Finite Group Databasebeta

← C2×#10595200 #11903845

Subgroups — C2×#10595200 #11903845

Order 1152.

2651 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64144C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic3C212yesmaximal, complemented
5C2×Dic3×#67C212yesmaximal, complemented
6C2×#63959C212yesmaximal, complemented
7C2×#63959C212yesmaximal, complemented
8#10595200C2116yesmaximal, direct product factor
9C2×#63884C212yesmaximal, complemented
10C2×#63837C212yesmaximal, complemented
11C2×#5713—31nomaximal
12C2×#5664—31nomaximal
13C22×C32×D4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yes—
17C23×C3×Dic3C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×#627C2212yes—
20C22×D3×Dic3C2212yes—
21C2×#3757C2211yescharacteristic
22C2×#3757C2212yes—
23#64144C2218yescomplemented
24C2×#3750C2212yes—
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2212yes—
27C3×#940C2218yes—
28C3×#935C2218yescomplemented
29C2×C3×Dic3⋊C4C2212yes—
30C2×C3×C4×Dic3C2211yescharacteristic
31#67⋊Dic3C22116yescomplemented
32Dic3×#67C22116yescomplemented
33C2×Dic3⋊Dic3C2212yes—
34C2×(C2×D3)⋊Dic3C2212yes—
35C2×(C2×D3)⋊Dic3C2212yes—
36C2×(C2×D3)⋊Dic3C2212yes—
37#63959C22116yescomplemented
38#63959C22116yescomplemented
39C2×Dic32C2212yes—
40C2×Dic32C2212yes—
41#63884C22116yescomplemented
42#63837C22116yescomplemented
43C2×C3×#127—31no—
44C2×C3×#123—31no—
45C2×#940D311yescharacteristic
46C2×#936—32no—
47C2×#936—32no—
48C2×#935—31no—
49C2×#935—31no—
50C2×#935—32no—
51C2×#935—61no—
52C2×#935D311yescharacteristic, complemented
53C2×D4×Dic3—32no—
54C2×D4×Dic3—32no—
55C2×C4×#67—32no—
56#5713—316no—
57#5664—316no—
58C2×#894—32no—
59C2×#887—32no—
60C2×#885—32no—
61C2×#885—32no—
62C2×#67⋊C4—32no—
63C2×C4×Dic6—32no—
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3×D3C2312yes—
67C2×C32×D4—42no—
68C2×C32×D4C2314yes—
69C22×C32×C4C2311yescharacteristic
70C22×C3⋊Dic3—42no—
71C22×C3⋊Dic3C2312yes—
72C22×C3⋊Dic3C2312yes—
73C22×C3⋊Dic3C2314yes—
74C2×C3×#67—28no—
75C2×C3×#67—28no—
76C2×C3×#67C2318yes—
77C2×C3×#67C2318yes—
78C22×C3×Dic3—42no—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2314yes—
82C22×C3×Dic3C2312yes—
83C2×C3×D12—42no—
84C2×C3×D12C2314yes—
85C2×#627—28no—
86C2×#627C2318yes—
87C2×D3×Dic3—44no—
88C2×D3×Dic3C2318yes—
89#3757C2314yes—
90#3757C2318yes—
91#3750C2318yes—
92C3×#217C2314yes—
93C3×#217C2318yes—
94C3×Dic3⋊C4C2318yes—
95C3×C4×Dic3C2314yes—
96Dic3⋊Dic3C2318yes—
97(C2×D3)⋊Dic3C2318yes—
98(C2×D3)⋊Dic3C2318yes—
99(C2×D3)⋊Dic3C2318yes—
100Dic32C2318yes—
101Dic32C2318yes—
102C2×#559—91noSylow
103C22×C3×D4—21no—
104C22×C3×D4—32no—
105C22×C3×D4—32no—
106C22×C3×D4—31no—
107C22×C3×D4C2×D311yescharacteristic
108C22×C3×D4C2×D311yescharacteristic
109C23×C3×C4—31no—
110C22×#67C2×D312yes—
111C22×#67C2×D312yes—
112C23×Dic3—31no—
113C23×Dic3—31no—
114C23×Dic3—32no—
115C23×Dic3—61no—
116C23×Dic3C2×D311yescharacteristic
117C22×D12C2×D311yescharacteristic
118C22×C4×D3—32no—
119C22×Dic6—32no—
120C22×Dic6—32no—
121C3×#127—38no—
122C3×#123—38no—
123C2×C3×C4⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—31no—
126C2×C3×C42—31no—
127C2×#217—31no—
128C2×#217—32no—
129C2×#217—32no—
130C2×#217—31no—
131C2×#217—32no—
132C2×#217—32no—
133C2×#217—32no—
134C2×#217—62no—
135C2×#217—61no—
136C2×#217C2×D312yes—
137C2×#217C2×D311yescharacteristic
138#940C2×D318yes—
139#936—316no—
140#936—316no—
141#935—38no—
142#935—38no—
143#935—316no—
144#935—68no—
145#935C2×D318yescomplemented
146D4×Dic3—316no—
147D4×Dic3—316no—
148C4×#67—316no—
149C2×(C2×D3)⋊C4—32no—
150C2×(C2×D3)⋊C4—32no—
151C2×(C2×D3)⋊C4—32no—
152C2×C4⋊Dic3—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4—32no—
156C2×Dic3⋊C4—62no—
157C2×Dic3⋊C4C2×D312yes—
158C2×C4×Dic3—32no—
159C2×C4×Dic3—32no—
160C2×C4×Dic3—32no—
161C2×C4×Dic3—32no—
162C2×C4×Dic3C2×D311yescharacteristic
163#894—316no—
164#887—316no—
165#885—316no—
166#885—316no—
167#67⋊C4—316no—
168C4×Dic6—316no—
169C23×C32—22no—
170C23×C32—24no—
171C23×C32—24no—
172C23×C32—22no—
173C23×C32C2412yes—
174C23×C32C2412yes—
175C23×C32C2411yescharacteristic
176C22×C3×D3—24no—
177C22×C3×D3—24no—
178C22×C3×D3—24no—
179C22×C3×D3C2414yes—
180C32×D4—44no—
181C2×C32×C4—22no—
182C2×C32×C4C2412yes—
183C2×C3⋊Dic3—24no—
184C2×C3⋊Dic3—24no—
185C2×C3⋊Dic3—44no—
186C2×C3⋊Dic3C2414yes—
187C2×C3⋊Dic3C2414yes—
188C3×#67—216no—
189C3×#67—216no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—24no—
192C2×C3×Dic3—44no—
193C2×C3×Dic3#4118yes—
194C2×C3×Dic3C2414yes—
195C2×C3×Dic3C2414yes—
196C2×C3×Dic3C2414yes—
197C3×D12—44no—
198#627—216no—
199D3×Dic3—48no—
200#559—916no—
201C2×#127—31no—
202C2×#124—92no—
203C2×#124—92no—
204C2×#123—31no—
205C2×#123—92no—
206C2×#123—91no—
207C2×C4×Q8—92no—
208C2×C4×D4—92no—
209C2×C4×D4—92no—
210C24×C3—21no—
211C24×C3—21no—
212C24×C3—32no—
213C24×C3C22×D311yescharacteristic
214C24×C3C22×D311yescharacteristic
215C24×C3C22×D311yescharacteristic
216C24×C3C22×D311yescharacteristic
217C23×D3C22×D312yes—
218C2×C3×D4—24no—
219C2×C3×D4—38no—
220C2×C3×D4—38no—
221C2×C3×D4—34no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4—44no—
225C2×C3×D4—68no—
226C2×C3×D4—68no—
227C2×C3×D4—122no—
228C2×C3×D4C22×D314yes—
229C2×C3×D4C22×D314yes—
230C22×C3×C4—21no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—32no—
234C22×C3×C4—34no—
235C22×C3×C4—122no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—28no—
239C2×#67—28no—
240C2×#67C22×D318yes—
241C2×#67C22×D318yes—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—32no—
246C22×Dic3—34no—
247C22×Dic3—34no—
248C22×Dic3—38no—
249C22×Dic3—42no—
250C22×Dic3—62no—
251C22×Dic3—62no—
252C22×Dic3—64no—
253C22×Dic3—124no—
254C22×Dic3—122no—
255C22×Dic3—122no—
256C22×Dic3—124no—
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D314yes—
260C22×Dic3C22×D312yes—
261C2×D12—42no—
262C2×D12C22×D314yes—
263C2×C4×D3—38no—
264C2×C4×D3—124no—
265C2×Dic6—38no—
266C2×Dic6—38no—
267C2×Dic6—68no—
268C2×Dic6—68no—
269C3×C4⋊C4—38no—
270C3×C22⋊C4—38no—
271C3×C22⋊C4—34no—
272C3×C42—34no—
273#217—34no—
274#217—38no—
275#217—38no—
276#217—34no—
277#217—38no—
278#217—38no—
279#217—38no—
280#217—68no—
281#217—64no—
282#217C22×D318yes—
283#217C22×D314yes—
284(C2×D3)⋊C4—38no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4—38no—
287C4⋊Dic3—38no—
288Dic3⋊C4—38no—
289Dic3⋊C4—38no—
290Dic3⋊C4—38no—
291Dic3⋊C4—68no—
292Dic3⋊C4C22×D318yes—
293C4×Dic3—38no—
294C4×Dic3—38no—
295C4×Dic3—38no—
296C4×Dic3—38no—
297C4×Dic3C22×D314yes—
298C22×C32—22no—
299C22×C32—24no—
300C22×C32—24no—
301C22×C32—22no—
302C22×C32—44no—
303C22×C32—44no—
304C22×C32C2×#4114yes—
305C22×C32H(5,𝔽2)12yes—
306C22×C32C2511yescharacteristic
307C2×C3×D3—24no—
308C2×C3×D3—24no—
309C2×C3×D3—24no—
310C2×C3×D3—48no—
311C32×C4—22no—
312C3⋊Dic3—24no—
313C3⋊Dic3—24no—
314C3×Dic3—24no—
315C3×Dic3—24no—
316C3×Dic3C2×#4118yes—
317C22×Q8—92no—
318C22×D4—32no—
319C22×D4—32no—
320C22×D4—31no—
321C22×D4D3211yescharacteristic
322C23×C4—31no—
323C23×C4—92no—
324C23×C4—91no—
325#127—38no—
326#124—916no—
327#124—916no—
328#123—38no—
329#123—916no—
330#123—98no—
331C4×Q8—916no—
332C4×D4—916no—
333C4×D4—916no—
334C2×C4⋊C4—32no—
335C2×C4⋊C4—92no—
336C2×C4⋊C4—92no—
337C2×C22⋊C4—32no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—92no—
340C2×C22⋊C4—92no—
341C2×C22⋊C4—92no—
342C2×C22⋊C4—92no—
343C2×C22⋊C4—91no—
344C2×C42—31no—
345C2×C42—92no—
346C2×C42—92no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—24no—
355C23×C3—24no—
356C23×C3—22no—
357C23×C3—22no—
358C23×C3—21no—
359C23×C3—34no—
360C23×C3—44no—
361C23×C3—42no—
362C23×C3—44no—
363C23×C3—64no—
364C23×C3—64no—
365C23×C3—64no—
366C23×C3C23×D312yes—
367C23×C3C23×D312yes—
368C23×C3C23×D312yes—
369C23×C3C23×D312yes—
370C23×C3C23×D311yescharacteristic
371C23×C3C23×D311yescharacteristic
372C22×D3—24no—
373C22×D3—24no—
374C22×D3—24no—
375C22×D3C23×D314yes—
376C3×D4—44no—
377C3×D4—44no—
378C3×D4—48no—
379C3×D4—616no—
380C3×D4—616no—
381C3×D4—124no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—38no—
386C2×C3×C4—34no—
387C2×C3×C4—34no—
388C2×C3×C4—34no—
389C2×C3×C4—42no—
390C2×C3×C4—64no—
391C2×C3×C4—64no—
392C2×C3×C4—124no—
393C2×C3×C4C23×D312yes—
394C2×C3×C4C23×D312yes—
395#67—216no—
396#67—216no—
397C2×Dic3—24no—
398C2×Dic3—24no—
399C2×Dic3—34no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—44no—
404C2×Dic3—64no—
405C2×Dic3—64no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—64no—
409C2×Dic3—64no—
410C2×Dic3—124no—
411C2×Dic3—124no—
412C2×Dic3—128no—
413C2×Dic3—124no—
414C2×Dic3—124no—
415C2×Dic3—128no—
416C2×Dic3#23718yes—
417C2×Dic3C23×D314yes—
418C2×Dic3C23×D314yes—
419C2×Dic3C23×D314yes—
420D12—44no—
421C4×D3—128no—
422Dic6—616no—
423Dic6—616no—
424C2×C32—42no—
425C2×C32—42no—
426C2×C32#55914yescomplemented
427C2×C32C22×#4112yes—
428C2×C32C2×H(5,𝔽2)11yescharacteristic
429C3×D3—44no—
430C24—32no—
431C24C2×D3211yescharacteristic
432C24C2×D3211yescharacteristic
433C2×Q8—98no—
434C2×Q8—188no—
435C2×D4—38no—
436C2×D4—38no—
437C2×D4—34no—
438C2×D4—42no—
439C2×D4—68no—
440C2×D4—68no—
441C2×D4—122no—
442C2×D4C2×D3214yes—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—34no—
447C22×C4—98no—
448C22×C4—92no—
449C22×C4—92no—
450C22×C4—94no—
451C22×C4—122no—
452C22×C4—364no—
453C22×C4—362no—
454C22×C4C2×D3211yescharacteristic
455C4⋊C4—38no—
456C4⋊C4—98no—
457C4⋊C4—98no—
458C22⋊C4—38no—
459C22⋊C4—34no—
460C22⋊C4—98no—
461C22⋊C4—98no—
462C22⋊C4—98no—
463C22⋊C4—98no—
464C22⋊C4—94no—
465C42—34no—
466C42—98no—
467C42—98no—
468C22×C3—24no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—24no—
476C22×C3—24no—
477C22×C3—24no—
478C22×C3—22no—
479C22×C3—21no—
480C22×C3—44no—
481C22×C3—42no—
482C22×C3—44no—
483C22×C3—48no—
484C22×C3—44no—
485C22×C3—44no—
486C22×C3—44no—
487C22×C3—44no—
488C22×C3—64no—
489C22×C3—64no—
490C22×C3—64no—
491C22×C3—84no—
492C22×C3—128no—
493C22×C3C2×#23714yes—
494C22×C3#100412yes—
495C22×C3#100412yes—
496C22×C3D3×#4114yes—
497C22×C3C24×D311yescharacteristic
498C22×C3C24×D311yescharacteristic
499C2×D3—24no—
500C2×D3—24no—
501C2×D3—24no—
502C2×D3—48no—
503C3×C4—22no—
504C3×C4—22no—
505C3×C4—38no—
506C3×C4—42no—
507C3×C4—64no—
508C3×C4—64no—
509Dic3—24no—
510Dic3—24no—
511Dic3—64no—
512Dic3—64no—
513Dic3—64no—
514Dic3—64no—
515Dic3—124no—
516Dic3—124no—
517Dic3C2×#23718yes—
518C32C2×#55911yescharacteristic, complemented, Sylow
519C23—24no—
520C23—24no—
521C23—22no—
522C23—22no—
523C23—34no—
524C23—64no—
525C23—64no—
526C23—64no—
527C23C22×D3212yes—
528C23C22×D3212yes—
529C23C22×D3211yescharacteristic
530Q8—1816no—
531D4—44no—
532D4—616no—
533D4—616no—
534D4—124no—
535C2×C4—22no—
536C2×C4—38no—
537C2×C4—34no—
538C2×C4—34no—
539C2×C4—34no—
540C2×C4—64no—
541C2×C4—64no—
542C2×C4—94no—
543C2×C4—94no—
544C2×C4—124no—
545C2×C4—184no—
546C2×C4—184no—
547C2×C4—368no—
548C2×C4—364no—
549C2×C4C22×D3212yes—
550C2×C3—22no—
551C2×C3—21no—
552C2×C3—24no—
553C2×C3—44no—
554C2×C3—42no—
555C2×C3—42no—
556C2×C3—42no—
557C2×C3—42no—
558C2×C3—82no—
559C2×C3—124no—
560C2×C3#566414yescomplemented
561C2×C3#571314yescomplemented
562C2×C3C22×#23712yes—
563C2×C3C2×#100411yescharacteristic
564C2×C3C2×#100411yescharacteristic
565C2×C3C2×D3×#4112yes—
566D3—44no—
567C22—24no—
568C22—24no—
569C22—22no—
570C22—22no—
571C22—44no—
572C22—44no—
573C22—64no—
574C22—64no—
575C22—64no—
576C22—128no—
577C22D3×#23714yes—
578C22#6433012yes—
579C22C23×D3211yescharacteristic
580C4—22no—
581C4—38no—
582C4—64no—
583C4—64no—
584C4—184no—
585C4—184no—
586C3—21no—
587C3C2×#566411yescharacteristic, complemented
588C3C2×#571311yescharacteristic, complemented
589C2—42no—
590C2—42no—
591C2—124no—
592C2#1059520014yesdirect product factor
593C2C2×D3×#23712yes—
594C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32C2×#559
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64144C2semidirect
3. C2×C3×#935C2semidirect
4. C2×#67⋊Dic3C2semidirect
5. C2×Dic3×#67C2semidirect
6. C2×#63959C2semidirect
7. C2×#63959C2semidirect
8. #10595200C2direct (N × H)
9. C2×#63884C2semidirect
10. C2×#63837C2semidirect
23. #64144C22semidirect
28. C3×#935C22semidirect
31. #67⋊Dic3C22semidirect
32. Dic3×#67C22semidirect
37. #63959C22semidirect
38. #63959C22semidirect
41. #63884C22semidirect
42. #63837C22semidirect
52. C2×#935D3semidirect
145. #935C2×D3semidirect
426. C2×C32#559semidirect
518. C32C2×#559semidirect
560. C2×C3#5664semidirect
561. C2×C3#5713semidirect
587. C3C2×#5664semidirect
588. C3C2×#5713semidirect
592. C2#10595200direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641442
C2×C3×#9402
C2×C3×#9352
C2×#67⋊Dic32
C2×Dic3×#672
C2×#639592
#105952002
C2×#638842
C2×#638372
C2×#57133
C2×#56643