Finite Group Databasebeta

← C2×#10595153 #11900793

Subgroups — C2×#10595153 #11900793

Order 1152.

3705 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×#3799C211yesmaximal, characteristic, complemented
3C2×#64149C211yesmaximal, characteristic, complemented
4C2×C3×#936C211yesmaximal, characteristic, complemented
5C2×#63971C214yesmaximal, complemented
6C2×#63952C214yesmaximal, complemented
7#10595153C2116yesmaximal, direct product factor
8C2×C4×D3×Dic3C211yesmaximal, characteristic, complemented
9C2×#63873C211yesmaximal, characteristic, complemented
10C2×#63864C211yesmaximal, characteristic, complemented
11C2×#5832—31nomaximal
12C2×#5668—31nomaximal
13C22×C32×D4C2211yescharacteristic
14C22×#638C2214yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C3×#67C2212yes—
17C23×C3×Dic3C2212yes—
18C2×C3×#237—28no—
19C2×C3×#237C2218yescomplemented
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#626C2212yes—
24C22×#624C2212yes—
25C22×D3×Dic3C2212yes—
26C2×#3799—28no—
27C2×#3799C2218yescomplemented
28#64149C2218yescomplemented
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×#217C2214yes—
31C3×#936C2218yescomplemented
32C2×C3×C4×Dic3C2211yescharacteristic
33#63971C22132yescomplemented
34C2×#3724C2214yes—
35C2×#3722C2214yes—
36C2×Dic32C2212yes—
37#63952C22132yescomplemented
38C4×D3×Dic3C2218yescomplemented
39#63873C2218yescomplemented
40#63864C2218yescomplemented
41C22×C3×#41—31no—
42C22×#239—31no—
43C22×#237D311yescharacteristic, complemented
44C22×#235—31no—
45C2×C3×#124—31no—
46#5832—316no—
47C2×#947—31no—
48C2×#944—31no—
49C2×#944—31no—
50C2×#940—31no—
51C2×#940—31no—
52C2×#940—61no—
53C2×#939—34no—
54C2×#936D311yescharacteristic, complemented
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—
62C24×C32C2312yes—
63C23×C3⋊D3C2312yes—
64C23×C3×D3C2311yescharacteristic
65C2×C32×D4—24no—
66C2×C32×D4C2314yes—
67C22×C32×C4C2311yescharacteristic
68C2×#638—216no—
69C2×#638C23116yes—
70C22×C3⋊Dic3C2312yes—
71C2×C4⋊(C3⋊D3)—24no—
72C2×C4⋊(C3⋊D3)C2314yes—
73C2×C3×#67—28no—
74C2×C3×#67C2318yes—
75C22×C3×Dic3—28no—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2318yes—
80C22×C3×Dic3C2311yescharacteristic
81C3×#237—232no—
82C2×C3×C4×D3D418yescomplemented
83C2×C3×C4×D3C2314yes—
84C2×C3×Dic6—24no—
85C2×C3×Dic6—24no—
86C2×C3×Dic6C2314yes—
87C2×C3×Dic6C2314yes—
88C2×#626—28no—
89C2×#626C2318yes—
90C2×#624—28no—
91C2×#624C2318yes—
92C2×D3×Dic3—28no—
93C2×D3×Dic3C2318yes—
94#3799—232no—
95C4×C3⋊Dic3C2314yes—
96C3×#217C23116yes—
97C3×C4×Dic3C2314yes—
98#3724C23116yes—
99#3722C23116yes—
100Dic32C2318yes—
101C2×#532—91noSylow
102C2×C3×#41—38no—
103C2×C3×#41—68no—
104C22×C3×Q8—31no—
105C22×C3×Q8—31no—
106C22×C3×D4—21no—
107C22×C3×D4—32no—
108C22×C3×D4C2×D311yescharacteristic
109C22×C3×D4C2×D311yescharacteristic
110C23×C3×C4—31no—
111C23×C3×C4—32no—
112C22×#67—34no—
113C22×#67—34no—
114C22×#67—32no—
115C22×#67—64no—
116C22×#67C2×D312yes—
117C23×Dic3—32no—
118C23×Dic3C2×D312yes—
119C2×#239—38no—
120C2×#239—68no—
121C2×#237—28no—
122C2×#237C2×D318yescomplemented
123C2×#235—38no—
124C2×#235—68no—
125C22×D12—32no—
126C22×D12—31no—
127C22×D12—31no—
128C22×D12—61no—
129C22×C4×D3—32no—
130C22×C4×D3—32no—
131C22×C4×D3—32no—
132C22×C4×D3C2×D311yescharacteristic
133C22×Dic6C2×D311yescharacteristic
134C22×Dic6C2×D311yescharacteristic
135C3×#124—38no—
136C2×C3×C22⋊C4—34no—
137C2×C3×C42—31no—
138C2×#217C2×D314yes—
139#947—38no—
140#944—38no—
141#944—38no—
142#940—38no—
143#940—38no—
144#940—68no—
145#939—332no—
146#936C2×D318yescomplemented
147C4×#67—332no—
148C2×(C2×D3)⋊C4—34no—
149C2×(C2×D3)⋊C4—34no—
150C2×Dic3⋊C4—34no—
151C2×Dic3⋊C4—34no—
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×C32—24no—
164C23×C32—28no—
165C23×C32C2414yes—
166C23×C32C2411yescharacteristic
167C22×C3⋊D3—24no—
168C22×C3⋊D3—28no—
169C22×C3⋊D3C2414yes—
170C22×C3×D3—24no—
171C22×C3×D3C2×D414yes—
172C22×C3×D3C2412yes—
173C32×D4—28no—
174C2×C32×C4C2×D414yes—
175C2×C32×C4C2412yes—
176#638—232no—
177C2×C3⋊Dic3#4118yescomplemented
178C2×C3⋊Dic3C2414yes—
179C4⋊(C3⋊D3)—28no—
180C3×#67—216no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3—24no—
183C2×C3×Dic3—24no—
184C2×C3×Dic3—216no—
185C2×C3×Dic3C2×D414yes—
186C2×C3×Dic3C2414yes—
187C2×C3×Dic3C2414yes—
188C2×C3×Dic3C2414yes—
189C2×C3×Dic3C2412yes—
190C3×C4×D3C2×D4116yescomplemented
191C3×Dic6—28no—
192C3×Dic6—28no—
193#626—216no—
194#624—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—22no—
207C24×C3—31no—
208C24×C3C22×D312yes—
209C24×C3C22×D312yes—
210C23×D3—32no—
211C23×D3—32no—
212C23×D3—62no—
213C23×D3C22×D311yescharacteristic
214C3×#41—632no—
215C2×C3×Q8—34no—
216C2×C3×Q8—34no—
217C2×C3×Q8—64no—
218C2×C3×Q8—64no—
219C2×C3×D4—24no—
220C2×C3×D4—24no—
221C2×C3×D4—24no—
222C2×C3×D4—38no—
223C2×C3×D4—44no—
224C2×C3×D4—68no—
225C2×C3×D4C22×D314yes—
226C2×C3×D4C22×D314yes—
227C22×C3×C4—21no—
228C22×C3×C4—31no—
229C22×C3×C4—38no—
230C22×C3×C4—34no—
231C22×C3×C4—32no—
232C22×C3×C4—32no—
233C22×C3×C4—32no—
234C22×C3×C4—38no—
235C22×C3×C4—68no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—28no—
239C2×#67—316no—
240C2×#67—316no—
241C2×#67—38no—
242C2×#67—616no—
243C2×#67—68no—
244C2×#67—616no—
245C2×#67—616no—
246C2×#67—1216no—
247C2×#67C22×D318yes—
248C22×Dic3—28no—
249C22×Dic3—32no—
250C22×Dic3—32no—
251C22×Dic3—38no—
252C22×Dic3—62no—
253C22×Dic3—68no—
254C22×Dic3C22×D318yes—
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D311yescharacteristic
259#239—632no—
260#237—232no—
261#235—632no—
262C2×D12—38no—
263C2×D12—34no—
264C2×D12—34no—
265C2×D12—64no—
266C2×D12—68no—
267C2×D12—64no—
268C2×D12—64no—
269C2×D12—124no—
270C2×C4×D3—38no—
271C2×C4×D3—38no—
272C2×C4×D3—38no—
273C2×C4×D3—68no—
274C2×C4×D3—68no—
275C2×C4×D3—68no—
276C2×C4×D3#6718yescomplemented
277C2×C4×D3C22×D314yes—
278C2×Dic6—24no—
279C2×Dic6—24no—
280C2×Dic6C22×D314yes—
281C2×Dic6C22×D314yes—
282C3×C22⋊C4—316no—
283C3×C42—34no—
284#217C22×D3116yes—
285(C2×D3)⋊C4—316no—
286(C2×D3)⋊C4—316no—
287Dic3⋊C4—316no—
288Dic3⋊C4—316no—
289C4×Dic3—34no—
290C4×Dic3—34no—
291C4×Dic3—38no—
292C4×Dic3—38no—
293C4×Dic3—64no—
294C4×Dic3C22×D314yes—
295C22×C32—24no—
296C22×C32—28no—
297C22×C32—48no—
298C22×C32C22×D412yes—
299C22×C32C2×#4114yes—
300C22×C32C2511yescharacteristic
301C2×C3⋊D3—24no—
302C2×C3⋊D3—28no—
303C2×C3⋊D3—48no—
304C2×C3×D3—28no—
305C2×C3×D3—24no—
306C2×C3×D3C22×D414yes—
307C32×C4C22×D414yes—
308C3⋊Dic3C2×#4118yescomplemented
309C3×Dic3—24no—
310C3×Dic3—24no—
311C3×Dic3—24no—
312C3×Dic3C22×D414yes—
313C2×#41—38no—
314C2×#41—68no—
315C2×#41—98no—
316C2×#41—188no—
317C22×Q8—31no—
318C22×Q8—31no—
319C22×D4—32no—
320C22×D4—92no—
321C22×D4—94no—
322C22×D4—91no—
323C22×D4D3211yescharacteristic
324C23×C4—31no—
325C23×C4—32no—
326C23×C4—92no—
327C23×C4—92no—
328C4⋊Q8—98no—
329#127—98no—
330#124—38no—
331#124—98no—
332#121—932no—
333C4×D4—932no—
334C2×C4⋊C4—94no—
335C2×C22⋊C4—34no—
336C2×C22⋊C4—94no—
337C2×C42—31no—
338C2×C42—98no—
339C2×C42—92no—
340C2×C42—91no—
341C23×C3—24no—
342C23×C3—28no—
343C23×C3—28no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—21no—
347C23×C3—34no—
348C23×C3—32no—
349C23×C3—48no—
350C23×C3—44no—
351C23×C3—64no—
352C23×C3C23×D314yes—
353C23×C3C23×D314yes—
354C23×C3C23×D311yescharacteristic
355C23×C3C23×D311yescharacteristic
356C22×D3—24no—
357C22×D3—34no—
358C22×D3—34no—
359C22×D3—64no—
360C22×D3—64no—
361C22×D3—68no—
362C22×D3—68no—
363C22×D3—64no—
364C22×D3—124no—
365C22×D3—128no—
366C22×D3C2×#6714yes—
367C22×D3C23×D312yes—
368C3×Q8—68no—
369C3×Q8—68no—
370C3×D4—28no—
371C3×D4—28no—
372C3×D4—48no—
373C3×D4—616no—
374C2×C3×C4—22no—
375C2×C3×C4—24no—
376C2×C3×C4—34no—
377C2×C3×C4—32no—
378C2×C3×C4—316no—
379C2×C3×C4—34no—
380C2×C3×C4—34no—
381C2×C3×C4—34no—
382C2×C3×C4—616no—
383C2×C3×C4—64no—
384C2×C3×C4—64no—
385C2×C3×C4—64no—
386C2×C3×C4D3×D414yes—
387C2×C3×C4C2×#6714yes—
388C2×C3×C4C23×D312yes—
389C2×C3×C4C23×D312yes—
390#67—216no—
391#67—616no—
392#67—632no—
393#67—632no—
394#67—1232no—
395C2×Dic3—24no—
396C2×Dic3—24no—
397C2×Dic3—24no—
398C2×Dic3—216no—
399C2×Dic3—38no—
400C2×Dic3—38no—
401C2×Dic3—34no—
402C2×Dic3—34no—
403C2×Dic3—68no—
404C2×Dic3—64no—
405C2×Dic3—616no—
406C2×Dic3C2×#6714yes—
407C2×Dic3C23×D314yes—
408C2×Dic3C23×D314yes—
409C2×Dic3C23×D314yes—
410C2×Dic3C23×D312yes—
411D12—616no—
412D12—68no—
413D12—68no—
414D12—128no—
415C4×D3—616no—
416C4×D3—616no—
417C4×D3—616no—
418C4×D3C2×#67116yescomplemented
419Dic6—28no—
420Dic6—28no—
421C2×C32—44no—
422C2×C32#53214yescomplemented
423C2×C32C23×D411yescharacteristic
424C2×C32C22×#4112yes—
425C3⋊D3—44no—
426C3×D3—24no—
427C24—31no—
428C24—92no—
429C24C2×D3212yes—
430#41—632no—
431#41—1832no—
432C2×Q8—34no—
433C2×Q8—34no—
434C2×Q8—64no—
435C2×Q8—64no—
436C2×D4—24no—
437C2×D4—38no—
438C2×D4—68no—
439C2×D4—98no—
440C2×D4—916no—
441C2×D4—94no—
442C2×D4—188no—
443C2×D4—1816no—
444C2×D4—184no—
445C2×D4C2×D3214yes—
446C22×C4—31no—
447C22×C4—34no—
448C22×C4—38no—
449C22×C4—38no—
450C22×C4—32no—
451C22×C4—32no—
452C22×C4—32no—
453C22×C4—68no—
454C22×C4—98no—
455C22×C4—98no—
456C22×C4—92no—
457C22×C4—188no—
458C22×C4—188no—
459C22×C4C2×D3211yescharacteristic
460C4⋊C4—916no—
461C22⋊C4—316no—
462C22⋊C4—916no—
463C42—34no—
464C42—98no—
465C42—94no—
466C22×C3—24no—
467C22×C3—28no—
468C22×C3—28no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—22no—
472C22×C3—21no—
473C22×C3—34no—
474C22×C3—48no—
475C22×C3—44no—
476C22×C3—48no—
477C22×C3—48no—
478C22×C3—68no—
479C22×C3—64no—
480C22×C3—88no—
481C22×C3C2×D3×D412yes—
482C22×C3D3×#4114yes—
483C22×C3D3×#4114yes—
484C22×C3C22×#6712yes—
485C22×C3C24×D311yescharacteristic
486C22×C3C24×D311yescharacteristic
487C2×D3—24no—
488C2×D3—28no—
489C2×D3—64no—
490C2×D3—68no—
491C2×D3—68no—
492C2×D3—64no—
493C2×D3—124no—
494C2×D3—128no—
495C2×D3—128no—
496C2×D3—128no—
497C2×D3—248no—
498C2×D3C22×#6714yes—
499C3×C4—24no—
500C3×C4—34no—
501C3×C4—64no—
502C3×C4—64no—
503C3×C4—64no—
504C3×C4C2×D3×D414yes—
505C3×C4C22×#6714yes—
506Dic3—24no—
507Dic3—24no—
508Dic3—24no—
509Dic3—38no—
510Dic3—38no—
511Dic3—68no—
512Dic3C22×#6714yes—
513C32C2×#53211yescharacteristic, complemented, Sylow
514C23—28no—
515C23—24no—
516C23—34no—
517C23—32no—
518C23—64no—
519C23—94no—
520C23—188no—
521C23—184no—
522C23C22×D3214yes—
523C23C22×D3211yescharacteristic
524Q8—68no—
525Q8—68no—
526D4—28no—
527D4—616no—
528D4—1816no—
529D4—1832no—
530D4—188no—
531C2×C4—34no—
532C2×C4—32no—
533C2×C4—316no—
534C2×C4—34no—
535C2×C4—34no—
536C2×C4—34no—
537C2×C4—616no—
538C2×C4—64no—
539C2×C4—64no—
540C2×C4—64no—
541C2×C4—98no—
542C2×C4—94no—
543C2×C4—1816no—
544C2×C4—1816no—
545C2×C4D3×#6714yes—
546C2×C4C22×D3212yes—
547C2×C3—22no—
548C2×C3—24no—
549C2×C3—21no—
550C2×C3—44no—
551C2×C3—44no—
552C2×C3—64no—
553C2×C3—84no—
554C2×C3#566814yescomplemented
555C2×C3#583214yescomplemented
556C2×C3C22×D3×D411yescharacteristic
557C2×C3C2×D3×#4112yes—
558C2×C3C2×D3×#4112yes—
559C2×C3C23×#6711yescharacteristic
560D3—24no—
561D3—124no—
562D3—124no—
563D3—244no—
564C22—28no—
565C22—24no—
566C22—34no—
567C22—48no—
568C22—64no—
569C22—68no—
570C22—188no—
571C22—184no—
572C22—368no—
573C22#6431214yes—
574C22C2×D3×#6712yes—
575C22C23×D3211yescharacteristic
576C4—34no—
577C4—64no—
578C4—64no—
579C4—64no—
580C4—98no—
581C4C2×D3×#6714yes—
582C3—21no—
583C3C2×#566811yescharacteristic, complemented
584C3C2×#583211yescharacteristic, complemented
585C2—44no—
586C2—64no—
587C2—364no—
588C2#1059515314yesdirect product factor
589C2C2×#6431212yes—
590C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×#3799C2semidirect
3. C2×#64149C2semidirect
4. C2×C3×#936C2semidirect
5. C2×#63971C2semidirect
6. C2×#63952C2semidirect
7. #10595153C2direct (N × H)
8. C2×C4×D3×Dic3C2semidirect
9. C2×#63873C2semidirect
10. C2×#63864C2semidirect
19. C2×C3×#237C22semidirect
27. C2×#3799C22semidirect
28. #64149C22semidirect
31. C3×#936C22semidirect
33. #63971C22semidirect
37. #63952C22semidirect
38. C4×D3×Dic3C22semidirect
39. #63873C22semidirect
40. #63864C22semidirect
43. C22×#237D3semidirect
54. C2×#936D3semidirect
82. C2×C3×C4×D3D4semidirect
122. C2×#237C2×D3semidirect
146. #936C2×D3semidirect
177. C2×C3⋊Dic3#41semidirect
190. C3×C4×D3C2×D4semidirect
276. C2×C4×D3#67semidirect
308. C3⋊Dic3C2×#41semidirect
418. C4×D3C2×#67semidirect
422. C2×C32#532semidirect
513. C32C2×#532semidirect
554. C2×C3#5668semidirect
555. C2×C3#5832semidirect
583. C3C2×#5668semidirect
584. C3C2×#5832semidirect
588. C2#10595153direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×#37992
C2×#641492
C2×C3×#9362
C2×#639712
C2×#639522
#105951532
C2×C4×D3×Dic32
C2×#638732
C2×#638642
C2×#58323
C2×#56683