Finite Group Databasebeta

← C2×#10595508 #11901333

Subgroups — C2×#10595508 #11901333

Order 1152.

3009 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3757C211yesmaximal, characteristic, complemented
2C2×C3×#953C212yesmaximal, complemented
3C2×#63982C211yesmaximal, characteristic, complemented
4C2×#63980C211yesmaximal, characteristic, complemented
5#10595508C2116yesmaximal, direct product factor
6C2×#67⋊Dic3C212yesmaximal, complemented
7C2×#63970C212yesmaximal, complemented
8C2×#63969C212yesmaximal, complemented
9C2×#63959C212yesmaximal, complemented
10C2×#63956C212yesmaximal, complemented
11C2×#5593—32nomaximal
12C25×C32C2211yescharacteristic
13C23×C3⋊Dic3C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67C2212yes—
16C22×C3×#67C2212yes—
17C22×C3×#67C2212yes—
18C22×#627C2211yescharacteristic, complemented
19C22×#625C2211yescharacteristic, complemented
20C22×D3×Dic3C2212yescomplemented
21C2×#3757C2212yes—
22C2×#3757C2212yes—
23C2×#3757C2218yescomplemented
24C3×#953C22116yescomplemented
25C2×C3×#217C2212yes—
26C2×C3×#217C2212yes—
27C2×C3×#217C2212yes—
28#63982C2218yescomplemented
29#63980C2218yescomplemented
30#67⋊Dic3C22116yescomplemented
31#63970C22116yescomplemented
32#63969C22116yescomplemented
33C2×#3724C2211yescharacteristic, complemented
34C2×#3724C2211yescharacteristic, complemented
35C2×Dic3⋊Dic3C2212yescomplemented
36C2×Dic3⋊Dic3C2212yescomplemented
37C2×(C2×D3)⋊Dic3C2212yescomplemented
38C2×(C2×D3)⋊Dic3C2212yescomplemented
39#63959C22116yescomplemented
40#63956C22116yescomplemented
41C2×Dic32C2212yescomplemented
42C2×C3×#120—32no—
43C2×#953D312yescomplemented
44C22×#217—32no—
45C22×#217—61no—
46C2×#939—32no—
47C2×#939—32no—
48C2×#938—32no—
49C2×#936—32no—
50C2×#935—32no—
51C2×D4×Dic3—32no—
52#5593—332no—
53C2×#885—32no—
54C2×#883—32no—
55C2×#67⋊C4—32no—
56C2×#879—32no—
57C2×#879—32no—
58C2×#878—32no—
59C24×C32—24no—
60C24×C32—42no—
61C24×C32—42no—
62C24×C32C2312yes—
63C24×C32C2311yescharacteristic
64C24×C32C2314yes—
65C23×C3×D3C2312yes—
66C22×C3⋊Dic3—42no—
67C22×C3⋊Dic3—42no—
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C22×C3⋊Dic3C2311yescharacteristic
71C22×C3⋊Dic3C2314yes—
72C22×C3⋊Dic3C2314yes—
73C2×C3×#67—28no—
74C2×C3×#67—44no—
75C2×C3×#67—44no—
76C2×C3×#67C2318yes—
77C2×C3×#67C2318yes—
78C2×C3×#67C2318yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2312yes—
82C2×#627—42no—
83C2×#627C2314yescomplemented
84C2×#625—42no—
85C2×#625C2314yescomplemented
86C2×D3×Dic3—44no—
87C2×D3×Dic3C2318yescomplemented
88#3757C2318yes—
89#3757C2318yes—
90C3×#217C2318yes—
91C3×#217C2318yes—
92C3×#217C2318yes—
93#3724C2314yescomplemented
94#3724C2314yescomplemented
95Dic3⋊Dic3C2318yescomplemented
96Dic3⋊Dic3C2318yescomplemented
97(C2×D3)⋊Dic3C2318yescomplemented
98(C2×D3)⋊Dic3C2318yescomplemented
99Dic32C2318yescomplemented
100C2×#538—91noSylow
101C25×C3—21no—
102C25×C3C2×D312yes—
103C22×C3×D4—32no—
104C22×C3×D4—32no—
105C22×C3×D4—32no—
106C22×#67—32no—
107C22×#67C2×D312yes—
108C22×#67C2×D312yes—
109C22×#67C2×D312yes—
110C23×Dic3—32no—
111C23×Dic3—32no—
112C23×Dic3—32no—
113C23×Dic3—61no—
114C23×Dic3—61no—
115C22×C4×D3—32no—
116C22×Dic6—32no—
117C3×#120—316no—
118C2×C3×C22⋊C4—32no—
119C2×C3×C22⋊C4—32no—
120C2×C3×C22⋊C4—32no—
121#953C2×D3116yescomplemented
122C2×#217—32no—
123C2×#217—32no—
124C2×#217—32no—
125C2×#217—32no—
126C2×#217—316no—
127C2×#217—32no—
128C2×#217—32no—
129C2×#217—62no—
130C2×#217—62no—
131C2×#217—68no—
132C2×#217C2×D312yes—
133C2×#217C2×D312yes—
134C2×#217C2×D312yes—
135#939—316no—
136#939—316no—
137#938—316no—
138#936—316no—
139#935—316no—
140D4×Dic3—316no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×C4⋊Dic3—32no—
144C2×C4⋊Dic3—32no—
145C2×Dic3⋊C4—32no—
146C2×Dic3⋊C4—32no—
147C2×Dic3⋊C4—32no—
148C2×Dic3⋊C4—32no—
149C2×C4×Dic3—32no—
150C2×C4×Dic3—32no—
151#885—316no—
152#883—316no—
153#67⋊C4—316no—
154#879—316no—
155#879—316no—
156#878—316no—
157C23×C32—22no—
158C23×C32—22no—
159C23×C32—28no—
160C23×C32—24no—
161C23×C32—24no—
162C23×C32—24no—
163C23×C32—44no—
164C23×C32—44no—
165C23×C32—416no—
166C23×C32#4114yes—
167C23×C32C2414yes—
168C23×C32C2412yes—
169C23×C32C2411yescharacteristic
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3C2414yes—
174C2×C3⋊Dic3—24no—
175C2×C3⋊Dic3—22no—
176C2×C3⋊Dic3—22no—
177C2×C3⋊Dic3—44no—
178C2×C3⋊Dic3—44no—
179C2×C3⋊Dic3C2414yes—
180C2×C3⋊Dic3C2412yes—
181C2×C3⋊Dic3C2412yes—
182C3×#67—216no—
183C3×#67—48no—
184C3×#67—48no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—24no—
187C2×C3×Dic3—24no—
188C2×C3×Dic3C2414yes—
189C2×C3×Dic3C2414yes—
190C2×C3×Dic3C2414yes—
191#627—44no—
192#625—44no—
193D3×Dic3—48no—
194#538—916no—
195C2×#126—92no—
196C2×#124—92no—
197C2×#123—92no—
198C2×C22⋊Q8—91no—
199C2×#121—92no—
200C2×#121—91no—
201C2×#120—32no—
202C2×C4×D4—92no—
203C22×C22⋊C4—91no—
204C24×C3—28no—
205C24×C3—28no—
206C24×C3—21no—
207C24×C3—22no—
208C24×C3—24no—
209C24×C3—32no—
210C24×C3—44no—
211C24×C3—44no—
212C24×C3—44no—
213C24×C3—44no—
214C24×C3C22×D312yes—
215C24×C3C22×D312yes—
216C24×C3C22×D312yes—
217C24×C3C22×D318yes—
218C23×D3C22×D312yes—
219C2×C3×D4—38no—
220C2×C3×D4—38no—
221C2×C3×D4—38no—
222C2×C3×D4—68no—
223C2×C3×D4—124no—
224C2×C3×D4—124no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—32no—
228C2×#67—28no—
229C2×#67—38no—
230C2×#67—44no—
231C2×#67—44no—
232C2×#67—124no—
233C2×#67C22×D318yes—
234C2×#67C22×D318yes—
235C2×#67C22×D318yes—
236C22×Dic3—32no—
237C22×Dic3—32no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—38no—
241C22×Dic3—38no—
242C22×Dic3—38no—
243C22×Dic3—62no—
244C22×Dic3—61no—
245C22×Dic3—61no—
246C22×Dic3—64no—
247C22×Dic3—64no—
248C22×Dic3—124no—
249C22×Dic3—124no—
250C22×Dic3—124no—
251C22×Dic3—124no—
252C22×Dic3—124no—
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D312yes—
255C22×Dic3C22×D312yes—
256C2×C4×D3—38no—
257C2×C4×D3—124no—
258C2×Dic6—38no—
259C2×Dic6—124no—
260C3×C22⋊C4—38no—
261C3×C22⋊C4—38no—
262C3×C22⋊C4—38no—
263#217—38no—
264#217—38no—
265#217—38no—
266#217—38no—
267#217—38no—
268#217—38no—
269#217—68no—
270#217—68no—
271#217C22×D318yes—
272#217C22×D318yes—
273#217C22×D318yes—
274(C2×D3)⋊C4—38no—
275(C2×D3)⋊C4—38no—
276C4⋊Dic3—38no—
277C4⋊Dic3—38no—
278Dic3⋊C4—38no—
279Dic3⋊C4—38no—
280Dic3⋊C4—38no—
281Dic3⋊C4—38no—
282C4×Dic3—38no—
283C4×Dic3—38no—
284C22×C32—28no—
285C22×C32—22no—
286C22×C32—22no—
287C22×C32—24no—
288C22×C32—24no—
289C22×C32—24no—
290C22×C32—416no—
291C22×C32—48no—
292C22×C32C2×#4114yes—
293C22×C32C2×#4112yes—
294C22×C32H(5,𝔽2)12yes—
295C22×C32H(5,𝔽2)12yes—
296C22×C32C2511yescharacteristic
297C2×C3×D3—24no—
298C2×C3×D3—24no—
299C2×C3×D3—24no—
300C2×C3×D3—48no—
301C3⋊Dic3—24no—
302C3⋊Dic3—22no—
303C3⋊Dic3—22no—
304C3×Dic3—24no—
305C3×Dic3—24no—
306C3×Dic3—24no—
307C25D3211yescharacteristic
308C22×Q8—91no—
309C22×D4—32no—
310C22×D4—32no—
311C22×D4—32no—
312C22×D4—91no—
313C23×C4—92no—
314C23×C4—91no—
315C23×C4—91no—
316#126—916no—
317#124—916no—
318#123—916no—
319C22⋊Q8—98no—
320#121—916no—
321#121—98no—
322#120—316no—
323C4×D4—916no—
324C2×C4⋊C4—92no—
325C2×C4⋊C4—92no—
326C2×C4⋊C4—91no—
327C2×C4⋊C4—91no—
328C2×C22⋊C4—32no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—92no—
332C2×C22⋊C4—92no—
333C2×C22⋊C4—92no—
334C2×C22⋊C4—92no—
335C2×C22⋊C4—98no—
336C2×C42—92no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—216no—
342C23×C3—28no—
343C23×C3—216no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3—24no—
348C23×C3—24no—
349C23×C3—24no—
350C23×C3—22no—
351C23×C3—24no—
352C23×C3—21no—
353C23×C3—24no—
354C23×C3—34no—
355C23×C3—44no—
356C23×C3—44no—
357C23×C3—48no—
358C23×C3—48no—
359C23×C3—48no—
360C23×C3—48no—
361C23×C3—432no—
362C23×C3—432no—
363C23×C3—64no—
364C23×C3—64no—
365C23×C3—64no—
366C23×C3#23718yes—
367C23×C3C23×D314yes—
368C23×C3C23×D314yes—
369C23×C3C23×D314yes—
370C23×C3C23×D312yes—
371C22×D3—24no—
372C22×D3—24no—
373C22×D3—24no—
374C22×D3C23×D314yes—
375C3×D4—616no—
376C3×D4—128no—
377C3×D4—128no—
378C2×C3×C4—34no—
379C2×C3×C4—34no—
380C2×C3×C4—34no—
381C2×C3×C4—64no—
382C2×C3×C4—64no—
383C2×C3×C4—64no—
384#67—216no—
385#67—48no—
386#67—48no—
387#67—128no—
388C2×Dic3—24no—
389C2×Dic3—24no—
390C2×Dic3—24no—
391C2×Dic3—34no—
392C2×Dic3—34no—
393C2×Dic3—34no—
394C2×Dic3—34no—
395C2×Dic3—64no—
396C2×Dic3—62no—
397C2×Dic3—62no—
398C2×Dic3—64no—
399C2×Dic3—64no—
400C2×Dic3—64no—
401C2×Dic3—64no—
402C2×Dic3—124no—
403C2×Dic3—122no—
404C2×Dic3—122no—
405C2×Dic3—128no—
406C2×Dic3—128no—
407C2×Dic3—128no—
408C2×Dic3—128no—
409C2×Dic3—128no—
410C2×Dic3C23×D314yes—
411C2×Dic3C23×D314yes—
412C2×Dic3C23×D314yes—
413C4×D3—128no—
414Dic6—128no—
415C2×C32—24no—
416C2×C32—44no—
417C2×C32#53814yescomplemented
418C2×C32C22×#4111yescharacteristic
419C2×C32C2×H(5,𝔽2)11yescharacteristic
420C2×C32C2×H(5,𝔽2)11yescharacteristic
421C3×D3—44no—
422C24—24no—
423C24—32no—
424C24—42no—
425C24—42no—
426C24C2×D3212yes—
427C24C2×D3211yescharacteristic
428C24C2×D3214yes—
429C2×Q8—94no—
430C2×Q8—362no—
431C2×D4—38no—
432C2×D4—38no—
433C2×D4—38no—
434C2×D4—68no—
435C2×D4—94no—
436C2×D4—124no—
437C2×D4—124no—
438C2×D4—362no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—32no—
442C22×C4—98no—
443C22×C4—92no—
444C22×C4—91no—
445C22×C4—91no—
446C22×C4—94no—
447C22×C4—94no—
448C22×C4—364no—
449C22×C4—362no—
450C22×C4—362no—
451C4⋊C4—98no—
452C4⋊C4—98no—
453C4⋊C4—94no—
454C4⋊C4—94no—
455C22⋊C4—38no—
456C22⋊C4—38no—
457C22⋊C4—38no—
458C22⋊C4—98no—
459C22⋊C4—98no—
460C22⋊C4—98no—
461C22⋊C4—98no—
462C42—98no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3—216no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—216no—
469C22×C3—28no—
470C22×C3—24no—
471C22×C3—24no—
472C22×C3—24no—
473C22×C3—24no—
474C22×C3—24no—
475C22×C3—24no—
476C22×C3—24no—
477C22×C3—22no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—21no—
481C22×C3—44no—
482C22×C3—44no—
483C22×C3—432no—
484C22×C3—432no—
485C22×C3—416no—
486C22×C3—48no—
487C22×C3—48no—
488C22×C3—64no—
489C22×C3—64no—
490C22×C3—64no—
491C22×C3—128no—
492C22×C3C2×#23718yes—
493C22×C3C2×#23714yes—
494C22×C3#100414yes—
495C22×C3#100414yes—
496C22×C3C24×D312yes—
497C2×D3—24no—
498C2×D3—24no—
499C2×D3—24no—
500C2×D3—48no—
501C3×C4—64no—
502C3×C4—64no—
503C3×C4—64no—
504Dic3—24no—
505Dic3—24no—
506Dic3—24no—
507Dic3—64no—
508Dic3—64no—
509Dic3—64no—
510Dic3—64no—
511Dic3—124no—
512Dic3—122no—
513Dic3—122no—
514C32C2×#53811yescharacteristic, complemented, Sylow
515C23—22no—
516C23—22no—
517C23—28no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—34no—
522C23—44no—
523C23—44no—
524C23—416no—
525C23—64no—
526C23—64no—
527C23—64no—
528C23#380514yes—
529C23C22×D3214yes—
530C23C22×D3212yes—
531C23C22×D3211yescharacteristic
532Q8—364no—
533D4—616no—
534D4—128no—
535D4—128no—
536D4—364no—
537C2×C4—34no—
538C2×C4—34no—
539C2×C4—34no—
540C2×C4—64no—
541C2×C4—64no—
542C2×C4—64no—
543C2×C4—94no—
544C2×C4—92no—
545C2×C4—92no—
546C2×C4—184no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4—368no—
550C2×C4—364no—
551C2×C4—364no—
552C2×C3—28no—
553C2×C3—28no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—24no—
558C2×C3—48no—
559C2×C3—44no—
560C2×C3—44no—
561C2×C3—124no—
562C2×C3#559318yescomplemented
563C2×C3C22×#23712yes—
564C2×C3C2×#100412yes—
565C2×C3C2×#100412yes—
566D3—44no—
567C22—22no—
568C22—22no—
569C22—28no—
570C22—24no—
571C22—24no—
572C22—24no—
573C22—416no—
574C22—48no—
575C22—64no—
576C22—64no—
577C22—64no—
578C22—128no—
579C22C2×#380514yes—
580C22C2×#380512yes—
581C22#6433012yes—
582C22#6433012yes—
583C22C23×D3211yescharacteristic
584C4—64no—
585C4—64no—
586C4—64no—
587C4—184no—
588C4—182no—
589C4—182no—
590C3—21no—
591C3C2×#559312yescomplemented
592C2—24no—
593C2—44no—
594C2—124no—
595C2#1059550814yesdirect product factor
596C2C22×#380511yescharacteristic
597C2C2×#6433011yescharacteristic
598C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
hypercenterC25D32
hypocenterC32C2×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C22×#3757C2semidirect
2. C2×C3×#953C2semidirect
3. C2×#63982C2semidirect
4. C2×#63980C2semidirect
5. #10595508C2direct (N × H)
6. C2×#67⋊Dic3C2semidirect
7. C2×#63970C2semidirect
8. C2×#63969C2semidirect
9. C2×#63959C2semidirect
10. C2×#63956C2semidirect
18. C22×#627C22semidirect
19. C22×#625C22semidirect
20. C22×D3×Dic3C22semidirect
23. C2×#3757C22semidirect
24. C3×#953C22semidirect
28. #63982C22semidirect
29. #63980C22semidirect
30. #67⋊Dic3C22semidirect
31. #63970C22semidirect
32. #63969C22semidirect
33. C2×#3724C22semidirect
34. C2×#3724C22semidirect
35. C2×Dic3⋊Dic3C22semidirect
36. C2×Dic3⋊Dic3C22semidirect
37. C2×(C2×D3)⋊Dic3C22semidirect
38. C2×(C2×D3)⋊Dic3C22semidirect
39. #63959C22semidirect
40. #63956C22semidirect
41. C2×Dic32C22semidirect
43. C2×#953D3semidirect
83. C2×#627C23semidirect
85. C2×#625C23semidirect
87. C2×D3×Dic3C23semidirect
93. #3724C23semidirect
94. #3724C23semidirect
95. Dic3⋊Dic3C23semidirect
96. Dic3⋊Dic3C23semidirect
97. (C2×D3)⋊Dic3C23semidirect
98. (C2×D3)⋊Dic3C23semidirect
99. Dic32C23semidirect
121. #953C2×D3semidirect
417. C2×C32#538semidirect
514. C32C2×#538semidirect
562. C2×C3#5593semidirect
591. C3C2×#5593semidirect
595. C2#10595508direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37572
C2×C3×#9532
C2×#639822
C2×#639802
#105955082
C2×#67⋊Dic32
C2×#639702
C2×#639692
C2×#639592
C2×#639562
C2×#55933