Finite Group Databasebeta

← C2×#10590951 #11863627

Subgroups — C2×#10590951 #11863627

Order 1152.

1733 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic, complemented
2C22×#3744C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590951C218yesmaximal, direct product factor
9C2×#4806—31nomaximal
10C2×#4738—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#627—21no—
16C22×#626—21no—
17C22×D3×Dic3—21no—
18C2×D3×Dic6—24no—
19C2×D3×Dic6—22no—
20C2×D3×Dic6—24no—
21C2×D3×Dic6C2214yescomplemented
22C22×C32×C8C2211yescharacteristic
23C2×#3744—24no—
24C2×#3744C2214yescomplemented
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×#3722—21no—
28#63909—22no—
29#63909C2214yes—
30C2×#3717—24no—
31C2×#3717C2214yescomplemented
32C3×(C2×D3)⋊C8C2214yescomplemented
33C3×#816C2214yescomplemented
34#63567C2214yescomplemented
35C22×D3×Q8—31no—
36C23×Dic6—31no—
37C22×#215—31no—
38C2×#930—31no—
39C22×#204—31no—
40C22×#204—31no—
41C22×#204—31no—
42C22×#204—61no—
43C2×#895—31no—
44C2×C3×#103—31no—
45C2×C3×C22⋊C8—31no—
46C2×(C2×D3)⋊C8D311yescharacteristic, complemented
47C2×#816—31no—
48C2×#816D311yescharacteristic, complemented
49C2×#810—31no—
50#4806—38no—
51#4738—38no—
52C23×C3⋊D3—21no—
53C23×C3×D3D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×#634—21no—
61C2×#634—22no—
62C2×#634D414yescomplemented
63C2×#634C2312yes—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yescomplemented
74C2×C3×Dic6C2312yes—
75C2×#627—28no—
76C2×#627—24no—
77C2×#626—24no—
78C2×#626—44no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—24no—
81D3×Dic6—216no—
82D3×Dic6—28no—
83D3×Dic6—28no—
84C2×C32×C8—22no—
85C2×C32×C8C2312yes—
86#3744—28no—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91#3722—24no—
92#3717—28no—
93C2×#448—91noSylow
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C22×#67—61no—
97C23×Dic3—61no—
98C2×D3×Q8—34no—
99C2×D3×Q8—64no—
100C2×D3×Q8—64no—
101C2×D3×Q8—62no—
102C22×D12—31no—
103C22×D12—31no—
104C22×D12—61no—
105C22×D12—61no—
106C22×C4×D3—61no—
107C22×C4×D3C2×D311yescharacteristic
108C22×Dic6—31no—
109C22×Dic6—31no—
110C22×Dic6—34no—
111C22×Dic6—61no—
112C22×Dic6—64no—
113C22×Dic6—62no—
114C22×Dic6—61no—
115C22×Dic6—61no—
116C22×Dic6—64no—
117C22×Dic6C2×D311yescharacteristic
118C22×C3×C8—21no—
119C22×C3×C8—31no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C2×D311yescharacteristic
122C2×C3×C4⋊C4—31no—
123C2×#215—34no—
124C2×#215—64no—
125#930—34no—
126#930—62no—
127C2×(C2×D3)⋊C4—61no—
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C22×C3⋊C8C2×D311yescharacteristic
131C2×#204—34no—
132C2×#204—34no—
133C2×#204—34no—
134C2×#204—64no—
135C2×#204—64no—
136C2×#204—64no—
137C2×#204—68no—
138C2×#204—64no—
139#895—34no—
140#895—62no—
141C3×#103—34no—
142C3×C22⋊C8—34no—
143(C2×D3)⋊C8C2×D314yescomplemented
144#816—34no—
145#816C2×D314yescomplemented
146#810—34no—
147C23×C32C2×D411yescharacteristic
148C22×C3⋊D3—22no—
149C22×C3⋊D3—42no—
150C22×C3⋊D3—42no—
151C22×C3⋊D3—42no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3SD1614yescomplemented
155C22×C3×D3C2×D412yes—
156C2×C32×C4C2×D411yescharacteristic
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D412yes—
159C2×C32×C4C2411yescharacteristic
160C2×C3⋊Dic3—24no—
161C2×C3⋊Dic3—22no—
162C4⋊(C3⋊D3)—22no—
163C4⋊(C3⋊D3)—22no—
164C4⋊(C3⋊D3)—42no—
165#634—24no—
166#634—22no—
167#634C2×D414yescomplemented
168C2×C3×Dic3—24no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—42no—
173C2×C3×Dic3C2×D412yes—
174C3×C4×D3—24no—
175C3×C4×D3—22no—
176C3×C4×D3—22no—
177C3×Dic6—24no—
178C3×Dic6—22no—
179C3×Dic6C2×D414yescomplemented
180#627—216no—
181#626—48no—
182D3×Dic3—216no—
183C32×C8—22no—
184C3×C3⋊C8—22no—
185C23×Q8—91no—
186C22×SD16—91no—
187C22×SD16—91no—
188C2×#121—91no—
189#448—98no—
190C2×#103—31no—
191C2×#103—91no—
192C2×C22⋊C8—31no—
193C24×C3—31no—
194C23×D3—61no—
195C23×D3—61no—
196C23×D3—121no—
197C23×D3D1211yescharacteristic
198C2×C3×Q8—34no—
199C2×C3×Q8—32no—
200C2×C3×Q8—61no—
201C2×C3×Q8—62no—
202C22×C3×C4—21no—
203C22×C3×C4—31no—
204C22×C3×C4—32no—
205C22×C3×C4—32no—
206C22×C3×C4—61no—
207C22×C3×C4—62no—
208C22×C3×C4—62no—
209C22×C3×C4—61no—
210C22×C3×C4C22×D311yescharacteristic
211C22×C3×C4C22×D311yescharacteristic
212C2×#67—64no—
213C2×#67—124no—
214C22×Dic3—21no—
215C22×Dic3—21no—
216C22×Dic3—64no—
217C22×Dic3—68no—
218C22×Dic3—61no—
219C22×Dic3—61no—
220C22×Dic3—121no—
221C22×Dic3D1211yescharacteristic
222D3×Q8—68no—
223D3×Q8—68no—
224D3×Q8—616no—
225C2×D12—32no—
226C2×D12—32no—
227C2×D12—62no—
228C2×D12—64no—
229C2×D12—62no—
230C2×D12—62no—
231C2×D12—62no—
232C2×D12—62no—
233C2×D12—64no—
234C2×D12—61no—
235C2×D12—61no—
236C2×D12—122no—
237C2×D12—121no—
238C2×D12—124no—
239C2×C4×D3—22no—
240C2×C4×D3—22no—
241C2×C4×D3—68no—
242C2×C4×D3—64no—
243C2×C4×D3D1212yes—
244C2×C4×D3C22×D312yes—
245C2×Dic6—21no—
246C2×Dic6—22no—
247C2×Dic6—34no—
248C2×Dic6—34no—
249C2×Dic6—32no—
250C2×Dic6—32no—
251C2×Dic6—64no—
252C2×Dic6—62no—
253C2×Dic6—68no—
254C2×Dic6—616no—
255C2×Dic6—64no—
256C2×Dic6—68no—
257C2×Dic6—68no—
258C2×Dic6—62no—
259C2×Dic6—61no—
260C2×Dic6—61no—
261C2×Dic6—62no—
262C2×Dic6—64no—
263C2×Dic6—68no—
264C2×Dic6—121no—
265C2×Dic6—122no—
266C2×Dic6D1214yescomplemented
267C2×Dic6C22×D312yes—
268C2×C3×C8—24no—
269C2×C3×C8—22no—
270C2×C3×C8—22no—
271C2×C3×C8—22no—
272C2×C3×C8—32no—
273C2×C3×C8—62no—
274C2×C3×C8C22×D312yes—
275C2×C3×C8C22×D312yes—
276C3×C4⋊C4—32no—
277C3×C4⋊C4—61no—
278#215—68no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281C4⋊Dic3—21no—
282C4⋊Dic3C22×D312yes—
283C2×C3⋊C8—22no—
284C2×C3⋊C8C22×D312yes—
285#204—68no—
286#204—68no—
287#204—616no—
288#204—68no—
289C22×C32#12012yes—
290C22×C32C2×SD1612yes—
291C22×C32#13712yes—
292C22×C32C22×D411yescharacteristic
293C2×C3⋊D3—42no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—42no—
296C2×C3⋊D3—84no—
297C2×C3×D3—22no—
298C2×C3×D3—22no—
299C2×C3×D3—28no—
300C2×C3×D3C2×SD1614yescomplemented
301C32×C4#12012yes—
302C32×C4C22×D411yescharacteristic
303C32×C4C22×D411yescharacteristic
304C3⋊Dic3—24no—
305C3×Dic3—24no—
306C3×Dic3—22no—
307C3×Dic3—42no—
308C22×Q8—31no—
309C22×Q8—94no—
310C22×Q8—91no—
311C22×Q8—181no—
312C22×Q8—182no—
313C22×Q8—184no—
314C22×Q8—184no—
315C22×D4—91no—
316C22×D4—181no—
317C23×C4—31no—
318C23×C4—181no—
319C2×SD16—94no—
320C2×SD16—94no—
321C2×SD16—184no—
322C2×SD16—184no—
323C22×C8—31no—
324C22×C8D3211yescharacteristic
325#121—94no—
326#121—182no—
327C2×C4⋊C4—31no—
328C2×C22⋊C4—181no—
329#103—34no—
330#103—94no—
331C22⋊C8—34no—
332C23×C3—21no—
333C23×C3—34no—
334C23×C3—32no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3C2×D1211yescharacteristic
338C23×C3D3×D411yescharacteristic
339C22×D3—22no—
340C22×D3—22no—
341C22×D3—62no—
342C22×D3—62no—
343C22×D3—122no—
344C22×D3—124no—
345C22×D3—122no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—122no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3—242no—
352C22×D3—242no—
353C22×D3#20414yescomplemented
354C22×D3C2×D1212yes—
355C3×Q8—34no—
356C3×Q8—64no—
357C3×Q8—62no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—32no—
363C2×C3×C4—62no—
364C2×C3×C4—64no—
365C2×C3×C4—62no—
366C2×C3×C4—64no—
367C2×C3×C4—62no—
368C2×C3×C4—62no—
369C2×C3×C4—62no—
370C2×C3×C4—122no—
371C2×C3×C4C2×D1211yescharacteristic
372C2×C3×C4C2×D1212yes—
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D412yes—
375C2×C3×C4D3×D412yes—
376C2×C3×C4D3×D412yes—
377C2×C3×C4C23×D311yescharacteristic
378C2×C3×C4C23×D311yescharacteristic
379#67—128no—
380C2×Dic3—24no—
381C2×Dic3—22no—
382C2×Dic3—22no—
383C2×Dic3—22no—
384C2×Dic3—42no—
385C2×Dic3—616no—
386C2×Dic3—64no—
387C2×Dic3—64no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—122no—
391C2×Dic3—124no—
392C2×Dic3C2×D1212yes—
393D12—64no—
394D12—62no—
395D12—62no—
396D12—62no—
397D12—62no—
398D12—122no—
399D12—124no—
400D12—128no—
401D12—122no—
402D12—122no—
403C4×D3—24no—
404C4×D3—22no—
405C4×D3—22no—
406C4×D3—616no—
407Dic6—24no—
408Dic6—22no—
409Dic6—34no—
410Dic6—34no—
411Dic6—64no—
412Dic6—616no—
413Dic6—616no—
414Dic6—64no—
415Dic6—64no—
416Dic6—62no—
417Dic6—62no—
418Dic6—122no—
419Dic6—124no—
420Dic6C2×D1214yescomplemented
421C3×C8—24no—
422C3×C8—22no—
423C3×C8—22no—
424C3×C8—62no—
425C3⋊C8—22no—
426C2×C32#44814yescomplemented
427C2×C32C2×#12011yescharacteristic
428C2×C32C22×SD1611yescharacteristic
429C2×C32C2×#13711yescharacteristic
430C3⋊D3—82no—
431C3×D3—24no—
432C24—31no—
433C24—181no—
434C2×Q8—32no—
435C2×Q8—34no—
436C2×Q8—61no—
437C2×Q8—62no—
438C2×Q8—92no—
439C2×Q8—94no—
440C2×Q8—184no—
441C2×Q8—188no—
442C2×Q8—188no—
443C2×Q8—188no—
444C2×Q8—1816no—
445C2×Q8—181no—
446C2×Q8—182no—
447C2×D4—92no—
448C2×D4—184no—
449C2×D4—182no—
450C2×D4—181no—
451C2×D4—182no—
452C2×D4—364no—
453C22×C4—31no—
454C22×C4—32no—
455C22×C4—32no—
456C22×C4—61no—
457C22×C4—62no—
458C22×C4—62no—
459C22×C4—61no—
460C22×C4—184no—
461C22×C4—188no—
462C22×C4—181no—
463C22×C4C2×D3211yescharacteristic
464SD16—188no—
465SD16—188no—
466C2×C8—22no—
467C2×C8—32no—
468C2×C8—62no—
469C2×C8C2×D3212yes—
470C4⋊C4—32no—
471C4⋊C4—61no—
472C22⋊C4—184no—
473C22×C3—21no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—34no—
478C22×C3—62no—
479C22×C3—62no—
480C22×C3—68no—
481C22×C3#88212yes—
482C22×C3#88212yes—
483C22×C3C2×#20412yes—
484C22×C3#90912yes—
485C22×C3D3×SD1612yes—
486C22×C3#91812yes—
487C22×C3C22×D1211yescharacteristic
488C22×C3C2×D3×D411yescharacteristic
489C2×D3—22no—
490C2×D3—22no—
491C2×D3—28no—
492C2×D3—124no—
493C2×D3—122no—
494C2×D3—122no—
495C2×D3—122no—
496C2×D3—122no—
497C2×D3—122no—
498C2×D3—122no—
499C2×D3—242no—
500C2×D3—242no—
501C2×D3—248no—
502C2×D3—244no—
503C2×D3—244no—
504C2×D3C2×#20414yescomplemented
505C3×C4—21no—
506C3×C4—21no—
507C3×C4—22no—
508C3×C4—62no—
509C3×C4—64no—
510C3×C4—122no—
511C3×C4#88212yes—
512C3×C4#88212yes—
513C3×C4C22×D1211yescharacteristic
514C3×C4C2×D3×D411yescharacteristic
515C3×C4C2×D3×D411yescharacteristic
516C3×C4C2×D3×D411yescharacteristic
517Dic3—24no—
518Dic3—22no—
519Dic3—42no—
520Dic3—64no—
521Dic3—64no—
522Dic3—124no—
523C32C2×#44811yescharacteristic, complemented, Sylow
524C23—32no—
525C23—34no—
526C23—62no—
527C23—62no—
528C23—182no—
529C23—362no—
530C23—362no—
531C23—362no—
532C23D3×D1211yescharacteristic
533Q8—34no—
534Q8—62no—
535Q8—64no—
536Q8—94no—
537Q8—1816no—
538Q8—182no—
539Q8—184no—
540D4—182no—
541D4—182no—
542D4—368no—
543D4—362no—
544C2×C4—32no—
545C2×C4—62no—
546C2×C4—62no—
547C2×C4—64no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—64no—
551C2×C4—62no—
552C2×C4—122no—
553C2×C4—1816no—
554C2×C4—182no—
555C2×C4—184no—
556C2×C4D3×D1212yes—
557C2×C4D3×D1211yescharacteristic
558C2×C4#381112yes—
559C2×C4C22×D3211yescharacteristic
560C8—22no—
561C8—62no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—24no—
565C2×C3—21no—
566C2×C3—64no—
567C2×C3#473814yescomplemented
568C2×C3#480614yescomplemented
569C2×C3C2×#88211yescharacteristic
570C2×C3C2×#88211yescharacteristic
571C2×C3C22×#20411yescharacteristic
572C2×C3C2×#90911yescharacteristic
573C2×C3C2×D3×SD1611yescharacteristic
574C2×C3C2×#91811yescharacteristic
575D3—24no—
576D3—244no—
577D3—242no—
578D3—242no—
579C22—34no—
580C22—62no—
581C22—68no—
582C22—62no—
583C22—362no—
584C22—362no—
585C22—362no—
586C22—724no—
587C22D3×#20412yes—
588C22#6380112yes—
589C22#6392312yes—
590C22C2×D3×D1211yescharacteristic
591C4—62no—
592C4—64no—
593C4—122no—
594C4—184no—
595C4#6392312yes—
596C4C2×D3×D1211yescharacteristic
597C4C2×#381111yescharacteristic
598C3—21no—
599C3C2×#473811yescharacteristic, complemented
600C3C2×#480611yescharacteristic, complemented
601C2—64no—
602C2—722no—
603C2#1059095114yesdirect product factor
604C2C2×D3×#20411yescharacteristic
605C2C2×#6380111yescharacteristic
606C2C2×#6392311yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63909C2
hypercenterC22×C8D32
hypocenterC32C2×#448
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×D3×Dic6C2semidirect
2. C22×#3744C2semidirect
4. C22×#3717C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63567C2semidirect
8. #10590951C2direct (N × H)
21. C2×D3×Dic6C22semidirect
24. C2×#3744C22semidirect
31. C2×#3717C22semidirect
32. C3×(C2×D3)⋊C8C22semidirect
33. C3×#816C22semidirect
34. #63567C22semidirect
46. C2×(C2×D3)⋊C8D3semidirect
48. C2×#816D3semidirect
62. C2×#634D4semidirect
73. C2×C3×Dic6D4semidirect
143. (C2×D3)⋊C8C2×D3semidirect
145. #816C2×D3semidirect
154. C22×C3×D3SD16semidirect
167. #634C2×D4semidirect
179. C3×Dic6C2×D4semidirect
266. C2×Dic6D12semidirect
300. C2×C3×D3C2×SD16semidirect
353. C22×D3#204semidirect
420. Dic6C2×D12semidirect
426. C2×C32#448semidirect
504. C2×D3C2×#204semidirect
523. C32C2×#448semidirect
567. C2×C3#4738semidirect
568. C2×C3#4806semidirect
599. C3C2×#4738semidirect
600. C3C2×#4806semidirect
603. C2#10590951direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C22×#37442
C2×#639092
C22×#37172
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C2×#635672
#105909512
C2×#48063
C2×#47383