Finite Group Databasebeta

← C2×#10591163 #11863722

Subgroups — C2×#10591163 #11863722

Order 1152.

1837 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×#64139C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C2×C3×#830C211yesmaximal, characteristic, complemented
6#10591163C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×#63563C211yesmaximal, characteristic, complemented
9C2×#5238—31nomaximal
10C2×#4734—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×#638—21no—
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C3×#67—21no—
15C2×C3×#235—22no—
16C2×C3×#235—24no—
17C2×C3×#235—24no—
18C2×C3×#235C2214yescomplemented
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3—21no—
21C22×C3×Dic6C2211yescharacteristic
22#64139—22no—
23#64139C2214yescomplemented
24C2×#3752—21no—
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3717—24no—
29C2×#3717C2214yescomplemented
30C2×#3714—24no—
31C2×#3714C2214yescomplemented
32C3×#830C2214yescomplemented
33#63566C2214yescomplemented
34#63563C2214yescomplemented
35C22×C3×#41—31no—
36C22×#235D311yescharacteristic, complemented
37C22×#215—31no—
38C22×#213—31no—
39C2×#930—31no—
40C2×#930—31no—
41C2×#930—61no—
42C22×D24—31no—
43C22×#204—31no—
44C2×C3×C22⋊C8—31no—
45#5238—38no—
46C2×#835—31no—
47C2×#832—31no—
48C2×#830D311yescharacteristic, complemented
49C2×#821—31no—
50C2×#816—31no—
51#4734—38no—
52C24×C32D411yescharacteristic
53C23×C3⋊D3—21no—
54C23×C3×D3—21no—
55C22×C32×C4—22no—
56C22×C32×C4—22no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4D412yes—
59C22×C32×C4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×#638—24no—
62C2×#638—44no—
63C22×C3⋊Dic3—21no—
64C2×C4⋊(C3⋊D3)—22no—
65C2×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)C2312yes—
68C2×C3×#67—28no—
69C2×C3×#67—24no—
70C22×C3×Dic3—21no—
71C3×#235—216no—
72C3×#235—28no—
73C3×#235—28no—
74C2×C3×D12—21no—
75C2×C3×D12—22no—
76C2×C3×D12D414yescomplemented
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—28no—
79C2×C3×C4×D3—24no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6—22no—
82C2×C3×Dic6D414yescomplemented
83C2×C3×Dic6C2312yes—
84#3752—24no—
85C4⋊(C3⋊Dic3)—21no—
86C4⋊(C3⋊Dic3)C2312yes—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8—22no—
89C2×C3×C3⋊C8C2312yes—
90C2×C3×C3⋊C8C2312yes—
91#3717—28no—
92#3714—28no—
93C2×#449—91noSylow
94C2×C3×#41—34no—
95C2×C3×#41—64no—
96C2×C3×#41—64no—
97C2×C3×#41—62no—
98C22×C3×Q8—31no—
99C22×C3×D4—31no—
100C22×C3×D4—61no—
101C23×C3×C4—21no—
102C23×C3×C4—61no—
103C23×C3×C4C2×D311yescharacteristic
104C23×C3×C4C2×D311yescharacteristic
105C22×#67—21no—
106C22×#67—62no—
107C22×#67—61no—
108C22×#67—61no—
109C2×#235—22no—
110C2×#235—24no—
111C2×#235—24no—
112C2×#235C2×D314yescomplemented
113C22×D12—31no—
114C22×D12—31no—
115C22×D12—61no—
116C22×D12C2×D311yescharacteristic
117C22×C4×D3—21no—
118C22×Dic6C2×D311yescharacteristic
119C22×C3×C8—31no—
120C22×C3×C8—31no—
121C2×#215—34no—
122C2×#215—64no—
123C2×#213—34no—
124C2×#213—64no—
125#930—34no—
126#930—34no—
127#930—64no—
128#930—64no—
129#930—62no—
130#930—62no—
131C2×(C2×D3)⋊C4—62no—
132C2×(C2×D3)⋊C4—61no—
133C2×(C2×D3)⋊C4—61no—
134C2×C4⋊Dic3—31no—
135C2×C4⋊Dic3—31no—
136C2×C4⋊Dic3—61no—
137C22×C3⋊C8C2×D311yescharacteristic
138C22×C3⋊C8C2×D311yescharacteristic
139C2×D24—34no—
140C2×D24—64no—
141C2×#204—34no—
142C2×#204—64no—
143C3×C22⋊C8—34no—
144#835—34no—
145#832—34no—
146#830C2×D314yescomplemented
147#821—34no—
148#816—34no—
149C23×C32—22no—
150C23×C32—22no—
151C23×C32—22no—
152C23×C32C2×D412yes—
153C23×C32C2×D411yescharacteristic
154C22×C3⋊D3—22no—
155C22×C3⋊D3—42no—
156C22×C3⋊D3—42no—
157C22×C3⋊D3—42no—
158C22×C3×D3—24no—
159C22×C3×D3—22no—
160C22×C3×D3—42no—
161C22×C3×D3—42no—
162C2×C32×C4—22no—
163C2×C32×C4—24no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D412yes—
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2411yescharacteristic
171#638—48no—
172C2×C3⋊Dic3—22no—
173C2×C3⋊Dic3—42no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)—22no—
176C4⋊(C3⋊D3)—42no—
177C3×#67—216no—
178C2×C3×Dic3—24no—
179C2×C3×Dic3—22no—
180C3×D12—24no—
181C3×D12—22no—
182C3×D12C2×D414yescomplemented
183C3×C4×D3—216no—
184C3×Dic6—24no—
185C3×Dic6—22no—
186C3×Dic6C2×D414yescomplemented
187C3×C3⋊C8—22no—
188C3×C3⋊C8—22no—
189C22×#41—31no—
190C22×SD16—91no—
191C22×D8—91no—
192C2×#121—91no—
193#449—98no—
194C2×#103—91no—
195C2×#102—91no—
196C2×C22⋊C8—31no—
197C24×C3—21no—
198C24×C3—61no—
199C24×C3D1211yescharacteristic
200C24×C3#6711yescharacteristic
201C23×D3—21no—
202C23×D3—62no—
203C23×D3—61no—
204C23×D3—61no—
205C3×#41—68no—
206C3×#41—68no—
207C3×#41—616no—
208C2×C3×Q8—34no—
209C2×C3×Q8—32no—
210C2×C3×Q8—61no—
211C2×C3×Q8—62no—
212C2×C3×D4—34no—
213C2×C3×D4—32no—
214C2×C3×D4—68no—
215C2×C3×D4—64no—
216C2×C3×D4—61no—
217C2×C3×D4—62no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—21no—
225C22×C3×C4—22no—
226C22×C3×C4—42no—
227C22×C3×C4—42no—
228C22×C3×C4—68no—
229C22×C3×C4—61no—
230C22×C3×C4—64no—
231C22×C3×C4D1211yescharacteristic
232C22×C3×C4D1212yes—
233C22×C3×C4#6711yescharacteristic
234C22×C3×C4#6712yes—
235C22×C3×C4C22×D312yes—
236C22×C3×C4C22×D312yes—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—28no—
240C2×#67—24no—
241C2×#67—68no—
242C2×#67—64no—
243C2×#67—64no—
244C2×#67—128no—
245C2×#67—124no—
246C2×#67—124no—
247C22×Dic3—21no—
248C22×Dic3—62no—
249C22×Dic3—61no—
250C22×Dic3—61no—
251#235—216no—
252#235—28no—
253#235—28no—
254C2×D12—21no—
255C2×D12—22no—
256C2×D12—32no—
257C2×D12—32no—
258C2×D12—62no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—62no—
262C2×D12—62no—
263C2×D12—62no—
264C2×D12—61no—
265C2×D12—61no—
266C2×D12—122no—
267C2×D12—122no—
268C2×D12#6714yescomplemented
269C2×D12C22×D312yes—
270C2×C4×D3—28no—
271C2×C4×D3—24no—
272C2×Dic6—21no—
273C2×Dic6—22no—
274C2×Dic6#6714yescomplemented
275C2×Dic6C22×D312yes—
276C2×C3×C8—32no—
277C2×C3×C8—32no—
278C2×C3×C8—62no—
279C2×C3×C8—62no—
280#215—68no—
281#213—68no—
282(C2×D3)⋊C4—68no—
283(C2×D3)⋊C4—64no—
284(C2×D3)⋊C4—64no—
285C4⋊Dic3—32no—
286C4⋊Dic3—32no—
287C4⋊Dic3—62no—
288C4⋊Dic3—62no—
289C4⋊Dic3—61no—
290C4⋊Dic3—61no—
291C2×C3⋊C8—22no—
292C2×C3⋊C8—22no—
293C2×C3⋊C8C22×D312yes—
294C2×C3⋊C8C22×D312yes—
295D24—68no—
296#204—68no—
297C22×C32—22no—
298C22×C32—22no—
299C22×C32—22no—
300C22×C32—44no—
301C22×C32#12012yes—
302C22×C32#13512yes—
303C22×C32AGL(1,ℤ/8)12yes—
304C22×C32C22×D411yescharacteristic
305C2×C3⋊D3—42no—
306C2×C3⋊D3—42no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—84no—
309C2×C3×D3—24no—
310C2×C3×D3—42no—
311C2×C3×D3—42no—
312C2×C3×D3—48no—
313C32×C4—22no—
314C32×C4#12012yes—
315C32×C4C22×D411yescharacteristic
316C32×C4C22×D411yescharacteristic
317C3⋊Dic3—42no—
318C3×Dic3—24no—
319C2×#41—34no—
320C2×#41—64no—
321C2×#41—64no—
322C2×#41—62no—
323C22×Q8—31no—
324C22×D4—31no—
325C22×D4—61no—
326C22×D4—91no—
327C22×D4—181no—
328C23×C4—61no—
329C23×C4D3211yescharacteristic
330C2×SD16—94no—
331C2×SD16—184no—
332C2×D8—94no—
333C2×D8—184no—
334C22×C8—31no—
335C22×C8—31no—
336#121—94no—
337#121—182no—
338C2×C4⋊C4—91no—
339C2×C22⋊C4—181no—
340#103—94no—
341#102—94no—
342C22⋊C8—34no—
343C23×C3—24no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—21no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—64no—
355C23×C3—62no—
356C23×C3—122no—
357C23×C3—122no—
358C23×C3C2×D1212yes—
359C23×C3C2×D1211yescharacteristic
360C23×C3C2×#6712yes—
361C23×C3C2×#6711yescharacteristic
362C22×D3—24no—
363C22×D3—22no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—64no—
367C22×D3—62no—
368C22×D3—62no—
369C22×D3—124no—
370C22×D3—124no—
371C22×D3—124no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—122no—
378C3×Q8—34no—
379C3×Q8—64no—
380C3×Q8—62no—
381C3×D4—34no—
382C3×D4—616no—
383C3×D4—64no—
384C3×D4—62no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—44no—
401C2×C3×C4—42no—
402C2×C3×C4—616no—
403C2×C3×C4—64no—
404C2×C3×C4—62no—
405C2×C3×C4C2×D1212yes—
406C2×C3×C4C2×D1211yescharacteristic
407C2×C3×C4D3×D412yes—
408C2×C3×C4D3×D412yes—
409C2×C3×C4C2×#6712yes—
410C2×C3×C4C2×#6711yescharacteristic
411C2×C3×C4C2×#6712yes—
412C2×C3×C4C2×#6712yes—
413C2×C3×C4C23×D311yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415#67—216no—
416#67—1216no—
417#67—128no—
418#67—128no—
419C2×Dic3—24no—
420C2×Dic3—22no—
421C2×Dic3—64no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—124no—
425C2×Dic3—122no—
426C2×Dic3—122no—
427D12—24no—
428D12—22no—
429D12—62no—
430D12—62no—
431D12—62no—
432D12—62no—
433D12—122no—
434D12—122no—
435D12—124no—
436D12—122no—
437D12—122no—
438D12C2×#6714yescomplemented
439C4×D3—216no—
440Dic6—24no—
441Dic6—22no—
442Dic6C2×#6714yescomplemented
443C3×C8—62no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8—22no—
447C2×C32—42no—
448C2×C32#44914yescomplemented
449C2×C32C2×#12011yescharacteristic
450C2×C32C2×#13511yescharacteristic
451C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
452C3⋊D3—82no—
453C3×D3—44no—
454C24—61no—
455C24—181no—
456C24#62611yescharacteristic
457#41—68no—
458#41—68no—
459#41—616no—
460C2×Q8—32no—
461C2×Q8—34no—
462C2×Q8—61no—
463C2×Q8—62no—
464C2×D4—32no—
465C2×D4—34no—
466C2×D4—68no—
467C2×D4—64no—
468C2×D4—61no—
469C2×D4—62no—
470C2×D4—92no—
471C2×D4—184no—
472C2×D4—181no—
473C2×D4—182no—
474C2×D4—182no—
475C2×D4—364no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—68no—
479C22×C4—61no—
480C22×C4—64no—
481C22×C4—181no—
482C22×C4#62612yes—
483C22×C4#62611yescharacteristic
484C22×C4C2×D3212yes—
485C22×C4C2×D3211yescharacteristic
486SD16—188no—
487D8—188no—
488C2×C8—32no—
489C2×C8—32no—
490C2×C8—62no—
491C2×C8—62no—
492C4⋊C4—92no—
493C4⋊C4—181no—
494C22⋊C4—184no—
495C22×C3—24no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—42no—
507C22×C3—42no—
508C22×C3—48no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—64no—
512C22×C3—122no—
513C22×C3—122no—
514C22×C3—128no—
515C22×C3#88212yes—
516C22×C3#90412yes—
517C22×C3#90812yes—
518C22×C3#94912yes—
519C22×C3#95012yes—
520C22×C3#95312yes—
521C22×C3C22×D1211yescharacteristic
522C22×C3C22×#6711yescharacteristic
523C2×D3—24no—
524C2×D3—48no—
525C2×D3—42no—
526C2×D3—42no—
527C2×D3—124no—
528C2×D3—124no—
529C2×D3—124no—
530C2×D3—122no—
531C2×D3—122no—
532C2×D3—122no—
533C2×D3—122no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—248no—
537C2×D3—244no—
538C2×D3—244no—
539C3×C4—22no—
540C3×C4—22no—
541C3×C4—21no—
542C3×C4—21no—
543C3×C4—22no—
544C3×C4—42no—
545C3×C4—64no—
546C3×C4#88212yes—
547C3×C4#95312yes—
548C3×C4C2×D3×D411yescharacteristic
549C3×C4C2×D3×D411yescharacteristic
550C3×C4C22×#6711yescharacteristic
551C3×C4C22×#6711yescharacteristic
552Dic3—24no—
553Dic3—124no—
554Dic3—122no—
555Dic3—122no—
556C32C2×#44911yescharacteristic, complemented, Sylow
557C23—22no—
558C23—22no—
559C23—22no—
560C23—62no—
561C23—64no—
562C23—122no—
563C23—122no—
564C23—182no—
565C23—362no—
566C23—362no—
567C23—362no—
568C23C2×#62612yes—
569C23C2×#62611yescharacteristic
570Q8—34no—
571Q8—62no—
572Q8—64no—
573D4—34no—
574D4—616no—
575D4—62no—
576D4—64no—
577D4—182no—
578D4—182no—
579D4—368no—
580D4—362no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—616no—
586C2×C4—62no—
587C2×C4—64no—
588C2×C4—182no—
589C2×C4—362no—
590C2×C4C2×#62612yes—
591C2×C4C2×#62611yescharacteristic
592C2×C4D3×#6712yes—
593C2×C4D3×#6712yes—
594C2×C4C22×D3211yescharacteristic
595C8—62no—
596C8—62no—
597C2×C3—21no—
598C2×C3—24no—
599C2×C3—21no—
600C2×C3—21no—
601C2×C3—44no—
602C2×C3—42no—
603C2×C3—42no—
604C2×C3—124no—
605C2×C3#473414yescomplemented
606C2×C3#523814yescomplemented
607C2×C3C2×#88211yescharacteristic
608C2×C3C2×#90411yescharacteristic
609C2×C3C2×#90811yescharacteristic
610C2×C3C2×#94911yescharacteristic
611C2×C3C2×#95011yescharacteristic
612C2×C3C2×#95311yescharacteristic
613D3—44no—
614D3—244no—
615D3—242no—
616D3—242no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—44no—
621C22—64no—
622C22—128no—
623C22—122no—
624C22—122no—
625C22—362no—
626C22—362no—
627C22—362no—
628C22—724no—
629C22#6382512yes—
630C22#6382912yes—
631C22#6397712yes—
632C22C22×#62611yescharacteristic
633C4—22no—
634C4—64no—
635C4—362no—
636C4#6397712yes—
637C4C2×D3×#6711yescharacteristic
638C4C2×D3×#6711yescharacteristic
639C3—21no—
640C3C2×#473411yescharacteristic, complemented
641C3C2×#523811yescharacteristic, complemented
642C2—42no—
643C2—124no—
644C2—722no—
645C2#1059116314yesdirect product factor
646C2C2×#6382511yescharacteristic
647C2C2×#6382911yescharacteristic
648C2C2×#6397711yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
hypercenterC23×C4D32
hypocenterC32C2×#449
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
1. C22×C3×#235C2semidirect
2. C2×#64139C2semidirect
3. C22×#3717C2semidirect
4. C22×#3714C2semidirect
5. C2×C3×#830C2semidirect
6. #10591163C2direct (N × H)
7. C2×#63566C2semidirect
8. C2×#63563C2semidirect
18. C2×C3×#235C22semidirect
23. #64139C22semidirect
29. C2×#3717C22semidirect
31. C2×#3714C22semidirect
32. C3×#830C22semidirect
33. #63566C22semidirect
34. #63563C22semidirect
36. C22×#235D3semidirect
48. C2×#830D3semidirect
76. C2×C3×D12D4semidirect
82. C2×C3×Dic6D4semidirect
112. C2×#235C2×D3semidirect
146. #830C2×D3semidirect
182. C3×D12C2×D4semidirect
186. C3×Dic6C2×D4semidirect
268. C2×D12#67semidirect
274. C2×Dic6#67semidirect
438. D12C2×#67semidirect
442. Dic6C2×#67semidirect
448. C2×C32#449semidirect
556. C32C2×#449semidirect
605. C2×C3#4734semidirect
606. C2×C3#5238semidirect
640. C3C2×#4734semidirect
641. C3C2×#5238semidirect
645. C2#10591163direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×#641392
C22×#37172
C22×#37142
C2×C3×#8302
#105911632
C2×#635662
C2×#635632
C2×#52383
C2×#47343