Finite Group Databasebeta

← C2×#10591184 #11863787

Subgroups — C2×#10591184 #11863787

Order 1152.

1965 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic
2C2×C3×#924C211yesmaximal, characteristic, complemented
3C22×#3719C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×C3×#830C211yesmaximal, characteristic, complemented
6#10591184C218yesmaximal, direct product factor
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63564C211yesmaximal, characteristic, complemented
9C2×#5047—31nomaximal
10C2×#4733—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C2×#3828—22no—
14C2×#3828—24no—
15C2×#3828—24no—
16C2×#3828C2214yes—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4×C3⋊D3—21no—
19C22×#634C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×C3×#217—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C3×#924—22no—
24C3×#924C2214yescomplemented
25C2×C3×Dic3⋊C4—21no—
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3719—24no—
29C2×#3719C2214yescomplemented
30C2×#3717—24no—
31C2×#3717C2214yescomplemented
32C3×#830C2214yescomplemented
33#63567C2214yescomplemented
34#63564C2214yescomplemented
35C22×#235—31no—
36C22×#235—31no—
37C22×#235—61no—
38C2×C3×C22⋊Q8—31no—
39C22×#216—31no—
40C22×#215—31no—
41C2×#924D311yescharacteristic, complemented
42C22×Dic12—31no—
43C22×#204—31no—
44C2×C3×C22⋊C8—31no—
45C2×#830D311yescharacteristic, complemented
46C2×#821—31no—
47C2×#816—31no—
48#5047—38no—
49C2×#810—31no—
50C2×#809—31no—
51#4733—38no—
52C24×C32D411yescharacteristic
53C23×C3⋊D3—21no—
54C22×C32×C4—22no—
55C22×C32×C4—22no—
56C22×C32×C4D411yescharacteristic
57C22×C32×C4D412yes—
58C22×C32×C4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×#638—28no—
61C2×#638—24no—
62C22×C3⋊Dic3—21no—
63#3828—216no—
64#3828—28no—
65#3828—28no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—22no—
68C2×C4⋊(C3⋊D3)D414yes—
69C2×C4⋊(C3⋊D3)C2312yes—
70C2×C4×C3⋊D3—28no—
71C2×C4×C3⋊D3—24no—
72C2×#634—21no—
73C2×#634—22no—
74C2×#634D414yes—
75C2×#634C2312yes—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2312yes—
82C3×#217—24no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C3×Dic3⋊C4—24no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89C2×C3×C3⋊C8C2312yes—
90#3719—28no—
91#3717—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C23×C3×C4—21no—
95C23×C3×C4C2×D311yescharacteristic
96C23×C3×C4C2×D311yescharacteristic
97C22×#67—62no—
98C22×#67—61no—
99C22×#67—61no—
100C2×#235—34no—
101C2×#235—34no—
102C2×#235—64no—
103C2×#235—64no—
104C2×#235—64no—
105C2×#235—64no—
106C2×#235—64no—
107C2×#235—68no—
108C2×#235—68no—
109C2×#235—64no—
110C2×#235—62no—
111C2×#235—62no—
112C22×D12—31no—
113C22×D12—31no—
114C22×D12—61no—
115C22×C4×D3—62no—
116C22×C4×D3—61no—
117C22×C4×D3—61no—
118C22×Dic6—31no—
119C22×Dic6—31no—
120C22×Dic6—61no—
121C22×Dic6C2×D311yescharacteristic
122C22×C3×C8—31no—
123C22×C3×C8—31no—
124C3×C22⋊Q8—34no—
125C3×C22⋊Q8—62no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C4⋊C4—61no—
128C2×C3×C22⋊C4—61no—
129C2×#217—21no—
130C2×#216—34no—
131C2×#216—64no—
132C2×#215—34no—
133C2×#215—64no—
134C2×C4⋊Dic3C2×D311yescharacteristic
135#924—22no—
136#924C2×D314yescomplemented
137C2×Dic3⋊C4—21no—
138C22×C3⋊C8C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140C2×Dic12—34no—
141C2×Dic12—64no—
142C2×#204—34no—
143C2×#204—64no—
144C3×C22⋊C8—34no—
145#830C2×D314yescomplemented
146#821—34no—
147#816—34no—
148#810—34no—
149#809—34no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32—22no—
153C23×C32C2×D412yes—
154C23×C32C2×D411yescharacteristic
155C22×C3⋊D3—24no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—42no—
158C22×C3⋊D3—42no—
159C2×C32×C4—22no—
160C2×C32×C4—24no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2411yescharacteristic
168#638—216no—
169C2×C3⋊Dic3—24no—
170C2×C3⋊Dic3—22no—
171C4⋊(C3⋊D3)—24no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)C2×D414yes—
174C4×C3⋊D3—216no—
175#634—24no—
176#634—22no—
177#634C2×D414yes—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—42no—
181C2×C3×Dic3—42no—
182C3×Dic6—22no—
183C3×Dic6—22no—
184C3×Dic6—42no—
185C3×C3⋊C8—22no—
186C3×C3⋊C8—22no—
187C22×#41—91no—
188C22×Q16—91no—
189C22×SD16—91no—
190C2×C22⋊Q8—31no—
191#452—98no—
192C2×#103—91no—
193C2×#102—91no—
194C2×C22⋊C8—31no—
195C24×C3—21no—
196C24×C3D1211yescharacteristic
197C24×C3#6711yescharacteristic
198C23×D3—62no—
199C23×D3—61no—
200C23×D3—61no—
201C2×C3×Q8—32no—
202C2×C3×Q8—61no—
203C2×C3×Q8—62no—
204C2×C3×Q8—62no—
205C22×C3×C4—24no—
206C22×C3×C4—24no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—21no—
212C22×C3×C4—22no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4D1211yescharacteristic
218C22×C3×C4D1212yes—
219C22×C3×C4#6711yescharacteristic
220C22×C3×C4#6712yes—
221C22×C3×C4C22×D312yes—
222C22×C3×C4C22×D312yes—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67—616no—
226C2×#67—68no—
227C2×#67—68no—
228C2×#67—68no—
229C2×#67—64no—
230C2×#67—64no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—62no—
234C22×Dic3—61no—
235C22×Dic3—61no—
236#235—68no—
237#235—68no—
238#235—68no—
239#235—68no—
240#235—616no—
241#235—616no—
242#235—632no—
243#235—616no—
244#235—616no—
245C2×D12—34no—
246C2×D12—34no—
247C2×D12—32no—
248C2×D12—32no—
249C2×D12—64no—
250C2×D12—62no—
251C2×D12—62no—
252C2×D12—64no—
253C2×D12—61no—
254C2×D12—62no—
255C2×D12—62no—
256C2×D12—61no—
257C2×C4×D3—616no—
258C2×C4×D3—68no—
259C2×C4×D3—68no—
260C2×C4×D3—68no—
261C2×C4×D3—64no—
262C2×C4×D3—64no—
263C2×Dic6—22no—
264C2×Dic6—22no—
265C2×Dic6—21no—
266C2×Dic6—34no—
267C2×Dic6—34no—
268C2×Dic6—32no—
269C2×Dic6—32no—
270C2×Dic6—64no—
271C2×Dic6—62no—
272C2×Dic6—62no—
273C2×Dic6—64no—
274C2×Dic6—61no—
275C2×Dic6—62no—
276C2×Dic6—62no—
277C2×Dic6—61no—
278C2×Dic6C22×D312yes—
279C2×C3×C8—32no—
280C2×C3×C8—32no—
281C2×C3×C8—62no—
282C2×C3×C8—62no—
283C3×C4⋊C4—32no—
284C3×C4⋊C4—64no—
285C3×C4⋊C4—61no—
286C3×C22⋊C4—64no—
287#217—24no—
288#216—68no—
289#215—68no—
290C4⋊Dic3—21no—
291C4⋊Dic3C22×D312yes—
292Dic3⋊C4—24no—
293C2×C3⋊C8—22no—
294C2×C3⋊C8—22no—
295C2×C3⋊C8C22×D312yes—
296C2×C3⋊C8C22×D312yes—
297Dic12—68no—
298#204—68no—
299C22×C32—22no—
300C22×C32—22no—
301C22×C32—22no—
302C22×C32—44no—
303C22×C32#12012yes—
304C22×C32#13512yes—
305C22×C32#13712yes—
306C22×C32C22×D411yescharacteristic
307C2×C3⋊D3—24no—
308C2×C3⋊D3—42no—
309C2×C3⋊D3—42no—
310C2×C3⋊D3—48no—
311C32×C4—22no—
312C32×C4#12012yes—
313C32×C4C22×D411yescharacteristic
314C32×C4C22×D411yescharacteristic
315C3⋊Dic3—24no—
316C3×Dic3—42no—
317C3×Dic3—42no—
318C2×#41—94no—
319C2×#41—184no—
320C2×#41—184no—
321C2×#41—182no—
322C22×Q8—31no—
323C22×Q8—91no—
324C22×D4—91no—
325C22×D4—181no—
326C23×C4—181no—
327C23×C4D3211yescharacteristic
328C2×Q16—94no—
329C2×Q16—184no—
330C2×SD16—94no—
331C2×SD16—184no—
332C22×C8—31no—
333C22×C8—31no—
334C22⋊Q8—34no—
335C22⋊Q8—62no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—61no—
338C2×C22⋊C4—61no—
339#103—94no—
340#102—94no—
341C22⋊C8—34no—
342C23×C3—24no—
343C23×C3—22no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—21no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3C2×D1212yes—
354C23×C3C2×D1211yescharacteristic
355C23×C3C2×#6712yes—
356C23×C3C2×#6711yescharacteristic
357C22×D3—64no—
358C22×D3—68no—
359C22×D3—64no—
360C22×D3—64no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—124no—
364C22×D3—124no—
365C22×D3—122no—
366C22×D3—122no—
367C22×D3—122no—
368C22×D3—122no—
369C3×Q8—62no—
370C3×Q8—62no—
371C3×Q8—122no—
372C2×C3×C4—24no—
373C2×C3×C4—24no—
374C2×C3×C4—24no—
375C2×C3×C4—28no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—24no—
379C2×C3×C4—24no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—62no—
390C2×C3×C4—62no—
391C2×C3×C4—122no—
392C2×C3×C4—122no—
393C2×C3×C4C2×D1212yes—
394C2×C3×C4C2×D1211yescharacteristic
395C2×C3×C4D3×D412yes—
396C2×C3×C4D3×D412yes—
397C2×C3×C4D3×D412yes—
398C2×C3×C4D3×D412yes—
399C2×C3×C4C2×#6712yes—
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403#67—632no—
404#67—616no—
405#67—616no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—42no—
409C2×Dic3—42no—
410C2×Dic3—64no—
411C2×Dic3—68no—
412C2×Dic3—64no—
413C2×Dic3—64no—
414C2×Dic3—62no—
415C2×Dic3—62no—
416D12—34no—
417D12—34no—
418D12—64no—
419D12—64no—
420D12—68no—
421D12—64no—
422D12—64no—
423D12—62no—
424D12—62no—
425C4×D3—632no—
426C4×D3—616no—
427C4×D3—616no—
428Dic6—22no—
429Dic6—22no—
430Dic6—34no—
431Dic6—34no—
432Dic6—42no—
433Dic6—64no—
434Dic6—64no—
435Dic6—68no—
436Dic6—64no—
437Dic6—64no—
438Dic6—62no—
439Dic6—62no—
440C3×C8—62no—
441C3×C8—62no—
442C3⋊C8—22no—
443C3⋊C8—22no—
444C2×C32—42no—
445C2×C32#45214yescomplemented
446C2×C32C2×#12011yescharacteristic
447C2×C32C2×#13511yescharacteristic
448C2×C32C2×#13711yescharacteristic
449C3⋊D3—44no—
450C24—181no—
451C24#62611yescharacteristic
452#41—188no—
453#41—188no—
454#41—1816no—
455C2×Q8—32no—
456C2×Q8—61no—
457C2×Q8—62no—
458C2×Q8—62no—
459C2×Q8—92no—
460C2×Q8—94no—
461C2×Q8—181no—
462C2×Q8—182no—
463C2×D4—92no—
464C2×D4—94no—
465C2×D4—188no—
466C2×D4—184no—
467C2×D4—181no—
468C2×D4—182no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—61no—
472C22×C4—61no—
473C22×C4—188no—
474C22×C4—181no—
475C22×C4—184no—
476C22×C4#62612yes—
477C22×C4#62611yescharacteristic
478C22×C4C2×D3212yes—
479C22×C4C2×D3211yescharacteristic
480Q16—188no—
481SD16—188no—
482C2×C8—32no—
483C2×C8—32no—
484C2×C8—62no—
485C2×C8—62no—
486C4⋊C4—32no—
487C4⋊C4—61no—
488C4⋊C4—64no—
489C22⋊C4—64no—
490C22×C3—24no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—21no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—48no—
504C22×C3—44no—
505C22×C3—44no—
506C22×C3#88212yes—
507C22×C3#90412yes—
508C22×C3#90912yes—
509C22×C3#93712yes—
510C22×C3#94212yes—
511C22×C3#95012yes—
512C22×C3C22×D1211yescharacteristic
513C22×C3C22×#6711yescharacteristic
514C2×D3—68no—
515C2×D3—64no—
516C2×D3—64no—
517C2×D3—1216no—
518C2×D3—124no—
519C2×D3—124no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—128no—
523C2×D3—122no—
524C2×D3—128no—
525C2×D3—122no—
526C3×C4—24no—
527C3×C4—22no—
528C3×C4—22no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—122no—
533C3×C4—122no—
534C3×C4#88212yes—
535C3×C4#93712yes—
536C3×C4C2×D3×D411yescharacteristic
537C3×C4C2×D3×D411yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540Dic3—42no—
541Dic3—42no—
542Dic3—68no—
543Dic3—64no—
544Dic3—64no—
545C32C2×#45211yescharacteristic, complemented, Sylow
546C23—22no—
547C23—22no—
548C23—22no—
549C23—182no—
550C23—184no—
551C23—362no—
552C23—362no—
553C23C2×#62612yes—
554C23C2×#62611yescharacteristic
555Q8—62no—
556Q8—62no—
557Q8—94no—
558Q8—122no—
559Q8—182no—
560Q8—184no—
561D4—94no—
562D4—1816no—
563D4—182no—
564D4—184no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—122no—
572C2×C4—122no—
573C2×C4—1816no—
574C2×C4—182no—
575C2×C4—184no—
576C2×C4C2×#62612yes—
577C2×C4C2×#62611yescharacteristic
578C2×C4#381112yes—
579C2×C4#381112yes—
580C2×C4C22×D3211yescharacteristic
581C8—62no—
582C8—62no—
583C2×C3—21no—
584C2×C3—24no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—44no—
588C2×C3—42no—
589C2×C3—42no—
590C2×C3#473314yescomplemented
591C2×C3#504714yescomplemented
592C2×C3C2×#88211yescharacteristic
593C2×C3C2×#90411yescharacteristic
594C2×C3C2×#90911yescharacteristic
595C2×C3C2×#93711yescharacteristic
596C2×C3C2×#94211yescharacteristic
597C2×C3C2×#95011yescharacteristic
598D3—128no—
599D3—124no—
600D3—124no—
601C22—22no—
602C22—22no—
603C22—22no—
604C22—44no—
605C22—184no—
606C22—368no—
607C22—362no—
608C22—362no—
609C22#6382912yes—
610C22#6383312yes—
611C22#6398112yes—
612C22C22×#62611yescharacteristic
613C4—22no—
614C4—122no—
615C4—122no—
616C4—184no—
617C4#6398112yes—
618C4C2×#381111yescharacteristic
619C4C2×#381111yescharacteristic
620C3—21no—
621C3C2×#473311yescharacteristic, complemented
622C3C2×#504711yescharacteristic, complemented
623C2—42no—
624C2—364no—
625C2#1059118414yesdirect product factor
626C2C2×#6382911yescharacteristic
627C2C2×#6383311yescharacteristic
628C2C2×#6398111yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
prime radicalC22×#3828C2
hypercenterC23×C4D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#924C2semidirect
3. C22×#3719C2semidirect
4. C22×#3717C2semidirect
5. C2×C3×#830C2semidirect
6. #10591184C2direct (N × H)
7. C2×#63567C2semidirect
8. C2×#63564C2semidirect
24. C3×#924C22semidirect
29. C2×#3719C22semidirect
31. C2×#3717C22semidirect
32. C3×#830C22semidirect
33. #63567C22semidirect
34. #63564C22semidirect
41. C2×#924D3semidirect
45. C2×#830D3semidirect
136. #924C2×D3semidirect
145. #830C2×D3semidirect
445. C2×C32#452semidirect
545. C32C2×#452semidirect
590. C2×C3#4733semidirect
591. C2×C3#5047semidirect
621. C3C2×#4733semidirect
622. C3C2×#5047semidirect
625. C2#10591184direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38282
C2×C3×#9242
C22×#37192
C22×#37172
C2×C3×#8302
#105911842
C2×#635672
C2×#635642
C2×#50473
C2×#47333