Finite Group Databasebeta

← C2×#10595208 #11902955

Subgroups — C2×#10595208 #11902955

Order 1152.

2987 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic
2C2×C3×#936C211yesmaximal, characteristic, complemented
3C2×C3×#935C211yesmaximal, characteristic, complemented
4C2×#63975C212yesmaximal, complemented
5C2×#63974C212yesmaximal, complemented
6C2×#63956C212yesmaximal, complemented
7C2×#63952C212yesmaximal, complemented
8#10595208C2116yesmaximal, direct product factor
9C2×#63888C212yesmaximal, complemented
10C2×#63836C212yesmaximal, complemented
11C2×#5679—31nomaximal
12C2×#5659—31nomaximal
13C24×C3⋊D3C2211yescharacteristic
14C22×C32×D4C2211yescharacteristic
15C22×#638C2212yes—
16C23×C3×Dic3C2211yescharacteristic, complemented
17C22×C3×Dic6C2211yescharacteristic, complemented
18C22×#624C2212yes—
19C22×#624C2212yes—
20C2×#3757C2211yescharacteristic
21#64146C2218yes—
22C2×#3752C2212yes—
23C2×C3×#217C2212yes—
24C2×C3×#217C2212yes—
25C2×C3×#217C2211yescharacteristic, complemented
26C2×C3×#217C2212yescomplemented
27C3×#936C2218yescomplemented
28C3×#935C2218yescomplemented
29C2×C3×Dic3⋊C4C2212yescomplemented
30C2×C3×C4×Dic3C2211yescharacteristic, complemented
31#63975C22116yescomplemented
32#63974C22116yescomplemented
33C2×#3724C2212yescomplemented
34C2×Dic3⋊Dic3C2212yescomplemented
35C2×Dic3⋊Dic3C2212yescomplemented
36C2×#3722C2212yes—
37C2×#3722C2212yes—
38#63956C22116yescomplemented
39C2×Dic32C2212yescomplemented
40#63952C22116yescomplemented
41#63888C22116yescomplemented
42#63836C22116yescomplemented
43C2×C3×#124—31no—
44C2×C3×#123—31no—
45C2×#946—32no—
46C2×#937—31no—
47C2×#937—31no—
48C2×#937—61no—
49C2×#936D311yescharacteristic, complemented
50C2×#935D311yescharacteristic, complemented
51C2×C4×#67—32no—
52#5679—316no—
53#5659—316no—
54C2×#896—32no—
55C2×#892—32no—
56C2×#883—32no—
57C2×#883—32no—
58C2×#67⋊C4—32no—
59C2×D3×C22⋊C4—32no—
60C2×D3×C22⋊C4—32no—
61C2×#879—32no—
62C2×#879—32no—
63C2×#872—32no—
64C24×C32C2311yescharacteristic
65C24×C32C2311yescharacteristic
66C23×C3⋊D3—28no—
67C23×C3⋊D3—42no—
68C23×C3⋊D3C2314yes—
69C23×C3⋊D3C2312yes—
70C2×C32×D4—42no—
71C2×C32×D4C2314yes—
72C22×C32×C4C2311yescharacteristic
73C2×#638—28no—
74C2×#638C2318yes—
75C22×C3⋊Dic3C2312yes—
76C22×C3×Dic3—42no—
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C22×C3×Dic3C2312yes—
81C22×C3×Dic3C2314yescomplemented
82C2×C3×Dic6—42no—
83C2×C3×Dic6C2314yescomplemented
84C2×#624—28no—
85C2×#624—44no—
86C2×#624C2318yes—
87C2×#624C2318yes—
88#3757C2314yes—
89#3752C2318yes—
90C3×#217C2318yes—
91C3×#217C2318yes—
92C3×#217C2314yescomplemented
93C3×#217C2318yescomplemented
94C3×Dic3⋊C4C2318yescomplemented
95C3×C4×Dic3C2314yescomplemented
96#3724C2318yescomplemented
97Dic3⋊Dic3C2318yescomplemented
98Dic3⋊Dic3C2318yescomplemented
99#3722C2318yes—
100#3722C2318yes—
101Dic32C2318yescomplemented
102C2×#551—91noSylow
103C24×D3—31no—
104C24×D3—31no—
105C24×D3—61no—
106C22×C3×Q8—31no—
107C22×C3×D4—21no—
108C22×C3×D4C2×D311yescharacteristic
109C22×C3×D4C2×D311yescharacteristic
110C23×C3×C4—31no—
111C22×#67—32no—
112C22×#67—32no—
113C22×#67—62no—
114C23×Dic3C2×D311yescharacteristic, complemented
115C22×C4×D3—32no—
116C22×C4×D3—32no—
117C22×C4×D3—32no—
118C22×C4×D3—32no—
119C22×Dic6C2×D311yescharacteristic, complemented
120C3×#124—38no—
121C3×#123—38no—
122C2×C3×C4⋊C4—32no—
123C2×C3×C22⋊C4—32no—
124C2×C3×C22⋊C4—32no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4—31no—
127C2×C3×C42—31no—
128C2×#217—31no—
129C2×#217—31no—
130C2×#217—61no—
131C2×#217C2×D312yes—
132C2×#217C2×D312yes—
133C2×#217C2×D311yescharacteristic, complemented
134C2×#217C2×D312yescomplemented
135#946—316no—
136#937—38no—
137#937—38no—
138#937—68no—
139#936C2×D318yescomplemented
140#935C2×D318yescomplemented
141C4×#67—316no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4—32no—
146C2×(C2×D3)⋊C4—32no—
147C2×(C2×D3)⋊C4—32no—
148C2×(C2×D3)⋊C4—62no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—32no—
153C2×Dic3⋊C4—32no—
154C2×Dic3⋊C4—32no—
155C2×Dic3⋊C4C2×D312yescomplemented
156C2×C4×Dic3—32no—
157C2×C4×Dic3—32no—
158C2×C4×Dic3C2×D311yescharacteristic, complemented
159#896—316no—
160#892—316no—
161#883—316no—
162#883—316no—
163#67⋊C4—316no—
164D3×C22⋊C4—316no—
165D3×C22⋊C4—316no—
166#879—316no—
167#879—316no—
168#872—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—216no—
179C22×C3⋊D3—44no—
180C22×C3⋊D3—416no—
181C22×C3⋊D3#4118yes—
182C22×C3⋊D3C2414yes—
183C32×D4—44no—
184C2×C32×C4—22no—
185C2×C32×C4C2412yes—
186#638—216no—
187C2×C3⋊Dic3—24no—
188C2×C3⋊Dic3C2414yes—
189C2×C3×Dic3—24no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—24no—
192C2×C3×Dic3—24no—
193C2×C3×Dic3—44no—
194C2×C3×Dic3C2414yes—
195C2×C3×Dic3C2414yes—
196C2×C3×Dic3C2414yes—
197C2×C3×Dic3C2414yes—
198C3×Dic6—44no—
199#624—216no—
200#624—48no—
201#551—916no—
202C2×#126—92no—
203C2×#124—31no—
204C2×#123—31no—
205C2×#123—92no—
206C2×C22⋊Q8—92no—
207C2×#120—91no—
208C2×C4×D4—92no—
209C2×#117—92no—
210C22×C22⋊C4—92no—
211C24×C3—21no—
212C24×C3—21no—
213C24×C3C22×D311yescharacteristic
214C24×C3C22×D311yescharacteristic
215C24×C3C22×D311yescharacteristic
216C24×C3C22×D311yescharacteristic
217C23×D3—32no—
218C23×D3—32no—
219C23×D3—34no—
220C23×D3—34no—
221C23×D3—62no—
222C23×D3—64no—
223C23×D3—68no—
224C23×D3—68no—
225C23×D3—128no—
226C23×D3—122no—
227C23×D3—122no—
228C23×D3—124no—
229C2×C3×Q8—34no—
230C2×C3×Q8—122no—
231C2×C3×D4—24no—
232C2×C3×D4—42no—
233C2×C3×D4—42no—
234C2×C3×D4—44no—
235C2×C3×D4C22×D314yes—
236C2×C3×D4C22×D314yes—
237C22×C3×C4—21no—
238C22×C3×C4—32no—
239C22×C3×C4—32no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—34no—
243C22×C3×C4—122no—
244C22×C3×C4C22×D311yescharacteristic
245C22×C3×C4C22×D311yescharacteristic
246C2×#67—38no—
247C2×#67—38no—
248C2×#67—68no—
249C2×#67—68no—
250C2×#67—68no—
251C2×#67—128no—
252C22×Dic3—32no—
253C22×Dic3—32no—
254C22×Dic3—42no—
255C22×Dic3—62no—
256C22×Dic3C22×D312yes—
257C22×Dic3C22×D312yes—
258C22×Dic3C22×D312yes—
259C22×Dic3C22×D312yes—
260C22×Dic3C22×D314yescomplemented
261C2×C4×D3—38no—
262C2×C4×D3—38no—
263C2×C4×D3—38no—
264C2×C4×D3—38no—
265C2×C4×D3—68no—
266C2×C4×D3—68no—
267C2×C4×D3—124no—
268C2×C4×D3—124no—
269C2×Dic6—42no—
270C2×Dic6C22×D314yescomplemented
271C3×C4⋊C4—38no—
272C3×C22⋊C4—38no—
273C3×C22⋊C4—38no—
274C3×C22⋊C4—38no—
275C3×C22⋊C4—34no—
276C3×C42—34no—
277#217—34no—
278#217—34no—
279#217—64no—
280#217C22×D318yes—
281#217C22×D318yes—
282#217C22×D314yescomplemented
283#217C22×D318yescomplemented
284(C2×D3)⋊C4—38no—
285(C2×D3)⋊C4—38no—
286(C2×D3)⋊C4—38no—
287(C2×D3)⋊C4—38no—
288(C2×D3)⋊C4—38no—
289(C2×D3)⋊C4—38no—
290(C2×D3)⋊C4—68no—
291C4⋊Dic3—38no—
292C4⋊Dic3—38no—
293Dic3⋊C4—38no—
294Dic3⋊C4—38no—
295Dic3⋊C4—38no—
296Dic3⋊C4—38no—
297Dic3⋊C4C22×D318yescomplemented
298C4×Dic3—38no—
299C4×Dic3—38no—
300C4×Dic3C22×D314yescomplemented
301C22×C32—22no—
302C22×C32—24no—
303C22×C32—24no—
304C22×C32—22no—
305C22×C32—44no—
306C22×C32—44no—
307C22×C32C2×#4114yes—
308C22×C32H(5,𝔽2)12yes—
309C22×C32C2511yescharacteristic
310C2×C3⋊D3—216no—
311C2×C3⋊D3—24no—
312C2×C3⋊D3—24no—
313C2×C3⋊D3—416no—
314C2×C3⋊D3C2×#4118yes—
315C32×C4—22no—
316C3⋊Dic3—24no—
317C3×Dic3—24no—
318C3×Dic3—24no—
319C3×Dic3—24no—
320C3×Dic3—24no—
321C25—91no—
322C22×Q8—31no—
323C22×D4—92no—
324C22×D4D3211yescharacteristic
325C23×C4—31no—
326C23×C4—92no—
327C23×C4—92no—
328#126—916no—
329#124—38no—
330#123—38no—
331#123—916no—
332C22⋊Q8—916no—
333#120—98no—
334C4×D4—916no—
335#117—916no—
336C2×C4⋊C4—32no—
337C2×C4⋊C4—92no—
338C2×C4⋊C4—92no—
339C2×C4⋊C4—92no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—32no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—916no—
345C2×C22⋊C4—92no—
346C2×C22⋊C4—92no—
347C2×C22⋊C4—91no—
348C2×C22⋊C4—92no—
349C2×C42—31no—
350C2×C42—92no—
351C23×C3—24no—
352C23×C3—22no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—22no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—24no—
359C23×C3—24no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—21no—
363C23×C3—44no—
364C23×C3—44no—
365C23×C3—42no—
366C23×C3C23×D312yes—
367C23×C3C23×D312yes—
368C23×C3C23×D312yes—
369C23×C3C23×D312yes—
370C23×C3C23×D311yescharacteristic
371C23×C3C23×D311yescharacteristic
372C22×D3—38no—
373C22×D3—38no—
374C22×D3—34no—
375C22×D3—34no—
376C22×D3—68no—
377C22×D3—64no—
378C22×D3—616no—
379C22×D3—616no—
380C22×D3—64no—
381C22×D3—64no—
382C22×D3—64no—
383C22×D3—64no—
384C22×D3—1216no—
385C22×D3—124no—
386C22×D3—124no—
387C22×D3—124no—
388C22×D3—124no—
389C22×D3—1216no—
390C22×D3—1216no—
391C22×D3—128no—
392C22×D3—1232no—
393C3×Q8—124no—
394C3×D4—44no—
395C3×D4—44no—
396C3×D4—48no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—34no—
401C2×C3×C4—34no—
402C2×C3×C4—34no—
403C2×C3×C4—34no—
404C2×C3×C4—42no—
405C2×C3×C4—64no—
406C2×C3×C4—64no—
407C2×C3×C4—64no—
408C2×C3×C4—64no—
409C2×C3×C4—124no—
410C2×C3×C4C23×D312yes—
411C2×C3×C4C23×D312yes—
412#67—616no—
413#67—616no—
414#67—1216no—
415C2×Dic3—24no—
416C2×Dic3—24no—
417C2×Dic3—24no—
418C2×Dic3—24no—
419C2×Dic3—34no—
420C2×Dic3—34no—
421C2×Dic3—44no—
422C2×Dic3—64no—
423C2×Dic3—64no—
424C2×Dic3—64no—
425C2×Dic3—124no—
426C2×Dic3C23×D314yes—
427C2×Dic3C23×D314yes—
428C2×Dic3C23×D314yes—
429C2×Dic3C23×D314yes—
430C4×D3—616no—
431C4×D3—616no—
432C4×D3—128no—
433C4×D3—128no—
434Dic6—44no—
435C2×C32—42no—
436C2×C32—42no—
437C2×C32#55114yescomplemented
438C2×C32C22×#4112yes—
439C2×C32C2×H(5,𝔽2)11yescharacteristic
440C3⋊D3—28no—
441C24—92no—
442C24—94no—
443C24—188no—
444C24—362no—
445C24C2×D3211yescharacteristic
446C24C2×D3211yescharacteristic
447C2×Q8—34no—
448C2×Q8—122no—
449C2×D4—42no—
450C2×D4—98no—
451C2×D4—188no—
452C2×D4C2×D3214yes—
453C22×C4—32no—
454C22×C4—32no—
455C22×C4—32no—
456C22×C4—32no—
457C22×C4—34no—
458C22×C4—98no—
459C22×C4—98no—
460C22×C4—92no—
461C22×C4—122no—
462C22×C4—188no—
463C22×C4—364no—
464C22×C4C2×D3211yescharacteristic
465C4⋊C4—38no—
466C4⋊C4—98no—
467C4⋊C4—98no—
468C4⋊C4—98no—
469C22⋊C4—38no—
470C22⋊C4—38no—
471C22⋊C4—38no—
472C22⋊C4—34no—
473C22⋊C4—98no—
474C22⋊C4—98no—
475C22⋊C4—94no—
476C22⋊C4—98no—
477C42—34no—
478C42—98no—
479C22×C3—24no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—24no—
485C22×C3—24no—
486C22×C3—24no—
487C22×C3—24no—
488C22×C3—24no—
489C22×C3—22no—
490C22×C3—21no—
491C22×C3—44no—
492C22×C3—44no—
493C22×C3—42no—
494C22×C3—48no—
495C22×C3—44no—
496C22×C3—44no—
497C22×C3—44no—
498C22×C3—44no—
499C22×C3—84no—
500C22×C3#100412yes—
501C22×C3#100412yes—
502C22×C3D3×#4114yes—
503C22×C3D3×#4114yes—
504C22×C3C24×D311yescharacteristic
505C22×C3C24×D311yescharacteristic
506C2×D3—38no—
507C2×D3—38no—
508C2×D3—68no—
509C2×D3—616no—
510C2×D3—616no—
511C2×D3—64no—
512C2×D3—64no—
513C2×D3—64no—
514C2×D3—64no—
515C2×D3—124no—
516C2×D3—124no—
517C2×D3—1216no—
518C2×D3—1216no—
519C2×D3—1216no—
520C2×D3—1232no—
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—42no—
524C3×C4—64no—
525C3×C4—64no—
526C3×C4—64no—
527C3×C4—64no—
528Dic3—24no—
529Dic3—24no—
530Dic3—24no—
531Dic3—24no—
532Dic3—64no—
533Dic3—64no—
534Dic3—124no—
535C32C2×#55111yescharacteristic, complemented, Sylow
536C23—24no—
537C23—24no—
538C23—22no—
539C23—22no—
540C23—98no—
541C23—94no—
542C23—1816no—
543C23—184no—
544C23—184no—
545C23—364no—
546C23—3616no—
547C23C22×D3212yes—
548C23C22×D3212yes—
549C23C22×D3211yescharacteristic
550Q8—124no—
551D4—44no—
552D4—1816no—
553C2×C4—22no—
554C2×C4—34no—
555C2×C4—34no—
556C2×C4—34no—
557C2×C4—34no—
558C2×C4—64no—
559C2×C4—64no—
560C2×C4—64no—
561C2×C4—64no—
562C2×C4—94no—
563C2×C4—124no—
564C2×C4—1816no—
565C2×C4—184no—
566C2×C4—368no—
567C2×C4C22×D3212yes—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—24no—
571C2×C3—44no—
572C2×C3—42no—
573C2×C3—42no—
574C2×C3—42no—
575C2×C3—42no—
576C2×C3—82no—
577C2×C3#565914yescomplemented
578C2×C3#567914yescomplemented
579C2×C3C2×#100411yescharacteristic
580C2×C3C2×#100411yescharacteristic
581C2×C3C2×D3×#4112yes—
582C2×C3C2×D3×#4112yes—
583D3—68no—
584D3—68no—
585D3—128no—
586C22—24no—
587C22—24no—
588C22—22no—
589C22—22no—
590C22—44no—
591C22—44no—
592C22—98no—
593C22—184no—
594C22—184no—
595C22—1816no—
596C22—3616no—
597C22#6431214yes—
598C22#6433012yes—
599C22C23×D3211yescharacteristic
600C4—22no—
601C4—64no—
602C4—64no—
603C4—64no—
604C4—64no—
605C4—184no—
606C3—21no—
607C3C2×#565911yescharacteristic, complemented
608C3C2×#567911yescharacteristic, complemented
609C2—42no—
610C2—42no—
611C2—188no—
612C2#1059520814yesdirect product factor
613C2C2×#6431212yes—
614C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
prime radicalC2×#64146C2
hypercenterC22×D4D32
hypocenterC32C2×#551
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#936C2semidirect
3. C2×C3×#935C2semidirect
4. C2×#63975C2semidirect
5. C2×#63974C2semidirect
6. C2×#63956C2semidirect
7. C2×#63952C2semidirect
8. #10595208C2direct (N × H)
9. C2×#63888C2semidirect
10. C2×#63836C2semidirect
16. C23×C3×Dic3C22semidirect
17. C22×C3×Dic6C22semidirect
25. C2×C3×#217C22semidirect
26. C2×C3×#217C22semidirect
27. C3×#936C22semidirect
28. C3×#935C22semidirect
29. C2×C3×Dic3⋊C4C22semidirect
30. C2×C3×C4×Dic3C22semidirect
31. #63975C22semidirect
32. #63974C22semidirect
33. C2×#3724C22semidirect
34. C2×Dic3⋊Dic3C22semidirect
35. C2×Dic3⋊Dic3C22semidirect
38. #63956C22semidirect
39. C2×Dic32C22semidirect
40. #63952C22semidirect
41. #63888C22semidirect
42. #63836C22semidirect
49. C2×#936D3semidirect
50. C2×#935D3semidirect
81. C22×C3×Dic3C23semidirect
83. C2×C3×Dic6C23semidirect
92. C3×#217C23semidirect
93. C3×#217C23semidirect
94. C3×Dic3⋊C4C23semidirect
95. C3×C4×Dic3C23semidirect
96. #3724C23semidirect
97. Dic3⋊Dic3C23semidirect
98. Dic3⋊Dic3C23semidirect
101. Dic32C23semidirect
114. C23×Dic3C2×D3semidirect
119. C22×Dic6C2×D3semidirect
133. C2×#217C2×D3semidirect
134. C2×#217C2×D3semidirect
139. #936C2×D3semidirect
140. #935C2×D3semidirect
155. C2×Dic3⋊C4C2×D3semidirect
158. C2×C4×Dic3C2×D3semidirect
260. C22×Dic3C22×D3semidirect
270. C2×Dic6C22×D3semidirect
282. #217C22×D3semidirect
283. #217C22×D3semidirect
297. Dic3⋊C4C22×D3semidirect
300. C4×Dic3C22×D3semidirect
437. C2×C32#551semidirect
535. C32C2×#551semidirect
577. C2×C3#5659semidirect
578. C2×C3#5679semidirect
607. C3C2×#5659semidirect
608. C3C2×#5679semidirect
612. C2#10595208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641462
C2×C3×#9362
C2×C3×#9352
C2×#639752
C2×#639742
C2×#639562
C2×#639522
#105952082
C2×#638882
C2×#638362
C2×#56793
C2×#56593