Finite Group Databasebeta

← C2×#10590969 #11863800

Subgroups — C2×#10590969 #11863800

Order 1152.

1649 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3795C211yesmaximal, characteristic
2C22×#3746C211yesmaximal, characteristic, complemented
3C2×#63857C211yesmaximal, characteristic, complemented
4C22×#3716C211yesmaximal, characteristic, complemented
5C2×C3×#821C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
7C2×#63567C211yesmaximal, characteristic, complemented
8#10590969C218yesmaximal, direct product factor
9C2×#4783—31nomaximal
10C2×#4733—31nomaximal
11C22×#634C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C22×#625—21no—
16C22×D3×Dic3—21no—
17C2×#3795—24no—
18C2×#3795—24no—
19C2×#3795—22no—
20C2×#3795C2214yes—
21C22×C32×C8C2211yescharacteristic
22C2×#3746—24no—
23C2×#3746C2214yescomplemented
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×Dic3⋊Dic3—21no—
27C2×(C2×D3)⋊Dic3—21no—
28#63857—22no—
29#63857C2214yescomplemented
30C2×#3716—24no—
31C2×#3716C2214yescomplemented
32C3×#821C2214yescomplemented
33C3×(C2×D3)⋊C8C2214yescomplemented
34#63567C2214yescomplemented
35C22×#237—31no—
36C22×#235—31no—
37C22×#214—31no—
38C2×#924—31no—
39C22×Dic12—31no—
40C22×Dic12—31no—
41C22×Dic12—61no—
42C22×#204—31no—
43C2×#897—31no—
44C2×C3×#102—31no—
45C2×C3×C22⋊C8—31no—
46C2×#821D311yescharacteristic, complemented
47C2×(C2×D3)⋊C8D311yescharacteristic, complemented
48C2×#816—31no—
49C2×#810—31no—
50#4783—38no—
51#4733—38no—
52C23×C3×D3—21no—
53C23×C3×D3D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3—21no—
57C2×#634—21no—
58C2×#634—22no—
59C2×#634—22no—
60C2×#634—22no—
61C2×#634—21no—
62C2×#634D414yes—
63C2×#634C2312yes—
64C2×#634C2312yes—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×D12—21no—
68C2×C3×D12—22no—
69C2×C3×D12D414yes—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×C4×D3—22no—
73C2×C3×C4×D3D412yes—
74C2×C3×C4×D3C2312yes—
75C2×#625—28no—
76C2×#625—24no—
77C2×D3×Dic3—28no—
78C2×D3×Dic3—24no—
79#3795—216no—
80#3795—28no—
81#3795—28no—
82C2×C32×C8—22no—
83C2×C32×C8C2312yes—
84#3746—28no—
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#3716—28no—
92C2×#452—91noSylow
93C22×C3×D4—31no—
94C23×C3×C4—31no—
95C22×#67—61no—
96C22×#67—61no—
97C23×Dic3—61no—
98C2×#237—34no—
99C2×#237—64no—
100C2×#237—64no—
101C2×#237—62no—
102C2×#235—34no—
103C2×#235—64no—
104C2×#235—62no—
105C2×#235—64no—
106C22×D12C2×D311yescharacteristic
107C22×C4×D3—61no—
108C22×C4×D3C2×D311yescharacteristic
109C22×Dic6—31no—
110C22×Dic6—31no—
111C22×Dic6—31no—
112C22×Dic6—31no—
113C22×Dic6—61no—
114C22×Dic6—61no—
115C22×C3×C8—21no—
116C22×C3×C8—31no—
117C22×C3×C8C2×D311yescharacteristic
118C22×C3×C8C2×D311yescharacteristic
119C2×C3×C4⋊C4—31no—
120C2×#217—61no—
121C2×#214—34no—
122C2×#214—64no—
123C2×(C2×D3)⋊C4—61no—
124C2×C4⋊Dic3—61no—
125C2×C4⋊Dic3C2×D311yescharacteristic
126#924—34no—
127#924—62no—
128C2×Dic3⋊C4—61no—
129C22×C3⋊C8C2×D311yescharacteristic
130C2×Dic12—34no—
131C2×Dic12—34no—
132C2×Dic12—64no—
133C2×Dic12—64no—
134C2×Dic12—64no—
135C2×Dic12—68no—
136C2×#204—34no—
137C2×#204—64no—
138#897—34no—
139#897—62no—
140C3×#102—34no—
141C3×C22⋊C8—34no—
142#821C2×D314yescomplemented
143(C2×D3)⋊C8C2×D314yescomplemented
144#816—34no—
145#810—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—42no—
153C22×C3×D3—42no—
154C22×C3×D3C2×D412yes—
155C2×C32×C4C2×D411yescharacteristic
156C2×C32×C4C2×D412yes—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2411yescharacteristic
159C2×C3⋊Dic3—24no—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—42no—
163#634—22no—
164#634—24no—
165#634—22no—
166#634—22no—
167#634—42no—
168#634C2×D414yes—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—42no—
172C2×C3×Dic3C2×D412yes—
173C3×D12—24no—
174C3×D12—22no—
175C3×D12C2×D414yes—
176C3×C4×D3—24no—
177C3×C4×D3—22no—
178C3×C4×D3—22no—
179#625—216no—
180D3×Dic3—216no—
181C32×C8—22no—
182C3×C3⋊C8—22no—
183C22×#41—91no—
184C22×Q16—91no—
185C22×SD16—91no—
186C2×C22⋊Q8—91no—
187#452—98no—
188C2×#103—91no—
189C2×#102—31no—
190C2×C22⋊C8—31no—
191C24×C3—31no—
192C24×C3—61no—
193C23×D3—21no—
194C23×D3D1211yescharacteristic
195C2×C3×D4—34no—
196C2×C3×D4—32no—
197C2×C3×D4—61no—
198C2×C3×D4—62no—
199C22×C3×C4—21no—
200C22×C3×C4—31no—
201C22×C3×C4—32no—
202C22×C3×C4—32no—
203C22×C3×C4—62no—
204C22×C3×C4—62no—
205C22×C3×C4—61no—
206C22×C3×C4C22×D311yescharacteristic
207C22×C3×C4C22×D311yescharacteristic
208C2×#67—64no—
209C2×#67—68no—
210C2×#67—68no—
211C2×#67—64no—
212C22×Dic3—21no—
213C22×Dic3—68no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—64no—
217C22×Dic3—61no—
218C22×Dic3—61no—
219C22×Dic3—121no—
220C22×Dic3—121no—
221C22×Dic3D1211yescharacteristic
222#237—68no—
223#237—68no—
224#237—616no—
225#235—68no—
226#235—616no—
227#235—68no—
228C2×D12—21no—
229C2×D12—22no—
230C2×D12D1214yes—
231C2×D12C22×D312yes—
232C2×C4×D3—22no—
233C2×C4×D3—22no—
234C2×C4×D3—64no—
235C2×C4×D3—68no—
236C2×C4×D3D1212yes—
237C2×C4×D3C22×D312yes—
238C2×Dic6—34no—
239C2×Dic6—34no—
240C2×Dic6—32no—
241C2×Dic6—32no—
242C2×Dic6—32no—
243C2×Dic6—32no—
244C2×Dic6—64no—
245C2×Dic6—62no—
246C2×Dic6—62no—
247C2×Dic6—62no—
248C2×Dic6—61no—
249C2×Dic6—61no—
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—121no—
261C2×Dic6—122no—
262C2×C3×C8—24no—
263C2×C3×C8—22no—
264C2×C3×C8—22no—
265C2×C3×C8—22no—
266C2×C3×C8—32no—
267C2×C3×C8—62no—
268C2×C3×C8C22×D312yes—
269C2×C3×C8C22×D312yes—
270C3×C4⋊C4—32no—
271C3×C4⋊C4—61no—
272#217—64no—
273#214—68no—
274(C2×D3)⋊C4—64no—
275C4⋊Dic3—21no—
276C4⋊Dic3—64no—
277C4⋊Dic3C22×D312yes—
278Dic3⋊C4—64no—
279C2×C3⋊C8—22no—
280C2×C3⋊C8C22×D312yes—
281Dic12—68no—
282Dic12—68no—
283Dic12—616no—
284#204—68no—
285C22×C32#12012yes—
286C22×C32#13512yes—
287C22×C32#13712yes—
288C22×C32C22×D411yescharacteristic
289C2×C3×D3—24no—
290C2×C3×D3—22no—
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C2×C3×D3—44no—
296C2×C3×D3—48no—
297C32×C4#12012yes—
298C32×C4C22×D411yescharacteristic
299C32×C4C22×D411yescharacteristic
300C3⋊Dic3—24no—
301C3⋊Dic3—42no—
302C3×Dic3—22no—
303C3×Dic3—42no—
304C2×#41—94no—
305C2×#41—182no—
306C2×#41—184no—
307C2×#41—184no—
308C22×Q8—91no—
309C22×Q8—91no—
310C22×D4—31no—
311C22×D4—181no—
312C23×C4—31no—
313C23×C4—181no—
314C2×Q16—94no—
315C2×Q16—184no—
316C2×SD16—94no—
317C2×SD16—184no—
318C22×C8—31no—
319C22×C8D3211yescharacteristic
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—34no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—64no—
331C23×C3—62no—
332C23×C3—62no—
333C23×C3—62no—
334C23×C3—62no—
335C23×C3—122no—
336C23×C3—122no—
337C23×C3C2×D1211yescharacteristic
338C23×C3D3×D411yescharacteristic
339C22×D3—22no—
340C22×D3—24no—
341C22×D3—22no—
342C22×D3—22no—
343C22×D3—22no—
344C22×D3—42no—
345C22×D3—42no—
346C22×D3C2×D1212yes—
347C3×D4—34no—
348C3×D4—64no—
349C3×D4—62no—
350C2×C3×C4—21no—
351C2×C3×C4—22no—
352C2×C3×C4—21no—
353C2×C3×C4—22no—
354C2×C3×C4—32no—
355C2×C3×C4—62no—
356C2×C3×C4—64no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—122no—
361C2×C3×C4C2×D1211yescharacteristic
362C2×C3×C4C2×D1212yes—
363C2×C3×C4D3×D411yescharacteristic
364C2×C3×C4D3×D412yes—
365C2×C3×C4D3×D412yes—
366C2×C3×C4D3×D412yes—
367C2×C3×C4C23×D311yescharacteristic
368C2×C3×C4C23×D311yescharacteristic
369#67—616no—
370#67—616no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—42no—
374C2×Dic3—616no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—122no—
382C2×Dic3—124no—
383C2×Dic3—122no—
384C2×Dic3—124no—
385C2×Dic3—122no—
386C2×Dic3—122no—
387C2×Dic3C2×D1212yes—
388D12—24no—
389D12—22no—
390D12C2×D1214yes—
391C4×D3—24no—
392C4×D3—22no—
393C4×D3—22no—
394C4×D3—616no—
395Dic6—34no—
396Dic6—34no—
397Dic6—64no—
398Dic6—64no—
399Dic6—64no—
400Dic6—62no—
401Dic6—62no—
402Dic6—64no—
403Dic6—62no—
404Dic6—62no—
405Dic6—62no—
406Dic6—62no—
407Dic6—122no—
408Dic6—124no—
409Dic6—122no—
410Dic6—124no—
411Dic6—122no—
412Dic6—122no—
413C3×C8—24no—
414C3×C8—22no—
415C3×C8—22no—
416C3×C8—62no—
417C3⋊C8—22no—
418C2×C32#45214yescomplemented
419C2×C32C2×#12011yescharacteristic
420C2×C32C2×#13511yescharacteristic
421C2×C32C2×#13711yescharacteristic
422C3×D3—42no—
423C3×D3—44no—
424C24—31no—
425C24—61no—
426#41—188no—
427#41—188no—
428#41—1816no—
429C2×Q8—92no—
430C2×Q8—92no—
431C2×Q8—94no—
432C2×Q8—181no—
433C2×Q8—182no—
434C2×Q8—181no—
435C2×Q8—182no—
436C2×Q8—182no—
437C2×D4—32no—
438C2×D4—34no—
439C2×D4—61no—
440C2×D4—62no—
441C2×D4—184no—
442C2×D4—188no—
443C22×C4—31no—
444C22×C4—32no—
445C22×C4—32no—
446C22×C4—62no—
447C22×C4—62no—
448C22×C4—61no—
449C22×C4—184no—
450C22×C4—188no—
451C22×C4—181no—
452C22×C4—181no—
453C22×C4C2×D3211yescharacteristic
454Q16—188no—
455SD16—188no—
456C2×C8—22no—
457C2×C8—32no—
458C2×C8—62no—
459C2×C8C2×D3212yes—
460C4⋊C4—32no—
461C4⋊C4—61no—
462C4⋊C4—184no—
463C22⋊C4—184no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—22no—
467C22×C3—22no—
468C22×C3—64no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3—62no—
472C22×C3—122no—
473C22×C3—122no—
474C22×C3—128no—
475C22×C3—124no—
476C22×C3#88212yes—
477C22×C3#88212yes—
478C22×C3#90412yes—
479C22×C3#90912yes—
480C22×C3#91212yes—
481C22×C3#91512yes—
482C22×C3C22×D1211yescharacteristic
483C22×C3C2×D3×D411yescharacteristic
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—24no—
487C2×D3—22no—
488C2×D3—42no—
489C2×D3—44no—
490C2×D3—42no—
491C2×D3—48no—
492C3×C4—21no—
493C3×C4—21no—
494C3×C4—22no—
495C3×C4—62no—
496C3×C4—122no—
497C3×C4#88212yes—
498C3×C4#88212yes—
499C3×C4C22×D1211yescharacteristic
500C3×C4C2×D3×D411yescharacteristic
501C3×C4C2×D3×D411yescharacteristic
502C3×C4C2×D3×D411yescharacteristic
503Dic3—22no—
504Dic3—42no—
505Dic3—64no—
506Dic3—64no—
507Dic3—124no—
508Dic3—124no—
509Dic3—122no—
510Dic3—122no—
511C32C2×#45211yescharacteristic, complemented, Sylow
512C23—32no—
513C23—62no—
514C23—62no—
515C23—62no—
516C23—62no—
517C23—64no—
518C23—122no—
519C23—122no—
520C23D3×D1211yescharacteristic
521Q8—94no—
522Q8—182no—
523Q8—184no—
524Q8—182no—
525Q8—182no—
526Q8—362no—
527D4—34no—
528D4—62no—
529D4—64no—
530D4—1816no—
531C2×C4—32no—
532C2×C4—62no—
533C2×C4—62no—
534C2×C4—62no—
535C2×C4—64no—
536C2×C4—62no—
537C2×C4—122no—
538C2×C4—1816no—
539C2×C4—182no—
540C2×C4—184no—
541C2×C4—182no—
542C2×C4—362no—
543C2×C4D3×D1212yes—
544C2×C4D3×D1211yescharacteristic
545C2×C4#381112yes—
546C2×C4C22×D3211yescharacteristic
547C8—22no—
548C8—62no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—24no—
552C2×C3—21no—
553C2×C3—124no—
554C2×C3—122no—
555C2×C3#473314yescomplemented
556C2×C3#478314yescomplemented
557C2×C3C2×#88211yescharacteristic
558C2×C3C2×#88211yescharacteristic
559C2×C3C2×#90411yescharacteristic
560C2×C3C2×#90911yescharacteristic
561C2×C3C2×#91211yescharacteristic
562C2×C3C2×#91511yescharacteristic
563D3—42no—
564D3—44no—
565C22—62no—
566C22—62no—
567C22—62no—
568C22—64no—
569C22—122no—
570C22—122no—
571C22—124no—
572C22—128no—
573C22#6380012yes—
574C22#6380712yes—
575C22#6392312yes—
576C22C2×D3×D1211yescharacteristic
577C4—62no—
578C4—122no—
579C4—184no—
580C4—362no—
581C4#6392312yes—
582C4C2×D3×D1211yescharacteristic
583C4C2×#381111yescharacteristic
584C3—21no—
585C3C2×#473311yescharacteristic, complemented
586C3C2×#478311yescharacteristic, complemented
587C2—122no—
588C2—124no—
589C2#1059096914yesdirect product factor
590C2C2×#6380011yescharacteristic
591C2C2×#6380711yescharacteristic
592C2C2×#6392311yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3795C2
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×#3746C2semidirect
3. C2×#63857C2semidirect
4. C22×#3716C2semidirect
5. C2×C3×#821C2semidirect
6. C2×C3×(C2×D3)⋊C8C2semidirect
7. C2×#63567C2semidirect
8. #10590969C2direct (N × H)
23. C2×#3746C22semidirect
29. #63857C22semidirect
31. C2×#3716C22semidirect
32. C3×#821C22semidirect
33. C3×(C2×D3)⋊C8C22semidirect
34. #63567C22semidirect
46. C2×#821D3semidirect
47. C2×(C2×D3)⋊C8D3semidirect
142. #821C2×D3semidirect
143. (C2×D3)⋊C8C2×D3semidirect
418. C2×C32#452semidirect
511. C32C2×#452semidirect
555. C2×C3#4733semidirect
556. C2×C3#4783semidirect
585. C3C2×#4733semidirect
586. C3C2×#4783semidirect
589. C2#10590969direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37952
C22×#37462
C2×#638572
C22×#37162
C2×C3×#8212
C2×C3×(C2×D3)⋊C82
C2×#635672
#105909692
C2×#47833
C2×#47333