Finite Group Databasebeta

← C2×#10591463 #11863783

Subgroups — C2×#10591463 #11863783

Order 1152.

1669 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2C22×#3754C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic, complemented
4C22×#3719C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591463C218yesmaximal, direct product factor
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5239—31nomaximal
10C2×#4783—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×#67—21no—
14C23×C3×Dic3—21no—
15C2×C3×#237—24no—
16C2×C3×#237—22no—
17C2×C3×#237—24no—
18C2×C3×#237C2214yes—
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C2×#3754—24no—
22C2×#3754C2214yescomplemented
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×Dic3⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63857—22no—
29#63857C2214yescomplemented
30C2×#3719—24no—
31C2×#3719C2214yescomplemented
32C3×#832C2214yescomplemented
33#63565C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×C3×#41—31no—
36C22×#237D311yescharacteristic
37C22×#216—31no—
38C22×#214—31no—
39C22×#214—31no—
40C22×#214—61no—
41C2×#924—31no—
42C22×Dic12—31no—
43C2×#897—31no—
44C2×C3×#102—31no—
45#5239—38no—
46C2×#835—31no—
47C2×#832D311yescharacteristic, complemented
48C2×#830—31no—
49C2×(C2×D3)⋊C8—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
59C22×C3⋊Dic3—21no—
60C2×#634—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634C2312yes—
64C2×C3×#67—28no—
65C2×C3×#67—24no—
66C22×C3×Dic3—28no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—24no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3D411yescharacteristic
71C3×#237—216no—
72C3×#237—28no—
73C3×#237—28no—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3D412yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×Dic6—21no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6D414yes—
81C2×C3×Dic6C2312yes—
82#3754—28no—
83C2×C3⋊(C3⋊C8)—22no—
84C2×C3⋊(C3⋊C8)C2312yes—
85C3×C4⋊Dic3—21no—
86C3×C4⋊Dic3C2312yes—
87C2×C3×C3⋊C8—22no—
88C2×C3×C3⋊C8C2312yes—
89Dic3⋊Dic3—24no—
90(C2×D3)⋊Dic3—24no—
91#3719—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×D4—21no—
99C22×C3×D4—61no—
100C22×C3×D4C2×D311yescharacteristic
101C22×C3×D4C2×D311yescharacteristic
102C23×C3×C4—31no—
103C23×C3×C4—61no—
104C22×#67—21no—
105C23×Dic3—21no—
106C2×#237—24no—
107C2×#237—22no—
108C2×#237—24no—
109C2×#237C2×D314yes—
110C22×C4×D3C2×D311yescharacteristic
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C22×Dic6C2×D311yescharacteristic
115C22×C3×C8—31no—
116C2×C3×C4⋊C4—31no—
117C2×#217—61no—
118C2×#216—34no—
119C2×#216—64no—
120C2×#214—34no—
121C2×#214—34no—
122C2×#214—64no—
123C2×#214—68no—
124C2×#214—64no—
125C2×#214—64no—
126C2×(C2×D3)⋊C4—61no—
127C2×C4⋊Dic3—61no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129#924—34no—
130#924—62no—
131C2×Dic3⋊C4—61no—
132C22×C3⋊C8—31no—
133C22×C3⋊C8—31no—
134C22×C3⋊C8—61no—
135C22×C3⋊C8C2×D311yescharacteristic
136C2×Dic12—34no—
137C2×Dic12—64no—
138#897—34no—
139#897—62no—
140C3×#102—34no—
141#835—34no—
142#832C2×D314yescomplemented
143#830—34no—
144(C2×D3)⋊C8—34no—
145#810—34no—
146C23×C32—24no—
147C23×C32—22no—
148C23×C32—42no—
149C23×C32—42no—
150C23×C32C2×D411yescharacteristic
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3C2×D412yes—
155C32×D4—24no—
156C32×D4—22no—
157C32×D4C2×D414yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2×D411yescharacteristic
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2411yescharacteristic
162C2×C3⋊Dic3—22no—
163C2×C3⋊Dic3—42no—
164#634—22no—
165#634—22no—
166#634—42no—
167C3×#67—216no—
168C2×C3×Dic3—216no—
169C2×C3×Dic3—24no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—42no—
174C2×C3×Dic3C2×D412yes—
175C3×C4×D3—24no—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×Dic6—24no—
179C3×Dic6—22no—
180C3×Dic6C2×D414yes—
181C3⋊(C3⋊C8)—22no—
182C3×C3⋊C8—22no—
183C22×#41—31no—
184C22×Q16—91no—
185C22×SD16—91no—
186C2×C22⋊Q8—91no—
187#452—98no—
188C2×#103—91no—
189C2×#102—31no—
190C2×C22⋊C8—91no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3—31no—
194C24×C3—41no—
195C23×D3#6711yescharacteristic
196C3×#41—68no—
197C3×#41—616no—
198C3×#41—68no—
199C2×C3×Q8—34no—
200C2×C3×Q8—32no—
201C2×C3×Q8—62no—
202C2×C3×Q8—61no—
203C2×C3×D4—21no—
204C2×C3×D4—22no—
205C2×C3×D4—21no—
206C2×C3×D4—22no—
207C2×C3×D4—24no—
208C2×C3×D4—22no—
209C2×C3×D4—42no—
210C2×C3×D4—41no—
211C2×C3×D4—64no—
212C2×C3×D4—68no—
213C2×C3×D4D1214yes—
214C2×C3×D4#6714yes—
215C2×C3×D4C22×D312yes—
216C2×C3×D4C22×D312yes—
217C22×C3×C4—21no—
218C22×C3×C4—31no—
219C22×C3×C4—32no—
220C22×C3×C4—32no—
221C22×C3×C4—64no—
222C22×C3×C4—68no—
223C22×C3×C4—61no—
224C22×C3×C4—62no—
225C22×C3×C4—62no—
226C22×C3×C4—61no—
227C22×C3×C4C22×D311yescharacteristic
228C22×C3×C4C22×D311yescharacteristic
229C2×#67—28no—
230C2×#67—24no—
231C22×Dic3—28no—
232C22×Dic3—21no—
233C22×Dic3—24no—
234C22×Dic3—21no—
235C22×Dic3—61no—
236C22×Dic3—61no—
237C22×Dic3—121no—
238C22×Dic3#6711yescharacteristic
239#237—216no—
240#237—28no—
241#237—28no—
242C2×C4×D3—22no—
243C2×C4×D3—22no—
244C2×C4×D3#6712yes—
245C2×C4×D3C22×D312yes—
246C2×Dic6—22no—
247C2×Dic6—21no—
248C2×Dic6—32no—
249C2×Dic6—32no—
250C2×Dic6—62no—
251C2×Dic6—64no—
252C2×Dic6—62no—
253C2×Dic6—62no—
254C2×Dic6—62no—
255C2×Dic6—62no—
256C2×Dic6—61no—
257C2×Dic6—61no—
258C2×Dic6—121no—
259C2×Dic6—122no—
260C2×Dic6#6714yes—
261C2×Dic6C22×D312yes—
262C2×C3×C8—32no—
263C2×C3×C8—62no—
264C3×C4⋊C4—32no—
265C3×C4⋊C4—61no—
266#217—64no—
267#216—68no—
268#214—616no—
269#214—68no—
270#214—68no—
271(C2×D3)⋊C4—64no—
272C4⋊Dic3—21no—
273C4⋊Dic3—64no—
274C4⋊Dic3C22×D312yes—
275Dic3⋊C4—64no—
276C2×C3⋊C8—22no—
277C2×C3⋊C8—32no—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—64no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8C22×D312yes—
284Dic12—68no—
285C22×C32—24no—
286C22×C32—42no—
287C22×C32—42no—
288C22×C32—48no—
289C22×C32#12012yes—
290C22×C32#13512yes—
291C22×C32#13712yes—
292C22×C32C22×D411yescharacteristic
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—22no—
296C2×C3×D3—44no—
297C32×C4#12012yes—
298C32×C4C22×D411yescharacteristic
299C32×C4C22×D411yescharacteristic
300C3⋊Dic3—42no—
301C3×Dic3—24no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C2×#41—34no—
305C2×#41—62no—
306C2×#41—64no—
307C2×#41—64no—
308C22×Q8—31no—
309C22×Q8—91no—
310C22×D4—61no—
311C22×D4D3211yescharacteristic
312C23×C4—31no—
313C23×C4—61no—
314C2×Q16—94no—
315C2×Q16—184no—
316C2×SD16—94no—
317C2×SD16—184no—
318C22×C8—31no—
319C22×C8—91no—
320C22⋊Q8—94no—
321C22⋊Q8—182no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—181no—
324C2×C22⋊C4—181no—
325#103—94no—
326#102—34no—
327C22⋊C8—94no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—32no—
334C23×C3—42no—
335C23×C3—44no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—42no—
340C23×C3—62no—
341C23×C3—62no—
342C23×C3—62no—
343C23×C3—82no—
344C23×C3—82no—
345C23×C3D3×D411yescharacteristic
346C23×C3C2×#6711yescharacteristic
347C22×D3—22no—
348C22×D3—22no—
349C22×D3—22no—
350C22×D3C2×#6712yes—
351C3×Q8—34no—
352C3×Q8—64no—
353C3×Q8—62no—
354C3×D4—24no—
355C3×D4—24no—
356C3×D4—22no—
357C3×D4—22no—
358C3×D4—24no—
359C3×D4—42no—
360C3×D4—44no—
361C3×D4—616no—
362C3×D4C2×D1214yes—
363C3×D4C2×#6714yes—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—21no—
368C2×C3×C4—32no—
369C2×C3×C4—616no—
370C2×C3×C4—62no—
371C2×C3×C4—64no—
372C2×C3×C4—62no—
373C2×C3×C4—64no—
374C2×C3×C4—62no—
375C2×C3×C4—62no—
376C2×C3×C4—62no—
377C2×C3×C4—122no—
378C2×C3×C4C2×D1212yes—
379C2×C3×C4D3×D411yescharacteristic
380C2×C3×C4D3×D412yes—
381C2×C3×C4C2×#6712yes—
382C2×C3×C4C2×#6711yescharacteristic
383C2×C3×C4C2×#6712yes—
384C2×C3×C4C23×D311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386#67—216no—
387C2×Dic3—216no—
388C2×Dic3—24no—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—22no—
392C2×Dic3—42no—
393C2×Dic3—62no—
394C2×Dic3—62no—
395C2×Dic3—122no—
396C2×Dic3—124no—
397C2×Dic3—122no—
398C2×Dic3—122no—
399C2×Dic3C2×#6712yes—
400C4×D3—24no—
401C4×D3—22no—
402C4×D3—22no—
403Dic6—24no—
404Dic6—22no—
405Dic6—64no—
406Dic6—62no—
407Dic6—62no—
408Dic6—62no—
409Dic6—62no—
410Dic6—122no—
411Dic6—124no—
412Dic6—122no—
413Dic6—122no—
414Dic6C2×#6714yes—
415C3×C8—62no—
416C3⋊C8—22no—
417C3⋊C8—64no—
418C3⋊C8—62no—
419C3⋊C8—62no—
420C2×C32—44no—
421C2×C32#45214yescomplemented
422C2×C32C2×#12011yescharacteristic
423C2×C32C2×#13511yescharacteristic
424C2×C32C2×#13711yescharacteristic
425C3×D3—42no—
426C24—21no—
427C24—31no—
428#41—68no—
429#41—616no—
430#41—68no—
431C2×Q8—32no—
432C2×Q8—34no—
433C2×Q8—62no—
434C2×Q8—61no—
435C2×Q8—92no—
436C2×Q8—181no—
437C2×Q8—182no—
438C2×Q8—182no—
439C2×D4—22no—
440C2×D4—21no—
441C2×D4—64no—
442C2×D4—68no—
443C2×D4#62614yes—
444C2×D4C2×D3212yes—
445C22×C4—31no—
446C22×C4—32no—
447C22×C4—32no—
448C22×C4—64no—
449C22×C4—68no—
450C22×C4—61no—
451C22×C4—62no—
452C22×C4—62no—
453C22×C4—61no—
454C22×C4—181no—
455C22×C4C2×D3211yescharacteristic
456Q16—188no—
457SD16—188no—
458C2×C8—32no—
459C2×C8—62no—
460C2×C8—92no—
461C2×C8—182no—
462C4⋊C4—32no—
463C4⋊C4—61no—
464C4⋊C4—184no—
465C22⋊C4—184no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—21no—
469C22×C3—22no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—44no—
473C22×C3—48no—
474C22×C3—42no—
475C22×C3—42no—
476C22×C3—48no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3—62no—
482C22×C3—82no—
483C22×C3—82no—
484C22×C3—88no—
485C22×C3—124no—
486C22×C3#88212yes—
487C22×C3#91212yes—
488C22×C3#91512yes—
489C22×C3#95012yes—
490C22×C3#95112yes—
491C22×C3#95312yes—
492C22×C3C2×D3×D411yescharacteristic
493C22×C3C22×#6711yescharacteristic
494C2×D3—22no—
495C2×D3—22no—
496C2×D3—22no—
497C2×D3—44no—
498C3×C4—21no—
499C3×C4—21no—
500C3×C4—22no—
501C3×C4—62no—
502C3×C4—64no—
503C3×C4—122no—
504C3×C4#88212yes—
505C3×C4#95312yes—
506C3×C4C22×D1211yescharacteristic
507C3×C4C2×D3×D411yescharacteristic
508C3×C4C22×#6711yescharacteristic
509C3×C4C22×#6711yescharacteristic
510Dic3—24no—
511Dic3—22no—
512Dic3—42no—
513Dic3—124no—
514Dic3—122no—
515Dic3—122no—
516C32C2×#45211yescharacteristic, complemented, Sylow
517C23—22no—
518C23—24no—
519C23—32no—
520C23—42no—
521C23—42no—
522C23—62no—
523C23—62no—
524C23—62no—
525C23D3×#6711yescharacteristic
526Q8—34no—
527Q8—62no—
528Q8—64no—
529Q8—182no—
530Q8—182no—
531Q8—362no—
532D4—22no—
533D4—24no—
534D4—616no—
535D4C2×#62614yes—
536C2×C4—32no—
537C2×C4—616no—
538C2×C4—62no—
539C2×C4—62no—
540C2×C4—64no—
541C2×C4—62no—
542C2×C4—62no—
543C2×C4—64no—
544C2×C4—62no—
545C2×C4—122no—
546C2×C4—182no—
547C2×C4—362no—
548C2×C4C2×#62612yes—
549C2×C4D3×#6712yes—
550C2×C4D3×#6711yescharacteristic
551C2×C4C22×D3211yescharacteristic
552C8—62no—
553C8—182no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—24no—
558C2×C3—44no—
559C2×C3—44no—
560C2×C3—84no—
561C2×C3—122no—
562C2×C3#478314yescomplemented
563C2×C3#523914yescomplemented
564C2×C3C2×#88211yescharacteristic
565C2×C3C2×#91211yescharacteristic
566C2×C3C2×#91511yescharacteristic
567C2×C3C2×#95011yescharacteristic
568C2×C3C2×#95111yescharacteristic
569C2×C3C2×#95311yescharacteristic
570D3—42no—
571C22—24no—
572C22—42no—
573C22—42no—
574C22—48no—
575C22—62no—
576C22—62no—
577C22—62no—
578C22—124no—
579C22#6392912yes—
580C22#6393312yes—
581C22#6397712yes—
582C22C2×D3×#6711yescharacteristic
583C4—62no—
584C4—64no—
585C4—122no—
586C4—362no—
587C4#6397712yes—
588C4C22×#62611yescharacteristic
589C4C2×D3×#6711yescharacteristic
590C3—21no—
591C3C2×#478311yescharacteristic, complemented
592C3C2×#523911yescharacteristic, complemented
593C2—44no—
594C2—122no—
595C2#1059146314yesdirect product factor
596C2C2×#6392911yescharacteristic
597C2C2×#6393311yescharacteristic
598C2C2×#6397711yescharacteristic
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×#3754C2semidirect
3. C2×#63857C2semidirect
4. C22×#3719C2semidirect
5. C2×C3×#832C2semidirect
6. #10591463C2direct (N × H)
7. C2×#63565C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
22. C2×#3754C22semidirect
29. #63857C22semidirect
31. C2×#3719C22semidirect
32. C3×#832C22semidirect
33. #63565C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
47. C2×#832D3semidirect
142. #832C2×D3semidirect
421. C2×C32#452semidirect
516. C32C2×#452semidirect
562. C2×C3#4783semidirect
563. C2×C3#5239semidirect
591. C3C2×#4783semidirect
592. C3C2×#5239semidirect
595. C2#10591463direct (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×#37542
C2×#638572
C22×#37192
C2×C3×#8322
#105914632
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52393
C2×#47833