Finite Group Databasebeta

← C2×#10591461 #11863785

Subgroups — C2×#10591461 #11863785

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 593 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C22×C3×#214C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic, complemented
4C22×#3718C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10591461C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5239—31nomaximal
10C2×#5173—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C23×C3×Dic3—21no—
14C2×C3×#237—24no—
15C2×C3×#237—22no—
16C2×C3×#237—24no—
17C2×C3×#237C2214yes—
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C2×C3×#214—24no—
24C2×C3×#214C2214yescomplemented
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3724—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63856—22no—
29#63856C2214yescomplemented
30C2×#3718—24no—
31C2×#3718C2214yescomplemented
32#63659C2214yescomplemented
33#63566C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×C3×#41—31no—
36C22×#237D311yescharacteristic
37C22×C3×SD16—31no—
38C2×#946—31no—
39C22×#216—31no—
40C22×#216—31no—
41C22×#214D311yescharacteristic, complemented
42C2×#924—31no—
43#5239—38no—
44C2×#835—31no—
45C2×#832—31no—
46C2×#832—31no—
47C2×#832—61no—
48C2×#830—31no—
49#5173—38no—
50C2×(C2×D3)⋊C8—31no—
51C2×#816—31no—
52C24×C32—21no—
53C23×C3×D3D411yescharacteristic
54C2×C32×D4—21no—
55C2×C32×D4—22no—
56C2×C32×D4D414yes—
57C2×C32×D4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3—21no—
60C2×C3×#67—28no—
61C2×C3×#67—24no—
62C22×C3×Dic3—28no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3—24no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C3×#237—216no—
68C3×#237—28no—
69C3×#237—28no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3D412yes—
73C2×C3×C4×D3C2312yes—
74C2×C3×Dic6—21no—
75C2×C3×Dic6—22no—
76C2×C3×Dic6—22no—
77C2×C3×Dic6—22no—
78C2×C3×Dic6—21no—
79C2×C3×Dic6D414yes—
80C2×C3×Dic6C2312yes—
81C2×C3×Dic6C2312yes—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2312yes—
86C3×#214—28no—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89#3724—24no—
90(C2×D3)⋊Dic3—24no—
91#3718—28no—
92C2×#452—91noSylow
93C2×C3×#41—34no—
94C2×C3×#41—62no—
95C2×C3×#41—64no—
96C2×C3×#41—64no—
97C22×C3×Q8—31no—
98C22×C3×Q8—31no—
99C22×C3×D4—21no—
100C22×C3×D4—61no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C2×D311yescharacteristic
103C23×C3×C4—31no—
104C23×C3×C4—61no—
105C22×#67—21no—
106C23×Dic3—21no—
107C2×#237—24no—
108C2×#237—22no—
109C2×#237—24no—
110C2×#237C2×D314yes—
111C22×C4×D3C2×D311yescharacteristic
112C22×Dic6C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C2×C3×SD16—34no—
115C2×C3×SD16—64no—
116C22×C3×C8—31no—
117C2×#217—61no—
118#946—34no—
119#946—62no—
120C2×#216—34no—
121C2×#216—34no—
122C2×#216—64no—
123C2×#216—64no—
124C2×#214—24no—
125C2×#214C2×D314yescomplemented
126C2×(C2×D3)⋊C4—61no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—31no—
129C2×C4⋊Dic3—61no—
130#924—34no—
131#924—62no—
132C2×Dic3⋊C4—61no—
133C2×Dic3⋊C4—61no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—61no—
137C22×C3⋊C8C2×D311yescharacteristic
138#835—34no—
139#832—34no—
140#832—34no—
141#832—64no—
142#830—34no—
143(C2×D3)⋊C8—34no—
144#816—34no—
145C23×C32—24no—
146C23×C32—22no—
147C23×C32—42no—
148C23×C32—42no—
149C23×C32C2×D411yescharacteristic
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3C2×D412yes—
154C32×D4—24no—
155C32×D4—22no—
156C32×D4C2×D414yes—
157C2×C32×C4C2×D411yescharacteristic
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2411yescharacteristic
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—42no—
163C3×#67—216no—
164C2×C3×Dic3—216no—
165C2×C3×Dic3—24no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—42no—
170C2×C3×Dic3C2×D412yes—
171C3×C4×D3—24no—
172C3×C4×D3—22no—
173C3×C4×D3—22no—
174C3×Dic6—24no—
175C3×Dic6—22no—
176C3×Dic6—22no—
177C3×Dic6—22no—
178C3×Dic6—42no—
179C3×Dic6C2×D414yes—
180C3⋊(C3⋊C8)—22no—
181C3×C3⋊C8—22no—
182C22×#41—31no—
183C22×Q16—91no—
184C22×SD16—31no—
185C2×C22⋊Q8—91no—
186#452—98no—
187C2×#103—91no—
188C2×#102—91no—
189C2×C22⋊C8—91no—
190C24×C3—21no—
191C24×C3—21no—
192C24×C3—31no—
193C24×C3—41no—
194C23×D3#6711yescharacteristic
195C3×#41—68no—
196C3×#41—616no—
197C3×#41—68no—
198C2×C3×Q8—34no—
199C2×C3×Q8—32no—
200C2×C3×Q8—32no—
201C2×C3×Q8—61no—
202C2×C3×Q8—62no—
203C2×C3×Q8—61no—
204C2×C3×Q8—62no—
205C2×C3×Q8—62no—
206C2×C3×D4—21no—
207C2×C3×D4—22no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—24no—
211C2×C3×D4—22no—
212C2×C3×D4—42no—
213C2×C3×D4—41no—
214C2×C3×D4—64no—
215C2×C3×D4—68no—
216C2×C3×D4#6714yes—
217C2×C3×D4#6714yes—
218C2×C3×D4C22×D312yes—
219C2×C3×D4C22×D312yes—
220C22×C3×C4—21no—
221C22×C3×C4—31no—
222C22×C3×C4—32no—
223C22×C3×C4—32no—
224C22×C3×C4—64no—
225C22×C3×C4—68no—
226C22×C3×C4—61no—
227C22×C3×C4—62no—
228C22×C3×C4—62no—
229C22×C3×C4—61no—
230C22×C3×C4C22×D311yescharacteristic
231C22×C3×C4C22×D311yescharacteristic
232C2×#67—28no—
233C2×#67—24no—
234C22×Dic3—28no—
235C22×Dic3—21no—
236C22×Dic3—24no—
237C22×Dic3—21no—
238C22×Dic3—61no—
239C22×Dic3—61no—
240C22×Dic3—121no—
241C22×Dic3#6711yescharacteristic
242#237—216no—
243#237—28no—
244#237—28no—
245C2×C4×D3—22no—
246C2×C4×D3—22no—
247C2×C4×D3#6712yes—
248C2×C4×D3C22×D312yes—
249C2×Dic6—22no—
250C2×Dic6—21no—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—21no—
254C2×Dic6#6714yes—
255C2×Dic6C22×D312yes—
256C2×Dic6C22×D312yes—
257C3×SD16—68no—
258C2×C3×C8—32no—
259C2×C3×C8—62no—
260#217—64no—
261#216—68no—
262#216—68no—
263#214—28no—
264(C2×D3)⋊C4—64no—
265C4⋊Dic3—32no—
266C4⋊Dic3—32no—
267C4⋊Dic3—62no—
268C4⋊Dic3—61no—
269C4⋊Dic3—61no—
270C4⋊Dic3—121no—
271Dic3⋊C4—64no—
272Dic3⋊C4—64no—
273C2×C3⋊C8—22no—
274C2×C3⋊C8—32no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—62no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—122no—
280C2×C3⋊C8C22×D312yes—
281C22×C32—24no—
282C22×C32—42no—
283C22×C32—42no—
284C22×C32—48no—
285C22×C32#12012yes—
286C22×C32#13512yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—22no—
291C2×C3×D3—22no—
292C2×C3×D3—44no—
293C32×C4#12012yes—
294C32×C4C22×D411yescharacteristic
295C32×C4C22×D411yescharacteristic
296C3⋊Dic3—42no—
297C3×Dic3—24no—
298C3×Dic3—22no—
299C3×Dic3—42no—
300C2×#41—34no—
301C2×#41—62no—
302C2×#41—64no—
303C2×#41—64no—
304C22×Q8—31no—
305C22×Q8—31no—
306C22×D4—61no—
307C22×D4D3211yescharacteristic
308C23×C4—31no—
309C23×C4—61no—
310C2×Q16—94no—
311C2×Q16—184no—
312C2×SD16—34no—
313C2×SD16—64no—
314C22×C8—31no—
315C22×C8—91no—
316C22⋊Q8—94no—
317C22⋊Q8—182no—
318C2×C4⋊C4—91no—
319C2×C4⋊C4—181no—
320C2×C22⋊C4—181no—
321#103—94no—
322#102—94no—
323C22⋊C8—94no—
324C23×C3—24no—
325C23×C3—24no—
326C23×C3—22no—
327C23×C3—22no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—42no—
331C23×C3—44no—
332C23×C3—42no—
333C23×C3—42no—
334C23×C3—42no—
335C23×C3—42no—
336C23×C3—62no—
337C23×C3—62no—
338C23×C3—62no—
339C23×C3—82no—
340C23×C3—82no—
341C23×C3D3×D411yescharacteristic
342C23×C3C2×#6711yescharacteristic
343C22×D3—22no—
344C22×D3—22no—
345C22×D3—22no—
346C22×D3C2×#6712yes—
347C3×Q8—34no—
348C3×Q8—64no—
349C3×Q8—62no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C3×D4—24no—
354C3×D4—24no—
355C3×D4—22no—
356C3×D4—22no—
357C3×D4—24no—
358C3×D4—42no—
359C3×D4—44no—
360C3×D4—616no—
361C3×D4C2×#6714yes—
362C3×D4C2×#6714yes—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—22no—
366C2×C3×C4—21no—
367C2×C3×C4—32no—
368C2×C3×C4—616no—
369C2×C3×C4—62no—
370C2×C3×C4—64no—
371C2×C3×C4—62no—
372C2×C3×C4—64no—
373C2×C3×C4—62no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—122no—
377C2×C3×C4D3×D411yescharacteristic
378C2×C3×C4D3×D412yes—
379C2×C3×C4C2×#6712yes—
380C2×C3×C4C2×#6712yes—
381C2×C3×C4C2×#6711yescharacteristic
382C2×C3×C4C2×#6712yes—
383C2×C3×C4C23×D311yescharacteristic
384C2×C3×C4C23×D311yescharacteristic
385#67—216no—
386C2×Dic3—216no—
387C2×Dic3—24no—
388C2×Dic3—22no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—42no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—122no—
395C2×Dic3—122no—
396C2×Dic3—122no—
397C2×Dic3—242no—
398C2×Dic3C2×#6712yes—
399C4×D3—24no—
400C4×D3—22no—
401C4×D3—22no—
402Dic6—24no—
403Dic6—22no—
404Dic6—22no—
405Dic6—22no—
406Dic6—42no—
407Dic6C2×#6714yes—
408C3×C8—62no—
409C3⋊C8—22no—
410C3⋊C8—62no—
411C3⋊C8—62no—
412C3⋊C8—122no—
413C2×C32—44no—
414C2×C32#45214yescomplemented
415C2×C32C2×#12011yescharacteristic
416C2×C32C2×#13511yescharacteristic
417C2×C32C2×#13711yescharacteristic
418C3×D3—42no—
419C24—21no—
420C24—31no—
421#41—68no—
422#41—616no—
423#41—68no—
424C2×Q8—32no—
425C2×Q8—32no—
426C2×Q8—34no—
427C2×Q8—62no—
428C2×Q8—61no—
429C2×Q8—61no—
430C2×Q8—62no—
431C2×Q8—62no—
432C2×D4—22no—
433C2×D4—21no—
434C2×D4—64no—
435C2×D4—68no—
436C2×D4#62514yes—
437C2×D4C2×D3212yes—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—64no—
442C22×C4—68no—
443C22×C4—61no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—61no—
447C22×C4—181no—
448C22×C4C2×D3211yescharacteristic
449Q16—188no—
450SD16—68no—
451C2×C8—32no—
452C2×C8—62no—
453C2×C8—92no—
454C2×C8—182no—
455C4⋊C4—92no—
456C4⋊C4—184no—
457C4⋊C4—181no—
458C22⋊C4—184no—
459C22×C3—24no—
460C22×C3—24no—
461C22×C3—21no—
462C22×C3—22no—
463C22×C3—22no—
464C22×C3—22no—
465C22×C3—44no—
466C22×C3—48no—
467C22×C3—48no—
468C22×C3—42no—
469C22×C3—42no—
470C22×C3—42no—
471C22×C3—42no—
472C22×C3—62no—
473C22×C3—62no—
474C22×C3—62no—
475C22×C3—82no—
476C22×C3—82no—
477C22×C3—88no—
478C22×C3—124no—
479C22×C3#91512yes—
480C22×C3#91612yes—
481C22×C3#93712yes—
482C22×C3#95012yes—
483C22×C3#95112yes—
484C22×C3#95312yes—
485C22×C3C2×D3×D411yescharacteristic
486C22×C3C22×#6711yescharacteristic
487C2×D3—22no—
488C2×D3—22no—
489C2×D3—22no—
490C2×D3—44no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—62no—
495C3×C4—64no—
496C3×C4—122no—
497C3×C4#93712yes—
498C3×C4#95312yes—
499C3×C4C2×D3×D411yescharacteristic
500C3×C4C22×#6711yescharacteristic
501C3×C4C22×#6711yescharacteristic
502C3×C4C22×#6711yescharacteristic
503Dic3—24no—
504Dic3—22no—
505Dic3—42no—
506Dic3—122no—
507Dic3—122no—
508Dic3—242no—
509C32C2×#45211yescharacteristic, complemented, Sylow
510C23—22no—
511C23—24no—
512C23—32no—
513C23—42no—
514C23—42no—
515C23—62no—
516C23—62no—
517C23—62no—
518C23D3×#6711yescharacteristic
519Q8—34no—
520Q8—62no—
521Q8—64no—
522Q8—62no—
523Q8—62no—
524Q8—122no—
525D4—22no—
526D4—24no—
527D4—616no—
528D4C2×#62514yes—
529C2×C4—32no—
530C2×C4—616no—
531C2×C4—62no—
532C2×C4—62no—
533C2×C4—64no—
534C2×C4—62no—
535C2×C4—62no—
536C2×C4—64no—
537C2×C4—62no—
538C2×C4—122no—
539C2×C4—182no—
540C2×C4—362no—
541C2×C4C2×#62512yes—
542C2×C4D3×#6712yes—
543C2×C4D3×#6711yescharacteristic
544C2×C4C22×D3211yescharacteristic
545C8—62no—
546C8—182no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—24no—
551C2×C3—44no—
552C2×C3—44no—
553C2×C3—84no—
554C2×C3—122no—
555C2×C3#517314yescomplemented
556C2×C3#523914yescomplemented
557C2×C3C2×#91511yescharacteristic
558C2×C3C2×#91611yescharacteristic
559C2×C3C2×#93711yescharacteristic
560C2×C3C2×#95011yescharacteristic
561C2×C3C2×#95111yescharacteristic
562C2×C3C2×#95311yescharacteristic
563D3—42no—
564C22—24no—
565C22—42no—
566C22—42no—
567C22—48no—
568C22—62no—
569C22—62no—
570C22—62no—
571C22—124no—
572C22#6392912yes—
573C22#6393512yes—
574C22#6397612yes—
575C22C2×D3×#6711yescharacteristic
576C4—62no—
577C4—64no—
578C4—122no—
579C4—362no—
580C4#6397612yes—
581C4C22×#62511yescharacteristic
582C4C2×D3×#6711yescharacteristic
583C3—21no—
584C3C2×#517311yescharacteristic, complemented
585C3C2×#523911yescharacteristic, complemented
586C2—44no—
587C2—122no—
588C2#1059146114yesdirect product factor
589C2C2×#6392911yescharacteristic
590C2C2×#6393511yescharacteristic
591C2C2×#6397611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#237C2
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×#63856C2semidirect
4. C22×#3718C2semidirect
5. C2×#63659C2semidirect
6. #10591461C2direct (N × H)
7. C2×#63566C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
24. C2×C3×#214C22semidirect
29. #63856C22semidirect
31. C2×#3718C22semidirect
32. #63659C22semidirect
33. #63566C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
41. C22×#214D3semidirect
125. C2×#214C2×D3semidirect
414. C2×C32#452semidirect
509. C32C2×#452semidirect
555. C2×C3#5173semidirect
556. C2×C3#5239semidirect
584. C3C2×#5173semidirect
585. C3C2×#5239semidirect
588. C2#10591461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×C3×#2142
C2×#638562
C22×#37182
C2×#636592
#105914612
C2×#635662
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52393
C2×#51733