Finite Group Databasebeta

← C2×#10595359 #11900796

Subgroups — C2×#10595359 #11900796

Order 1152.

3601 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C22×#3795C211yesmaximal, characteristic, complemented
3C2×#64153C211yesmaximal, characteristic, complemented
4C2×C3×#947C211yesmaximal, characteristic, complemented
5#10595359C2116yesmaximal, direct product factor
6C2×#63914C211yesmaximal, characteristic, complemented
7C2×#63885C214yesmaximal, complemented
8C2×#63879C214yesmaximal, complemented
9C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
10C2×#63860C211yesmaximal, characteristic, complemented
11C2×#5832—31nomaximal
12C2×#5668—31nomaximal
13C22×C32×Q8C2211yescharacteristic
14C22×#634C2211yescharacteristic
15C2×C3×#239—28no—
16C2×C3×#239C2218yescomplemented
17C22×C3×D12C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2212yes—
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2211yescharacteristic
22C22×#625C2212yes—
23C22×#625C2214yes—
24C22×D3×Dic3C2212yes—
25C22×D3×Dic3C2212yes—
26C2×#3795—28no—
27C2×#3795C2218yescomplemented
28#64153C2218yescomplemented
29C2×#3750C2214yes—
30C2×C4×C3⋊Dic3C2211yescharacteristic
31C3×#947C2218yescomplemented
32C2×C3×(C2×D3)⋊C4C2214yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2214yes—
35C2×Dic32C2212yes—
36#63914C2218yescomplemented
37#63885C22132yescomplemented
38#63879C22132yescomplemented
39C4×D3×Dic3C2218yescomplemented
40#63860C2218yescomplemented
41C22×C3×#41—31no—
42C22×#239D311yescharacteristic, complemented
43C22×#237—31no—
44C22×#235—31no—
45C2×C3×#124—31no—
46#5832—316no—
47C2×#947D311yescharacteristic, complemented
48C2×#944—31no—
49C2×#944—31no—
50C2×#944—61no—
51C2×#940—31no—
52C2×#940—31no—
53C2×#939—34no—
54C2×#936—31no—
55C2×C4×#67—34no—
56C22×C4×Dic3—31no—
57#5668—316no—
58C2×#884—34no—
59C2×#67⋊C4—34no—
60C2×#875—31no—
61C2×C42×D3—31no—
62C23×C3×D3C2312yes—
63C23×C3×D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C2×C32×Q8—24no—
66C2×C32×Q8C2314yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2312yes—
71C2×#634—24no—
72C2×#634C2314yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2311yescharacteristic
75C3×#239—232no—
76C2×C3×D12—28no—
77C2×C3×D12—24no—
78C2×C3×D12—24no—
79C2×C3×D12C2314yes—
80C2×C3×D12C2314yes—
81C2×C3×D12C2318yes—
82C2×C3×C4×D3—28no—
83C2×C3×C4×D3D418yescomplemented
84C2×C3×C4×D3C2318yes—
85C2×C3×C4×D3C2314yes—
86C2×#625—28no—
87C2×#625—216no—
88C2×#625C2318yes—
89C2×#625C23116yes—
90C2×D3×Dic3—28no—
91C2×D3×Dic3—28no—
92C2×D3×Dic3C2318yes—
93C2×D3×Dic3C2318yes—
94#3795—232no—
95#3750C23116yes—
96C4×C3⋊Dic3C2314yes—
97C3×(C2×D3)⋊C4C23116yes—
98C3×C4×Dic3C2314yes—
99(C2×D3)⋊Dic3C23116yes—
100Dic32C2318yes—
101C2×#532—91noSylow
102C2×C3×#41—38no—
103C2×C3×#41—68no—
104C22×C3×Q8—21no—
105C22×C3×Q8C2×D311yescharacteristic
106C22×C3×Q8C2×D311yescharacteristic
107C22×C3×D4—31no—
108C22×C3×D4—31no—
109C22×C3×D4—32no—
110C23×C3×C4—31no—
111C23×C3×C4—32no—
112C22×#67—32no—
113C22×#67—32no—
114C22×#67—34no—
115C22×#67—34no—
116C23×Dic3—32no—
117C23×Dic3—32no—
118C2×#239—28no—
119C2×#239C2×D318yescomplemented
120C2×#237—38no—
121C2×#237—68no—
122C2×#235—38no—
123C2×#235—68no—
124C22×D12C2×D311yescharacteristic
125C22×D12C2×D311yescharacteristic
126C22×D12C2×D312yes—
127C22×C4×D3—32no—
128C22×C4×D3—32no—
129C22×C4×D3C2×D312yes—
130C22×C4×D3C2×D311yescharacteristic
131C22×Dic6—31no—
132C22×Dic6—31no—
133C22×Dic6—61no—
134C3×#124—38no—
135C2×C3×C22⋊C4—34no—
136C2×C3×C42—31no—
137C2×#217—34no—
138#947C2×D318yescomplemented
139#944—38no—
140#944—38no—
141#944—68no—
142#940—38no—
143#940—38no—
144#939—332no—
145#936—38no—
146C4×#67—332no—
147C2×(C2×D3)⋊C4—34no—
148C2×(C2×D3)⋊C4C2×D314yes—
149C2×Dic3⋊C4—34no—
150C2×Dic3⋊C4—34no—
151C2×Dic3⋊C4—64no—
152C2×C4×Dic3—31no—
153C2×C4×Dic3—31no—
154C2×C4×Dic3—32no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3—38no—
157C2×C4×Dic3—61no—
158C2×C4×Dic3C2×D311yescharacteristic
159#884—332no—
160#67⋊C4—332no—
161#875—38no—
162C42×D3—38no—
163C23×C32C2411yescharacteristic
164C22×C3×D3—24no—
165C22×C3×D3—24no—
166C22×C3×D3—24no—
167C22×C3×D3—28no—
168C22×C3×D3—28no—
169C22×C3×D3C2×D414yes—
170C22×C3×D3C2414yes—
171C22×C3×D3C2414yes—
172C22×C3×D3C2412yes—
173C32×Q8—28no—
174C2×C32×C4—24no—
175C2×C32×C4C2×D414yes—
176C2×C32×C4C2414yes—
177C2×C32×C4C2412yes—
178C2×C3⋊Dic3—24no—
179C2×C3⋊Dic3#4118yescomplemented
180C2×C3⋊Dic3C2414yes—
181C2×C3⋊Dic3C2414yes—
182#634—28no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3C2×D414yes—
185C2×C3×Dic3C2414yes—
186C2×C3×Dic3C2412yes—
187C3×D12—216no—
188C3×D12—28no—
189C3×D12—28no—
190C3×C4×D3—216no—
191C3×C4×D3C2×D4116yescomplemented
192#625—216no—
193#625—232no—
194D3×Dic3—216no—
195D3×Dic3—216no—
196C22×#41—31no—
197C22×#41—91no—
198#532—916no—
199C2×C4⋊Q8—91no—
200C2×#127—91no—
201C2×#124—31no—
202C2×#124—91no—
203C2×#121—94no—
204C2×C4×D4—94no—
205C22×C42—91no—
206C24×C3—31no—
207C24×C3—32no—
208C24×C3—32no—
209C23×D3C22×D312yes—
210C23×D3C22×D312yes—
211C23×D3C22×D311yescharacteristic
212C3×#41—632no—
213C2×C3×Q8—24no—
214C2×C3×Q8—24no—
215C2×C3×Q8—24no—
216C2×C3×Q8—44no—
217C2×C3×Q8C22×D314yes—
218C2×C3×Q8C22×D314yes—
219C2×C3×D4—34no—
220C2×C3×D4—38no—
221C2×C3×D4—34no—
222C2×C3×D4—68no—
223C2×C3×D4—64no—
224C2×C3×D4—64no—
225C22×C3×C4—21no—
226C22×C3×C4—22no—
227C22×C3×C4—31no—
228C22×C3×C4—38no—
229C22×C3×C4—34no—
230C22×C3×C4—32no—
231C22×C3×C4—38no—
232C22×C3×C4—68no—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D312yes—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—316no—
238C2×#67—38no—
239C2×#67—316no—
240C2×#67—38no—
241C2×#67—616no—
242C2×#67—616no—
243C2×#67—68no—
244C2×#67—68no—
245C22×Dic3—32no—
246C22×Dic3—32no—
247C22×Dic3—32no—
248C22×Dic3—32no—
249C22×Dic3—38no—
250C22×Dic3—38no—
251C22×Dic3—62no—
252C22×Dic3—62no—
253C22×Dic3—68no—
254C22×Dic3—68no—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D311yescharacteristic
257#239—232no—
258#237—632no—
259#235—632no—
260C2×D12—28no—
261C2×D12—24no—
262C2×D12—24no—
263C2×D12C22×D314yes—
264C2×D12C22×D318yes—
265C2×D12C22×D314yes—
266C2×C4×D3—28no—
267C2×C4×D3—38no—
268C2×C4×D3—38no—
269C2×C4×D3—68no—
270C2×C4×D3—68no—
271C2×C4×D3#6718yescomplemented
272C2×C4×D3C22×D318yes—
273C2×C4×D3C22×D314yes—
274C2×Dic6—34no—
275C2×Dic6—34no—
276C2×Dic6—64no—
277C2×Dic6—64no—
278C2×Dic6—64no—
279C2×Dic6—124no—
280C3×C22⋊C4—316no—
281C3×C42—34no—
282#217—316no—
283(C2×D3)⋊C4—316no—
284(C2×D3)⋊C4C22×D3116yes—
285Dic3⋊C4—316no—
286Dic3⋊C4—316no—
287Dic3⋊C4—616no—
288C4×Dic3—34no—
289C4×Dic3—34no—
290C4×Dic3—38no—
291C4×Dic3—38no—
292C4×Dic3—64no—
293C4×Dic3C22×D314yes—
294C22×C32C22×D412yes—
295C22×C32C2×#4114yes—
296C22×C32C2511yescharacteristic
297C2×C3×D3—28no—
298C2×C3×D3—24no—
299C2×C3×D3—24no—
300C2×C3×D3—24no—
301C2×C3×D3—28no—
302C2×C3×D3—28no—
303C2×C3×D3—48no—
304C2×C3×D3—48no—
305C2×C3×D3C22×D414yes—
306C32×C4—24no—
307C32×C4C22×D414yes—
308C3⋊Dic3—24no—
309C3⋊Dic3C2×#4118yescomplemented
310C3×Dic3—24no—
311C3×Dic3C22×D414yes—
312C2×#41—38no—
313C2×#41—68no—
314C2×#41—98no—
315C2×#41—188no—
316C22×Q8—91no—
317C22×Q8D3211yescharacteristic
318C22×D4—32no—
319C22×D4—31no—
320C22×D4—31no—
321C22×D4—94no—
322C22×D4—92no—
323C23×C4—31no—
324C23×C4—32no—
325C23×C4—92no—
326C23×C4—92no—
327C4⋊Q8—98no—
328#127—98no—
329#124—38no—
330#124—98no—
331#121—932no—
332C4×D4—932no—
333C2×C4⋊C4—94no—
334C2×C22⋊C4—34no—
335C2×C22⋊C4—94no—
336C2×C42—31no—
337C2×C42—98no—
338C2×C42—92no—
339C2×C42—91no—
340C23×C3—21no—
341C23×C3—34no—
342C23×C3—32no—
343C23×C3—34no—
344C23×C3—34no—
345C23×C3—64no—
346C23×C3—64no—
347C23×C3—68no—
348C23×C3—68no—
349C23×C3—64no—
350C23×C3C23×D311yescharacteristic
351C23×C3C23×D311yescharacteristic
352C22×D3—24no—
353C22×D3—24no—
354C22×D3—28no—
355C22×D3—28no—
356C22×D3—24no—
357C22×D3C2×#6714yes—
358C22×D3C23×D314yes—
359C22×D3C23×D314yes—
360C22×D3C23×D312yes—
361C3×Q8—28no—
362C3×Q8—28no—
363C3×Q8—48no—
364C3×D4—616no—
365C3×D4—68no—
366C3×D4—68no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—22no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—34no—
373C2×C3×C4—32no—
374C2×C3×C4—316no—
375C2×C3×C4—34no—
376C2×C3×C4—44no—
377C2×C3×C4—616no—
378C2×C3×C4—64no—
379C2×C3×C4D3×D414yes—
380C2×C3×C4C2×#6714yes—
381C2×C3×C4C23×D314yes—
382C2×C3×C4C23×D314yes—
383C2×C3×C4C23×D312yes—
384C2×C3×C4C23×D312yes—
385#67—632no—
386#67—632no—
387#67—616no—
388#67—616no—
389C2×Dic3—24no—
390C2×Dic3—38no—
391C2×Dic3—38no—
392C2×Dic3—34no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—34no—
396C2×Dic3—68no—
397C2×Dic3—64no—
398C2×Dic3—64no—
399C2×Dic3—616no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—616no—
403C2×Dic3—124no—
404C2×Dic3C2×#6714yes—
405C2×Dic3C23×D314yes—
406C2×Dic3C23×D312yes—
407D12—216no—
408D12—28no—
409D12—28no—
410C4×D3—216no—
411C4×D3—616no—
412C4×D3—616no—
413C4×D3C2×#67116yescomplemented
414Dic6—68no—
415Dic6—68no—
416Dic6—128no—
417C2×C32#53214yescomplemented
418C2×C32C23×D411yescharacteristic
419C2×C32C22×#4112yes—
420C3×D3—24no—
421C3×D3—44no—
422C3×D3—44no—
423C24—31no—
424C24—32no—
425C24—32no—
426#41—632no—
427#41—1832no—
428C2×Q8—24no—
429C2×Q8—94no—
430C2×Q8—184no—
431C2×Q8C2×D3214yes—
432C2×D4—38no—
433C2×D4—34no—
434C2×D4—34no—
435C2×D4—68no—
436C2×D4—64no—
437C2×D4—64no—
438C2×D4—916no—
439C2×D4—98no—
440C2×D4—1816no—
441C2×D4—188no—
442C22×C4—31no—
443C22×C4—34no—
444C22×C4—38no—
445C22×C4—32no—
446C22×C4—38no—
447C22×C4—68no—
448C22×C4—98no—
449C22×C4—98no—
450C22×C4—92no—
451C22×C4—92no—
452C22×C4—188no—
453C22×C4—188no—
454C22×C4C2×D3212yes—
455C22×C4C2×D3211yescharacteristic
456C4⋊C4—916no—
457C22⋊C4—316no—
458C22⋊C4—916no—
459C42—34no—
460C42—98no—
461C42—94no—
462C22×C3—24no—
463C22×C3—22no—
464C22×C3—21no—
465C22×C3—34no—
466C22×C3—68no—
467C22×C3—64no—
468C22×C3—64no—
469C22×C3—68no—
470C22×C3—68no—
471C22×C3—64no—
472C22×C3—128no—
473C22×C3—128no—
474C22×C3C2×D3×D412yes—
475C22×C3D3×#4114yes—
476C22×C3D3×#4114yes—
477C22×C3C22×#6712yes—
478C22×C3C24×D311yescharacteristic
479C22×C3C24×D311yescharacteristic
480C2×D3—24no—
481C2×D3—28no—
482C2×D3—24no—
483C2×D3—28no—
484C2×D3—28no—
485C2×D3—24no—
486C2×D3—48no—
487C2×D3—48no—
488C2×D3C22×#6714yes—
489C3×C4—24no—
490C3×C4—24no—
491C3×C4—24no—
492C3×C4—34no—
493C3×C4—44no—
494C3×C4—64no—
495C3×C4C2×D3×D414yes—
496C3×C4C22×#6714yes—
497Dic3—24no—
498Dic3—38no—
499Dic3—38no—
500Dic3—68no—
501Dic3—64no—
502Dic3—64no—
503Dic3—124no—
504Dic3C22×#6714yes—
505C32C2×#53211yescharacteristic, complemented, Sylow
506C23—34no—
507C23—32no—
508C23—34no—
509C23—34no—
510C23—64no—
511C23—68no—
512C23—68no—
513C23—64no—
514C23—64no—
515C23C22×D3211yescharacteristic
516Q8—28no—
517Q8—188no—
518D4—616no—
519D4—68no—
520D4—68no—
521D4—1832no—
522D4—1816no—
523C2×C4—24no—
524C2×C4—34no—
525C2×C4—32no—
526C2×C4—316no—
527C2×C4—34no—
528C2×C4—616no—
529C2×C4—64no—
530C2×C4—98no—
531C2×C4—94no—
532C2×C4—94no—
533C2×C4—1816no—
534C2×C4—1816no—
535C2×C4—184no—
536C2×C4D3×#6714yes—
537C2×C4C22×D3214yes—
538C2×C4C22×D3212yes—
539C2×C3—24no—
540C2×C3—22no—
541C2×C3—21no—
542C2×C3—64no—
543C2×C3—124no—
544C2×C3—124no—
545C2×C3#566814yescomplemented
546C2×C3#583214yescomplemented
547C2×C3C22×D3×D411yescharacteristic
548C2×C3C2×D3×#4112yes—
549C2×C3C2×D3×#4112yes—
550C2×C3C23×#6711yescharacteristic
551D3—24no—
552D3—44no—
553D3—44no—
554C22—34no—
555C22—68no—
556C22—64no—
557C22—68no—
558C22—68no—
559C22—64no—
560C22—64no—
561C22—128no—
562C22—128no—
563C22#6431914yes—
564C22C2×D3×#6712yes—
565C22C23×D3211yescharacteristic
566C4—24no—
567C4—34no—
568C4—64no—
569C4—98no—
570C4—184no—
571C4C2×D3×#6714yes—
572C3—21no—
573C3C2×#566811yescharacteristic, complemented
574C3C2×#583211yescharacteristic, complemented
575C2—64no—
576C2—124no—
577C2—124no—
578C2#1059535914yesdirect product factor
579C2C2×#6431912yes—
580C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×Q8C22
socleC23×C32C24
hypercenterC22×Q8D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C22×#3795C2semidirect
3. C2×#64153C2semidirect
4. C2×C3×#947C2semidirect
5. #10595359C2direct (N × H)
6. C2×#63914C2semidirect
7. C2×#63885C2semidirect
8. C2×#63879C2semidirect
9. C2×C4×D3×Dic3C2semidirect
10. C2×#63860C2semidirect
16. C2×C3×#239C22semidirect
27. C2×#3795C22semidirect
28. #64153C22semidirect
31. C3×#947C22semidirect
36. #63914C22semidirect
37. #63885C22semidirect
38. #63879C22semidirect
39. C4×D3×Dic3C22semidirect
40. #63860C22semidirect
42. C22×#239D3semidirect
47. C2×#947D3semidirect
83. C2×C3×C4×D3D4semidirect
119. C2×#239C2×D3semidirect
138. #947C2×D3semidirect
179. C2×C3⋊Dic3#41semidirect
191. C3×C4×D3C2×D4semidirect
271. C2×C4×D3#67semidirect
309. C3⋊Dic3C2×#41semidirect
413. C4×D3C2×#67semidirect
417. C2×C32#532semidirect
505. C32C2×#532semidirect
545. C2×C3#5668semidirect
546. C2×C3#5832semidirect
573. C3C2×#5668semidirect
574. C3C2×#5832semidirect
578. C2#10595359direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×#37952
C2×#641532
C2×C3×#9472
#105953592
C2×#639142
C2×#638852
C2×#638792
C2×C4×D3×Dic32
C2×#638602
C2×#58323
C2×#56683