Finite Group Databasebeta

← C2×#10590961 #11863790

Subgroups — C2×#10590961 #11863790

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C22×C3×#204C211yesmaximal, characteristic, complemented
3C2×#63871C211yesmaximal, characteristic, complemented
4C22×#3718C211yesmaximal, characteristic, complemented
5C2×#63647C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590961C218yesmaximal, direct product factor
9C2×#5173—31nomaximal
10C2×#4808—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×D3×Dic3—21no—
17C2×#3796—22no—
18C2×#3796—24no—
19C2×#3796—24no—
20C2×#3796C2214yes—
21C22×C32×C8C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#204—24no—
25C2×C3×#204C2214yescomplemented
26C2×Dic3⋊Dic3—21no—
27C2×#3722—21no—
28#63871—22no—
29#63871C2214yescomplemented
30C2×#3718—24no—
31C2×#3718C2214yescomplemented
32#63647C2214yescomplemented
33C3×#816C2214yescomplemented
34#63562C2214yescomplemented
35C22×#239—31no—
36C22×#237—31no—
37C22×C3×SD16—31no—
38C2×#946—31no—
39C22×#216—31no—
40C22×#216—31no—
41C22×#204D311yescharacteristic, complemented
42C2×#897—31no—
43C2×C3×#103—31no—
44C2×#832—31no—
45#5173—38no—
46C2×(C2×D3)⋊C8—31no—
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—61no—
49C2×#816D311yescharacteristic, complemented
50C2×#809—31no—
51#4808—38no—
52C23×C3⋊D3D411yescharacteristic
53C23×C3×D3—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3D411yescharacteristic
56C2×C4×C3⋊D3—22no—
57C2×C4×C3⋊D3—22no—
58C2×C4×C3⋊D3D412yes—
59C2×C4×C3⋊D3C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3—21no—
63C2×C3×D12—21no—
64C2×C3×D12—22no—
65C2×C3×D12D414yes—
66C2×C3×D12C2312yes—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D414yes—
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×D3×Dic3—28no—
78C2×D3×Dic3—24no—
79#3796—216no—
80#3796—28no—
81#3796—28no—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×C4⋊Dic3—21no—
87C3×C4⋊Dic3C2312yes—
88C3×#204—28no—
89Dic3⋊Dic3—24no—
90#3722—24no—
91#3718—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C22×C3×Q8—31no—
95C22×C3×D4—31no—
96C22×#67—61no—
97C23×Dic3—61no—
98C2×#239—34no—
99C2×#239—62no—
100C2×#239—64no—
101C2×#239—64no—
102C2×#237—34no—
103C2×#237—62no—
104C2×#237—64no—
105C2×#237—64no—
106C22×D12—61no—
107C22×D12C2×D311yescharacteristic
108C22×C4×D3—31no—
109C22×C4×D3—31no—
110C22×C4×D3—61no—
111C22×C4×D3—61no—
112C22×Dic6C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C2×C3×SD16—34no—
115C2×C3×SD16—64no—
116C22×C3×C8—21no—
117C22×C3×C8C2×D311yescharacteristic
118C22×C3×C8C2×D311yescharacteristic
119C2×C3×C4⋊C4—31no—
120#946—34no—
121#946—62no—
122C2×#216—34no—
123C2×#216—34no—
124C2×#216—64no—
125C2×#216—64no—
126C2×(C2×D3)⋊C4—61no—
127C2×(C2×D3)⋊C4—61no—
128C2×C4⋊Dic3—61no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×Dic3⋊C4—61no—
131C22×C3⋊C8—31no—
132C22×C3⋊C8—31no—
133C22×C3⋊C8—61no—
134C2×#204—24no—
135C2×#204C2×D314yescomplemented
136#897—34no—
137#897—62no—
138C3×#103—34no—
139#832—34no—
140(C2×D3)⋊C8—34no—
141(C2×D3)⋊C8—34no—
142(C2×D3)⋊C8—64no—
143#816C2×D314yescomplemented
144#809—34no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—22no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—22no—
149C22×C3⋊D3C2×D412yes—
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C22×C3×D3—42no—
153C22×C3×D3—42no—
154C2×C32×C4C2×D412yes—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C2×D412yes—
160C4×C3⋊D3—24no—
161C4×C3⋊D3—22no—
162C4×C3⋊D3—22no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3—42no—
169C3×D12—24no—
170C3×D12—22no—
171C3×D12C2×D414yes—
172C3×Dic6—24no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C3×Dic6—42no—
177C3×Dic6C2×D414yes—
178#626—216no—
179D3×Dic3—216no—
180C32×C8—22no—
181C3⋊(C3⋊C8)—22no—
182C22×#41—91no—
183C22×Q16—91no—
184C22×SD16—31no—
185C2×C22⋊Q8—91no—
186#452—98no—
187C2×#103—31no—
188C2×#102—91no—
189C2×C22⋊C8—91no—
190C24×C3—61no—
191C23×D3—21no—
192C23×D3—31no—
193C23×D3—31no—
194C23×D3—61no—
195C2×C3×Q8—34no—
196C2×C3×Q8—32no—
197C2×C3×Q8—32no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—62no—
201C2×C3×Q8—62no—
202C2×C3×Q8—62no—
203C2×C3×D4—34no—
204C2×C3×D4—32no—
205C2×C3×D4—62no—
206C2×C3×D4—61no—
207C22×C3×C4—21no—
208C22×C3×C4—61no—
209C22×C3×C4—61no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—64no—
214C2×#67—68no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—31no—
219C22×Dic3—31no—
220C22×Dic3—61no—
221C22×Dic3—64no—
222C22×Dic3—68no—
223#239—68no—
224#239—616no—
225#239—68no—
226#237—68no—
227#237—616no—
228#237—68no—
229C2×D12—22no—
230C2×D12—21no—
231C2×D12—64no—
232C2×D12—68no—
233C2×D12#6714yes—
234C2×D12C22×D312yes—
235C2×C4×D3—32no—
236C2×C4×D3—32no—
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3—62no—
240C2×C4×D3—62no—
241C2×C4×D3—64no—
242C2×C4×D3—68no—
243C2×C4×D3—62no—
244C2×C4×D3—62no—
245C2×C4×D3—62no—
246C2×C4×D3—62no—
247C2×C4×D3—122no—
248C2×C4×D3—122no—
249C2×Dic6—21no—
250C2×Dic6—22no—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—21no—
254C2×Dic6D1214yes—
255C2×Dic6C22×D312yes—
256C2×Dic6C22×D312yes—
257C3×SD16—68no—
258C2×C3×C8—22no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8—42no—
262C2×C3×C8C22×D312yes—
263C2×C3×C8C22×D312yes—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—61no—
266#216—68no—
267#216—68no—
268(C2×D3)⋊C4—64no—
269(C2×D3)⋊C4—64no—
270C4⋊Dic3—21no—
271C4⋊Dic3—64no—
272C4⋊Dic3C22×D312yes—
273Dic3⋊C4—64no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—122no—
280#204—28no—
281C22×C32#12012yes—
282C22×C32#13512yes—
283C22×C32#13712yes—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—22no—
286C2×C3⋊D3—22no—
287C2×C3⋊D3—22no—
288C2×C3⋊D3—44no—
289C2×C3×D3—24no—
290C2×C3×D3—42no—
291C2×C3×D3—42no—
292C2×C3×D3—48no—
293C32×C4#12012yes—
294C32×C4C22×D411yescharacteristic
295C32×C4C22×D411yescharacteristic
296C3⋊Dic3—22no—
297C3×Dic3—24no—
298C3×Dic3—42no—
299C3×Dic3—42no—
300C2×#41—94no—
301C2×#41—182no—
302C2×#41—184no—
303C2×#41—184no—
304C22×Q8—31no—
305C22×Q8—31no—
306C22×D4—31no—
307C22×D4—181no—
308C23×C4—91no—
309C23×C4—181no—
310C2×Q16—94no—
311C2×Q16—184no—
312C2×SD16—34no—
313C2×SD16—64no—
314C22×C8—91no—
315C22×C8D3211yescharacteristic
316C22⋊Q8—94no—
317C22⋊Q8—182no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—181no—
320C2×C22⋊C4—181no—
321#103—34no—
322#102—94no—
323C22⋊C8—94no—
324C23×C3—21no—
325C23×C3—64no—
326C23×C3—62no—
327C23×C3—122no—
328C23×C3—122no—
329C23×C3D3×D411yescharacteristic
330C23×C3D3×D411yescharacteristic
331C22×D3—24no—
332C22×D3—22no—
333C22×D3—32no—
334C22×D3—32no—
335C22×D3—42no—
336C22×D3—42no—
337C22×D3—62no—
338C22×D3—64no—
339C22×D3—62no—
340C22×D3—62no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—122no—
346C22×D3—122no—
347C3×Q8—34no—
348C3×Q8—64no—
349C3×Q8—62no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C3×D4—34no—
354C3×D4—64no—
355C3×D4—62no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—64no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—122no—
365C2×C3×C4—122no—
366C2×C3×C4C2×D1212yes—
367C2×C3×C4D3×D412yes—
368C2×C3×C4D3×D411yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D412yes—
371C2×C3×C4C2×#6712yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—616no—
375C2×Dic3—24no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—32no—
380C2×Dic3—32no—
381C2×Dic3—42no—
382C2×Dic3—42no—
383C2×Dic3—62no—
384C2×Dic3—616no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—122no—
388D12—24no—
389D12—22no—
390D12—616no—
391D12C2×#6714yes—
392C4×D3—616no—
393C4×D3—64no—
394C4×D3—64no—
395C4×D3—62no—
396C4×D3—62no—
397C4×D3—62no—
398C4×D3—62no—
399C4×D3—122no—
400C4×D3—122no—
401C4×D3—124no—
402Dic6—24no—
403Dic6—22no—
404Dic6—22no—
405Dic6—22no—
406Dic6—42no—
407Dic6C2×D1214yes—
408C3×C8—22no—
409C3×C8—22no—
410C3×C8—42no—
411C3⋊C8—62no—
412C3⋊C8—62no—
413C3⋊C8—122no—
414C2×C32#45214yescomplemented
415C2×C32C2×#12011yescharacteristic
416C2×C32C2×#13511yescharacteristic
417C2×C32C2×#13711yescharacteristic
418C3⋊D3—42no—
419C3×D3—44no—
420C24—61no—
421C24—91no—
422#41—188no—
423#41—188no—
424#41—1816no—
425C2×Q8—32no—
426C2×Q8—32no—
427C2×Q8—34no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—62no—
431C2×Q8—62no—
432C2×Q8—62no—
433C2×D4—32no—
434C2×D4—34no—
435C2×D4—62no—
436C2×D4—61no—
437C2×D4—184no—
438C2×D4—188no—
439C22×C4—61no—
440C22×C4—61no—
441C22×C4—61no—
442C22×C4—91no—
443C22×C4—92no—
444C22×C4—92no—
445C22×C4—184no—
446C22×C4—188no—
447C22×C4—182no—
448C22×C4—182no—
449C22×C4C2×D3211yescharacteristic
450Q16—188no—
451SD16—68no—
452C2×C8—22no—
453C2×C8—92no—
454C2×C8—182no—
455C2×C8C2×D3212yes—
456C4⋊C4—32no—
457C4⋊C4—61no—
458C4⋊C4—184no—
459C22⋊C4—184no—
460C22×C3—21no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—64no—
465C22×C3—122no—
466C22×C3—122no—
467C22×C3—128no—
468C22×C3#88212yes—
469C22×C3#91512yes—
470C22×C3#91612yes—
471C22×C3#91612yes—
472C22×C3#91812yes—
473C22×C3#93712yes—
474C22×C3C2×D3×D411yescharacteristic
475C22×C3C2×D3×D411yescharacteristic
476C2×D3—24no—
477C2×D3—48no—
478C2×D3—42no—
479C2×D3—42no—
480C2×D3—64no—
481C2×D3—62no—
482C2×D3—62no—
483C2×D3—62no—
484C2×D3—62no—
485C2×D3—62no—
486C2×D3—62no—
487C2×D3—122no—
488C2×D3—122no—
489C2×D3—128no—
490C2×D3—124no—
491C2×D3—124no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—64no—
496C3×C4—122no—
497C3×C4—122no—
498C3×C4#88212yes—
499C3×C4#93712yes—
500C3×C4C22×D1211yescharacteristic
501C3×C4C2×D3×D411yescharacteristic
502C3×C4C2×D3×D411yescharacteristic
503C3×C4C22×#6711yescharacteristic
504Dic3—24no—
505Dic3—42no—
506Dic3—42no—
507Dic3—62no—
508Dic3—62no—
509Dic3—122no—
510C32C2×#45211yescharacteristic, complemented, Sylow
511C23—62no—
512C23—64no—
513C23—92no—
514C23—122no—
515C23—122no—
516C23—182no—
517C23—182no—
518C23—182no—
519C23#380211yescharacteristic
520Q8—34no—
521Q8—62no—
522Q8—64no—
523Q8—62no—
524Q8—62no—
525Q8—122no—
526D4—34no—
527D4—62no—
528D4—64no—
529D4—1816no—
530C2×C4—62no—
531C2×C4—64no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—92no—
535C2×C4—122no—
536C2×C4—122no—
537C2×C4—1816no—
538C2×C4—182no—
539C2×C4—182no—
540C2×C4—182no—
541C2×C4—184no—
542C2×C4D3×D1212yes—
543C2×C4#380211yescharacteristic
544C2×C4D3×#6712yes—
545C2×C4C22×D3211yescharacteristic
546C8—22no—
547C8—182no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—24no—
551C2×C3—21no—
552C2×C3—124no—
553C2×C3#480814yescomplemented
554C2×C3#517314yescomplemented
555C2×C3C2×#88211yescharacteristic
556C2×C3C2×#91511yescharacteristic
557C2×C3C2×#91611yescharacteristic
558C2×C3C2×#91611yescharacteristic
559C2×C3C2×#91811yescharacteristic
560C2×C3C2×#93711yescharacteristic
561D3—44no—
562D3—124no—
563D3—122no—
564D3—122no—
565C22—64no—
566C22—122no—
567C22—122no—
568C22—128no—
569C22—182no—
570C22—182no—
571C22—182no—
572C22—364no—
573C22#6380912yes—
574C22#6381112yes—
575C22#6392212yes—
576C22C2×#380211yescharacteristic
577C4—64no—
578C4—122no—
579C4—122no—
580C4—182no—
581C4#6392212yes—
582C4C2×D3×D1211yescharacteristic
583C4C2×D3×#6711yescharacteristic
584C3—21no—
585C3C2×#480811yescharacteristic, complemented
586C3C2×#517311yescharacteristic, complemented
587C2—124no—
588C2—362no—
589C2#1059096114yesdirect product factor
590C2C2×#6380911yescharacteristic
591C2C2×#6381111yescharacteristic
592C2C2×#6392211yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3796C2
hypercenterC22×C8D32
hypocenterC32C2×#452
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×C3×#204C2semidirect
3. C2×#63871C2semidirect
4. C22×#3718C2semidirect
5. C2×#63647C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63562C2semidirect
8. #10590961C2direct (N × H)
25. C2×C3×#204C22semidirect
29. #63871C22semidirect
31. C2×#3718C22semidirect
32. #63647C22semidirect
33. C3×#816C22semidirect
34. #63562C22semidirect
41. C22×#204D3semidirect
49. C2×#816D3semidirect
135. C2×#204C2×D3semidirect
143. #816C2×D3semidirect
414. C2×C32#452semidirect
510. C32C2×#452semidirect
553. C2×C3#4808semidirect
554. C2×C3#5173semidirect
585. C3C2×#4808semidirect
586. C3C2×#5173semidirect
589. C2#10590961direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C22×C3×#2042
C2×#638712
C22×#37182
C2×#636472
C2×C3×#8162
C2×#635622
#105909612
C2×#51733
C2×#48083