Finite Group Databasebeta

← C2×#10590611 #11857794

Subgroups — C2×#10590611 #11857794

Order 1152.

1749 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3796C211yesmaximal, characteristic
2C2×#64101C211yesmaximal, characteristic, complemented
3C22×#3710C211yesmaximal, characteristic, complemented
4C2×C3×#810C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×#63566C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590611C218yesmaximal, direct product factor
9C2×#4804—31nomaximal
10C2×#4772—31nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626—21no—
15C22×D3×Dic3—21no—
16C2×#3796—22no—
17C2×#3796—24no—
18C2×#3796C418yescomplemented
19C2×#3796C2214yes—
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×C4×C3⋊Dic3—21no—
24#64101—22no—
25#64101C2214yescomplemented
26C22×C3×C3⋊C8C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C2×#3710—24no—
29C2×#3710C2214yescomplemented
30C3×#810C2214yescomplemented
31C3×#809C2214yescomplemented
32#63566C2214yescomplemented
33#63563C2214yescomplemented
34C22×#239—31no—
35C22×#237—31no—
36C22×D3×C8—31no—
37C22×D3×C8—31no—
38C2×#892—31no—
39C2×#892—31no—
40C2×#892—61no—
41C2×C3×#103—31no—
42C2×C3×#102—31no—
43C2×#835—31no—
44C2×#832—31no—
45C2×#821—31no—
46C2×#816—31no—
47C2×#810D311yescharacteristic, complemented
48C2×#809D311yescharacteristic, complemented
49#4804—38no—
50#4772—38no—
51C23×C3⋊D3D411yescharacteristic
52C23×C3×D3—21no—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C22×C3⋊Dic3D411yescharacteristic
57C2×C4×C3⋊D3C2×C414yes—
58C2×C4×C3⋊D3D412yes—
59C2×C4×C3⋊D3D414yes—
60C2×C4×C3⋊D3C2312yes—
61C22×C3×Dic3—21no—
62C2×C3×D12—21no—
63C2×C3×D12—22no—
64C2×C3×D12C2×C414yes—
65C2×C3×D12C2312yes—
66C2×C3×Dic6—21no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6C2×C414yes—
69C2×C3×Dic6C2312yes—
70C2×#626—28no—
71C2×#626—24no—
72C2×D3×Dic3—28no—
73C2×D3×Dic3—24no—
74#3796—216no—
75#3796—28no—
76#3796C2×C4116yescomplemented
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2312yes—
79#3752—24no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)C2312yes—
82C4×C3⋊Dic3—24no—
83C2×C3×C3⋊C8—22no—
84C2×C3×C3⋊C8—22no—
85C2×C3×C3⋊C8C2312yes—
86C2×C3×C3⋊C8C2312yes—
87#3710—28no—
88C2×#416—91noSylow
89C22×C3×Q8—31no—
90C22×C3×D4—31no—
91C22×#67—61no—
92C23×Dic3—61no—
93C2×#239—38no—
94C2×#239—34no—
95C2×#239—62no—
96C2×#239—64no—
97C2×#237—38no—
98C2×#237—34no—
99C2×#237—62no—
100C2×#237—64no—
101C22×D12—61no—
102C22×D12C2×D311yescharacteristic
103C22×C4×D3—31no—
104C22×C4×D3—31no—
105C22×C4×D3—61no—
106C22×C4×D3—61no—
107C22×Dic6C2×D311yescharacteristic
108C22×C3×C8—31no—
109C22×C3×C8—31no—
110C2×C3×C4⋊C4—21no—
111C2×C3×C4⋊C4C2×D311yescharacteristic
112C2×C3×C4⋊C4C2×D311yescharacteristic
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×(C2×D3)⋊C4—62no—
116C2×C4⋊Dic3—31no—
117C2×C4⋊Dic3—31no—
118C2×C4⋊Dic3—61no—
119C2×C4×Dic3—61no—
120C2×C4×Dic3—61no—
121C2×C4×Dic3—62no—
122C22×C3⋊C8C2×D311yescharacteristic
123C22×C3⋊C8C2×D311yescharacteristic
124C2×D3×C8—34no—
125C2×D3×C8—34no—
126C2×D3×C8—64no—
127C2×D3×C8—64no—
128#892—34no—
129#892—34no—
130#892—64no—
131#892—62no—
132#892—62no—
133#892—64no—
134C3×#103—34no—
135C3×#102—34no—
136#835—34no—
137#832—34no—
138#821—34no—
139#816—34no—
140#810C2×D314yescomplemented
141#809C2×D314yescomplemented
142C23×C32C2×D411yescharacteristic
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3C22⋊C414yes—
146C22×C3⋊D3C2×D412yes—
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—42no—
150C22×C3×D3—42no—
151C2×C32×C4—22no—
152C2×C32×C4—42no—
153C2×C32×C4C22×C412yes—
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4C2×D412yes—
156C2×C32×C4C2411yescharacteristic
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3—42no—
159C2×C3⋊Dic3C22⋊C414yes—
160C2×C3⋊Dic3C2×D412yes—
161C4×C3⋊D3C22⋊C418yes—
162C4×C3⋊D3C22×C414yes—
163C4×C3⋊D3C2×D414yes—
164C2×C3×Dic3—24no—
165C2×C3×Dic3—22no—
166C3×D12—24no—
167C3×D12—22no—
168C3×D12C22×C414yes—
169C3×Dic6—24no—
170C3×Dic6—22no—
171C3×Dic6C22×C414yes—
172#626—216no—
173D3×Dic3—216no—
174C3×C3⋊C8—22no—
175C3×C3⋊C8—22no—
176C22×#41—91no—
177C23×C8—91no—
178C2×#117—91no—
179#416—98no—
180C2×#103—31no—
181C2×#103—91no—
182C2×#102—31no—
183C2×#102—91no—
184C24×C3—61no—
185C23×D3—21no—
186C23×D3—31no—
187C23×D3—31no—
188C23×D3—61no—
189C2×C3×Q8—34no—
190C2×C3×Q8—32no—
191C2×C3×Q8—62no—
192C2×C3×Q8—61no—
193C2×C3×D4—34no—
194C2×C3×D4—32no—
195C2×C3×D4—62no—
196C2×C3×D4—61no—
197C22×C3×C4—22no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—61no—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67—68no—
205C2×#67—64no—
206C22×Dic3—21no—
207C22×Dic3—31no—
208C22×Dic3—31no—
209C22×Dic3—61no—
210C22×Dic3—68no—
211C22×Dic3—64no—
212C22×Dic3—62no—
213C22×Dic3—61no—
214C22×Dic3—61no—
215#239—316no—
216#239—616no—
217#239—68no—
218#237—316no—
219#237—616no—
220#237—68no—
221C2×D12—22no—
222C2×D12—21no—
223C2×D12—68no—
224C2×D12—64no—
225C2×D12C4×D314yes—
226C2×D12C22×D312yes—
227C2×C4×D3—34no—
228C2×C4×D3—34no—
229C2×C4×D3—32no—
230C2×C4×D3—32no—
231C2×C4×D3—34no—
232C2×C4×D3—34no—
233C2×C4×D3—32no—
234C2×C4×D3—32no—
235C2×C4×D3—62no—
236C2×C4×D3—62no—
237C2×C4×D3—64no—
238C2×C4×D3—64no—
239C2×C4×D3—68no—
240C2×C4×D3—64no—
241C2×Dic6—22no—
242C2×Dic6—21no—
243C2×Dic6C4×D314yes—
244C2×Dic6C22×D312yes—
245C2×C3×C8—32no—
246C2×C3×C8—32no—
247C2×C3×C8—62no—
248C2×C3×C8—62no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—22no—
253C3×C4⋊C4C22×D312yes—
254C3×C4⋊C4C22×D312yes—
255(C2×D3)⋊C4—64no—
256(C2×D3)⋊C4—64no—
257(C2×D3)⋊C4—68no—
258C4⋊Dic3—32no—
259C4⋊Dic3—32no—
260C4⋊Dic3—62no—
261C4⋊Dic3—62no—
262C4⋊Dic3—61no—
263C4⋊Dic3—61no—
264C4×Dic3—64no—
265C4×Dic3—64no—
266C4×Dic3—68no—
267C2×C3⋊C8—22no—
268C2×C3⋊C8—22no—
269C2×C3⋊C8C22×D312yes—
270C2×C3⋊C8C22×D312yes—
271D3×C8—68no—
272D3×C8—68no—
273C22×C32C2×C22⋊C412yes—
274C22×C32#13512yes—
275C22×C32#13512yes—
276C22×C32C22×D411yescharacteristic
277C2×C3⋊D3—22no—
278C2×C3⋊D3—22no—
279C2×C3⋊D3—28no—
280C2×C3⋊D3C2×C22⋊C414yes—
281C2×C3×D3—24no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—48no—
285C32×C4—42no—
286C32×C4C2×C22⋊C412yes—
287C32×C4C23×C411yescharacteristic
288C32×C4C22×D411yescharacteristic
289C3⋊Dic3—42no—
290C3⋊Dic3C2×C22⋊C414yes—
291C3×Dic3—24no—
292C2×#41—94no—
293C2×#41—98no—
294C2×#41—184no—
295C2×#41—182no—
296C22×Q8—31no—
297C22×D4—31no—
298C22×D4—181no—
299C23×C4—91no—
300C23×C4—181no—
301C22×C8—31no—
302C22×C8—31no—
303C22×C8—94no—
304C22×C8—184no—
305#117—94no—
306#117—182no—
307C2×C4⋊C4—91no—
308C2×C4⋊C4D3211yescharacteristic
309C2×C22⋊C4—181no—
310C2×C42—181no—
311#103—34no—
312#103—94no—
313#102—34no—
314#102—94no—
315C23×C3—21no—
316C23×C3—64no—
317C23×C3—62no—
318C23×C3—122no—
319C23×C3—122no—
320C23×C3D3×D411yescharacteristic
321C23×C3D3×D411yescharacteristic
322C22×D3—24no—
323C22×D3—22no—
324C22×D3—34no—
325C22×D3—34no—
326C22×D3—32no—
327C22×D3—32no—
328C22×D3—42no—
329C22×D3—42no—
330C22×D3—64no—
331C22×D3—62no—
332C22×D3—62no—
333C22×D3—62no—
334C22×D3—62no—
335C22×D3—62no—
336C22×D3—122no—
337C22×D3—122no—
338C3×Q8—34no—
339C3×Q8—64no—
340C3×Q8—62no—
341C3×D4—34no—
342C3×D4—64no—
343C3×D4—62no—
344C2×C3×C4—24no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—21no—
348C2×C3×C4—22no—
349C2×C3×C4—22no—
350C2×C3×C4—21no—
351C2×C3×C4—44no—
352C2×C3×C4—42no—
353C2×C3×C4—42no—
354C2×C3×C4—64no—
355C2×C3×C4—62no—
356C2×C3×C4C2×C4×D312yes—
357C2×C3×C4C2×C4×D312yes—
358C2×C3×C4D3×D412yes—
359C2×C3×C4D3×D412yes—
360C2×C3×C4D3×D411yescharacteristic
361C2×C3×C4D3×D411yescharacteristic
362C2×C3×C4C23×D311yescharacteristic
363C2×C3×C4C23×D311yescharacteristic
364#67—616no—
365C2×Dic3—24no—
366C2×Dic3—22no—
367C2×Dic3—34no—
368C2×Dic3—34no—
369C2×Dic3—32no—
370C2×Dic3—32no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—616no—
374C2×Dic3—64no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—124no—
378C2×Dic3—122no—
379C2×Dic3—122no—
380D12—24no—
381D12—22no—
382D12—616no—
383D12C2×C4×D314yes—
384C4×D3—38no—
385C4×D3—38no—
386C4×D3—34no—
387C4×D3—34no—
388C4×D3—34no—
389C4×D3—34no—
390C4×D3—68no—
391C4×D3—64no—
392C4×D3—64no—
393C4×D3—616no—
394Dic6—24no—
395Dic6—22no—
396Dic6C2×C4×D314yes—
397C3×C8—62no—
398C3×C8—62no—
399C3⋊C8—22no—
400C3⋊C8—22no—
401C2×C32#41614yescomplemented
402C2×C32C22×C22⋊C411yescharacteristic
403C2×C32C2×#13511yescharacteristic
404C2×C32C2×#13511yescharacteristic
405C3⋊D3—24no—
406C3×D3—44no—
407C24—61no—
408C24—91no—
409#41—916no—
410#41—188no—
411#41—1816no—
412C2×Q8—32no—
413C2×Q8—34no—
414C2×Q8—62no—
415C2×Q8—61no—
416C2×D4—32no—
417C2×D4—34no—
418C2×D4—62no—
419C2×D4—61no—
420C2×D4—184no—
421C2×D4—188no—
422C22×C4—21no—
423C22×C4—61no—
424C22×C4—91no—
425C22×C4—92no—
426C22×C4—94no—
427C22×C4—94no—
428C22×C4—92no—
429C22×C4—184no—
430C22×C4—188no—
431C22×C4—181no—
432C22×C4C2×D3211yescharacteristic
433C2×C8—32no—
434C2×C8—32no—
435C2×C8—62no—
436C2×C8—62no—
437C2×C8—188no—
438C4⋊C4—21no—
439C4⋊C4—92no—
440C4⋊C4—181no—
441C4⋊C4C2×D3212yes—
442C22⋊C4—184no—
443C42—184no—
444C22×C3—21no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—22no—
448C22×C3—64no—
449C22×C3—122no—
450C22×C3—122no—
451C22×C3—128no—
452C22×C3D3×C22⋊C412yes—
453C22×C3D3×C22⋊C412yes—
454C22×C3#91212yes—
455C22×C3#91612yes—
456C22×C3#91612yes—
457C22×C3#91912yes—
458C22×C3C2×D3×D411yescharacteristic
459C22×C3C2×D3×D411yescharacteristic
460C2×D3—24no—
461C2×D3—34no—
462C2×D3—34no—
463C2×D3—42no—
464C2×D3—42no—
465C2×D3—48no—
466C2×D3—64no—
467C2×D3—62no—
468C2×D3—62no—
469C2×D3—62no—
470C2×D3—62no—
471C2×D3—68no—
472C2×D3—68no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—128no—
476C3×C4—21no—
477C3×C4—21no—
478C3×C4—22no—
479C3×C4—44no—
480C3×C4—42no—
481C3×C4—42no—
482C3×C4—64no—
483C3×C4D3×C22⋊C412yes—
484C3×C4D3×C22⋊C412yes—
485C3×C4C22×C4×D311yescharacteristic
486C3×C4C22×C4×D311yescharacteristic
487C3×C4C2×D3×D411yescharacteristic
488C3×C4C2×D3×D411yescharacteristic
489Dic3—24no—
490Dic3—34no—
491Dic3—34no—
492Dic3—64no—
493Dic3—124no—
494Dic3—122no—
495Dic3—122no—
496C32C2×#41611yescharacteristic, complemented, Sylow
497C23—62no—
498C23—64no—
499C23—92no—
500C23—94no—
501C23—122no—
502C23—122no—
503C23—182no—
504C23—182no—
505C23#381111yescharacteristic
506Q8—34no—
507Q8—62no—
508Q8—64no—
509D4—34no—
510D4—62no—
511D4—64no—
512D4—1816no—
513C2×C4—22no—
514C2×C4—42no—
515C2×C4—62no—
516C2×C4—64no—
517C2×C4—92no—
518C2×C4—94no—
519C2×C4—94no—
520C2×C4—94no—
521C2×C4—98no—
522C2×C4—1816no—
523C2×C4—182no—
524C2×C4—362no—
525C2×C4C4×D3212yes—
526C2×C4#380212yes—
527C2×C4#381111yescharacteristic
528C2×C4C22×D3211yescharacteristic
529C8—62no—
530C8—62no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—24no—
534C2×C3—21no—
535C2×C3—124no—
536C2×C3#477214yescomplemented
537C2×C3#480414yescomplemented
538C2×C3C2×D3×C22⋊C411yescharacteristic
539C2×C3C2×D3×C22⋊C411yescharacteristic
540C2×C3C2×#91211yescharacteristic
541C2×C3C2×#91611yescharacteristic
542C2×C3C2×#91611yescharacteristic
543C2×C3C2×#91911yescharacteristic
544D3—44no—
545D3—64no—
546D3—64no—
547D3—124no—
548C22—64no—
549C22—94no—
550C22—122no—
551C22—122no—
552C22—128no—
553C22—182no—
554C22—182no—
555C22—188no—
556C22#6392112yes—
557C22#6393612yes—
558C22#6395012yes—
559C22C2×#381111yescharacteristic
560C4—42no—
561C4—64no—
562C4—94no—
563C4—362no—
564C4#6392112yes—
565C4C2×C4×D3211yescharacteristic
566C4C2×#380211yescharacteristic
567C3—21no—
568C3C2×#477211yescharacteristic, complemented
569C3C2×#480411yescharacteristic, complemented
570C2—124no—
571C2—184no—
572C2#1059061114yesdirect product factor
573C2C2×#6392111yescharacteristic
574C2C2×#6393611yescharacteristic
575C2C2×#6395011yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3796C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#416
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#64101C2semidirect
3. C22×#3710C2semidirect
4. C2×C3×#810C2semidirect
5. C2×C3×#809C2semidirect
6. C2×#63566C2semidirect
7. C2×#63563C2semidirect
8. #10590611C2direct (N × H)
18. C2×#3796C4semidirect
25. #64101C22semidirect
29. C2×#3710C22semidirect
30. C3×#810C22semidirect
31. C3×#809C22semidirect
32. #63566C22semidirect
33. #63563C22semidirect
47. C2×#810D3semidirect
48. C2×#809D3semidirect
76. #3796C2×C4semidirect
140. #810C2×D3semidirect
141. #809C2×D3semidirect
401. C2×C32#416semidirect
496. C32C2×#416semidirect
536. C2×C3#4772semidirect
537. C2×C3#4804semidirect
568. C3C2×#4772semidirect
569. C3C2×#4804semidirect
572. C2#10590611direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37962
C2×#641012
C22×#37102
C2×C3×#8102
C2×C3×#8092
C2×#635662
C2×#635632
#105906112
C2×#48043
C2×#47723