Finite Group Databasebeta

← C2×D3×#944 #11900721

Subgroups — C2×D3×#944 #11900721

Order 1152.

3393 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×Q8C211yesmaximal, characteristic
2C22×D3×Dic6C211yesmaximal, characteristic
3C2×#64153C211yesmaximal, characteristic, complemented
4C2×C3×#944C211yesmaximal, characteristic, complemented
5D3×#944C2116yesmaximal, direct product factor
6C2×D3×Dic3⋊C4C214yesmaximal
7C2×C4×D3×Dic3C211yesmaximal, characteristic
8C2×#63873C211yesmaximal, characteristic, complemented
9C2×#63866C211yesmaximal, characteristic, complemented
10C2×#63839C214yesmaximal, complemented
11C22×#944—31nomaximal
12C2×D3×C4⋊Q8—31nomaximal
13C22×C32×Q8C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C3×D3×Q8—28no—
16C2×C3×D3×Q8C2218yes—
17C22×C3×C4×D3C2212yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2212yes—
22C22×#627C2212yes—
23C22×D3×Dic3C2212yes—
24C22×D3×Dic3C2212yes—
25C2×D3×Dic6—28no—
26C2×D3×Dic6C2218yes—
27#64153C2218yescomplemented
28C2×#3750C2214yes—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C3×#944C2218yescomplemented
31C2×C3×Dic3⋊C4C2214yes—
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2214yes—
34C2×Dic3⋊Dic3C2214yes—
35C2×Dic32C2212yes—
36D3×Dic3⋊C4C22132yes—
37C4×D3×Dic3C2218yes—
38#63873C2218yescomplemented
39#63866C2218yescomplemented
40#63839C22132yescomplemented
41C23×C3×Q8—31no—
42C22×D3×Q8—31no—
43C22×D3×Q8D311yescharacteristic
44C23×Dic6—31no—
45C2×C3×C4⋊Q8—31no—
46C2×#944—31no—
47C2×#944—31no—
48C2×#944—31no—
49C2×#944—31no—
50C2×#944—316no—
51C2×#944—34no—
52C2×#944—31no—
53C2×#944—61no—
54C2×#944D311yescharacteristic, direct product factor
55C22×Dic3⋊C4—34no—
56C22×C4×Dic3—31no—
57D3×C4⋊Q8—316no—
58C2×D3×C4⋊C4—34no—
59C2×#888—34no—
60C2×C42×D3—31no—
61C2×#869—31no—
62C23×C3×D3C2311yescharacteristic
63C2×C32×Q8—24no—
64C2×C32×Q8C2314yes—
65C22×C32×C4C2312yes—
66C22×C32×C4C2311yescharacteristic
67C22×C3⋊Dic3C2312yes—
68C22×C3⋊Dic3C2312yes—
69C2×#634—24no—
70C2×#634C2314yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C3×D3×Q8—232no—
76C2×C3×C4×D3—28no—
77C2×C3×C4×D3D418yes—
78C2×C3×C4×D3C2318yes—
79C2×C3×C4×D3C2314yes—
80C2×C3×Dic6—24no—
81C2×C3×Dic6—24no—
82C2×C3×Dic6—28no—
83C2×C3×Dic6C2314yes—
84C2×C3×Dic6C2318yes—
85C2×C3×Dic6C2314yes—
86C2×#627—28no—
87C2×#627C2318yes—
88C2×D3×Dic3—28no—
89C2×D3×Dic3Q8116yescomplemented
90C2×D3×Dic3C2318yes—
91C2×D3×Dic3C2318yes—
92D3×Dic6—232no—
93#3750C23116yes—
94C4×C3⋊Dic3C2314yes—
95C3×Dic3⋊C4C23116yes—
96C3×C4×Dic3C2314yes—
97#3724C23116yes—
98Dic3⋊Dic3C23116yes—
99Dic32C2318yes—
100C22×C4⋊Q8—91noSylow
101C22×C3×Q8—21no—
102C22×C3×Q8—38no—
103C22×C3×Q8—31no—
104C22×C3×Q8—32no—
105C22×C3×Q8—31no—
106C22×C3×Q8—68no—
107C22×C3×Q8C2×D311yescharacteristic
108C22×C3×Q8C2×D311yescharacteristic
109C23×C3×C4—31no—
110C23×C3×C4—32no—
111C23×Dic3—32no—
112C23×Dic3—32no—
113C2×D3×Q8—28no—
114C2×D3×Q8—38no—
115C2×D3×Q8—68no—
116C2×D3×Q8C2×D318yes—
117C22×C4×D3—32no—
118C22×C4×D3—32no—
119C22×C4×D3C2×D312yes—
120C22×C4×D3C2×D311yescharacteristic
121C22×Dic6—31no—
122C22×Dic6—31no—
123C22×Dic6—32no—
124C22×Dic6—32no—
125C22×Dic6—38no—
126C22×Dic6—61no—
127C22×Dic6—68no—
128C22×Dic6C2×D311yescharacteristic
129C22×Dic6C2×D311yescharacteristic
130C22×Dic6C2×D312yes—
131C3×C4⋊Q8—38no—
132C2×C3×C4⋊C4—34no—
133C2×C3×C42—31no—
134#944—38no—
135#944—38no—
136#944—38no—
137#944—38no—
138#944—332no—
139#944—38no—
140#944—68no—
141#944C2×D318yesdirect product factor
142C2×C4⋊Dic3—34no—
143C2×Dic3⋊C4—34no—
144C2×Dic3⋊C4—34no—
145C2×Dic3⋊C4—34no—
146C2×Dic3⋊C4—34no—
147C2×Dic3⋊C4—34no—
148C2×Dic3⋊C4—332no—
149C2×Dic3⋊C4—64no—
150C2×Dic3⋊C4C2×D314yes—
151C2×C4×Dic3—31no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3—38no—
156C2×C4×Dic3—61no—
157C2×C4×Dic3C2×D311yescharacteristic
158D3×C4⋊C4—332no—
159#888—332no—
160C42×D3—38no—
161#869—38no—
162C23×C32C2411yescharacteristic
163C22×C3×D3C2×D414yes—
164C22×C3×D3C2×Q818yes—
165C22×C3×D3C2412yes—
166C32×Q8—28no—
167C2×C32×C4—24no—
168C2×C32×C4C2×D414yes—
169C2×C32×C4C2414yes—
170C2×C32×C4C2412yes—
171C2×C3⋊Dic3—24no—
172C2×C3⋊Dic3C2×Q818yescomplemented
173C2×C3⋊Dic3C2414yes—
174C2×C3⋊Dic3C2414yes—
175#634—28no—
176C2×C3×Dic3—24no—
177C2×C3×Dic3—24no—
178C2×C3×Dic3C2×D414yes—
179C2×C3×Dic3C2×Q818yescomplemented
180C2×C3×Dic3C2414yes—
181C2×C3×Dic3C2414yes—
182C2×C3×Dic3C2412yes—
183C2×C3×Dic3C2414yes—
184C3×C4×D3—216no—
185C3×C4×D3C2×D4116yes—
186C3×Dic6—28no—
187C3×Dic6—28no—
188C3×Dic6—216no—
189#627—216no—
190D3×Dic3—216no—
191D3×Dic3C2×Q8132yescomplemented
192C23×Q8—31no—
193C23×Q8—91no—
194C2×C4⋊Q8—31no—
195C2×C4⋊Q8—91no—
196C2×C4⋊Q8—94no—
197C2×C4⋊Q8—916no—
198C2×C4⋊Q8—91no—
199C2×C4⋊Q8—91no—
200C22×C4⋊C4—94no—
201C22×C42—91no—
202C24×C3—31no—
203C23×D3C22×D311yescharacteristic
204C2×C3×Q8—24no—
205C2×C3×Q8—24no—
206C2×C3×Q8—24no—
207C2×C3×Q8—38no—
208C2×C3×Q8—34no—
209C2×C3×Q8—34no—
210C2×C3×Q8—44no—
211C2×C3×Q8—68no—
212C2×C3×Q8—632no—
213C2×C3×Q8—64no—
214C2×C3×Q8—64no—
215C2×C3×Q8C22×D314yes—
216C2×C3×Q8C22×D314yes—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—31no—
220C22×C3×C4—32no—
221C22×C3×C4—38no—
222C22×C3×C4—34no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—38no—
226C22×C3×C4—68no—
227C22×C3×C4C22×D312yes—
228C22×C3×C4C22×D312yes—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C22×Dic3—32no—
232C22×Dic3—32no—
233C22×Dic3—316no—
234C22×Dic3—38no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—38no—
238C22×Dic3—62no—
239C22×Dic3—62no—
240C22×Dic3—68no—
241C22×Dic3C22×D312yes—
242C22×Dic3C22×D312yes—
243C22×Dic3C22×D312yes—
244C22×Dic3C22×D311yescharacteristic
245D3×Q8—232no—
246D3×Q8—632no—
247C2×C4×D3—28no—
248C2×C4×D3—316no—
249C2×C4×D3—38no—
250C2×C4×D3—38no—
251C2×C4×D3—68no—
252C2×C4×D3#6718yes—
253C2×C4×D3C22×D318yes—
254C2×C4×D3C22×D314yes—
255C2×Dic6—24no—
256C2×Dic6—24no—
257C2×Dic6—28no—
258C2×Dic6—34no—
259C2×Dic6—34no—
260C2×Dic6—38no—
261C2×Dic6—38no—
262C2×Dic6—64no—
263C2×Dic6—632no—
264C2×Dic6—68no—
265C2×Dic6—64no—
266C2×Dic6—64no—
267C2×Dic6—68no—
268C2×Dic6—124no—
269C2×Dic6C22×D314yes—
270C2×Dic6C22×D318yes—
271C2×Dic6C22×D314yes—
272C3×C4⋊C4—316no—
273C3×C42—34no—
274C4⋊Dic3—316no—
275Dic3⋊C4—316no—
276Dic3⋊C4—316no—
277Dic3⋊C4—316no—
278Dic3⋊C4—316no—
279Dic3⋊C4—316no—
280Dic3⋊C4—616no—
281Dic3⋊C4C22×D3116yes—
282C4×Dic3—34no—
283C4×Dic3—34no—
284C4×Dic3—38no—
285C4×Dic3—38no—
286C4×Dic3—64no—
287C4×Dic3C22×D314yes—
288C22×C32C22×D412yes—
289C22×C32C22×Q814yes—
290C22×C32C2511yescharacteristic
291C2×C3×D3C4⋊Q8116yescomplemented
292C2×C3×D3C22×D414yes—
293C2×C3×D3C22×Q818yes—
294C32×C4—24no—
295C32×C4C22×D414yes—
296C3⋊Dic3—24no—
297C3⋊Dic3C22×Q818yescomplemented
298C3×Dic3—24no—
299C3×Dic3—24no—
300C3×Dic3C22×D414yes—
301C3×Dic3C22×Q818yescomplemented
302C22×Q8—38no—
303C22×Q8—31no—
304C22×Q8—32no—
305C22×Q8—31no—
306C22×Q8—68no—
307C22×Q8—92no—
308C22×Q8—98no—
309C22×Q8—91no—
310C22×Q8—188no—
311C22×Q8D3211yescharacteristic
312C23×C4—31no—
313C23×C4—32no—
314C23×C4—92no—
315C23×C4—92no—
316C4⋊Q8—38no—
317C4⋊Q8—98no—
318C4⋊Q8—932no—
319C4⋊Q8—98no—
320C4⋊Q8—98no—
321C2×C4⋊C4—34no—
322C2×C4⋊C4—932no—
323C2×C4⋊C4—94no—
324C2×C4⋊C4—94no—
325C2×C4⋊C4—94no—
326C2×C42—31no—
327C2×C42—98no—
328C2×C42—92no—
329C2×C42—91no—
330C23×C3—21no—
331C23×C3—34no—
332C23×C3—38no—
333C23×C3—32no—
334C23×C3C23×D311yescharacteristic
335C23×C3C23×D311yescharacteristic
336C22×D3D3×Q818yes—
337C22×D3C2×#6714yes—
338C22×D3C23×D312yes—
339C3×Q8—28no—
340C3×Q8—28no—
341C3×Q8—48no—
342C3×Q8—616no—
343C3×Q8—68no—
344C3×Q8—68no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—22no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—34no—
351C2×C3×C4—38no—
352C2×C3×C4—32no—
353C2×C3×C4—34no—
354C2×C3×C4—316no—
355C2×C3×C4—34no—
356C2×C3×C4—34no—
357C2×C3×C4—44no—
358C2×C3×C4—616no—
359C2×C3×C4—64no—
360C2×C3×C4—64no—
361C2×C3×C4D3×D414yes—
362C2×C3×C4C2×#6714yes—
363C2×C3×C4C23×D314yes—
364C2×C3×C4C23×D314yes—
365C2×C3×C4C23×D312yes—
366C2×C3×C4C23×D312yes—
367C2×Dic3—24no—
368C2×Dic3—24no—
369C2×Dic3—38no—
370C2×Dic3—38no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—332no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—68no—
377C2×Dic3—64no—
378C2×Dic3—64no—
379C2×Dic3—616no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—124no—
383C2×Dic3D3×Q818yescomplemented
384C2×Dic3C2×#6714yes—
385C2×Dic3C23×D314yes—
386C2×Dic3C23×D314yes—
387C2×Dic3C23×D314yes—
388C2×Dic3C23×D312yes—
389C4×D3—216no—
390C4×D3—332no—
391C4×D3—616no—
392C4×D3C2×#67116yes—
393Dic6—28no—
394Dic6—28no—
395Dic6—216no—
396Dic6—616no—
397Dic6—68no—
398Dic6—68no—
399Dic6—616no—
400Dic6—128no—
401C2×C32C2×C4⋊Q814yescomplemented
402C2×C32C23×D411yescharacteristic
403C2×C32C23×Q812yes—
404C3×D3C2×C4⋊Q818yescomplemented
405C24—31no—
406C2×Q8—24no—
407C2×Q8—34no—
408C2×Q8—38no—
409C2×Q8—34no—
410C2×Q8—68no—
411C2×Q8—632no—
412C2×Q8—64no—
413C2×Q8—64no—
414C2×Q8—98no—
415C2×Q8—94no—
416C2×Q8—188no—
417C2×Q8—1832no—
418C2×Q8—184no—
419C2×Q8C2×D3214yes—
420C22×C4—32no—
421C22×C4—31no—
422C22×C4—34no—
423C22×C4—38no—
424C22×C4—32no—
425C22×C4—32no—
426C22×C4—38no—
427C22×C4—68no—
428C22×C4—98no—
429C22×C4—916no—
430C22×C4—98no—
431C22×C4—92no—
432C22×C4—92no—
433C22×C4—188no—
434C22×C4C2×D3212yes—
435C22×C4C2×D3211yescharacteristic
436C4⋊C4—316no—
437C4⋊C4—916no—
438C4⋊C4—916no—
439C4⋊C4—916no—
440C42—34no—
441C42—98no—
442C42—94no—
443C22×C3—24no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—34no—
447C22×C3—38no—
448C22×C3—316no—
449C22×C3C2×D3×D412yes—
450C22×C3C2×D3×Q814yes—
451C22×C3C2×D3×Q814yes—
452C22×C3C22×#6712yes—
453C22×C3C24×D311yescharacteristic
454C22×C3C24×D311yescharacteristic
455C2×D3#944116yesdirect product factor
456C2×D3C2×D3×Q818yes—
457C2×D3C22×#6714yes—
458C3×C4—24no—
459C3×C4—24no—
460C3×C4—24no—
461C3×C4—34no—
462C3×C4—38no—
463C3×C4—44no—
464C3×C4—64no—
465C3×C4—64no—
466C3×C4C2×D3×D414yes—
467C3×C4C22×#6714yes—
468Dic3—24no—
469Dic3—24no—
470Dic3—38no—
471Dic3—38no—
472Dic3—68no—
473Dic3—64no—
474Dic3—64no—
475Dic3—124no—
476Dic3C2×D3×Q818yescomplemented
477Dic3C22×#6714yes—
478C32C22×C4⋊Q811yescharacteristic, complemented, Sylow
479C23—38no—
480C23—34no—
481C23—32no—
482C23C22×D3211yescharacteristic
483Q8—28no—
484Q8—616no—
485Q8—68no—
486Q8—68no—
487Q8—1816no—
488Q8—188no—
489C2×C4—24no—
490C2×C4—38no—
491C2×C4—34no—
492C2×C4—34no—
493C2×C4—32no—
494C2×C4—316no—
495C2×C4—34no—
496C2×C4—34no—
497C2×C4—616no—
498C2×C4—64no—
499C2×C4—64no—
500C2×C4—932no—
501C2×C4—98no—
502C2×C4—94no—
503C2×C4—94no—
504C2×C4—1816no—
505C2×C4—184no—
506C2×C4D3×#6714yes—
507C2×C4C22×D3214yes—
508C2×C4C22×D3212yes—
509C2×C3—24no—
510C2×C3—22no—
511C2×C3—21no—
512C2×C3—38no—
513C2×C3D3×C4⋊Q814yescomplemented
514C2×C3C2×#94414yescomplemented
515C2×C3C22×D3×D411yescharacteristic
516C2×C3C22×D3×Q812yes—
517C2×C3C22×D3×Q812yes—
518C2×C3C23×#6711yescharacteristic
519D3C2×#94418yesdirect product factor
520C22—316no—
521C22—38no—
522C22—34no—
523C22D32×Q814yes—
524C22C2×D3×#6712yes—
525C22C23×D3211yescharacteristic
526C4—24no—
527C4—38no—
528C4—34no—
529C4—64no—
530C4—64no—
531C4—98no—
532C4—184no—
533C4C2×D3×#6714yes—
534C3—21no—
535C3C2×D3×C4⋊Q811yescharacteristic, complemented
536C3C22×#94411yescharacteristic, complemented
537C2—38no—
538C2D3×#94414yesdirect product factor
539C2C2×D32×Q812yes—
540C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
prime radicalC23×C3×D3C23
hypercenterC22×Q8D32
hypocenterC32C22×C4⋊Q8
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
3. C2×#64153C2semidirect
4. C2×C3×#944C2semidirect
5. D3×#944C2direct (N × H)
8. C2×#63873C2semidirect
9. C2×#63866C2semidirect
10. C2×#63839C2semidirect
27. #64153C22semidirect
30. C3×#944C22semidirect
38. #63873C22semidirect
39. #63866C22semidirect
40. #63839C22semidirect
54. C2×#944D3direct (N × H)
89. C2×D3×Dic3Q8semidirect
141. #944C2×D3direct (N × H)
172. C2×C3⋊Dic3C2×Q8semidirect
179. C2×C3×Dic3C2×Q8semidirect
191. D3×Dic3C2×Q8semidirect
291. C2×C3×D3C4⋊Q8semidirect
297. C3⋊Dic3C22×Q8semidirect
301. C3×Dic3C22×Q8semidirect
383. C2×Dic3D3×Q8semidirect
401. C2×C32C2×C4⋊Q8semidirect
404. C3×D3C2×C4⋊Q8semidirect
455. C2×D3#944direct (N × H)
476. Dic3C2×D3×Q8semidirect
478. C32C22×C4⋊Q8semidirect
513. C2×C3D3×C4⋊Q8semidirect
514. C2×C3C2×#944semidirect
519. D3C2×#944direct (N × H)
535. C3C2×D3×C4⋊Q8semidirect
536. C3C22×#944semidirect
538. C2D3×#944direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×Q82
C22×D3×Dic62
C2×#641532
C2×C3×#9442
D3×#9442
C2×D3×Dic3⋊C42
C2×C4×D3×Dic32
C2×#638732
C2×#638662
C2×#638392
C22×#9443
C2×D3×C4⋊Q83