Finite Group Databasebeta

← C2×#10591466 #11863784

Subgroups — C2×#10591466 #11863784

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×#3830C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×#63871C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591466C218yesmaximal, direct product factor
7C2×#63567C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic, complemented
9C2×#5173—31nomaximal
10C2×#4783—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#638—21no—
13C23×C3⋊Dic3—21no—
14C2×#3830—24no—
15C2×#3830—22no—
16C2×#3830—24no—
17C2×#3830C2214yes—
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×C3×#214—24no—
22C2×C3×#214C2214yescomplemented
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×Dic3⋊Dic3—21no—
27C2×#3722—21no—
28#63871—22no—
29#63871C2214yescomplemented
30C2×#3719—24no—
31C2×#3719C2214yescomplemented
32C3×#832C2214yescomplemented
33#63567C2214yescomplemented
34#63557C2214yescomplemented
35C22×#237—31no—
36C22×#237—31no—
37C22×#237—61no—
38C22×C3×SD16—31no—
39C2×#946—31no—
40C22×#216—31no—
41C22×#214D311yescharacteristic, complemented
42C22×Dic12—31no—
43C2×#897—31no—
44C2×C3×#102—31no—
45C2×#832D311yescharacteristic, complemented
46#5173—38no—
47C2×(C2×D3)⋊C8—31no—
48C2×(C2×D3)⋊C8—31no—
49C2×#816—31no—
50C2×#810—31no—
51#4783—38no—
52C24×C32—21no—
53C23×C3⋊D3D411yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4D414yes—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C2×#638—28no—
60C2×#638—24no—
61C22×C3⋊Dic3—28no—
62C22×C3⋊Dic3—21no—
63C22×C3⋊Dic3—24no—
64C22×C3⋊Dic3D411yescharacteristic
65#3830—216no—
66#3830—28no—
67#3830—28no—
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3D412yes—
71C2×C4×C3⋊D3C2312yes—
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×#214—28no—
83C3×C4⋊Dic3—21no—
84C3×C4⋊Dic3C2312yes—
85C2×C3×C3⋊C8—22no—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88C2×C3×C3⋊C8C2312yes—
89Dic3⋊Dic3—24no—
90#3722—24no—
91#3719—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C22×C3×D4—21no—
95C22×C3×D4C2×D311yescharacteristic
96C22×C3×D4C2×D311yescharacteristic
97C22×#67—61no—
98C22×#67—61no—
99C22×#67—62no—
100C23×Dic3—61no—
101C23×Dic3—61no—
102C23×Dic3—62no—
103C2×#237—34no—
104C2×#237—34no—
105C2×#237—64no—
106C2×#237—64no—
107C2×#237—64no—
108C2×#237—62no—
109C2×#237—62no—
110C2×#237—64no—
111C2×#237—68no—
112C2×#237—68no—
113C2×#237—64no—
114C2×#237—64no—
115C22×C4×D3—31no—
116C22×C4×D3—31no—
117C22×C4×D3—61no—
118C22×Dic6—31no—
119C22×Dic6—31no—
120C22×Dic6—61no—
121C22×Dic6C2×D311yescharacteristic
122C2×C3×SD16—34no—
123C2×C3×SD16—64no—
124C22×C3×C8—31no—
125C22×C3×C8—31no—
126C2×C3×C4⋊C4—31no—
127#946—34no—
128#946—62no—
129C2×#216—34no—
130C2×#216—64no—
131C2×#214—24no—
132C2×#214C2×D314yescomplemented
133C2×(C2×D3)⋊C4—61no—
134C2×(C2×D3)⋊C4—61no—
135C2×C4⋊Dic3—61no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C2×Dic3⋊C4—61no—
138C22×C3⋊C8C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140C2×Dic12—34no—
141C2×Dic12—64no—
142#897—34no—
143#897—62no—
144C3×#102—34no—
145#832C2×D314yescomplemented
146(C2×D3)⋊C8—34no—
147(C2×D3)⋊C8—34no—
148#816—34no—
149#810—34no—
150C23×C32—24no—
151C23×C32—22no—
152C23×C32—42no—
153C23×C32—42no—
154C23×C32C2×D411yescharacteristic
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3C2×D412yes—
159C32×D4—24no—
160C32×D4—22no—
161C32×D4C2×D414yes—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2411yescharacteristic
166#638—216no—
167C2×C3⋊Dic3—216no—
168C2×C3⋊Dic3—24no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—22no—
171C2×C3⋊Dic3C2×D412yes—
172C4×C3⋊D3—24no—
173C4×C3⋊D3—22no—
174C4×C3⋊D3—22no—
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—31no—
190C2×C22⋊Q8—91no—
191#452—98no—
192C2×#103—91no—
193C2×#102—31no—
194C2×C22⋊C8—91no—
195C24×C3—22no—
196C24×C3—21no—
197C24×C3—21no—
198C23×D3—31no—
199C23×D3—31no—
200C23×D3—61no—
201C2×C3×Q8—32no—
202C2×C3×Q8—61no—
203C2×C3×Q8—62no—
204C2×C3×Q8—62no—
205C2×C3×D4—24no—
206C2×C3×D4—22no—
207C2×C3×D4—21no—
208C2×C3×D4—22no—
209C2×C3×D4—21no—
210C2×C3×D4—22no—
211C2×C3×D4—24no—
212C2×C3×D4—22no—
213C2×C3×D4D1214yes—
214C2×C3×D4#6714yes—
215C2×C3×D4C22×D312yes—
216C2×C3×D4C22×D312yes—
217C22×C3×C4—21no—
218C22×C3×C4—61no—
219C22×C3×C4—61no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C2×#67—64no—
223C2×#67—64no—
224C2×#67—68no—
225C2×#67—616no—
226C2×#67—68no—
227C2×#67—68no—
228C22×Dic3—21no—
229C22×Dic3—21no—
230C22×Dic3—31no—
231C22×Dic3—31no—
232C22×Dic3—61no—
233C22×Dic3—64no—
234C22×Dic3—64no—
235C22×Dic3—62no—
236C22×Dic3—68no—
237C22×Dic3—616no—
238C22×Dic3—68no—
239C22×Dic3—68no—
240C22×Dic3—61no—
241C22×Dic3—61no—
242#237—68no—
243#237—68no—
244#237—616no—
245#237—632no—
246#237—616no—
247#237—616no—
248#237—616no—
249#237—68no—
250#237—68no—
251C2×C4×D3—32no—
252C2×C4×D3—32no—
253C2×C4×D3—32no—
254C2×C4×D3—32no—
255C2×C4×D3—62no—
256C2×C4×D3—62no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—62no—
260C2×C4×D3—62no—
261C2×C4×D3—62no—
262C2×C4×D3—62no—
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—64no—
273C2×Dic6—62no—
274C2×Dic6—62no—
275C2×Dic6—61no—
276C2×Dic6—61no—
277C2×Dic6—62no—
278C2×Dic6C22×D312yes—
279C3×SD16—68no—
280C2×C3×C8—32no—
281C2×C3×C8—32no—
282C2×C3×C8—62no—
283C2×C3×C8—62no—
284C3×C4⋊C4—32no—
285C3×C4⋊C4—61no—
286#216—68no—
287#214—28no—
288(C2×D3)⋊C4—64no—
289(C2×D3)⋊C4—64no—
290C4⋊Dic3—21no—
291C4⋊Dic3—64no—
292C4⋊Dic3C22×D312yes—
293Dic3⋊C4—64no—
294C2×C3⋊C8—22no—
295C2×C3⋊C8—22no—
296C2×C3⋊C8C22×D312yes—
297C2×C3⋊C8C22×D312yes—
298Dic12—68no—
299C22×C32—24no—
300C22×C32—42no—
301C22×C32—42no—
302C22×C32—48no—
303C22×C32#12012yes—
304C22×C32#13512yes—
305C22×C32#13712yes—
306C22×C32C22×D411yescharacteristic
307C2×C3⋊D3—22no—
308C2×C3⋊D3—22no—
309C2×C3⋊D3—22no—
310C2×C3⋊D3—44no—
311C32×C4#12012yes—
312C32×C4C22×D411yescharacteristic
313C32×C4C22×D411yescharacteristic
314C3⋊Dic3—24no—
315C3⋊Dic3—22no—
316C3×Dic3—42no—
317C3×Dic3—42no—
318C2×#41—94no—
319C2×#41—182no—
320C2×#41—184no—
321C2×#41—184no—
322C22×Q8—31no—
323C22×Q8—91no—
324C22×D4—181no—
325C22×D4D3211yescharacteristic
326C23×C4—91no—
327C23×C4—181no—
328C2×Q16—94no—
329C2×Q16—184no—
330C2×SD16—34no—
331C2×SD16—64no—
332C22×C8—31no—
333C22×C8—31no—
334C22⋊Q8—94no—
335C22⋊Q8—182no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—181no—
338C2×C22⋊C4—181no—
339#103—94no—
340#102—34no—
341C22⋊C8—94no—
342C23×C3—24no—
343C23×C3—28no—
344C23×C3—24no—
345C23×C3—24no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—21no—
349C23×C3—44no—
350C23×C3—44no—
351C23×C3—42no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—42no—
355C23×C3D3×D411yescharacteristic
356C23×C3D3×D411yescharacteristic
357C22×D3—32no—
358C22×D3—32no—
359C22×D3—62no—
360C22×D3—64no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—62no—
365C22×D3—62no—
366C22×D3—62no—
367C22×D3—122no—
368C22×D3—122no—
369C3×Q8—62no—
370C3×Q8—62no—
371C3×Q8—122no—
372C3×D4—24no—
373C3×D4—28no—
374C3×D4—24no—
375C3×D4—24no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—24no—
379C3×D4C2×D1214yes—
380C3×D4C2×#6714yes—
381C2×C3×C4—21no—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—21no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—122no—
388C2×C3×C4—122no—
389C2×C3×C4C2×D1212yes—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D412yes—
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D412yes—
394C2×C3×C4C2×#6712yes—
395C2×C3×C4C23×D311yescharacteristic
396C2×C3×C4C23×D311yescharacteristic
397#67—632no—
398#67—616no—
399#67—616no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—32no—
403C2×Dic3—32no—
404C2×Dic3—42no—
405C2×Dic3—42no—
406C2×Dic3—62no—
407C2×Dic3—64no—
408C2×Dic3—68no—
409C2×Dic3—64no—
410C2×Dic3—632no—
411C2×Dic3—616no—
412C2×Dic3—616no—
413C2×Dic3—64no—
414C2×Dic3—62no—
415C2×Dic3—64no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—62no—
419C4×D3—64no—
420C4×D3—64no—
421C4×D3—68no—
422C4×D3—64no—
423C4×D3—64no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—62no—
427C4×D3—62no—
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—44no—
445C2×C32#45214yescomplemented
446C2×C32C2×#12011yescharacteristic
447C2×C32C2×#13511yescharacteristic
448C2×C32C2×#13711yescharacteristic
449C3⋊D3—42no—
450C24—21no—
451C24—91no—
452#41—188no—
453#41—1816no—
454#41—188no—
455C2×Q8—32no—
456C2×Q8—61no—
457C2×Q8—62no—
458C2×Q8—62no—
459C2×Q8—92no—
460C2×Q8—94no—
461C2×Q8—182no—
462C2×Q8—181no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—184no—
466C2×D4—188no—
467C2×D4#62614yes—
468C2×D4C2×D3212yes—
469C22×C4—61no—
470C22×C4—61no—
471C22×C4—91no—
472C22×C4—92no—
473C22×C4—92no—
474C22×C4—184no—
475C22×C4—188no—
476C22×C4—181no—
477C22×C4—182no—
478C22×C4—182no—
479C22×C4C2×D3211yescharacteristic
480Q16—188no—
481SD16—68no—
482C2×C8—32no—
483C2×C8—32no—
484C2×C8—62no—
485C2×C8—62no—
486C4⋊C4—32no—
487C4⋊C4—61no—
488C4⋊C4—184no—
489C22⋊C4—184no—
490C22×C3—28no—
491C22×C3—24no—
492C22×C3—24no—
493C22×C3—21no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—44no—
498C22×C3—44no—
499C22×C3—416no—
500C22×C3—48no—
501C22×C3—42no—
502C22×C3—42no—
503C22×C3—42no—
504C22×C3—42no—
505C22×C3—48no—
506C22×C3#88212yes—
507C22×C3#91212yes—
508C22×C3#91512yes—
509C22×C3#91512yes—
510C22×C3#91612yes—
511C22×C3#93712yes—
512C22×C3C2×D3×D411yescharacteristic
513C22×C3C2×D3×D411yescharacteristic
514C2×D3—64no—
515C2×D3—62no—
516C2×D3—62no—
517C2×D3—62no—
518C2×D3—62no—
519C2×D3—62no—
520C2×D3—62no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—128no—
524C2×D3—124no—
525C2×D3—124no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—22no—
529C3×C4—122no—
530C3×C4—122no—
531C3×C4#88212yes—
532C3×C4#93712yes—
533C3×C4C22×D1211yescharacteristic
534C3×C4C2×D3×D411yescharacteristic
535C3×C4C2×D3×D411yescharacteristic
536C3×C4C22×#6711yescharacteristic
537Dic3—42no—
538Dic3—42no—
539Dic3—68no—
540Dic3—64no—
541Dic3—64no—
542Dic3—62no—
543Dic3—64no—
544Dic3—62no—
545C32C2×#45211yescharacteristic, complemented, Sylow
546C23—22no—
547C23—24no—
548C23—42no—
549C23—42no—
550C23—92no—
551C23—182no—
552C23—182no—
553C23—182no—
554C23#381111yescharacteristic
555Q8—62no—
556Q8—62no—
557Q8—94no—
558Q8—122no—
559Q8—182no—
560Q8—184no—
561D4—22no—
562D4—24no—
563D4—1816no—
564D4C2×#62614yes—
565C2×C4—62no—
566C2×C4—62no—
567C2×C4—92no—
568C2×C4—122no—
569C2×C4—122no—
570C2×C4—1816no—
571C2×C4—182no—
572C2×C4—182no—
573C2×C4—184no—
574C2×C4—182no—
575C2×C4—182no—
576C2×C4—184no—
577C2×C4C2×#62612yes—
578C2×C4#381112yes—
579C2×C4#381111yescharacteristic
580C2×C4C22×D3211yescharacteristic
581C8—62no—
582C8—62no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—24no—
587C2×C3—48no—
588C2×C3—44no—
589C2×C3—44no—
590C2×C3#478314yescomplemented
591C2×C3#517314yescomplemented
592C2×C3C2×#88211yescharacteristic
593C2×C3C2×#91211yescharacteristic
594C2×C3C2×#91511yescharacteristic
595C2×C3C2×#91511yescharacteristic
596C2×C3C2×#91611yescharacteristic
597C2×C3C2×#93711yescharacteristic
598D3—124no—
599D3—122no—
600D3—122no—
601C22—24no—
602C22—42no—
603C22—42no—
604C22—48no—
605C22—182no—
606C22—182no—
607C22—182no—
608C22—364no—
609C22#6393112yes—
610C22#6393612yes—
611C22#6398112yes—
612C22C2×#381111yescharacteristic
613C4—122no—
614C4—122no—
615C4—182no—
616C4—184no—
617C4#6398112yes—
618C4C22×#62611yescharacteristic
619C4C2×#381111yescharacteristic
620C3—21no—
621C3C2×#478311yescharacteristic, complemented
622C3C2×#517311yescharacteristic, complemented
623C2—44no—
624C2—362no—
625C2#1059146614yesdirect product factor
626C2C2×#6393111yescharacteristic
627C2C2×#6393611yescharacteristic
628C2C2×#6398111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×#3830C2
hypercenterC22×D4D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C22×C3×#214C2semidirect
3. C2×#63871C2semidirect
4. C22×#3719C2semidirect
5. C2×C3×#832C2semidirect
6. #10591466C2direct (N × H)
7. C2×#63567C2semidirect
8. C2×#63557C2semidirect
22. C2×C3×#214C22semidirect
29. #63871C22semidirect
31. C2×#3719C22semidirect
32. C3×#832C22semidirect
33. #63567C22semidirect
34. #63557C22semidirect
41. C22×#214D3semidirect
45. C2×#832D3semidirect
132. C2×#214C2×D3semidirect
145. #832C2×D3semidirect
445. C2×C32#452semidirect
545. C32C2×#452semidirect
590. C2×C3#4783semidirect
591. C2×C3#5173semidirect
621. C3C2×#4783semidirect
622. C3C2×#5173semidirect
625. C2#10591466direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×C3×#2142
C2×#638712
C22×#37192
C2×C3×#8322
#105914662
C2×#635672
C2×#635572
C2×#51733
C2×#47833