no—
293C4×D4—182no—
294C2×C4⋊C4—91no—
295C2×C22⋊C4—181no—
296C2×C22⋊C4—181no—
297C2×C22⋊C4—181no—
298C2×C42—91no—
299C4⋊C8—94no—
300#103—94no—
301#102—94no—
302C23×C3—24no—
303C23×C3—28no—
304C23×C3—24no—
305C23×C3—24no—
306C23×C3—22no—
307C23×C3—22no—
308C23×C3—21no—
309C23×C3—44no—
310C23×C3—44no—
311C23×C3—42no—
312C23×C3—42no—
313C23×C3—42no—
314C23×C3—42no—
315C23×C3—62no—
316C23×C3—122no—
317C23×C3—122no—
318C23×C3—122no—
319C23×C3D3×D411yescharacteristic
320C23×C3D3×D411yescharacteristic
321C22×D3—22no—
322C22×D3—42no—
323C22×D3—42no—
324C22×D3—42no—
325C3×Q8—62no—
326C3×Q8—62no—
327C3×Q8—122no—
328C3×D4—24no—
329C3×D4—28no—
330C3×D4—24no—
331C3×D4—24no—
332C3×D4—22no—
333C3×D4—22no—
334C3×D4—24no—
335C3×D4—62no—
336C3×D4—62no—
337C3×D4—122no—
338C3×D4C2×#6714yes—
339C3×D4C2×#6714yes—
340C2×C3×C4—21no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—21no—
344C2×C3×C4—62no—
345C2×C3×C4—122no—
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4D3×D411yescharacteristic
348C2×C3×C4#23712yes—
349C2×C3×C4#23712yes—
350C2×C3×C4C2×#6712yes—
351C2×C3×C4C2×#6712yes—
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3—22no—
355C2×Dic3—32no—
356C2×Dic3—32no—
357C2×Dic3—32no—
358C2×Dic3—32no—
359C2×Dic3—42no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—64no—
363C2×Dic3—62no—
364C2×Dic3—62no—
365C2×Dic3—62no—
366C2×Dic3—62no—
367C2×Dic3—64no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—122no—
371C2×Dic3—1216no—
372C2×Dic3—128no—
373C2×Dic3—128no—
374C2×Dic3—124no—
375C2×Dic3—122no—
376C2×Dic3—122no—
377D12—22no—
378D12—22no—
379D12—42no—
380Dic6—22no—
381Dic6—22no—
382Dic6—42no—
383C3×C8—62no—
384C3×C8—62no—
385C3⋊C8—22no—
386C3⋊C8—22no—
387C2×C32—44no—
388C2×C32#46314yescomplemented
389C2×C32C2×#12111yescharacteristic
390C2×C32C2×#13511yescharacteristic
391C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
392C3×D3—82no—
393C24—21no—
394C24—61no—
395C2×Q8—32no—
396C2×Q8—61no—
397C2×Q8—62no—
398C2×Q8—62no—
399C2×D4—22no—
400C2×D4—21no—
401C2×D4—32no—
402C2×D4—62no—
403C2×D4—62no—
404C2×D4—61no—
405C2×D4#62514yes—
406C2×D4C2×D3212yes—
407C22×C4—61no—
408C22×C4—91no—
409C22×C4—91no—
410C22×C4—184no—
411C22×C4—181no—
412C22×C4—364no—
413C22×C4C2×D3211yescharacteristic
414SD16—68no—
415D8—68no—
416C2×C8—32no—
417C2×C8—32no—
418C2×C8—62no—
419C2×C8—62no—
420C4⋊C4—92no—
421C4⋊C4—181no—
422C22⋊C4—184no—
423C22⋊C4—184no—
424C22⋊C4—184no—
425C42—92no—
426C42—92no—
427C22×C3—28no—
428C22×C3—24no—
429C22×C3—24no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—44no—
435C22×C3—44no—
436C22×C3—416no—
437C22×C3—48no—
438C22×C3—48no—
439C22×C3—42no—
440C22×C3—42no—
441C22×C3—42no—
442C22×C3—42no—
443C22×C3—122no—
444C22×C3—122no—
445C22×C3—122no—
446C22×C3—244no—
447C22×C3#91112yes—
448C22×C3#91212yes—
449C22×C3#91412yes—
450C22×C3#91612yes—
451C22×C3#93912yes—
452C22×C3#93912yes—
453C22×C3C2×D3×D411yescharacteristic
454C22×C3C2×D3×D411yescharacteristic
455C2×D3—42no—
456C2×D3—42no—
457C2×D3—42no—
458C2×D3—84no—
459C3×C4—21no—
460C3×C4—21no—
461C3×C4—22no—
462C3×C4—122no—
463C3×C4#93912yes—
464C3×C4#93912yes—
465C3×C4C2×#23711yescharacteristic
466C3×C4C2×#23711yescharacteristic
467C3×C4C22×#6711yescharacteristic
468C3×C4C22×#6711yescharacteristic
469Dic3—42no—
470Dic3—64no—
471Dic3—62no—
472Dic3—62no—
473Dic3—62no—
474Dic3—62no—
475Dic3—122no—
476Dic3—124no—
477Dic3—122no—
478Dic3—122no—
479C32C2×#46311yescharacteristic, complemented, Sylow
480C23—22no—
481C23—24no—
482C23—42no—
483C23—42no—
484C23—62no—
485C23—122no—
486C23—122no—
487C23—122no—
488C23#381111yescharacteristic
489Q8—62no—
490Q8—62no—
491Q8—122no—
492D4—22no—
493D4—24no—
494D4—62no—
495D4—62no—
496D4—122no—
497D4C2×#62514yes—
498C2×C4—62no—
499C2×C4—92no—
500C2×C4—92no—
501C2×C4—122no—
502C2×C4—182no—
503C2×C4—182no—
504C2×C4—182no—
505C2×C4—368no—
506C2×C4—362no—
507C2×C4#380512yes—
508C2×C4C2×#62512yes—
509C2×C4#381111yescharacteristic
510C2×C4C22×D3211yescharacteristic
511C8—62no—
512C8—62no—
513C2×C3—21no—
514C2×C3—21no—
515C2×C3—21no—
516C2×C3—24no—
517C2×C3—48no—
518C2×C3—44no—
519C2×C3—44no—
520C2×C3—242no—
521C2×C3#515314yescomplemented
522C2×C3#516514yescomplemented
523C2×C3C2×#91111yescharacteristic
524C2×C3C2×#91211yescharacteristic
525C2×C3C2×#91411yescharacteristic
526C2×C3C2×#91611yescharacteristic
527C2×C3C2×#93911yescharacteristic
528C2×C3C2×#93911yescharacteristic
529D3—82no—
530C22—24no—
531C22—42no—
532C22—42no—
533C22—48no—
534C22—122no—
535C22—122no—
536C22—122no—
537C22—244no—
538C22#6393612yes—
539C22#6393712yes—
540C22#6398012yes—
541C22C2×#381111yescharacteristic
542C4—122no—
543C4—182no—
544C4—182no—
545C4—362no—
546C4#6398012yes—
547C4C2×#380511yescharacteristic
548C4C22×#62511yescharacteristic
549C3—21no—
550C3C2×#515311yescharacteristic, complemented
551C3C2×#516511yescharacteristic, complemented
552C2—44no—
553C2—242no—
554C2#1059147614yesdirect product factor
555C2C2×#6393611yescharacteristic
556C2C2×#6393711yescharacteristic
557C2C2×#6398011yescharacteristic
subgroupG/H
centerC23#3811
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×D4×C3⋊Dic3C2semidirect
2. C22×C3×#214C2semidirect
4. C2×#63863C2semidirect
5. #10591476C2direct (N × H)
6. C2×#63572C2semidirect
7. C2×#63566C2semidirect
8. C2×#63563C2semidirect
17. D4×C3⋊Dic3C22semidirect
21. C2×C3×#214C22semidirect
29. #63863C22semidirect
30. #63572C22semidirect
31. #63566C22semidirect
32. #63563C22semidirect
40. C22×#214D3semidirect
117. C2×#214C2×D3semidirect
388. C2×C32#463semidirect
479. C32C2×#463semidirect
521. C2×C3#5153semidirect
522. C2×C3#5165semidirect
550. C3C2×#5153semidirect
551. C3C2×#5165semidirect
554. C2#10591476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C22×C3×#2142
C22×C3×#2132
C2×#638632
#105914762
C2×#635722
C2×#635662
C2×#635632
C2×#51653
C2×#51533