Finite Group Databasebeta

← C2×#10591602 #11863796

Subgroups — C2×#10591602 #11863796

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×#3832C211yesmaximal, characteristic
2C22×C3×#216C211yesmaximal, characteristic, complemented
3C2×#63871C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×C3×#835C211yesmaximal, characteristic, complemented
6#10591602C218yesmaximal, direct product factor
7C2×#63564C211yesmaximal, characteristic, complemented
8C2×#63557C211yesmaximal, characteristic, complemented
9C2×#5187—31nomaximal
10C2×#4808—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×#3832—24no—
13C2×#3832—24no—
14C2×#3832—22no—
15C2×#3832C2214yes—
16C22×C4⋊(C3⋊D3)—21no—
17C22×C4⋊(C3⋊D3)C2211yescharacteristic
18C22×C4×C3⋊D3—21no—
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×C3×#216—24no—
22C2×C3×#216C2214yescomplemented
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×#3717—24no—
31C2×#3717C2214yescomplemented
32C3×#835C2214yescomplemented
33#63564C2214yescomplemented
34#63557C2214yescomplemented
35C22×#239—31no—
36C22×#239—31no—
37C22×#239—61no—
38C22×C3×Q16—31no—
39C2×#946—31no—
40C22×#216D311yescharacteristic, complemented
41C22×#215—31no—
42C22×#204—31no—
43C2×#897—31no—
44C2×C3×#103—31no—
45C2×#835D311yescharacteristic, complemented
46#5187—38no—
47C2×#821—31no—
48C2×(C2×D3)⋊C8—31no—
49C2×(C2×D3)⋊C8—31no—
50C2×#809—31no—
51#4808—38no—
52C23×C3⋊D3—21no—
53C23×C3⋊D3D411yescharacteristic
54C2×C32×Q8—22no—
55C2×C32×Q8—21no—
56C2×C32×Q8D414yes—
57C2×C32×Q8C2312yes—
58C22×C32×C4—21no—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3D411yescharacteristic
61#3832—216no—
62#3832—28no—
63#3832—28no—
64C2×C4⋊(C3⋊D3)—28no—
65C2×C4⋊(C3⋊D3)—24no—
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—22no—
72C2×C4×C3⋊D3—22no—
73C2×C4×C3⋊D3—24no—
74C2×C4×C3⋊D3D412yes—
75C2×C4×C3⋊D3C2312yes—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C2×C3×Dic6—22no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6C2312yes—
82C3×#216—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#3717—28no—
92C2×#452—91noSylow
93C22×C3×Q8—21no—
94C22×C3×Q8—31no—
95C22×C3×Q8C2×D311yescharacteristic
96C22×C3×Q8C2×D311yescharacteristic
97C2×#239—34no—
98C2×#239—34no—
99C2×#239—64no—
100C2×#239—62no—
101C2×#239—62no—
102C2×#239—64no—
103C2×#239—64no—
104C2×#239—64no—
105C2×#239—68no—
106C2×#239—68no—
107C2×#239—64no—
108C2×#239—64no—
109C22×D12—31no—
110C22×D12—31no—
111C22×D12—61no—
112C22×D12—61no—
113C22×D12—61no—
114C22×D12—62no—
115C22×C4×D3—31no—
116C22×C4×D3—31no—
117C22×C4×D3—61no—
118C22×C4×D3—61no—
119C22×C4×D3—61no—
120C22×C4×D3—62no—
121C22×Dic6C2×D311yescharacteristic
122C2×C3×Q16—34no—
123C2×C3×Q16—64no—
124C22×C3×C8—31no—
125C22×C3×C8—31no—
126C2×C3×C4⋊C4—31no—
127#946—34no—
128#946—62no—
129C2×#216—24no—
130C2×#216C2×D314yescomplemented
131C2×#215—34no—
132C2×#215—64no—
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×#204—34no—
141C2×#204—64no—
142#897—34no—
143#897—62no—
144C3×#103—34no—
145#835C2×D314yescomplemented
146#821—34no—
147(C2×D3)⋊C8—34no—
148(C2×D3)⋊C8—34no—
149#809—34no—
150C23×C32C2×D411yescharacteristic
151C22×C3⋊D3—24no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—42no—
157C22×C3⋊D3—42no—
158C22×C3⋊D3C2×D412yes—
159C32×Q8—24no—
160C32×Q8—22no—
161C32×Q8C2×D414yes—
162C2×C32×C4—24no—
163C2×C32×C4—22no—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3C2×D412yes—
170C4⋊(C3⋊D3)—216no—
171C4⋊(C3⋊D3)—24no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)C2×D414yes—
174C4×C3⋊D3—216no—
175C4×C3⋊D3—24no—
176C4×C3⋊D3—22no—
177C4×C3⋊D3—22no—
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—31no—
189C22×SD16—91no—
190C2×C22⋊Q8—91no—
191#452—98no—
192C2×#103—31no—
193C2×#102—91no—
194C2×C22⋊C8—91no—
195C23×D3—31no—
196C23×D3—31no—
197C23×D3—61no—
198C23×D3—62no—
199C23×D3—61no—
200C23×D3—61no—
201C2×C3×Q8—22no—
202C2×C3×Q8—24no—
203C2×C3×Q8—22no—
204C2×C3×Q8—22no—
205C2×C3×Q8—21no—
206C2×C3×Q8—21no—
207C2×C3×Q8—24no—
208C2×C3×Q8—22no—
209C2×C3×Q8—32no—
210C2×C3×Q8—61no—
211C2×C3×Q8—62no—
212C2×C3×Q8—62no—
213C2×C3×Q8D1214yes—
214C2×C3×Q8#6714yes—
215C2×C3×Q8C22×D312yes—
216C2×C3×Q8C22×D312yes—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—61no—
222C22×C3×C4—61no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C22×Dic3—21no—
226C22×Dic3—21no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—61no—
230#239—68no—
231#239—68no—
232#239—616no—
233#239—632no—
234#239—616no—
235#239—616no—
236#239—616no—
237#239—68no—
238#239—68no—
239C2×D12—34no—
240C2×D12—34no—
241C2×D12—32no—
242C2×D12—32no—
243C2×D12—64no—
244C2×D12—62no—
245C2×D12—64no—
246C2×D12—64no—
247C2×D12—68no—
248C2×D12—616no—
249C2×D12—68no—
250C2×D12—68no—
251C2×D12—64no—
252C2×D12—62no—
253C2×D12—62no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—62no—
257C2×C4×D3—32no—
258C2×C4×D3—32no—
259C2×C4×D3—32no—
260C2×C4×D3—32no—
261C2×C4×D3—62no—
262C2×C4×D3—62no—
263C2×C4×D3—64no—
264C2×C4×D3—64no—
265C2×C4×D3—68no—
266C2×C4×D3—616no—
267C2×C4×D3—68no—
268C2×C4×D3—68no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—62no—
272C2×C4×D3—62no—
273C2×C4×D3—62no—
274C2×C4×D3—62no—
275C2×Dic6—22no—
276C2×Dic6—22no—
277C2×Dic6—21no—
278C2×Dic6C22×D312yes—
279C3×Q16—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—28no—
287#215—68no—
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—
298#204—68no—
299C22×C32#12012yes—
300C22×C32#13512yes—
301C22×C32#13712yes—
302C22×C32C22×D411yescharacteristic
303C2×C3⋊D3—22no—
304C2×C3⋊D3—24no—
305C2×C3⋊D3—22no—
306C2×C3⋊D3—22no—
307C2×C3⋊D3—42no—
308C2×C3⋊D3—42no—
309C2×C3⋊D3—44no—
310C2×C3⋊D3—48no—
311C32×C4—24no—
312C32×C4#12012yes—
313C32×C4C22×D411yescharacteristic
314C32×C4C22×D411yescharacteristic
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×Q8D3211yescharacteristic
324C22×D4—91no—
325C22×D4—181no—
326C23×C4—91no—
327C23×C4—181no—
328C2×Q16—34no—
329C2×Q16—64no—
330C2×SD16—94no—
331C2×SD16—184no—
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—34no—
340#102—94no—
341C22⋊C8—94no—
342C23×C3—21no—
343C23×C3D3×D411yescharacteristic
344C23×C3D3×D411yescharacteristic
345C22×D3—32no—
346C22×D3—32no—
347C22×D3—62no—
348C22×D3—64no—
349C22×D3—68no—
350C22×D3—64no—
351C22×D3—64no—
352C22×D3—62no—
353C22×D3—62no—
354C22×D3—62no—
355C22×D3—62no—
356C22×D3—62no—
357C22×D3—64no—
358C22×D3—62no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—122no—
362C22×D3—122no—
363C22×D3—124no—
364C22×D3—124no—
365C22×D3—122no—
366C22×D3—122no—
367C22×D3—122no—
368C22×D3—122no—
369C3×Q8—24no—
370C3×Q8—28no—
371C3×Q8—24no—
372C3×Q8—24no—
373C3×Q8—22no—
374C3×Q8—22no—
375C3×Q8—24no—
376C3×Q8—62no—
377C3×Q8—62no—
378C3×Q8—122no—
379C3×Q8C2×D1214yes—
380C3×Q8C2×#6714yes—
381C2×C3×C4—24no—
382C2×C3×C4—28no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—21no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—122no—
394C2×C3×C4—122no—
395C2×C3×C4C2×D1212yes—
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D412yes—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D412yes—
400C2×C3×C4C2×#6712yes—
401C2×C3×C4C23×D311yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—32no—
406C2×Dic3—32no—
407C2×Dic3—42no—
408C2×Dic3—42no—
409C2×Dic3—62no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413D12—34no—
414D12—34no—
415D12—64no—
416D12—632no—
417D12—616no—
418D12—616no—
419D12—64no—
420D12—68no—
421D12—64no—
422D12—64no—
423D12—62no—
424D12—62no—
425C4×D3—632no—
426C4×D3—616no—
427C4×D3—616no—
428C4×D3—64no—
429C4×D3—64no—
430C4×D3—68no—
431C4×D3—64no—
432C4×D3—64no—
433C4×D3—62no—
434C4×D3—62no—
435C4×D3—62no—
436C4×D3—62no—
437Dic6—22no—
438Dic6—22no—
439Dic6—42no—
440C3×C8—62no—
441C3×C8—62no—
442C3⋊C8—22no—
443C3⋊C8—22no—
444C2×C32#45214yescomplemented
445C2×C32C2×#12011yescharacteristic
446C2×C32C2×#13511yescharacteristic
447C2×C32C2×#13711yescharacteristic
448C3⋊D3—42no—
449C3⋊D3—44no—
450C24—91no—
451C24—181no—
452#41—188no—
453#41—1816no—
454#41—188no—
455C2×Q8—21no—
456C2×Q8—22no—
457C2×Q8—32no—
458C2×Q8—61no—
459C2×Q8—62no—
460C2×Q8—62no—
461C2×Q8#62614yes—
462C2×Q8C2×D3212yes—
463C2×D4—92no—
464C2×D4—94no—
465C2×D4—184no—
466C2×D4—188no—
467C2×D4—182no—
468C2×D4—181no—
469C22×C4—21no—
470C22×C4—61no—
471C22×C4—61no—
472C22×C4—91no—
473C22×C4—92no—
474C22×C4—92no—
475C22×C4—184no—
476C22×C4—188no—
477C22×C4—182no—
478C22×C4—182no—
479C22×C4C2×D3211yescharacteristic
480Q16—68no—
481SD16—188no—
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—21no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3#88212yes—
495C22×C3#91612yes—
496C22×C3#91812yes—
497C22×C3#91812yes—
498C22×C3#91912yes—
499C22×C3#93712yes—
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C2×D3—68no—
503C2×D3—64no—
504C2×D3—64no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—62no—
508C2×D3—62no—
509C2×D3—62no—
510C2×D3—64no—
511C2×D3—62no—
512C2×D3—122no—
513C2×D3—122no—
514C2×D3—124no—
515C2×D3—124no—
516C2×D3—128no—
517C2×D3—1216no—
518C2×D3—124no—
519C2×D3—128no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—124no—
525C2×D3—128no—
526C3×C4—28no—
527C3×C4—24no—
528C3×C4—24no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—122no—
533C3×C4—122no—
534C3×C4#88212yes—
535C3×C4#93712yes—
536C3×C4C22×D1211yescharacteristic
537C3×C4C2×D3×D411yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×#6711yescharacteristic
540Dic3—42no—
541Dic3—42no—
542Dic3—64no—
543Dic3—62no—
544Dic3—62no—
545C32C2×#45211yescharacteristic, complemented, Sylow
546C23—92no—
547C23—182no—
548C23—182no—
549C23—182no—
550C23—184no—
551C23—182no—
552C23—362no—
553C23—362no—
554C23#381111yescharacteristic
555Q8—22no—
556Q8—24no—
557Q8—62no—
558Q8—62no—
559Q8—122no—
560Q8C2×#62614yes—
561D4—94no—
562D4—1816no—
563D4—182no—
564D4—184no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—92no—
570C2×C4—122no—
571C2×C4—122no—
572C2×C4—1816no—
573C2×C4—182no—
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—24no—
586C2×C3—21no—
587C2×C3#480814yescomplemented
588C2×C3#518714yescomplemented
589C2×C3C2×#88211yescharacteristic
590C2×C3C2×#91611yescharacteristic
591C2×C3C2×#91811yescharacteristic
592C2×C3C2×#91811yescharacteristic
593C2×C3C2×#91911yescharacteristic
594C2×C3C2×#93711yescharacteristic
595D3—124no—
596D3—128no—
597D3—122no—
598D3—124no—
599D3—122no—
600D3—124no—
601C22—182no—
602C22—182no—
603C22—184no—
604C22—182no—
605C22—362no—
606C22—362no—
607C22—364no—
608C22—368no—
609C22#6394512yes—
610C22#6395012yes—
611C22#6398112yes—
612C22C2×#381111yescharacteristic
613C4—24no—
614C4—122no—
615C4—122no—
616C4—182no—
617C4#6398112yes—
618C4C22×#62611yescharacteristic
619C4C2×#381111yescharacteristic
620C3—21no—
621C3C2×#480811yescharacteristic, complemented
622C3C2×#518711yescharacteristic, complemented
623C2—362no—
624C2—364no—
625C2#1059160214yesdirect product factor
626C2C2×#6394511yescharacteristic
627C2C2×#6395011yescharacteristic
628C2C2×#6398111yescharacteristic
subgroupG/H
centerC23#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC22×#3832C2
hypercenterC22×Q8D32
hypocenterC32C2×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C22×C3×#216C2semidirect
3. C2×#63871C2semidirect
4. C22×#3717C2semidirect
5. C2×C3×#835C2semidirect
6. #10591602C2direct (N × H)
7. C2×#63564C2semidirect
8. C2×#63557C2semidirect
22. C2×C3×#216C22semidirect
29. #63871C22semidirect
31. C2×#3717C22semidirect
32. C3×#835C22semidirect
33. #63564C22semidirect
34. #63557C22semidirect
40. C22×#216D3semidirect
45. C2×#835D3semidirect
130. C2×#216C2×D3semidirect
145. #835C2×D3semidirect
444. C2×C32#452semidirect
545. C32C2×#452semidirect
587. C2×C3#4808semidirect
588. C2×C3#5187semidirect
621. C3C2×#4808semidirect
622. C3C2×#5187semidirect
625. C2#10591602direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38322
C22×C3×#2162
C2×#638712
C22×#37172
C2×C3×#8352
#105916022
C2×#635642
C2×#635572
C2×#51873
C2×#48083