Finite Group Databasebeta

← C2×#10590614 #11863794

Subgroups — C2×#10590614 #11863794

Order 1152.

1601 conjugacy classes of subgroups.

The subgroup lattice has 587 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C2×C3×#897C211yesmaximal, characteristic, complemented
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63637C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590614C218yesmaximal, direct product factor
9C2×#5047—31nomaximal
10C2×#4783—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#625—21no—
16C22×D3×Dic3—21no—
17C2×#3795—24no—
18C2×#3795—24no—
19C2×#3795—22no—
20C2×#3795C2214yes—
21C2×C32×C4⋊C4C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×(C2×D3)⋊C4—21no—
24C2×C3×C4⋊Dic3—21no—
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#897—22no—
27C3×#897C2214yescomplemented
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63637C2214yescomplemented
33C3×#809C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×#237—31no—
36C22×#235—31no—
37C2×C3×C22⋊Q8—31no—
38C22×#216—31no—
39C22×#215—31no—
40C22×#214—31no—
41C22×Dic12—31no—
42C2×#897D311yescharacteristic, complemented
43C2×C3×#102—31no—
44C2×#830—31no—
45C2×(C2×D3)⋊C8—31no—
46#5047—38no—
47C2×#810—31no—
48C2×#810—31no—
49C2×#810—61no—
50C2×#809D311yescharacteristic, complemented
51#4783—38no—
52C23×C3×D3—21no—
53C23×C3×D3D411yescharacteristic
54C22×C32×C4—21no—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C2×#634—21no—
58C2×#634—22no—
59C2×#634D414yes—
60C2×#634C2312yes—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×D12—21no—
64C2×C3×D12—22no—
65C2×C3×D12D414yes—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—22no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—21no—
74C2×C3×Dic6C2312yes—
75C2×#625—28no—
76C2×#625—24no—
77C2×D3×Dic3—28no—
78C2×D3×Dic3—24no—
79#3795—216no—
80#3795—28no—
81#3795—28no—
82C32×C4⋊C4—21no—
83C32×C4⋊C4C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×(C2×D3)⋊C4—24no—
87C3×C4⋊Dic3—24no—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90#3719—28no—
91#3715—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C22×C3×D4—31no—
95C23×C3×C4—31no—
96C22×#67—61no—
97C22×#67—61no—
98C23×Dic3—61no—
99C2×#237—34no—
100C2×#237—64no—
101C2×#237—64no—
102C2×#237—62no—
103C2×#235—34no—
104C2×#235—64no—
105C2×#235—62no—
106C2×#235—64no—
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—61no—
109C22×C4×D3C2×D311yescharacteristic
110C22×Dic6—31no—
111C22×Dic6—31no—
112C22×Dic6—61no—
113C22×Dic6C2×D311yescharacteristic
114C22×C3×C8—31no—
115C3×C22⋊Q8—34no—
116C3×C22⋊Q8—62no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—61no—
119C2×C3×C4⋊C4C2×D311yescharacteristic
120C2×C3×C4⋊C4C2×D311yescharacteristic
121C2×C3×C22⋊C4—61no—
122C2×#216—34no—
123C2×#216—64no—
124C2×#215—34no—
125C2×#215—64no—
126C2×#214—34no—
127C2×#214—64no—
128C2×(C2×D3)⋊C4—21no—
129C2×C4⋊Dic3—21no—
130C22×C3⋊C8—31no—
131C22×C3⋊C8—31no—
132C22×C3⋊C8—61no—
133C22×C3⋊C8C2×D311yescharacteristic
134C2×Dic12—34no—
135C2×Dic12—64no—
136#897—22no—
137#897C2×D314yescomplemented
138C3×#102—34no—
139#830—34no—
140(C2×D3)⋊C8—34no—
141#810—34no—
142#810—34no—
143#810—64no—
144#809C2×D314yescomplemented
145C23×C32C2×D411yescharacteristic
146C22×C3×D3—24no—
147C22×C3×D3—22no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—42no—
152C22×C3×D3—42no—
153C22×C3×D3C2×D412yes—
154C2×C32×C4—22no—
155C2×C32×C4—42no—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—24no—
161C2×C3⋊Dic3—22no—
162#634—24no—
163#634—22no—
164#634C2×D414yes—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3C2×D412yes—
169C3×D12—24no—
170C3×D12—22no—
171C3×D12C2×D414yes—
172C3×C4×D3—24no—
173C3×C4×D3—22no—
174C3×C4×D3—22no—
175C3×Dic6—22no—
176C3×Dic6—22no—
177C3×Dic6—42no—
178#625—216no—
179D3×Dic3—216no—
180C3⋊(C3⋊C8)—22no—
181C3×C3⋊C8—22no—
182C22×#41—91no—
183C22×Q16—91no—
184C22×SD16—91no—
185C2×C22⋊Q8—31no—
186#452—98no—
187C2×#103—91no—
188C2×#102—31no—
189C2×C22⋊C8—91no—
190C24×C3—31no—
191C24×C3—61no—
192C23×D3—21no—
193C23×D3#6711yescharacteristic
194C2×C3×Q8—32no—
195C2×C3×Q8—61no—
196C2×C3×Q8—62no—
197C2×C3×Q8—62no—
198C2×C3×D4—34no—
199C2×C3×D4—32no—
200C2×C3×D4—62no—
201C2×C3×D4—61no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—31no—
206C22×C3×C4—32no—
207C22×C3×C4—32no—
208C22×C3×C4—41no—
209C22×C3×C4—62no—
210C22×C3×C4—62no—
211C22×C3×C4—61no—
212C22×C3×C4C22×D311yescharacteristic
213C22×C3×C4C22×D311yescharacteristic
214C2×#67—64no—
215C2×#67—68no—
216C2×#67—68no—
217C2×#67—64no—
218C22×Dic3—21no—
219C22×Dic3—68no—
220C22×Dic3—61no—
221C22×Dic3—61no—
222C22×Dic3—64no—
223C22×Dic3—121no—
224C22×Dic3#6711yescharacteristic
225#237—68no—
226#237—68no—
227#237—616no—
228#235—68no—
229#235—616no—
230#235—68no—
231C2×D12—22no—
232C2×D12—21no—
233C2×D12D1214yes—
234C2×D12C22×D312yes—
235C2×C4×D3—22no—
236C2×C4×D3—22no—
237C2×C4×D3—64no—
238C2×C4×D3—68no—
239C2×C4×D3#6712yes—
240C2×C4×D3C22×D312yes—
241C2×Dic6—22no—
242C2×Dic6—22no—
243C2×Dic6—21no—
244C2×Dic6—34no—
245C2×Dic6—34no—
246C2×Dic6—32no—
247C2×Dic6—32no—
248C2×Dic6—62no—
249C2×Dic6—64no—
250C2×Dic6—62no—
251C2×Dic6—61no—
252C2×Dic6—62no—
253C2×Dic6—61no—
254C2×Dic6—122no—
255C2×Dic6—121no—
256C2×Dic6C22×D312yes—
257C2×C3×C8—32no—
258C2×C3×C8—62no—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—22no—
262C3×C4⋊C4—41no—
263C3×C4⋊C4—64no—
264C3×C4⋊C4C22×D312yes—
265C3×C4⋊C4C22×D312yes—
266C3×C22⋊C4—64no—
267#216—68no—
268#215—68no—
269#214—68no—
270(C2×D3)⋊C4—24no—
271C4⋊Dic3—24no—
272C2×C3⋊C8—22no—
273C2×C3⋊C8—32no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—62no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—122no—
279C2×C3⋊C8C22×D312yes—
280Dic12—68no—
281C22×C32#12012yes—
282C22×C32#13512yes—
283C22×C32#13712yes—
284C22×C32C22×D411yescharacteristic
285C2×C3×D3—24no—
286C2×C3×D3—22no—
287C2×C3×D3—22no—
288C2×C3×D3—22no—
289C2×C3×D3—42no—
290C2×C3×D3—42no—
291C2×C3×D3—44no—
292C2×C3×D3—48no—
293C32×C4—42no—
294C32×C4#12012yes—
295C32×C4C22×D411yescharacteristic
296C32×C4C22×D411yescharacteristic
297C3⋊Dic3—24no—
298C3×Dic3—22no—
299C3×Dic3—42no—
300C2×#41—94no—
301C2×#41—182no—
302C2×#41—184no—
303C2×#41—184no—
304C22×Q8—31no—
305C22×Q8—91no—
306C22×D4—31no—
307C22×D4—181no—
308C23×C4—31no—
309C23×C4—181no—
310C2×Q16—94no—
311C2×Q16—184no—
312C2×SD16—94no—
313C2×SD16—184no—
314C22×C8—31no—
315C22×C8—91no—
316C22⋊Q8—34no—
317C22⋊Q8—62no—
318C2×C4⋊C4—61no—
319C2×C4⋊C4D3211yescharacteristic
320C2×C22⋊C4—61no—
321#103—94no—
322#102—34no—
323C22⋊C8—94no—
324C23×C3—21no—
325C23×C3—32no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3—64no—
330C23×C3—62no—
331C23×C3—122no—
332C23×C3—122no—
333C23×C3D3×D411yescharacteristic
334C23×C3C2×#6711yescharacteristic
335C22×D3—24no—
336C22×D3—22no—
337C22×D3—22no—
338C22×D3—22no—
339C22×D3—22no—
340C22×D3—42no—
341C22×D3—42no—
342C22×D3C2×#6712yes—
343C3×Q8—62no—
344C3×Q8—62no—
345C3×Q8—122no—
346C3×D4—34no—
347C3×D4—64no—
348C3×D4—62no—
349C2×C3×C4—22no—
350C2×C3×C4—22no—
351C2×C3×C4—21no—
352C2×C3×C4—22no—
353C2×C3×C4—22no—
354C2×C3×C4—21no—
355C2×C3×C4—32no—
356C2×C3×C4—42no—
357C2×C3×C4—42no—
358C2×C3×C4—42no—
359C2×C3×C4—62no—
360C2×C3×C4—64no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—82no—
365C2×C3×C4—122no—
366C2×C3×C4C2×D1212yes—
367C2×C3×C4D3×D412yes—
368C2×C3×C4D3×D412yes—
369C2×C3×C4D3×D412yes—
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4C2×#6711yescharacteristic
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—616no—
375#67—616no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—42no—
379C2×Dic3—616no—
380C2×Dic3—64no—
381C2×Dic3—64no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—122no—
385C2×Dic3—124no—
386C2×Dic3C2×#6712yes—
387D12—24no—
388D12—22no—
389D12C2×D1214yes—
390C4×D3—24no—
391C4×D3—22no—
392C4×D3—22no—
393C4×D3—616no—
394Dic6—22no—
395Dic6—22no—
396Dic6—34no—
397Dic6—34no—
398Dic6—42no—
399Dic6—64no—
400Dic6—64no—
401Dic6—64no—
402Dic6—62no—
403Dic6—62no—
404Dic6—122no—
405Dic6—124no—
406C3×C8—62no—
407C3⋊C8—22no—
408C3⋊C8—62no—
409C3⋊C8—62no—
410C3⋊C8—122no—
411C2×C32#45214yescomplemented
412C2×C32C2×#12011yescharacteristic
413C2×C32C2×#13511yescharacteristic
414C2×C32C2×#13711yescharacteristic
415C3×D3—42no—
416C3×D3—44no—
417C24—31no—
418C24—61no—
419#41—188no—
420#41—188no—
421#41—1816no—
422C2×Q8—32no—
423C2×Q8—61no—
424C2×Q8—62no—
425C2×Q8—62no—
426C2×Q8—92no—
427C2×Q8—94no—
428C2×Q8—182no—
429C2×Q8—181no—
430C2×D4—32no—
431C2×D4—34no—
432C2×D4—62no—
433C2×D4—61no—
434C2×D4—184no—
435C2×D4—188no—
436C22×C4—21no—
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—32no—
440C22×C4—62no—
441C22×C4—62no—
442C22×C4—61no—
443C22×C4—184no—
444C22×C4—188no—
445C22×C4—181no—
446C22×C4C2×D3211yescharacteristic
447Q16—188no—
448SD16—188no—
449C2×C8—32no—
450C2×C8—62no—
451C2×C8—92no—
452C2×C8—182no—
453C4⋊C4—21no—
454C4⋊C4—64no—
455C4⋊C4C2×D3212yes—
456C22⋊C4—64no—
457C22×C3—21no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—62no—
462C22×C3—62no—
463C22×C3—62no—
464C22×C3—64no—
465C22×C3—124no—
466C22×C3—122no—
467C22×C3—128no—
468C22×C3—122no—
469C22×C3#88212yes—
470C22×C3#91212yes—
471C22×C3#91512yes—
472C22×C3#93712yes—
473C22×C3#94212yes—
474C22×C3#95012yes—
475C22×C3C2×D3×D411yescharacteristic
476C22×C3C22×#6711yescharacteristic
477C2×D3—24no—
478C2×D3—22no—
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—42no—
482C2×D3—42no—
483C2×D3—48no—
484C2×D3—44no—
485C3×C4—21no—
486C3×C4—21no—
487C3×C4—22no—
488C3×C4—42no—
489C3×C4—42no—
490C3×C4—62no—
491C3×C4—82no—
492C3×C4—122no—
493C3×C4#88212yes—
494C3×C4#93712yes—
495C3×C4C22×D1211yescharacteristic
496C3×C4C2×D3×D411yescharacteristic
497C3×C4C2×D3×D411yescharacteristic
498C3×C4C2×D3×D411yescharacteristic
499Dic3—22no—
500Dic3—42no—
501Dic3—64no—
502Dic3—64no—
503Dic3—124no—
504C32C2×#45211yescharacteristic, complemented, Sylow
505C23—32no—
506C23—62no—
507C23—62no—
508C23—64no—
509C23—62no—
510C23—62no—
511C23—122no—
512C23—122no—
513C23D3×#6711yescharacteristic
514Q8—62no—
515Q8—62no—
516Q8—94no—
517Q8—122no—
518Q8—182no—
519Q8—184no—
520D4—34no—
521D4—62no—
522D4—64no—
523D4—1816no—
524C2×C4—22no—
525C2×C4—32no—
526C2×C4—42no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—64no—
531C2×C4—62no—
532C2×C4—122no—
533C2×C4—1816no—
534C2×C4—182no—
535C2×C4—184no—
536C2×C4D3×D1212yes—
537C2×C4#380212yes—
538C2×C4D3×#6711yescharacteristic
539C2×C4C22×D3211yescharacteristic
540C8—62no—
541C8—182no—
542C2×C3—21no—
543C2×C3—21no—
544C2×C3—24no—
545C2×C3—21no—
546C2×C3—124no—
547C2×C3—122no—
548C2×C3#478314yescomplemented
549C2×C3#504714yescomplemented
550C2×C3C2×#88211yescharacteristic
551C2×C3C2×#91211yescharacteristic
552C2×C3C2×#91511yescharacteristic
553C2×C3C2×#93711yescharacteristic
554C2×C3C2×#94211yescharacteristic
555C2×C3C2×#95011yescharacteristic
556D3—42no—
557D3—44no—
558C22—62no—
559C22—62no—
560C22—62no—
561C22—64no—
562C22—122no—
563C22—122no—
564C22—124no—
565C22—128no—
566C22#6392212yes—
567C22#6393312yes—
568C22#6394612yes—
569C22C2×D3×#6711yescharacteristic
570C4—42no—
571C4—62no—
572C4—122no—
573C4—184no—
574C4#6392212yes—
575C4C2×D3×D1211yescharacteristic
576C4C2×#380211yescharacteristic
577C3—21no—
578C3C2×#478311yescharacteristic, complemented
579C3C2×#504711yescharacteristic, complemented
580C2—122no—
581C2—124no—
582C2#1059061414yesdirect product factor
583C2C2×#6392211yescharacteristic
584C2C2×#6393311yescharacteristic
585C2C2×#6394611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3795C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#897C2semidirect
3. C22×#3719C2semidirect
4. C22×#3715C2semidirect
5. C2×#63637C2semidirect
6. C2×C3×#809C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590614C2direct (N × H)
27. C3×#897C22semidirect
29. C2×#3719C22semidirect
31. C2×#3715C22semidirect
32. #63637C22semidirect
33. C3×#809C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
42. C2×#897D3semidirect
50. C2×#809D3semidirect
137. #897C2×D3semidirect
144. #809C2×D3semidirect
411. C2×C32#452semidirect
504. C32C2×#452semidirect
548. C2×C3#4783semidirect
549. C2×C3#5047semidirect
578. C3C2×#4783semidirect
579. C3C2×#5047semidirect
582. C2#10590614direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C2×C3×#8972
C22×#37192
C22×#37152
C2×#636372
C2×C3×#8092
C2×(C2×D3)⋊(C3⋊C8)2
#105906142
C2×#50473
C2×#47833