Finite Group Databasebeta

← C2×#10594006 #11900460

Subgroups — C2×#10594006 #11900460

Order 1152.

3925 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
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×#64081C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C212yesmaximal, complemented
5C2×#63922C212yesmaximal, complemented
6C2×C4×#625C212yesmaximal, complemented
7C2×#63899C212yesmaximal, complemented
8C2×#63885C212yesmaximal, complemented
9C2×#63854C212yesmaximal, complemented
10#10594006C2116yesmaximal, direct product factor
11C2×#5547—32nomaximal
12C23×D32C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×C3×D12C2212yes—
15C22×C3×C4×D3C2212yes—
16C22×C3×C4×D3C2212yescomplemented
17C22×#627C2211yescharacteristic, complemented
18C22×#626C2212yes—
19C22×#625C2212yes—
20C22×#625C2211yescharacteristic, complemented
21C22×#624C2211yescharacteristic
22C22×D3×Dic3C2212yes—
23C2×C4×D32—28no—
24C2×C4×D32C2218yescomplemented
25C2×#3798—28no—
26C2×#3798C2218yescomplemented
27C2×C32×C42C2211yescharacteristic, complemented
28C2×#3752C2212yes—
29C2×#3750C2212yescomplemented
30C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
31#64081C2218yescomplemented
32C2×C3×(C2×D3)⋊C4C2212yes—
33C2×C3×(C2×D3)⋊C4C2212yescomplemented
34C2×C3×C4⋊Dic3C2212yescomplemented
35C3×C4×D12C22116yescomplemented
36C2×#3724C2212yescomplemented
37C2×(C2×D3)⋊Dic3C2212yes—
38C2×(C2×D3)⋊Dic3C2212yescomplemented
39#63922C22116yescomplemented
40C4×#625C22116yescomplemented
41#63899C22116yescomplemented
42#63885C22116yescomplemented
43#63854C22116yescomplemented
44C22×#235—32no—
45C23×C4×D3—32no—
46C2×C3×C4×D4—32no—
47C2×#939—32no—
48C2×#937—32no—
49C2×C4×#67—32no—
50C2×C4×#67—32no—
51#5547—332no—
52C2×#896—32no—
53C2×#894—32no—
54C2×#884—32no—
55C2×#883—32no—
56C2×#882—32no—
57C2×#878—32no—
58C2×C4×D12D312yescomplemented
59C2×#872—32no—
60C2×#872—61no—
61C23×C3⋊D3C2311yescharacteristic
62C23×C3×D3C2312yes—
63C23×C3×D3C2312yes—
64C22×D32—24no—
65C22×D32—28no—
66C22×D32C2314yes—
67C22×C32×C4C2312yes—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2312yes—
70C22×C3⋊Dic3C2311yescharacteristic
71C2×C4×C3⋊D3D418yescomplemented
72C2×C4×C3⋊D3C2314yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×C3×D12—28no—
76C2×C3×D12C2318yes—
77C2×C3×C4×D3—28no—
78C2×C3×C4×D3—28no—
79C2×C3×C4×D3C2318yes—
80C2×C3×C4×D3C2318yescomplemented
81C2×#627—24no—
82C2×#627C2314yescomplemented
83C2×#626—28no—
84C2×#626C2318yes—
85C2×#625—28no—
86C2×#625—24no—
87C2×#625C2318yes—
88C2×#625C2314yescomplemented
89C2×#624—24no—
90C2×#624C2314yes—
91C2×D3×Dic3—28no—
92C2×D3×Dic3C2318yes—
93C4×D32—232no—
94#3798—232no—
95C32×C42C2314yescomplemented
96#3752C2318yes—
97#3750C2318yescomplemented
98C4×C3⋊Dic3C2314yescomplemented
99C3×(C2×D3)⋊C4C2318yes—
100C3×(C2×D3)⋊C4C2318yescomplemented
101C3×C4⋊Dic3C2318yescomplemented
102#3724C2318yescomplemented
103(C2×D3)⋊Dic3C2318yes—
104(C2×D3)⋊Dic3C2318yescomplemented
105C2×#525—91noSylow
106C24×D3—32no—
107C22×C3×D4—32no—
108C23×C3×C4—32no—
109C23×C3×C4—32no—
110C22×#67—32no—
111C22×#67—32no—
112C22×#67—32no—
113C22×#67—32no—
114C23×Dic3—32no—
115C2×#235—316no—
116C2×#235—616no—
117C22×D12—32no—
118C22×D12C2×D312yes—
119C22×C4×D3—32no—
120C22×C4×D3—32no—
121C22×C4×D3—32no—
122C22×C4×D3—316no—
123C22×C4×D3—61no—
124C22×C4×D3—616no—
125C22×C4×D3C2×D312yes—
126C22×C4×D3C2×D312yescomplemented
127C22×Dic6—32no—
128C3×C4×D4—316no—
129C2×C3×C4⋊C4—32no—
130C2×C3×C22⋊C4—32no—
131C2×C3×C22⋊C4—32no—
132C2×C3×C42—21no—
133C2×C3×C42C2×D312yescomplemented
134C2×#217—32no—
135C2×#217—32no—
136#939—316no—
137#937—316no—
138C4×#67—316no—
139C4×#67—316no—
140C2×(C2×D3)⋊C4—32no—
141C2×(C2×D3)⋊C4—32no—
142C2×(C2×D3)⋊C4—32no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—62no—
145C2×(C2×D3)⋊C4C2×D312yes—
146C2×(C2×D3)⋊C4C2×D312yescomplemented
147C2×C4⋊Dic3C2×D312yescomplemented
148C2×Dic3⋊C4—32no—
149C2×Dic3⋊C4—32no—
150C2×Dic3⋊C4—32no—
151C2×Dic3⋊C4—32no—
152C2×Dic3⋊C4—62no—
153C2×C4×Dic3—32no—
154C2×C4×Dic3—61no—
155#896—316no—
156#894—316no—
157#884—316no—
158#883—316no—
159#882—316no—
160#878—316no—
161C4×D12C2×D3116yescomplemented
162#872—316no—
163#872—68no—
164C23×C32C2411yescharacteristic
165C22×C3⋊D3—24no—
166C22×C3⋊D3C2×D414yes—
167C22×C3⋊D3C2412yes—
168C22×C3×D3—24no—
169C22×C3×D3—24no—
170C22×C3×D3—24no—
171C22×C3×D3—24no—
172C22×C3×D3—24no—
173C22×C3×D3#4118yescomplemented
174C22×C3×D3C2414yes—
175C22×C3×D3C2414yes—
176C2×D32—232no—
177C2×D32—28no—
178C2×D32—216no—
179C2×C32×C4—24no—
180C2×C32×C4C2×D414yes—
181C2×C32×C4C2414yes—
182C2×C32×C4C2412yes—
183C2×C3⋊Dic3—24no—
184C2×C3⋊Dic3C2×D414yes—
185C2×C3⋊Dic3C2414yes—
186C2×C3⋊Dic3C2412yes—
187C4×C3⋊D3C2×D4116yescomplemented
188C2×C3×Dic3—24no—
189C2×C3×Dic3—24no—
190C2×C3×Dic3C2414yes—
191C2×C3×Dic3C2414yes—
192C3×D12—216no—
193C3×C4×D3—216no—
194C3×C4×D3—216no—
195#627—28no—
196#626—216no—
197#625—216no—
198#625—28no—
199#624—28no—
200D3×Dic3—216no—
201C22×#41—91no—
202C24×C4—91no—
203#525—916no—
204C2×#123—92no—
205C2×C22⋊Q8—92no—
206C2×#121—92no—
207C2×#120—92no—
208C2×C4×D4—32no—
209C2×C4×D4—92no—
210C2×#117—91no—
211C24×C3—32no—
212C24×C3—32no—
213C23×D3—32no—
214C23×D3—38no—
215C23×D3—61no—
216C23×D3—68no—
217C23×D3—68no—
218C23×D3—68no—
219C23×D3C22×D312yes—
220C23×D3C22×D312yes—
221C2×C3×D4—38no—
222C2×C3×D4—68no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—32no—
226C22×C3×C4—32no—
227C22×C3×C4—38no—
228C22×C3×C4—38no—
229C22×C3×C4—68no—
230C22×C3×C4—68no—
231C22×C3×C4C22×D312yes—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D312yes—
234C2×#67—38no—
235C2×#67—38no—
236C2×#67—38no—
237C2×#67—38no—
238C2×#67—68no—
239C2×#67—68no—
240C2×#67—68no—
241C2×#67—68no—
242C22×Dic3—32no—
243C22×Dic3—32no—
244C22×Dic3—32no—
245C22×Dic3—38no—
246C22×Dic3—61no—
247C22×Dic3—62no—
248C22×Dic3—68no—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251#235—664no—
252C2×D12—28no—
253C2×D12—38no—
254C2×D12—68no—
255C2×D12C22×D318yes—
256C2×C4×D3—28no—
257C2×C4×D3—28no—
258C2×C4×D3—316no—
259C2×C4×D3—38no—
260C2×C4×D3—38no—
261C2×C4×D3—38no—
262C2×C4×D3—64no—
263C2×C4×D3—68no—
264C2×C4×D3—664no—
265C2×C4×D3—68no—
266C2×C4×D3—68no—
267C2×C4×D3C22×D318yes—
268C2×C4×D3C22×D318yescomplemented
269C2×Dic6—38no—
270C2×Dic6—68no—
271C3×C4⋊C4—38no—
272C3×C22⋊C4—38no—
273C3×C22⋊C4—38no—
274C3×C42—24no—
275C3×C42C22×D318yescomplemented
276#217—38no—
277#217—38no—
278(C2×D3)⋊C4—38no—
279(C2×D3)⋊C4—38no—
280(C2×D3)⋊C4—38no—
281(C2×D3)⋊C4—38no—
282(C2×D3)⋊C4—68no—
283(C2×D3)⋊C4C22×D318yes—
284(C2×D3)⋊C4C22×D318yescomplemented
285C4⋊Dic3C22×D318yescomplemented
286Dic3⋊C4—38no—
287Dic3⋊C4—38no—
288Dic3⋊C4—38no—
289Dic3⋊C4—38no—
290Dic3⋊C4—68no—
291C4×Dic3—38no—
292C4×Dic3—64no—
293C22×C32C22×D412yes—
294C22×C32C2×#4114yes—
295C22×C32C2511yescharacteristic
296C2×C3⋊D3—28no—
297C2×C3⋊D3—24no—
298C2×C3⋊D3C22×D414yes—
299C2×C3×D3—216no—
300C2×C3×D3—24no—
301C2×C3×D3—24no—
302C2×C3×D3—24no—
303C2×C3×D3—24no—
304C2×C3×D3—24no—
305C2×C3×D3—48no—
306C2×C3×D3C2×#4118yescomplemented
307D32—232no—
308C32×C4—24no—
309C32×C4C22×D414yes—
310C3⋊Dic3—24no—
311C3⋊Dic3C22×D414yes—
312C3×Dic3—24no—
313C3×Dic3—24no—
314C25—91no—
315C2×#41—98no—
316C2×#41—188no—
317C22×Q8—91no—
318C22×D4—32no—
319C22×D4—92no—
320C22×D4—92no—
321C22×D4—91no—
322C23×C4—32no—
323C23×C4—32no—
324C23×C4—91no—
325C23×C4—98no—
326C23×C4—92no—
327C23×C4—91no—
328C23×C4—188no—
329#123—916no—
330C22⋊Q8—916no—
331#121—916no—
332#120—916no—
333C4×D4—316no—
334C4×D4—916no—
335#117—98no—
336C2×C4⋊C4—32no—
337C2×C4⋊C4—92no—
338C2×C4⋊C4—92no—
339C2×C22⋊C4—32no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—92no—
342C2×C22⋊C4—92no—
343C2×C22⋊C4—92no—
344C2×C42—91no—
345C2×C42D3211yescharacteristic, complemented
346C23×C3—21no—
347C23×C3—38no—
348C23×C3—34no—
349C23×C3—34no—
350C23×C3—64no—
351C23×C3—64no—
352C23×C3—64no—
353C23×C3—64no—
354C23×C3—64no—
355C23×C3C23×D312yes—
356C22×D3—24no—
357C22×D3—24no—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3—38no—
362C22×D3—34no—
363C22×D3—64no—
364C22×D3—62no—
365C22×D3—616no—
366C22×D3—616no—
367C22×D3—664no—
368C22×D3—64no—
369C22×D3—64no—
370C22×D3—616no—
371C22×D3—124no—
372C22×D3#23518yescomplemented
373C22×D3C23×D314yes—
374C22×D3C23×D314yes—
375C3×D4—616no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—22no—
379C2×C3×C4—24no—
380C2×C3×C4—24no—
381C2×C3×C4—34no—
382C2×C3×C4—34no—
383C2×C3×C4—44no—
384C2×C3×C4—64no—
385C2×C3×C4—64no—
386C2×C3×C4—616no—
387C2×C3×C4—616no—
388C2×C3×C4D3×D418yes—
389C2×C3×C4C23×D314yes—
390C2×C3×C4C23×D314yes—
391C2×C3×C4C23×D314yes—
392#67—616no—
393#67—616no—
394#67—616no—
395#67—616no—
396C2×Dic3—24no—
397C2×Dic3—24no—
398C2×Dic3—38no—
399C2×Dic3—34no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—64no—
403C2×Dic3—62no—
404C2×Dic3—64no—
405C2×Dic3—616no—
406C2×Dic3—64no—
407C2×Dic3—64no—
408C2×Dic3—124no—
409C2×Dic3C23×D314yes—
410C2×Dic3C23×D314yes—
411D12—216no—
412D12—616no—
413C4×D3—216no—
414C4×D3—216no—
415C4×D3—332no—
416C4×D3—616no—
417C4×D3—616no—
418C4×D3—616no—
419Dic6—616no—
420C2×C32#52514yescomplemented
421C2×C32C23×D411yescharacteristic
422C2×C32C22×#4112yes—
423C3⋊D3—24no—
424C3×D3—28no—
425C3×D3—44no—
426C24—32no—
427C24—32no—
428C24—94no—
429C24—91no—
430C24—188no—
431C24—184no—
432#41—1832no—
433C2×Q8—94no—
434C2×Q8—184no—
435C2×D4—38no—
436C2×D4—68no—
437C2×D4—98no—
438C2×D4—98no—
439C2×D4—94no—
440C2×D4—188no—
441C2×D4—184no—
442C2×D4—188no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—38no—
446C22×C4—38no—
447C22×C4—68no—
448C22×C4—68no—
449C22×C4—94no—
450C22×C4—98no—
451C22×C4—91no—
452C22×C4—94no—
453C22×C4—98no—
454C22×C4—92no—
455C22×C4—1832no—
456C22×C4—184no—
457C22×C4—188no—
458C22×C4C2×D3212yes—
459C22×C4C2×D3211yescharacteristic
460C4⋊C4—38no—
461C4⋊C4—98no—
462C4⋊C4—98no—
463C22⋊C4—38no—
464C22⋊C4—38no—
465C22⋊C4—98no—
466C22⋊C4—98no—
467C22⋊C4—98no—
468C42—94no—
469C42C2×D3214yescomplemented
470C22×C3—22no—
471C22×C3—24no—
472C22×C3—21no—
473C22×C3—38no—
474C22×C3—64no—
475C22×C3—64no—
476C22×C3—616no—
477C22×C3—64no—
478C22×C3—64no—
479C22×C3—64no—
480C22×C3—128no—
481C22×C3C2×#23514yes—
482C22×C3C2×D3×D414yes—
483C22×C3D3×#4114yes—
484C22×C3C24×D312yes—
485C2×D3—24no—
486C2×D3—24no—
487C2×D3—216no—
488C2×D3—24no—
489C2×D3—24no—
490C2×D3—24no—
491C2×D3—38no—
492C2×D3—48no—
493C2×D3—64no—
494C2×D3—664no—
495C2×D3—64no—
496C2×D3—64no—
497C2×D3—616no—
498C2×D3—124no—
499C2×D3—128no—
500C2×D3C2×#23518yescomplemented
501C3×C4—24no—
502C3×C4—24no—
503C3×C4—24no—
504C3×C4—44no—
505C3×C4—64no—
506C3×C4—64no—
507C3×C4C2×D3×D418yes—
508Dic3—24no—
509Dic3—24no—
510Dic3—38no—
511Dic3—64no—
512Dic3—64no—
513Dic3—64no—
514Dic3—124no—
515C32C2×#52511yescharacteristic, complemented, Sylow
516C23—38no—
517C23—34no—
518C23—34no—
519C23—64no—
520C23—64no—
521C23—64no—
522C23—64no—
523C23—64no—
524C23—94no—
525C23—92no—
526C23—1816no—
527C23—188no—
528C23—1832no—
529C23—184no—
530C23C22×D3211yescharacteristic
531Q8—188no—
532D4—616no—
533D4—1816no—
534D4—188no—
535D4—1816no—
536C2×C4—24no—
537C2×C4—34no—
538C2×C4—34no—
539C2×C4—64no—
540C2×C4—64no—
541C2×C4—616no—
542C2×C4—616no—
543C2×C4—94no—
544C2×C4—92no—
545C2×C4—916no—
546C2×C4—94no—
547C2×C4—188no—
548C2×C4—1816no—
549C2×C4—184no—
550C2×C4#380214yes—
551C2×C4C22×D3214yes—
552C2×C4C22×D3212yes—
553C2×C3—21no—
554C2×C3—22no—
555C2×C3—24no—
556C2×C3—68no—
557C2×C3—124no—
558C2×C3#554718yescomplemented
559C2×C3C22×#23512yes—
560C2×C3C22×D3×D412yes—
561C2×C3C2×D3×#4112yes—
562D3—28no—
563D3—44no—
564D3—68no—
565D3—124no—
566C22—38no—
567C22—64no—
568C22—64no—
569C22—616no—
570C22—64no—
571C22—64no—
572C22—64no—
573C22—94no—
574C22—128no—
575C22—1832no—
576C22—184no—
577C22—188no—
578C22C2×#380212yes—
579C22D3×#23514yes—
580C22C23×D3211yescharacteristic
581C4—24no—
582C4—64no—
583C4—64no—
584C4—94no—
585C4—184no—
586C4C2×#380214yes—
587C3—21no—
588C3C2×#554712yescomplemented
589C2—68no—
590C2—124no—
591C2—184no—
592C2#1059400614yesdirect product factor
593C2C22×#380211yescharacteristic
594C2C2×D3×#23512yes—
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
2. C22×#3798C2semidirect
3. C2×#64081C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C2×#63922C2semidirect
6. C2×C4×#625C2semidirect
7. C2×#63899C2semidirect
8. C2×#63885C2semidirect
9. C2×#63854C2semidirect
10. #10594006C2direct (N × H)
16. C22×C3×C4×D3C22semidirect
17. C22×#627C22semidirect
20. C22×#625C22semidirect
24. C2×C4×D32C22semidirect
26. C2×#3798C22semidirect
27. C2×C32×C42C22semidirect
29. C2×#3750C22semidirect
30. C2×C4×C3⋊Dic3C22semidirect
31. #64081C22semidirect
33. C2×C3×(C2×D3)⋊C4C22semidirect
34. C2×C3×C4⋊Dic3C22semidirect
35. C3×C4×D12C22semidirect
36. C2×#3724C22semidirect
38. C2×(C2×D3)⋊Dic3C22semidirect
39. #63922C22semidirect
40. C4×#625C22semidirect
41. #63899C22semidirect
42. #63885C22semidirect
43. #63854C22semidirect
58. C2×C4×D12D3semidirect
71. C2×C4×C3⋊D3D4semidirect
80. C2×C3×C4×D3C23semidirect
82. C2×#627C23semidirect
88. C2×#625C23semidirect
95. C32×C42C23semidirect
97. #3750C23semidirect
98. C4×C3⋊Dic3C23semidirect
100. C3×(C2×D3)⋊C4C23semidirect
101. C3×C4⋊Dic3C23semidirect
102. #3724C23semidirect
104. (C2×D3)⋊Dic3C23semidirect
126. C22×C4×D3C2×D3semidirect
133. C2×C3×C42C2×D3semidirect
146. C2×(C2×D3)⋊C4C2×D3semidirect
147. C2×C4⋊Dic3C2×D3semidirect
161. C4×D12C2×D3semidirect
173. C22×C3×D3#41semidirect
187. C4×C3⋊D3C2×D4semidirect
268. C2×C4×D3C22×D3semidirect
275. C3×C42C22×D3semidirect
284. (C2×D3)⋊C4C22×D3semidirect
285. C4⋊Dic3C22×D3semidirect
306. C2×C3×D3C2×#41semidirect
345. C2×C42D32semidirect
372. C22×D3#235semidirect
420. C2×C32#525semidirect
469. C42C2×D32semidirect
500. C2×D3C2×#235semidirect
515. C32C2×#525semidirect
558. C2×C3#5547semidirect
588. C3C2×#5547semidirect
592. C2#10594006direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D322
C22×#37982
C2×#640812
C2×C3×C4×D122
C2×#639222
C2×C4×#6252
C2×#638992
C2×#638852
C2×#638542
#105940062
C2×#55473