Finite Group Databasebeta

← C2×#10591436 #11860167

Subgroups — C2×#10591436 #11860167

Order 1152.

1429 conjugacy classes of subgroups.

The subgroup lattice has 539 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic
3C2×#63898C211yesmaximal, characteristic, complemented
4C2×C3×#832C211yesmaximal, characteristic, complemented
5#10591436C218yesmaximal, direct product factor
6C2×#63573C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×#63555C211yesmaximal, characteristic, complemented
9C2×#5152—31nomaximal
10C2×#4785—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C23×C3⋊Dic3—21no—
13C22×C3×D12C2211yescharacteristic
14C22×D3×Dic3—21no—
15C2×#3757—21no—
16D4×C3⋊Dic3—22no—
17D4×C3⋊Dic3C2214yescomplemented
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C4×C3⋊Dic3C2211yescharacteristic
20C2×C3×#213C418yescomplemented
21C2×C3×#213C2214yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63898—22no—
27#63898C2214yescomplemented
28C3×#832C2214yescomplemented
29#63573C2214yescomplemented
30#63563C2214yescomplemented
31#63555C2214yescomplemented
32C22×C3×D8—31no—
33C2×D4×Dic3—31no—
34C2×D4×Dic3—31no—
35C2×D4×Dic3—31no—
36C2×D4×Dic3—61no—
37C22×#213D311yescharacteristic
38C2×#893—31no—
39C2×C3×#102—31no—
40C2×#832—31no—
41C2×#832D311yescharacteristic, complemented
42#5152—38no—
43C2×#821—31no—
44C2×#817—31no—
45C2×#815—31no—
46C2×#815—31no—
47C2×#808—31no—
48#4785—38no—
49C24×C32—21no—
50C23×C3×D3—21no—
51C2×C32×D4—21no—
52C2×C32×D4—22no—
53C2×C32×D4C2×C414yescomplemented
54C2×C32×D4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C3⋊Dic3—21no—
57C22×C3⋊Dic3—24no—
58C22×C3⋊Dic3—44no—
59C22×C3⋊Dic3D411yescharacteristic
60C22×C3⋊Dic3D411yescharacteristic
61C22×C3×Dic3—21no—
62C2×C3×D12—21no—
63C2×C3×D12—22no—
64C2×C3×D12C2×C414yescomplemented
65C2×C3×D12C2312yes—
66C2×D3×Dic3—24no—
67C2×D3×Dic3—44no—
68#3757—24no—
69C4⋊(C3⋊Dic3)—21no—
70C4⋊(C3⋊Dic3)C2312yes—
71C4×C3⋊Dic3D412yes—
72C4×C3⋊Dic3C2312yes—
73C3×#213C2×C4116yescomplemented
74C3×C4⋊Dic3—21no—
75C3×C4⋊Dic3C2312yes—
76C2×C3×C3⋊C8—22no—
77C2×C3×C3⋊C8C2×C414yescomplemented
78C2×C3×C3⋊C8C2312yes—
79C2×C3×C3⋊C8C2312yes—
80(C2×D3)⋊Dic3—24no—
81C2×#442—91noSylow
82C22×C3×D4—21no—
83C22×C3×D4—31no—
84C22×C3×D4C2×D311yescharacteristic
85C22×C3×D4C2×D311yescharacteristic
86C23×Dic3—61no—
87C23×Dic3—61no—
88C23×Dic3—61no—
89C23×Dic3—62no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—61no—
92C2×C3×D8—38no—
93C2×C3×D8—34no—
94C22×C3×C8—31no—
95C22×C3×C8—31no—
96C2×C3×C4⋊C4—31no—
97C2×#217—61no—
98C2×#217—61no—
99C2×#217—61no—
100C2×#217—62no—
101D4×Dic3—34no—
102D4×Dic3—34no—
103D4×Dic3—34no—
104D4×Dic3—64no—
105D4×Dic3—62no—
106D4×Dic3—62no—
107D4×Dic3—62no—
108D4×Dic3—64no—
109C2×#213Dic318yescomplemented
110C2×#213C2×D314yes—
111C2×(C2×D3)⋊C4—61no—
112C2×C4⋊Dic3—31no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—61no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—61no—
119C22×C3⋊C8C2×D311yescharacteristic
120C22×C3⋊C8C2×D311yescharacteristic
121#893—34no—
122#893—62no—
123C3×#102—34no—
124#832—34no—
125#832C2×D314yescomplemented
126#821—34no—
127#817—34no—
128#815—34no—
129#815—34no—
130#808—34no—
131C23×C32—24no—
132C23×C32—22no—
133C23×C32—42no—
134C23×C32—42no—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—24no—
137C22×C3×D3—22no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C32×D4—24no—
141C32×D4—22no—
142C32×D4C22×C414yescomplemented
143C2×C32×C4C22×C412yes—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—48no—
151C2×C3⋊Dic3—42no—
152C2×C3⋊Dic3C2×D412yes—
153C2×C3⋊Dic3C2×D412yes—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C3×D12—24no—
157C3×D12—22no—
158C3×D12C22×C414yescomplemented
159D3×Dic3—48no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8C22×C414yescomplemented
162C22×D8—31no—
163C2×C4×D4—91no—
164C2×C4×D4—91no—
165#442—98no—
166C2×#106—91no—
167C2×#102—31no—
168C2×#102—91no—
169C2×#97—91no—
170C24×C3—22no—
171C24×C3—21no—
172C24×C3—21no—
173C24×C3—61no—
174C23×D3—21no—
175C2×C3×D4—22no—
176C2×C3×D4—24no—
177C2×C3×D4—21no—
178C2×C3×D4—21no—
179C2×C3×D4—22no—
180C2×C3×D4—22no—
181C2×C3×D4—24no—
182C2×C3×D4—22no—
183C2×C3×D4—34no—
184C2×C3×D4—32no—
185C2×C3×D4—61no—
186C2×C3×D4—62no—
187C2×C3×D4C4×D314yescomplemented
188C2×C3×D4C2×Dic314yescomplemented
189C2×C3×D4C22×D312yes—
190C2×C3×D4C22×D312yes—
191C22×C3×C4—21no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—21no—
196C22×Dic3—31no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—31no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—64no—
203C22×Dic3—64no—
204C22×Dic3—64no—
205C22×Dic3—62no—
206C22×Dic3—68no—
207C22×Dic3—61no—
208C22×Dic3—61no—
209C22×Dic3—124no—
210C22×Dic3—128no—
211C22×Dic3—124no—
212C22×Dic3—124no—
213C2×D12—21no—
214C2×D12—22no—
215C2×D12C2×Dic314yescomplemented
216C2×D12C22×D312yes—
217C2×C4×D3—64no—
218C2×C4×D3—124no—
219C3×D8—316no—
220C2×C3×C8—34no—
221C2×C3×C8—32no—
222C2×C3×C8—32no—
223C2×C3×C8—62no—
224C3×C4⋊C4—32no—
225C3×C4⋊C4—61no—
226#217—64no—
227#217—64no—
228#217—64no—
229#217—68no—
230#213C2×Dic3116yescomplemented
231(C2×D3)⋊C4—64no—
232C4⋊Dic3—21no—
233C4⋊Dic3—32no—
234C4⋊Dic3—32no—
235C4⋊Dic3—62no—
236C4⋊Dic3—62no—
237C4⋊Dic3—61no—
238C4⋊Dic3—61no—
239C4⋊Dic3C22×D312yes—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—32no—
243C4×Dic3—32no—
244C4×Dic3—62no—
245C4×Dic3—62no—
246C2×C3⋊C8—22no—
247C2×C3⋊C8C2×Dic314yescomplemented
248C2×C3⋊C8C22×D312yes—
249C2×C3⋊C8C22×D312yes—
250C22×C32—24no—
251C22×C32—42no—
252C22×C32—42no—
253C22×C32—48no—
254C22×C32C4×D412yes—
255C22×C32AGL(1,ℤ/8)12yes—
256C22×C32AGL(1,ℤ/8)12yes—
257C22×C32C22×D411yescharacteristic
258C2×C3×D3—24no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—48no—
262C32×C4C4×D412yes—
263C32×C4C23×C411yescharacteristic
264C32×C4C2×#4111yescharacteristic
265C3⋊Dic3—22no—
266C3⋊Dic3—22no—
267C3⋊Dic3—42no—
268C3×Dic3—42no—
269C22×D4—31no—
270C22×D4D3211yescharacteristic
271C23×C4—181no—
272C23×C4—181no—
273C2×D8—38no—
274C2×D8—34no—
275C22×C8—31no—
276C22×C8—31no—
277C4×D4—94no—
278C4×D4—94no—
279C4×D4—182no—
280C4×D4—182no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—91no—
283C2×C22⋊C4—181no—
284C2×C22⋊C4—181no—
285C2×C42—91no—
286#106—94no—
287#102—34no—
288#102—94no—
289#97—94no—
290C23×C3—24no—
291C23×C3—28no—
292C23×C3—24no—
293C23×C3—24no—
294C23×C3—22no—
295C23×C3—22no—
296C23×C3—21no—
297C23×C3—44no—
298C23×C3—44no—
299C23×C3—42no—
300C23×C3—42no—
301C23×C3—42no—
302C23×C3—42no—
303C23×C3—64no—
304C23×C3—62no—
305C23×C3—122no—
306C23×C3—122no—
307C23×C3D3×D411yescharacteristic
308C23×C3D3×D411yescharacteristic
309C22×D3—24no—
310C22×D3—22no—
311C22×D3—42no—
312C22×D3—42no—
313C3×D4—24no—
314C3×D4—28no—
315C3×D4—24no—
316C3×D4—24no—
317C3×D4—22no—
318C3×D4—22no—
319C3×D4—24no—
320C3×D4—34no—
321C3×D4—64no—
322C3×D4—62no—
323C3×D4C2×C4×D314yescomplemented
324C3×D4C22×Dic314yescomplemented
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—62no—
330C2×C3×C4—122no—
331C2×C3×C4C2×C4×D312yes—
332C2×C3×C4D3×D411yescharacteristic
333C2×C3×C4D3×D411yescharacteristic
334C2×C3×C4#23712yes—
335C2×C3×C4#23712yes—
336C2×C3×C4C22×Dic312yes—
337C2×C3×C4C23×D311yescharacteristic
338C2×C3×C4C23×D311yescharacteristic
339C2×Dic3—22no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—32no—
343C2×Dic3—32no—
344C2×Dic3—42no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—64no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—64no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—122no—
356C2×Dic3—128no—
357C2×Dic3—1216no—
358C2×Dic3—128no—
359C2×Dic3—128no—
360C2×Dic3—124no—
361C2×Dic3—122no—
362C2×Dic3—122no—
363D12—24no—
364D12—22no—
365D12C22×Dic314yescomplemented
366C4×D3—128no—
367C3×C8—34no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8C22×Dic314yescomplemented
371C2×C32—44no—
372C2×C32#44214yescomplemented
373C2×C32C2×C4×D411yescharacteristic
374C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
375C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
376C3×D3—44no—
377C24—21no—
378C24—61no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—32no—
382C2×D4—34no—
383C2×D4—62no—
384C2×D4—61no—
385C2×D4D3×Dic314yescomplemented
386C2×D4C2×D3212yes—
387C22×C4—61no—
388C22×C4—91no—
389C22×C4—91no—
390C22×C4—184no—
391C22×C4—184no—
392C22×C4—181no—
393C22×C4—364no—
394C22×C4—364no—
395C22×C4C2×D3211yescharacteristic
396D8—316no—
397C2×C8—32no—
398C2×C8—34no—
399C2×C8—32no—
400C2×C8—62no—
401C4⋊C4—32no—
402C4⋊C4—61no—
403C4⋊C4—92no—
404C4⋊C4—181no—
405C22⋊C4—184no—
406C22⋊C4—184no—
407C42—92no—
408C42—92no—
409C22×C3—28no—
410C22×C3—24no—
411C22×C3—24no—
412C22×C3—21no—
413C22×C3—22no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—44no—
417C22×C3—44no—
418C22×C3—416no—
419C22×C3—48no—
420C22×C3—42no—
421C22×C3—42no—
422C22×C3—42no—
423C22×C3—42no—
424C22×C3—48no—
425C22×C3—64no—
426C22×C3—122no—
427C22×C3—122no—
428C22×C3—128no—
429C22×C3#67⋊C412yes—
430C22×C3#91112yes—
431C22×C3#91112yes—
432C22×C3#91112yes—
433C22×C3#91412yes—
434C22×C3D4×Dic312yes—
435C22×C3C2×D3×D411yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C2×D3—24no—
438C2×D3—48no—
439C2×D3—42no—
440C2×D3—42no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—122no—
445C3×C4#67⋊C412yes—
446C3×C4D4×Dic312yes—
447C3×C4C22×C4×D311yescharacteristic
448C3×C4C2×#23711yescharacteristic
449C3×C4C2×#23711yescharacteristic
450C3×C4C23×Dic311yescharacteristic
451Dic3—42no—
452Dic3—64no—
453Dic3—62no—
454Dic3—62no—
455Dic3—62no—
456Dic3—62no—
457Dic3—122no—
458Dic3—124no—
459Dic3—122no—
460Dic3—122no—
461C32C2×#44211yescharacteristic, complemented, Sylow
462C23—22no—
463C23—24no—
464C23—42no—
465C23—42no—
466C23—62no—
467C23—64no—
468C23—122no—
469C23—122no—
470C23#381111yescharacteristic
471D4—22no—
472D4—24no—
473D4—34no—
474D4—62no—
475D4—64no—
476D4C2×D3×Dic314yescomplemented
477C2×C4—62no—
478C2×C4—92no—
479C2×C4—92no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—182no—
484C2×C4—368no—
485C2×C4—368no—
486C2×C4—362no—
487C2×C4C2×D3×Dic312yes—
488C2×C4#380512yes—
489C2×C4#381111yescharacteristic
490C2×C4C22×D3211yescharacteristic
491C8—34no—
492C8—62no—
493C2×C3—21no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—24no—
497C2×C3—48no—
498C2×C3—44no—
499C2×C3—44no—
500C2×C3—124no—
501C2×C3#478514yescomplemented
502C2×C3#515214yescomplemented
503C2×C3C2×#67⋊C411yescharacteristic
504C2×C3C2×#91111yescharacteristic
505C2×C3C2×#91111yescharacteristic
506C2×C3C2×#91111yescharacteristic
507C2×C3C2×#91411yescharacteristic
508C2×C3C2×D4×Dic311yescharacteristic
509D3—44no—
510C22—24no—
511C22—42no—
512C22—42no—
513C22—48no—
514C22—64no—
515C22—122no—
516C22—122no—
517C22—128no—
518C22#6392712yes—
519C22#6393712yes—
520C22#67⋊Dic312yes—
521C22C2×#381111yescharacteristic
522C4—122no—
523C4—182no—
524C4—182no—
525C4—362no—
526C4#67⋊Dic312yes—
527C4C22×D3×Dic311yescharacteristic
528C4C2×#380511yescharacteristic
529C3—21no—
530C3C2×#478511yescharacteristic, complemented
531C3C2×#515211yescharacteristic, complemented
532C2—44no—
533C2—124no—
534C2#1059143614yesdirect product factor
535C2C2×#6392711yescharacteristic
536C2C2×#6393711yescharacteristic
537C2C2×#67⋊Dic311yescharacteristic
subgroupG/H
centerC23#3811
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
prime radicalC22×C3×#213C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32C2×#442
LCSG ▷ 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
1. C2×D4×C3⋊Dic3C2semidirect
3. C2×#63898C2semidirect
4. C2×C3×#832C2semidirect
5. #10591436C2direct (N × H)
6. C2×#63573C2semidirect
7. C2×#63563C2semidirect
8. C2×#63555C2semidirect
17. D4×C3⋊Dic3C22semidirect
20. C2×C3×#213C4semidirect
27. #63898C22semidirect
28. C3×#832C22semidirect
29. #63573C22semidirect
30. #63563C22semidirect
31. #63555C22semidirect
41. C2×#832D3semidirect
53. C2×C32×D4C2×C4semidirect
64. C2×C3×D12C2×C4semidirect
73. C3×#213C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
109. C2×#213Dic3semidirect
125. #832C2×D3semidirect
142. C32×D4C22×C4semidirect
158. C3×D12C22×C4semidirect
161. C3×C3⋊C8C22×C4semidirect
187. C2×C3×D4C4×D3semidirect
188. C2×C3×D4C2×Dic3semidirect
215. C2×D12C2×Dic3semidirect
230. #213C2×Dic3semidirect
247. C2×C3⋊C8C2×Dic3semidirect
323. C3×D4C2×C4×D3semidirect
324. C3×D4C22×Dic3semidirect
365. D12C22×Dic3semidirect
370. C3⋊C8C22×Dic3semidirect
372. C2×C32#442semidirect
385. C2×D4D3×Dic3semidirect
461. C32C2×#442semidirect
476. D4C2×D3×Dic3semidirect
501. C2×C3#4785semidirect
502. C2×C3#5152semidirect
530. C3C2×#4785semidirect
531. C3C2×#5152semidirect
534. C2#10591436direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C22×C3×#2132
C2×#638982
C2×C3×#8322
#105914362
C2×#635732
C2×#635632
C2×#635552
C2×#51523
C2×#47853