Finite Group Databasebeta

← C2×#10590952 #11863673

Subgroups — C2×#10590952 #11863673

Order 1152.

1609 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic
2C22×#3746C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590952C218yesmaximal, direct product factor
9C2×#4809—31nomaximal
10C2×#4739—31nomaximal
11C22×#634C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627—21no—
16C22×D3×Dic3—21no—
17C2×D3×Dic6—24no—
18C2×D3×Dic6—22no—
19C2×D3×Dic6—24no—
20C2×D3×Dic6C2214yes—
21C22×C32×C8C2211yescharacteristic
22C2×#3746—24no—
23C2×#3746C2214yescomplemented
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×Dic3⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63857—22no—
29#63857C2214yes—
30C2×#3719—24no—
31C2×#3719C2214yescomplemented
32C3×(C2×D3)⋊C8C2214yes—
33C3×#816C2214yescomplemented
34#63567C2214yescomplemented
35C22×D3×Q8—31no—
36C23×Dic6—31no—
37C22×#216—31no—
38C2×#924—31no—
39C22×Dic12—31no—
40C22×Dic12—31no—
41C22×Dic12—31no—
42C22×Dic12—61no—
43C2×#897—31no—
44C2×C3×#103—31no—
45C2×C3×C22⋊C8—31no—
46C2×(C2×D3)⋊C8D311yescharacteristic
47C2×#816—31no—
48C2×#816D311yescharacteristic, complemented
49C2×#810—31no—
50#4809—38no—
51#4739—38no—
52C23×C3×D3D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—22no—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634—21no—
61C2×#634D414yes—
62C2×#634C2312yes—
63C2×#634C2312yes—
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—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yes—
74C2×C3×Dic6C2312yes—
75C2×#627—28no—
76C2×#627—24no—
77C2×D3×Dic3—28no—
78C2×D3×Dic3—24no—
79D3×Dic6—216no—
80D3×Dic6—28no—
81D3×Dic6—28no—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84#3746—28no—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89Dic3⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91#3719—28no—
92C2×#451—91noSylow
93C22×C3×Q8—31no—
94C23×C3×C4—31no—
95C23×Dic3—61no—
96C2×D3×Q8—34no—
97C2×D3×Q8—64no—
98C2×D3×Q8—64no—
99C2×D3×Q8—62no—
100C22×C4×D3—61no—
101C22×C4×D3C2×D311yescharacteristic
102C22×Dic6—31no—
103C22×Dic6—31no—
104C22×Dic6—31no—
105C22×Dic6—31no—
106C22×Dic6—34no—
107C22×Dic6—61no—
108C22×Dic6—61no—
109C22×Dic6—64no—
110C22×Dic6—62no—
111C22×Dic6—61no—
112C22×Dic6—61no—
113C22×Dic6—64no—
114C22×Dic6C2×D311yescharacteristic
115C22×C3×C8—21no—
116C22×C3×C8—31no—
117C22×C3×C8C2×D311yescharacteristic
118C22×C3×C8C2×D311yescharacteristic
119C2×C3×C4⋊C4—31no—
120C2×#217—61no—
121C2×#216—34no—
122C2×#216—64no—
123C2×(C2×D3)⋊C4—61no—
124C2×C4⋊Dic3—61no—
125C2×C4⋊Dic3C2×D311yescharacteristic
126#924—34no—
127#924—62no—
128C2×Dic3⋊C4—61no—
129C22×C3⋊C8C2×D311yescharacteristic
130C2×Dic12—34no—
131C2×Dic12—34no—
132C2×Dic12—34no—
133C2×Dic12—64no—
134C2×Dic12—64no—
135C2×Dic12—64no—
136C2×Dic12—68no—
137C2×Dic12—64no—
138#897—34no—
139#897—62no—
140C3×#103—34no—
141C3×C22⋊C8—34no—
142(C2×D3)⋊C8C2×D314yes—
143#816—34no—
144#816C2×D314yescomplemented
145#810—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3Q1614yescomplemented
150C22×C3×D3C2×D412yes—
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D412yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2411yescharacteristic
155C2×C3⋊Dic3—24no—
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—42no—
159#634—22no—
160#634—24no—
161#634—22no—
162#634—22no—
163#634—42no—
164#634C2×D414yes—
165C2×C3×Dic3—24no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—42no—
170C2×C3×Dic3C2×D412yes—
171C3×C4×D3—24no—
172C3×C4×D3—22no—
173C3×C4×D3—22no—
174C3×Dic6—24no—
175C3×Dic6—22no—
176C3×Dic6C2×D414yes—
177#627—216no—
178D3×Dic3—216no—
179C32×C8—22no—
180C3×C3⋊C8—22no—
181C23×Q8—91no—
182C22×Q16—91no—
183C22×Q16—91no—
184C2×C22⋊Q8—91no—
185#451—98no—
186C2×#103—31no—
187C2×#103—91no—
188C2×C22⋊C8—31no—
189C24×C3—31no—
190C23×D3D1211yescharacteristic
191C2×C3×Q8—34no—
192C2×C3×Q8—32no—
193C2×C3×Q8—61no—
194C2×C3×Q8—62no—
195C22×C3×C4—21no—
196C22×C3×C4—31no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—61no—
200C22×C3×C4—62no—
201C22×C3×C4—62no—
202C22×C3×C4—61no—
203C22×C3×C4C22×D311yescharacteristic
204C22×C3×C4C22×D311yescharacteristic
205C22×Dic3—21no—
206C22×Dic3—21no—
207C22×Dic3—64no—
208C22×Dic3—68no—
209C22×Dic3—61no—
210C22×Dic3—61no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—121no—
214C22×Dic3—121no—
215C22×Dic3D1211yescharacteristic
216D3×Q8—68no—
217D3×Q8—68no—
218D3×Q8—616no—
219C2×C4×D3—22no—
220C2×C4×D3—22no—
221C2×C4×D3—68no—
222C2×C4×D3—64no—
223C2×C4×D3D1212yes—
224C2×C4×D3C22×D312yes—
225C2×Dic6—21no—
226C2×Dic6—22no—
227C2×Dic6—34no—
228C2×Dic6—34no—
229C2×Dic6—32no—
230C2×Dic6—32no—
231C2×Dic6—32no—
232C2×Dic6—32no—
233C2×Dic6—64no—
234C2×Dic6—62no—
235C2×Dic6—62no—
236C2×Dic6—68no—
237C2×Dic6—616no—
238C2×Dic6—64no—
239C2×Dic6—68no—
240C2×Dic6—68no—
241C2×Dic6—62no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—62no—
245C2×Dic6—64no—
246C2×Dic6—68no—
247C2×Dic6—64no—
248C2×Dic6—62no—
249C2×Dic6—62no—
250C2×Dic6—62no—
251C2×Dic6—62no—
252C2×Dic6—61no—
253C2×Dic6—61no—
254C2×Dic6—121no—
255C2×Dic6—122no—
256C2×Dic6—121no—
257C2×Dic6—122no—
258C2×Dic6D1214yes—
259C2×Dic6C22×D312yes—
260C2×C3×C8—24no—
261C2×C3×C8—22no—
262C2×C3×C8—22no—
263C2×C3×C8—22no—
264C2×C3×C8—32no—
265C2×C3×C8—62no—
266C2×C3×C8C22×D312yes—
267C2×C3×C8C22×D312yes—
268C3×C4⋊C4—32no—
269C3×C4⋊C4—61no—
270#217—64no—
271#216—68no—
272(C2×D3)⋊C4—64no—
273C4⋊Dic3—21no—
274C4⋊Dic3—64no—
275C4⋊Dic3C22×D312yes—
276Dic3⋊C4—64no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8C22×D312yes—
279Dic12—68no—
280Dic12—68no—
281Dic12—616no—
282Dic12—68no—
283C22×C32#12012yes—
284C22×C32C2×Q1612yes—
285C22×C32#13712yes—
286C22×C32C22×D411yescharacteristic
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—28no—
290C2×C3×D3C2×Q1614yescomplemented
291C32×C4#12012yes—
292C32×C4C22×D411yescharacteristic
293C32×C4C22×D411yescharacteristic
294C3⋊Dic3—24no—
295C3⋊Dic3—42no—
296C3×Dic3—24no—
297C3×Dic3—22no—
298C3×Dic3—42no—
299C22×Q8—31no—
300C22×Q8—94no—
301C22×Q8—91no—
302C22×Q8—91no—
303C22×Q8—181no—
304C22×Q8—182no—
305C22×Q8—184no—
306C22×Q8—184no—
307C23×C4—31no—
308C23×C4—181no—
309C2×Q16—94no—
310C2×Q16—94no—
311C2×Q16—184no—
312C2×Q16—184no—
313C22×C8—31no—
314C22×C8D3211yescharacteristic
315C22⋊Q8—94no—
316C22⋊Q8—182no—
317C2×C4⋊C4—31no—
318C2×C4⋊C4—181no—
319C2×C22⋊C4—181no—
320#103—34no—
321#103—94no—
322C22⋊C8—34no—
323C23×C3—21no—
324C23×C3—34no—
325C23×C3—32no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3C2×D1211yescharacteristic
329C23×C3D3×D411yescharacteristic
330C22×D3—22no—
331C22×D3—22no—
332C22×D3Dic1214yescomplemented
333C22×D3C2×D1212yes—
334C3×Q8—34no—
335C3×Q8—64no—
336C3×Q8—62no—
337C2×C3×C4—21no—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—22no—
341C2×C3×C4—32no—
342C2×C3×C4—62no—
343C2×C3×C4—64no—
344C2×C3×C4—62no—
345C2×C3×C4—64no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—122no—
350C2×C3×C4C2×D1211yescharacteristic
351C2×C3×C4C2×D1212yes—
352C2×C3×C4D3×D411yescharacteristic
353C2×C3×C4D3×D412yes—
354C2×C3×C4D3×D412yes—
355C2×C3×C4D3×D412yes—
356C2×C3×C4C23×D311yescharacteristic
357C2×C3×C4C23×D311yescharacteristic
358C2×Dic3—24no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—42no—
363C2×Dic3—616no—
364C2×Dic3—64no—
365C2×Dic3—64no—
366C2×Dic3—62no—
367C2×Dic3—62no—
368C2×Dic3—62no—
369C2×Dic3—62no—
370C2×Dic3—122no—
371C2×Dic3—124no—
372C2×Dic3—122no—
373C2×Dic3—124no—
374C2×Dic3—122no—
375C2×Dic3—122no—
376C2×Dic3C2×D1212yes—
377C4×D3—24no—
378C4×D3—22no—
379C4×D3—22no—
380C4×D3—616no—
381Dic6—24no—
382Dic6—22no—
383Dic6—34no—
384Dic6—34no—
385Dic6—64no—
386Dic6—616no—
387Dic6—616no—
388Dic6—64no—
389Dic6—64no—
390Dic6—62no—
391Dic6—62no—
392Dic6—64no—
393Dic6—62no—
394Dic6—62no—
395Dic6—62no—
396Dic6—62no—
397Dic6—122no—
398Dic6—124no—
399Dic6—122no—
400Dic6—124no—
401Dic6—122no—
402Dic6—122no—
403Dic6C2×D1214yes—
404C3×C8—24no—
405C3×C8—22no—
406C3×C8—22no—
407C3×C8—62no—
408C3⋊C8—22no—
409C2×C32#45114yescomplemented
410C2×C32C2×#12011yescharacteristic
411C2×C32C22×Q1611yescharacteristic
412C2×C32C2×#13711yescharacteristic
413C3×D3—24no—
414C24—31no—
415C2×Q8—32no—
416C2×Q8—34no—
417C2×Q8—61no—
418C2×Q8—62no—
419C2×Q8—92no—
420C2×Q8—92no—
421C2×Q8—94no—
422C2×Q8—184no—
423C2×Q8—188no—
424C2×Q8—188no—
425C2×Q8—188no—
426C2×Q8—1816no—
427C2×Q8—181no—
428C2×Q8—182no—
429C2×Q8—181no—
430C2×Q8—182no—
431C2×Q8—182no—
432C22×C4—31no—
433C22×C4—32no—
434C22×C4—32no—
435C22×C4—61no—
436C22×C4—62no—
437C22×C4—62no—
438C22×C4—61no—
439C22×C4—184no—
440C22×C4—188no—
441C22×C4—181no—
442C22×C4—181no—
443C22×C4C2×D3211yescharacteristic
444Q16—188no—
445Q16—188no—
446C2×C8—22no—
447C2×C8—32no—
448C2×C8—62no—
449C2×C8C2×D3212yes—
450C4⋊C4—32no—
451C4⋊C4—61no—
452C4⋊C4—184no—
453C22⋊C4—184no—
454C22×C3—21no—
455C22×C3—22no—
456C22×C3—22no—
457C22×C3—22no—
458C22×C3—34no—
459C22×C3—62no—
460C22×C3—62no—
461C22×C3—68no—
462C22×C3#88212yes—
463C22×C3#88212yes—
464C22×C3C2×Dic1212yes—
465C22×C3#90912yes—
466C22×C3#91512yes—
467C22×C3D3×Q1612yes—
468C22×C3C22×D1211yescharacteristic
469C22×C3C2×D3×D411yescharacteristic
470C2×D3—22no—
471C2×D3—22no—
472C2×D3—28no—
473C2×D3C2×Dic1214yescomplemented
474C3×C4—21no—
475C3×C4—21no—
476C3×C4—22no—
477C3×C4—62no—
478C3×C4—64no—
479C3×C4—122no—
480C3×C4#88212yes—
481C3×C4#88212yes—
482C3×C4C22×D1211yescharacteristic
483C3×C4C2×D3×D411yescharacteristic
484C3×C4C2×D3×D411yescharacteristic
485C3×C4C2×D3×D411yescharacteristic
486Dic3—24no—
487Dic3—22no—
488Dic3—42no—
489Dic3—64no—
490Dic3—64no—
491Dic3—124no—
492Dic3—124no—
493Dic3—122no—
494Dic3—122no—
495C32C2×#45111yescharacteristic, complemented, Sylow
496C23—32no—
497C23—34no—
498C23—62no—
499C23—62no—
500C23D3×D1211yescharacteristic
501Q8—34no—
502Q8—62no—
503Q8—64no—
504Q8—94no—
505Q8—1816no—
506Q8—182no—
507Q8—184no—
508Q8—182no—
509Q8—182no—
510Q8—362no—
511C2×C4—32no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—64no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—64no—
518C2×C4—62no—
519C2×C4—122no—
520C2×C4—1816no—
521C2×C4—182no—
522C2×C4—184no—
523C2×C4—182no—
524C2×C4—362no—
525C2×C4D3×D1212yes—
526C2×C4D3×D1211yescharacteristic
527C2×C4#381112yes—
528C2×C4C22×D3211yescharacteristic
529C8—22no—
530C8—62no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—24no—
534C2×C3—21no—
535C2×C3—64no—
536C2×C3#473914yescomplemented
537C2×C3#480914yescomplemented
538C2×C3C2×#88211yescharacteristic
539C2×C3C2×#88211yescharacteristic
540C2×C3C22×Dic1211yescharacteristic
541C2×C3C2×#90911yescharacteristic
542C2×C3C2×#91511yescharacteristic
543C2×C3C2×D3×Q1611yescharacteristic
544D3—24no—
545C22—34no—
546C22—62no—
547C22—68no—
548C22—62no—
549C22D3×Dic1212yes—
550C22#6380012yes—
551C22#6392312yes—
552C22C2×D3×D1211yescharacteristic
553C4—62no—
554C4—64no—
555C4—122no—
556C4—184no—
557C4—362no—
558C4#6392312yes—
559C4C2×D3×D1211yescharacteristic
560C4C2×#381111yescharacteristic
561C3—21no—
562C3C2×#473911yescharacteristic, complemented
563C3C2×#480911yescharacteristic, complemented
564C2—64no—
565C2#1059095214yesdirect product factor
566C2C2×D3×Dic1211yescharacteristic
567C2C2×#6380011yescharacteristic
568C2C2×#6392311yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×C8D32
hypocenterC32C2×#451
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×#3746C2semidirect
4. C22×#3719C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63567C2semidirect
8. #10590952C2direct (N × H)
23. C2×#3746C22semidirect
31. C2×#3719C22semidirect
33. C3×#816C22semidirect
34. #63567C22semidirect
48. C2×#816D3semidirect
144. #816C2×D3semidirect
149. C22×C3×D3Q16semidirect
290. C2×C3×D3C2×Q16semidirect
332. C22×D3Dic12semidirect
409. C2×C32#451semidirect
473. C2×D3C2×Dic12semidirect
495. C32C2×#451semidirect
536. C2×C3#4739semidirect
537. C2×C3#4809semidirect
562. C3C2×#4739semidirect
563. C3C2×#4809semidirect
565. C2#10590952direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C22×#37462
C2×#638572
C22×#37192
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C2×#635672
#105909522
C2×#48093
C2×#47393