Finite Group Databasebeta

← C2×#10590966 #11863798

Subgroups — C2×#10590966 #11863798

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×#3799C211yesmaximal, characteristic
2C22×C3×Dic12C211yesmaximal, characteristic, complemented
3C2×#63856C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590966C218yesmaximal, direct product factor
9C2×#5187—31nomaximal
10C2×#4733—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×#624—21no—
17C2×#3799—24no—
18C2×#3799—22no—
19C2×#3799—24no—
20C2×#3799C2214yes—
21C22×C32×C8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×C3×Dic12—24no—
25C2×C3×Dic12C2214yescomplemented
26C2×#3724—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63856—22no—
29#63856C2214yescomplemented
30C2×#3717—24no—
31C2×#3717C2214yescomplemented
32#63648C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63566C2214yescomplemented
35C22×#239—31no—
36C22×#235—31no—
37C22×C3×Q16—31no—
38C2×#946—31no—
39C22×#215—31no—
40C2×#924—31no—
41C22×Dic12D311yescharacteristic, complemented
42C22×#204—31no—
43C2×C3×C22⋊C8—31no—
44C2×#835—31no—
45#5187—38no—
46C2×#821—31no—
47C2×#821—31no—
48C2×#821—61no—
49C2×(C2×D3)⋊C8D311yescharacteristic, complemented
50C2×#816—31no—
51#4733—38no—
52C23×C3⋊D3—21no—
53C23×C3×D3D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)D414yes—
59C2×C4⋊(C3⋊D3)C2312yes—
60C22×C3×Dic3—21no—
61C22×C3×Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C2×C3×C4×D3—22no—
64C2×C3×C4×D3—22no—
65C2×C3×C4×D3D412yes—
66C2×C3×C4×D3C2312yes—
67C2×C3×Dic6—21no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6—22no—
71C2×C3×Dic6—21no—
72C2×C3×Dic6D414yes—
73C2×C3×Dic6C2312yes—
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×#624—28no—
78C2×#624—24no—
79#3799—216no—
80#3799—28no—
81#3799—28no—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C2×C3×C3⋊C8—22no—
87C2×C3×C3⋊C8C2312yes—
88C3×Dic12—28no—
89#3724—24no—
90(C2×D3)⋊Dic3—24no—
91#3717—28no—
92C2×#452—91noSylow
93C22×C3×Q8—31no—
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C22×#67—61no—
97C2×#239—34no—
98C2×#239—64no—
99C2×#239—64no—
100C2×#239—62no—
101C2×#235—34no—
102C2×#235—64no—
103C2×#235—62no—
104C2×#235—64no—
105C22×D12—31no—
106C22×D12—31no—
107C22×D12—61no—
108C22×D12—61no—
109C22×C4×D3—61no—
110C22×C4×D3—61no—
111C22×C4×D3C2×D311yescharacteristic
112C22×Dic6C2×D311yescharacteristic
113C22×Dic6C2×D311yescharacteristic
114C2×C3×Q16—34no—
115C2×C3×Q16—64no—
116C22×C3×C8—21no—
117C22×C3×C8—31no—
118C22×C3×C8C2×D311yescharacteristic
119C22×C3×C8C2×D311yescharacteristic
120C2×#217—61no—
121#946—34no—
122#946—62no—
123C2×#215—34no—
124C2×#215—64no—
125C2×(C2×D3)⋊C4—61no—
126C2×C4⋊Dic3—31no—
127C2×C4⋊Dic3—31no—
128C2×C4⋊Dic3—61no—
129#924—34no—
130#924—62no—
131C2×Dic3⋊C4—61no—
132C2×Dic3⋊C4—61no—
133C22×C3⋊C8C2×D311yescharacteristic
134C2×Dic12—24no—
135C2×Dic12C2×D314yescomplemented
136C2×#204—34no—
137C2×#204—64no—
138C3×C22⋊C8—34no—
139#835—34no—
140#821—34no—
141#821—34no—
142#821—64no—
143(C2×D3)⋊C8C2×D314yescomplemented
144#816—34no—
145C23×C32C2×D411yescharacteristic
146C22×C3⋊D3—24no—
147C22×C3⋊D3—22no—
148C22×C3⋊D3—42no—
149C22×C3⋊D3—42no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3C2×D412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2411yescharacteristic
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3—42no—
160C4⋊(C3⋊D3)—24no—
161C4⋊(C3⋊D3)—22no—
162C4⋊(C3⋊D3)C2×D414yes—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—42no—
168C2×C3×Dic3C2×D412yes—
169C3×C4×D3—24no—
170C3×C4×D3—22no—
171C3×C4×D3—22no—
172C3×Dic6—24no—
173C3×Dic6—22no—
174C3×Dic6—22no—
175C3×Dic6—22no—
176C3×Dic6—42no—
177C3×Dic6C2×D414yes—
178#626—216no—
179#624—216no—
180C32×C8—22no—
181C3×C3⋊C8—22no—
182C22×#41—91no—
183C22×Q16—31no—
184C22×SD16—91no—
185C2×C22⋊Q8—91no—
186#452—98no—
187C2×#103—91no—
188C2×#102—91no—
189C2×C22⋊C8—31no—
190C24×C3—31no—
191C23×D3—61no—
192C23×D3—61no—
193C23×D3—121no—
194C23×D3D1211yescharacteristic
195C2×C3×Q8—34no—
196C2×C3×Q8—32no—
197C2×C3×Q8—32no—
198C2×C3×Q8—61no—
199C2×C3×Q8—61no—
200C2×C3×Q8—62no—
201C2×C3×Q8—62no—
202C2×C3×Q8—62no—
203C22×C3×C4—21no—
204C22×C3×C4—31no—
205C22×C3×C4—32no—
206C22×C3×C4—32no—
207C22×C3×C4—61no—
208C22×C3×C4—62no—
209C22×C3×C4—62no—
210C22×C3×C4—61no—
211C22×C3×C4C22×D311yescharacteristic
212C22×C3×C4C22×D311yescharacteristic
213C2×#67—64no—
214C2×#67—68no—
215C22×Dic3—21no—
216C22×Dic3—21no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—121no—
220C22×Dic3D1211yescharacteristic
221#239—68no—
222#239—68no—
223#239—616no—
224#235—68no—
225#235—616no—
226#235—68no—
227C2×D12—34no—
228C2×D12—34no—
229C2×D12—32no—
230C2×D12—32no—
231C2×D12—62no—
232C2×D12—64no—
233C2×D12—68no—
234C2×D12—64no—
235C2×D12—61no—
236C2×D12—61no—
237C2×D12—62no—
238C2×D12—62no—
239C2×D12—121no—
240C2×D12—122no—
241C2×C4×D3—22no—
242C2×C4×D3—22no—
243C2×C4×D3—64no—
244C2×C4×D3—68no—
245C2×C4×D3—68no—
246C2×C4×D3—64no—
247C2×C4×D3D1212yes—
248C2×C4×D3C22×D312yes—
249C2×Dic6—21no—
250C2×Dic6—22no—
251C2×Dic6—22no—
252C2×Dic6—22no—
253C2×Dic6—21no—
254C2×Dic6#6714yes—
255C2×Dic6C22×D312yes—
256C2×Dic6C22×D312yes—
257C3×Q16—68no—
258C2×C3×C8—22no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8—32no—
262C2×C3×C8—42no—
263C2×C3×C8—62no—
264C2×C3×C8C22×D312yes—
265C2×C3×C8C22×D312yes—
266#217—64no—
267#215—68no—
268(C2×D3)⋊C4—64no—
269C4⋊Dic3—32no—
270C4⋊Dic3—32no—
271C4⋊Dic3—62no—
272C4⋊Dic3—61no—
273C4⋊Dic3—61no—
274C4⋊Dic3—121no—
275Dic3⋊C4—64no—
276Dic3⋊C4—64no—
277C2×C3⋊C8—22no—
278C2×C3⋊C8C22×D312yes—
279Dic12—28no—
280#204—68no—
281C22×C32#12012yes—
282C22×C32#13512yes—
283C22×C32#13712yes—
284C22×C32C22×D411yescharacteristic
285C2×C3⋊D3—24no—
286C2×C3⋊D3—42no—
287C2×C3⋊D3—42no—
288C2×C3⋊D3—48no—
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—22no—
298C3×Dic3—24no—
299C3×Dic3—42no—
300C2×#41—94no—
301C2×#41—182no—
302C2×#41—184no—
303C2×#41—184no—
304C22×Q8—31no—
305C22×Q8—31no—
306C22×D4—91no—
307C22×D4—181no—
308C23×C4—31no—
309C23×C4—181no—
310C2×Q16—34no—
311C2×Q16—64no—
312C2×SD16—94no—
313C2×SD16—184no—
314C22×C8—31no—
315C22×C8D3211yescharacteristic
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—34no—
324C23×C3—21no—
325C23×C3—32no—
326C23×C3—62no—
327C23×C3—62no—
328C23×C3—62no—
329C23×C3C2×D1211yescharacteristic
330C23×C3D3×D411yescharacteristic
331C22×D3—22no—
332C22×D3—22no—
333C22×D3—22no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—62no—
337C22×D3—62no—
338C22×D3—122no—
339C22×D3—124no—
340C22×D3—122no—
341C22×D3—122no—
342C22×D3—122no—
343C22×D3—122no—
344C22×D3—242no—
345C22×D3—242no—
346C22×D3C2×D1212yes—
347C3×Q8—34no—
348C3×Q8—64no—
349C3×Q8—62no—
350C3×Q8—62no—
351C3×Q8—62no—
352C3×Q8—122no—
353C2×C3×C4—21no—
354C2×C3×C4—21no—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—32no—
358C2×C3×C4—64no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—64no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—62no—
365C2×C3×C4—122no—
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4D3×D411yescharacteristic
368C2×C3×C4D3×D412yes—
369C2×C3×C4D3×D412yes—
370C2×C3×C4D3×D412yes—
371C2×C3×C4C2×#6712yes—
372C2×C3×C4C23×D311yescharacteristic
373C2×C3×C4C23×D311yescharacteristic
374#67—616no—
375C2×Dic3—22no—
376C2×Dic3—24no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—42no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—122no—
383C2×Dic3—122no—
384C2×Dic3—122no—
385C2×Dic3—242no—
386C2×Dic3C2×D1212yes—
387D12—34no—
388D12—34no—
389D12—64no—
390D12—616no—
391D12—64no—
392D12—64no—
393D12—62no—
394D12—62no—
395D12—122no—
396D12—124no—
397C4×D3—24no—
398C4×D3—22no—
399C4×D3—22no—
400C4×D3—616no—
401C4×D3—616no—
402Dic6—24no—
403Dic6—22no—
404Dic6—22no—
405Dic6—22no—
406Dic6—42no—
407Dic6C2×#6714yes—
408C3×C8—22no—
409C3×C8—22no—
410C3×C8—42no—
411C3×C8—62no—
412C3⋊C8—22no—
413C2×C32#45214yescomplemented
414C2×C32C2×#12011yescharacteristic
415C2×C32C2×#13511yescharacteristic
416C2×C32C2×#13711yescharacteristic
417C3⋊D3—44no—
418C3×D3—42no—
419C24—31no—
420C24—181no—
421#41—188no—
422#41—188no—
423#41—1816no—
424C2×Q8—32no—
425C2×Q8—32no—
426C2×Q8—34no—
427C2×Q8—61no—
428C2×Q8—61no—
429C2×Q8—62no—
430C2×Q8—62no—
431C2×Q8—62no—
432C2×D4—92no—
433C2×D4—94no—
434C2×D4—184no—
435C2×D4—188no—
436C2×D4—181no—
437C2×D4—182no—
438C22×C4—31no—
439C22×C4—32no—
440C22×C4—32no—
441C22×C4—61no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—61no—
445C22×C4—184no—
446C22×C4—188no—
447C22×C4—181no—
448C22×C4C2×D3211yescharacteristic
449Q16—68no—
450SD16—188no—
451C2×C8—22no—
452C2×C8—32no—
453C2×C8—62no—
454C2×C8C2×D3212yes—
455C4⋊C4—92no—
456C4⋊C4—184no—
457C4⋊C4—181no—
458C22⋊C4—184no—
459C22×C3—21no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—62no—
464C22×C3—62no—
465C22×C3—62no—
466C22×C3—124no—
467C22×C3#88212yes—
468C22×C3#90412yes—
469C22×C3#90912yes—
470C22×C3#91812yes—
471C22×C3#91912yes—
472C22×C3#93712yes—
473C22×C3C22×D1211yescharacteristic
474C22×C3C2×D3×D411yescharacteristic
475C2×D3—22no—
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—44no—
479C2×D3—64no—
480C2×D3—64no—
481C2×D3—124no—
482C2×D3—128no—
483C2×D3—122no—
484C2×D3—122no—
485C2×D3—128no—
486C2×D3—122no—
487C2×D3—122no—
488C2×D3—242no—
489C2×D3—242no—
490C2×D3—248no—
491C3×C4—21no—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—64no—
495C3×C4—62no—
496C3×C4—122no—
497C3×C4#88212yes—
498C3×C4#93712yes—
499C3×C4C2×D3×D411yescharacteristic
500C3×C4C2×D3×D411yescharacteristic
501C3×C4C2×D3×D411yescharacteristic
502C3×C4C22×#6711yescharacteristic
503Dic3—22no—
504Dic3—24no—
505Dic3—42no—
506Dic3—122no—
507Dic3—122no—
508Dic3—242no—
509C32C2×#45211yescharacteristic, complemented, Sylow
510C23—32no—
511C23—62no—
512C23—62no—
513C23—62no—
514C23—182no—
515C23—184no—
516C23—362no—
517C23—362no—
518C23D3×D1211yescharacteristic
519Q8—34no—
520Q8—62no—
521Q8—64no—
522Q8—62no—
523Q8—62no—
524Q8—122no—
525D4—94no—
526D4—1816no—
527D4—182no—
528D4—184no—
529C2×C4—32no—
530C2×C4—62no—
531C2×C4—62no—
532C2×C4—64no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—64no—
536C2×C4—62no—
537C2×C4—122no—
538C2×C4—1816no—
539C2×C4—182no—
540C2×C4—362no—
541C2×C4D3×D1211yescharacteristic
542C2×C4#380212yes—
543C2×C4D3×#6712yes—
544C2×C4C22×D3211yescharacteristic
545C8—22no—
546C8—62no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—24no—
551C2×C3—122no—
552C2×C3#473314yescomplemented
553C2×C3#518714yescomplemented
554C2×C3C2×#88211yescharacteristic
555C2×C3C2×#90411yescharacteristic
556C2×C3C2×#90911yescharacteristic
557C2×C3C2×#91811yescharacteristic
558C2×C3C2×#91911yescharacteristic
559C2×C3C2×#93711yescharacteristic
560D3—42no—
561D3—124no—
562D3—124no—
563D3—244no—
564C22—62no—
565C22—62no—
566C22—62no—
567C22—124no—
568C22—184no—
569C22—362no—
570C22—362no—
571C22—368no—
572C22#6380112yes—
573C22#6380812yes—
574C22#6392212yes—
575C22C2×D3×D1211yescharacteristic
576C4—62no—
577C4—64no—
578C4—122no—
579C4—362no—
580C4#6392212yes—
581C4C2×#380211yescharacteristic
582C4C2×D3×#6711yescharacteristic
583C3—21no—
584C3C2×#473311yescharacteristic, complemented
585C3C2×#518711yescharacteristic, complemented
586C2—122no—
587C2—364no—
588C2#1059096614yesdirect product factor
589C2C2×#6380111yescharacteristic
590C2C2×#6380811yescharacteristic
591C2C2×#6392211yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3799C2
hypercenterC22×C8D32
hypocenterC32C2×#452
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
2. C22×C3×Dic12C2semidirect
3. C2×#63856C2semidirect
4. C22×#3717C2semidirect
5. C2×#63648C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63566C2semidirect
8. #10590966C2direct (N × H)
25. C2×C3×Dic12C22semidirect
29. #63856C22semidirect
31. C2×#3717C22semidirect
32. #63648C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63566C22semidirect
41. C22×Dic12D3semidirect
49. C2×(C2×D3)⋊C8D3semidirect
135. C2×Dic12C2×D3semidirect
143. (C2×D3)⋊C8C2×D3semidirect
413. C2×C32#452semidirect
509. C32C2×#452semidirect
552. C2×C3#4733semidirect
553. C2×C3#5187semidirect
584. C3C2×#4733semidirect
585. C3C2×#5187semidirect
588. C2#10590966direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×C3×Dic122
C2×#638562
C22×#37172
C2×#636482
C2×C3×(C2×D3)⋊C82
C2×#635662
#105909662
C2×#51873
C2×#47333