Finite Group Databasebeta

← C2×#10591460 #11866692

Subgroups — C2×#10591460 #11866692

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×#938C211yesmaximal, characteristic
3C2×#63857C211yesmaximal, characteristic, complemented
4C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591460C218yesmaximal, direct product factor
7C2×#63574C211yesmaximal, characteristic, complemented
8C2×#63567C211yesmaximal, characteristic, complemented
9C2×#5041—31nomaximal
10C2×#4778—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×C4×D3C2211yescharacteristic
15C2×#3754—24no—
16C2×#3754C2214yescomplemented
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×#217—21no—
19C3×#938—22no—
20C3×#938C2214yes—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63857—22no—
27#63857C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30C3×#832C2214yescomplemented
31#63574C2214yescomplemented
32#63567C2214yescomplemented
33C2×C3×#121—31no—
34C2×#938D311yescharacteristic
35C22×#214—31no—
36C22×#214—31no—
37C22×#214—61no—
38C2×#924—31no—
39C23×C3⋊C8—31no—
40C22×D3×C8—31no—
41C2×#897—31no—
42C2×C3×#102—31no—
43C2×#832D311yescharacteristic, complemented
44C2×#816—31no—
45#5041—38no—
46C2×#810—31no—
47C2×#808—31no—
48C2×#808—31no—
49#4778—38no—
50C24×C32—21no—
51C23×C3×D3D411yescharacteristic
52C2×C32×D4—22no—
53C2×C32×D4—21no—
54C2×C32×D4—22no—
55C2×C32×D4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3—21no—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634—21no—
61C2×#634C2312yes—
62C2×C3×#67—24no—
63C2×C3×#67—44no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71#3754—28no—
72C2×C3⋊(C3⋊C8)D414yescomplemented
73C2×C3⋊(C3⋊C8)C2312yes—
74C3×#217—24no—
75C3×C4⋊Dic3—21no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C3×C4⋊Dic3C2312yes—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81Dic3⋊Dic3—24no—
82(C2×D3)⋊Dic3—24no—
83D3×C3⋊C8—28no—
84C2×#465—91noSylow
85C22×C3×D4—21no—
86C22×C3×D4—61no—
87C22×C3×D4C2×D311yescharacteristic
88C22×C3×D4C2×D311yescharacteristic
89C23×C3×C4—31no—
90C22×#67—21no—
91C22×C4×D3C2×D311yescharacteristic
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C22×C3×C8—31no—
96C3×#121—34no—
97C3×#121—62no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C22⋊C4—61no—
101C2×#217—21no—
102C2×#217—61no—
103#938—22no—
104#938C2×D314yes—
105C2×#214—34no—
106C2×#214—34no—
107C2×#214—64no—
108C2×#214—64no—
109C2×#214—64no—
110C2×#214—68no—
111C2×(C2×D3)⋊C4—61no—
112C2×C4⋊Dic3—61no—
113C2×C4⋊Dic3C2×D311yescharacteristic
114C2×C4⋊Dic3C2×D311yescharacteristic
115#924—34no—
116#924—62no—
117C2×Dic3⋊C4—61no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—34no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8—64no—
123C22×C3⋊C8C2×D311yescharacteristic
124C2×D3×C8—34no—
125C2×D3×C8—64no—
126#897—34no—
127#897—62no—
128C3×#102—34no—
129#832C2×D314yescomplemented
130#816—34no—
131#810—34no—
132#808—34no—
133#808—34no—
134C23×C32—22no—
135C23×C32—42no—
136C23×C32—42no—
137C23×C32—42no—
138C23×C32C2×D411yescharacteristic
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3SD1614yescomplemented
142C22×C3×D3C2×D412yes—
143C32×D4—22no—
144C32×D4—22no—
145C32×D4—42no—
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—
155C3×#67—48no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—42no—
160C2×C3×Dic3—42no—
161C2×C3×Dic3C2×D412yes—
162C3×C4×D3—24no—
163C3×C4×D3—22no—
164C3×C4×D3—22no—
165C3⋊(C3⋊C8)C2×D414yescomplemented
166C3×C3⋊C8—22no—
167C22×SD16—91no—
168C23×C8—91no—
169C2×C22⋊Q8—91no—
170C2×#121—31no—
171#465—98no—
172C2×#106—91no—
173C2×#103—91no—
174C2×#102—31no—
175C24×C3—21no—
176C24×C3—21no—
177C24×C3—31no—
178C24×C3—41no—
179C23×D3#6711yescharacteristic
180C2×C3×D4—24no—
181C2×C3×D4—22no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—21no—
187C2×C3×D4—22no—
188C2×C3×D4—42no—
189C2×C3×D4—41no—
190C2×C3×D4—64no—
191C2×C3×D4—124no—
192C2×C3×D4C22×D312yes—
193C2×C3×D4C22×D312yes—
194C22×C3×C4—21no—
195C22×C3×C4—31no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—62no—
199C22×C3×C4—62no—
200C22×C3×C4—61no—
201C22×C3×C4—61no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67—24no—
205C2×#67—44no—
206C22×Dic3—21no—
207C22×Dic3—21no—
208C22×Dic3—61no—
209C22×Dic3—61no—
210C22×Dic3—121no—
211C22×Dic3#6711yescharacteristic
212C2×C4×D3—22no—
213C2×C4×D3—22no—
214C2×C4×D3#6712yes—
215C2×C4×D3C22×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—
228C2×C3×C8—32no—
229C2×C3×C8—62no—
230C3×C4⋊C4—32no—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—61no—
233C3×C4⋊C4—61no—
234C3×C22⋊C4—64no—
235#217—24no—
236#217—64no—
237#214—68no—
238#214—68no—
239#214—616no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—21no—
242C4⋊Dic3—21no—
243C4⋊Dic3—64no—
244C4⋊Dic3C22×D312yes—
245C4⋊Dic3C22×D312yes—
246Dic3⋊C4—64no—
247C2×C3⋊C8—22no—
248C2×C3⋊C8—34no—
249C2×C3⋊C8—34no—
250C2×C3⋊C8—32no—
251C2×C3⋊C8—32no—
252C2×C3⋊C8—64no—
253C2×C3⋊C8—62no—
254C2×C3⋊C8—68no—
255C2×C3⋊C8C22×D312yes—
256D3×C8—68no—
257C22×C32—42no—
258C22×C32—42no—
259C22×C32—42no—
260C22×C32—84no—
261C22×C32#12112yes—
262C22×C32C2×SD1612yes—
263C22×C32#13512yes—
264C22×C32C22×D411yescharacteristic
265C2×C3×D3—22no—
266C2×C3×D3—22no—
267C2×C3×D3—28no—
268C2×C3×D3C2×SD1614yescomplemented
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—42no—
273C3×Dic3—22no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C22×Q8—91no—
277C22×D4—61no—
278C22×D4D3211yescharacteristic
279C23×C4—31no—
280C2×SD16—94no—
281C2×SD16—184no—
282C22×C8—31no—
283C22×C8—94no—
284C22×C8—91no—
285C22×C8—184no—
286C22⋊Q8—94no—
287C22⋊Q8—182no—
288#121—34no—
289#121—62no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—31no—
292C2×C4⋊C4—181no—
293C2×C22⋊C4—61no—
294C2×C22⋊C4—181no—
295#106—94no—
296#103—94no—
297#102—34no—
298C23×C3—22no—
299C23×C3—22no—
300C23×C3—21no—
301C23×C3—34no—
302C23×C3—32no—
303C23×C3—42no—
304C23×C3—44no—
305C23×C3—42no—
306C23×C3—42no—
307C23×C3—42no—
308C23×C3—42no—
309C23×C3—42no—
310C23×C3—42no—
311C23×C3—62no—
312C23×C3—62no—
313C23×C3—82no—
314C23×C3—82no—
315C23×C3D3×D411yescharacteristic
316C23×C3C2×#6711yescharacteristic
317C22×D3—22no—
318C22×D3—22no—
319C22×D3#21414yescomplemented
320C22×D3C2×#6712yes—
321C3×D4—24no—
322C3×D4—22no—
323C3×D4—22no—
324C3×D4—22no—
325C3×D4—22no—
326C3×D4—42no—
327C3×D4—44no—
328C3×D4—42no—
329C3×D4—42no—
330C3×D4—128no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—32no—
336C2×C3×C4—62no—
337C2×C3×C4—64no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—62no—
342C2×C3×C4—122no—
343C2×C3×C4—122no—
344C2×C3×C4#23512yes—
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D412yes—
347C2×C3×C4D3×D412yes—
348C2×C3×C4#23712yes—
349C2×C3×C4C2×#6711yescharacteristic
350C2×C3×C4C23×D311yescharacteristic
351C2×C3×C4C23×D311yescharacteristic
352#67—48no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—22no—
356C2×Dic3—42no—
357C2×Dic3—42no—
358C2×Dic3—62no—
359C2×Dic3—62no—
360C2×Dic3—122no—
361C2×Dic3—124no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364C2×Dic3C2×#6712yes—
365C4×D3—24no—
366C4×D3—22no—
367C4×D3—22no—
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—34no—
380C3⋊C8—34no—
381C3⋊C8—64no—
382C2×C32—82no—
383C2×C32#46514yescomplemented
384C2×C32C2×#12111yescharacteristic
385C2×C32C22×SD1611yescharacteristic
386C2×C32C2×#13511yescharacteristic
387C3×D3—24no—
388C24—21no—
389C24—31no—
390C2×Q8—92no—
391C2×Q8—181no—
392C2×Q8—182no—
393C2×Q8—182no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4—64no—
398C2×D4—124no—
399C2×D4C2×D3212yes—
400C22×C4—31no—
401C22×C4—32no—
402C22×C4—32no—
403C22×C4—62no—
404C22×C4—62no—
405C22×C4—61no—
406C22×C4—61no—
407C22×C4—181no—
408C22×C4C2×D3211yescharacteristic
409SD16—188no—
410C2×C8—32no—
411C2×C8—62no—
412C2×C8—92no—
413C2×C8—94no—
414C2×C8—188no—
415C4⋊C4—32no—
416C4⋊C4—32no—
417C4⋊C4—61no—
418C4⋊C4—61no—
419C4⋊C4—184no—
420C22⋊C4—64no—
421C22⋊C4—184no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—34no—
427C22×C3—44no—
428C22×C3—42no—
429C22×C3—42no—
430C22×C3—42no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—62no—
435C22×C3—62no—
436C22×C3—68no—
437C22×C3—82no—
438C22×C3—82no—
439C22×C3—88no—
440C22×C3—84no—
441C22×C3—84no—
442C22×C3#88412yes—
443C22×C3#91212yes—
444C22×C3D3×SD1612yes—
445C22×C3C2×#21412yes—
446C22×C3#93912yes—
447C22×C3#95012yes—
448C22×C3C2×D3×D411yescharacteristic
449C22×C3C22×#6711yescharacteristic
450C2×D3—22no—
451C2×D3—28no—
452C2×D3—22no—
453C2×D3C2×#21414yescomplemented
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—62no—
458C3×C4—122no—
459C3×C4—122no—
460C3×C4#88412yes—
461C3×C4#93912yes—
462C3×C4C2×#23511yescharacteristic
463C3×C4C2×D3×D411yescharacteristic
464C3×C4C2×D3×D411yescharacteristic
465C3×C4C2×#23711yescharacteristic
466Dic3—22no—
467Dic3—42no—
468Dic3—42no—
469Dic3—124no—
470Dic3—122no—
471Dic3—122no—
472C32C2×#46511yescharacteristic, complemented, Sylow
473C23—22no—
474C23—32no—
475C23—34no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—62no—
480C23—62no—
481C23D3×#6711yescharacteristic
482Q8—182no—
483Q8—182no—
484Q8—362no—
485D4—22no—
486D4—22no—
487D4—42no—
488D4—128no—
489C2×C4—32no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—64no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—122no—
497C2×C4—122no—
498C2×C4—182no—
499C2×C4—362no—
500C2×C4#380412yes—
501C2×C4D3×#6711yescharacteristic
502C2×C4#381112yes—
503C2×C4C22×D3211yescharacteristic
504C8—62no—
505C8—94no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—24no—
510C2×C3—64no—
511C2×C3—84no—
512C2×C3—82no—
513C2×C3—82no—
514C2×C3#477814yescomplemented
515C2×C3#504114yescomplemented
516C2×C3C2×#88411yescharacteristic
517C2×C3C2×#91211yescharacteristic
518C2×C3C2×D3×SD1611yescharacteristic
519C2×C3C22×#21411yescharacteristic
520C2×C3C2×#93911yescharacteristic
521C2×C3C2×#95011yescharacteristic
522D3—24no—
523C22—34no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—62no—
528C22—62no—
529C22—68no—
530C22—84no—
531C22D3×#21412yes—
532C22#6393312yes—
533C22#6397112yes—
534C22C2×D3×#6711yescharacteristic
535C4—62no—
536C4—122no—
537C4—122no—
538C4—362no—
539C4#6397112yes—
540C4C2×#380411yescharacteristic
541C4C2×#381111yescharacteristic
542C3—21no—
543C3C2×#477811yescharacteristic, complemented
544C3C2×#504111yescharacteristic, complemented
545C2—64no—
546C2—82no—
547C2#1059146014yesdirect product factor
548C2C2×D3×#21411yescharacteristic
549C2C2×#6393311yescharacteristic
550C2C2×#6397111yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC2×C3×#938C2
hypercenterC22×D4D32
hypocenterC32C2×#465
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
3. C2×#63857C2semidirect
4. C22×D3×C3⋊C8C2semidirect
5. C2×C3×#832C2semidirect
6. #10591460C2direct (N × H)
7. C2×#63574C2semidirect
8. C2×#63567C2semidirect
16. C2×#3754C22semidirect
27. #63857C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. C3×#832C22semidirect
31. #63574C22semidirect
32. #63567C22semidirect
43. C2×#832D3semidirect
72. C2×C3⋊(C3⋊C8)D4semidirect
129. #832C2×D3semidirect
141. C22×C3×D3SD16semidirect
165. C3⋊(C3⋊C8)C2×D4semidirect
268. C2×C3×D3C2×SD16semidirect
319. C22×D3#214semidirect
383. C2×C32#465semidirect
453. C2×D3C2×#214semidirect
472. C32C2×#465semidirect
514. C2×C3#4778semidirect
515. C2×C3#5041semidirect
543. C3C2×#4778semidirect
544. C3C2×#5041semidirect
547. C2#10591460direct (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×#9382
C2×#638572
C22×D3×C3⋊C82
C2×C3×#8322
#105914602
C2×#635742
C2×#635672
C2×#50413
C2×#47783