Finite Group Databasebeta

← C2×#10590346 #11860169

Subgroups — C2×#10590346 #11860169

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×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic
4C2×C3×#803C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590346C218yesmaximal, direct product factor
9C2×#5014—31nomaximal
10C2×#4711—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3—21no—
15C2×C32×C42C2211yescharacteristic
16C2×#3752—21no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C4×C4⋊(C3⋊D3)—22no—
19C4×C4⋊(C3⋊D3)C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×C4×D12—22no—
25C3×C4×D12C2214yescomplemented
26C2×#3714C418yescomplemented
27C2×#3714C2214yes—
28C3×#803C2214yescomplemented
29#63573C2214yescomplemented
30#63564C2214yescomplemented
31#63563C2214yescomplemented
32C2×C3×C4×D4—31no—
33C22×#213—31no—
34C22×D24—31no—
35C2×C4×D12—31no—
36C2×C4×D12—31no—
37C2×C4×D12—61no—
38C2×C4×D12D311yescharacteristic, complemented
39C2×C3×#97—31no—
40C2×#832—31no—
41C2×#821—31no—
42C2×#821—31no—
43C2×#817—31no—
44#5014—38no—
45C2×#809—31no—
46C2×#808—31no—
47C2×#803D311yescharacteristic, complemented
48#4711—38no—
49C23×C3⋊D3—21no—
50C23×C3×D3—21no—
51C22×C32×C4D411yescharacteristic
52C22×C32×C4D411yescharacteristic
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×C4⋊(C3⋊D3)—21no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)C2×C414yescomplemented
58C2×C4⋊(C3⋊D3)C2312yes—
59C2×C4×C3⋊D3—24no—
60C2×C4×C3⋊D3—44no—
61C22×C3×Dic3—21no—
62C2×C3×D12—21no—
63C2×C3×D12—22no—
64C2×C3×D12C2×C414yescomplemented
65C2×C3×D12C2312yes—
66C2×C3×C4×D3—24no—
67C2×C3×C4×D3—44no—
68C32×C42D412yes—
69C32×C42C2312yes—
70#3752—24no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C3×(C2×D3)⋊C4—24no—
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#3714C2×C4116yescomplemented
81C2×#442—91noSylow
82C22×C3×D4—31no—
83C23×C3×C4—61no—
84C22×D12—31no—
85C22×D12—31no—
86C22×D12—61no—
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3—62no—
90C22×C4×D3—61no—
91C22×C4×D3—61no—
92C22×C3×C8—31no—
93C22×C3×C8—31no—
94C3×C4×D4—34no—
95C3×C4×D4—62no—
96C2×C3×C4⋊C4—31no—
97C2×C3×C22⋊C4—61no—
98C2×C3×C42—21no—
99C2×C3×C42C2×D311yescharacteristic
100C2×C3×C42C2×D311yescharacteristic
101C2×#213—38no—
102C2×#213—34no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—62no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—61no—
110C2×C4⋊Dic3C2×D311yescharacteristic
111C22×C3⋊C8C2×D311yescharacteristic
112C22×C3⋊C8C2×D311yescharacteristic
113C2×D24—38no—
114C2×D24—34no—
115C4×D12—22no—
116C4×D12—34no—
117C4×D12—34no—
118C4×D12—64no—
119C4×D12—64no—
120C4×D12—62no—
121C4×D12—62no—
122C4×D12C2×D314yescomplemented
123C3×#97—34no—
124#832—34no—
125#821—34no—
126#821—34no—
127#817—34no—
128#809—34no—
129#808—34no—
130#803C2×D314yescomplemented
131C23×C32C2×D411yescharacteristic
132C22×C3⋊D3—24no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—42no—
135C22×C3⋊D3—42no—
136C22×C3×D3—24no—
137C22×C3×D3—22no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C2×C32×C4—22no—
141C2×C32×C4—22no—
142C2×C32×C4C22×C412yes—
143C2×C32×C4C2×D412yes—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150C4⋊(C3⋊D3)—24no—
151C4⋊(C3⋊D3)—22no—
152C4⋊(C3⋊D3)C22×C414yescomplemented
153C4×C3⋊D3—48no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—42no—
156C3×D12—24no—
157C3×D12—22no—
158C3×D12C22×C414yescomplemented
159C3×C4×D3—48no—
160C3×C3⋊C8—22no—
161C3×C3⋊C8C22×C414yescomplemented
162C22×D8—91no—
163C2×C4×D4—31no—
164C2×C4×D4—91no—
165#442—98no—
166C2×#106—91no—
167C2×#102—91no—
168C2×#102—91no—
169C2×#97—31no—
170C24×C3—61no—
171C23×D3—21no—
172C23×D3—62no—
173C23×D3—61no—
174C23×D3—61no—
175C2×C3×D4—34no—
176C2×C3×D4—32no—
177C2×C3×D4—61no—
178C2×C3×D4—62no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—61no—
183C22×C3×C4—64no—
184C22×C3×C4—124no—
185C22×C3×C4D1211yescharacteristic
186C22×C3×C4D1211yescharacteristic
187C22×C3×C4#6711yescharacteristic
188C22×C3×C4#6711yescharacteristic
189C22×C3×C4C22×D311yescharacteristic
190C22×C3×C4C22×D311yescharacteristic
191C22×Dic3—21no—
192C22×Dic3—62no—
193C22×Dic3—61no—
194C22×Dic3—61no—
195C2×D12—22no—
196C2×D12—21no—
197C2×D12—34no—
198C2×D12—34no—
199C2×D12—32no—
200C2×D12—32no—
201C2×D12—62no—
202C2×D12—64no—
203C2×D12—62no—
204C2×D12—64no—
205C2×D12—61no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—61no—
209C2×D12C4×D314yescomplemented
210C2×D12C22×D312yes—
211C2×C4×D3—24no—
212C2×C4×D3—44no—
213C2×C4×D3—68no—
214C2×C4×D3—64no—
215C2×C4×D3—64no—
216C2×C4×D3—128no—
217C2×C4×D3—124no—
218C2×C4×D3—124no—
219C2×C3×C8—34no—
220C2×C3×C8—32no—
221C2×C3×C8—32no—
222C2×C3×C8—62no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4—61no—
225C3×C22⋊C4—64no—
226C3×C42—22no—
227C3×C42—22no—
228C3×C42D1212yes—
229C3×C42#6712yes—
230C3×C42C22×D312yes—
231C3×C42C22×D312yes—
232#213—316no—
233(C2×D3)⋊C4—24no—
234(C2×D3)⋊C4—68no—
235(C2×D3)⋊C4—64no—
236(C2×D3)⋊C4—64no—
237C4⋊Dic3—21no—
238C4⋊Dic3—32no—
239C4⋊Dic3—32no—
240C4⋊Dic3—62no—
241C4⋊Dic3—62no—
242C4⋊Dic3—61no—
243C4⋊Dic3—61no—
244C4⋊Dic3C22×D312yes—
245C2×C3⋊C8—22no—
246C2×C3⋊C8C4×D314yescomplemented
247C2×C3⋊C8C22×D312yes—
248C2×C3⋊C8C22×D312yes—
249D24—316no—
250C22×C32C4×D412yes—
251C22×C32AGL(1,ℤ/8)12yes—
252C22×C32AGL(1,ℤ/8)12yes—
253C22×C32C22×D411yescharacteristic
254C2×C3⋊D3—24no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3—42no—
257C2×C3⋊D3—48no—
258C2×C3×D3—24no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—48no—
262C32×C4—22no—
263C32×C4—22no—
264C32×C4C4×D412yes—
265C32×C4C23×C411yescharacteristic
266C32×C4C2×#4111yescharacteristic
267C3⋊Dic3—42no—
268C3×Dic3—42no—
269C22×D4—31no—
270C22×D4—91no—
271C23×C4—61no—
272C23×C4—181no—
273C2×D8—98no—
274C2×D8—94no—
275C22×C8—31no—
276C22×C8—31no—
277C4×D4—34no—
278C4×D4—62no—
279C4×D4—94no—
280C4×D4—182no—
281C2×C4⋊C4—31no—
282C2×C4⋊C4—91no—
283C2×C22⋊C4—61no—
284C2×C22⋊C4—181no—
285C2×C42D3211yescharacteristic
286#106—94no—
287#102—94no—
288#102—94no—
289#97—34no—
290C23×C3—21no—
291C23×C3—64no—
292C23×C3—62no—
293C23×C3—122no—
294C23×C3—122no—
295C23×C3C2×D1211yescharacteristic
296C23×C3C2×#6711yescharacteristic
297C22×D3—24no—
298C22×D3—22no—
299C22×D3—42no—
300C22×D3—42no—
301C22×D3—64no—
302C22×D3—68no—
303C22×D3—64no—
304C22×D3—64no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—124no—
308C22×D3—124no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—122no—
313C3×D4—34no—
314C3×D4—64no—
315C3×D4—62no—
316C2×C3×C4—24no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—21no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—21no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—42no—
328C2×C3×C4—62no—
329C2×C3×C4—128no—
330C2×C3×C4—122no—
331C2×C3×C4C2×C4×D312yes—
332C2×C3×C4C2×C4×D312yes—
333C2×C3×C4C2×D1212yes—
334C2×C3×C4C2×D1212yes—
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4#23512yes—
337C2×C3×C4#23512yes—
338C2×C3×C4C2×#6712yes—
339C2×C3×C4C2×#6712yes—
340C2×C3×C4C2×#6711yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×C3×C4C23×D311yescharacteristic
343C2×Dic3—22no—
344C2×Dic3—42no—
345C2×Dic3—64no—
346C2×Dic3—62no—
347C2×Dic3—62no—
348C2×Dic3—124no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351D12—24no—
352D12—22no—
353D12—34no—
354D12—34no—
355D12—64no—
356D12—64no—
357D12—68no—
358D12—64no—
359D12—64no—
360D12—62no—
361D12—62no—
362D12C2×C4×D314yescomplemented
363C4×D3—48no—
364C4×D3—1216no—
365C4×D3—128no—
366C4×D3—128no—
367C3×C8—34no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8C2×C4×D314yescomplemented
371C2×C32#44214yescomplemented
372C2×C32C2×C4×D411yescharacteristic
373C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
374C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
375C3⋊D3—44no—
376C3×D3—44no—
377C24—61no—
378C24—181no—
379C2×D4—32no—
380C2×D4—34no—
381C2×D4—62no—
382C2×D4—61no—
383C2×D4—92no—
384C2×D4—94no—
385C2×D4—182no—
386C2×D4—181no—
387C22×C4—61no—
388C22×C4—64no—
389C22×C4—124no—
390C22×C4—181no—
391C22×C4—184no—
392C22×C4—364no—
393C22×C4#62611yescharacteristic
394C22×C4#62611yescharacteristic
395C22×C4C2×D3211yescharacteristic
396D8—916no—
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—64no—
406C22⋊C4—184no—
407C42#62612yes—
408C42C2×D3212yes—
409C22×C3—21no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—64no—
414C22×C3—128no—
415C22×C3—122no—
416C22×C3—122no—
417C22×C3C4×D1212yes—
418C22×C3#90812yes—
419C22×C3#90812yes—
420C22×C3C4×#6712yes—
421C22×C3#93212yes—
422C22×C3#94912yes—
423C22×C3C22×D1211yescharacteristic
424C22×C3C22×#6711yescharacteristic
425C2×D3—24no—
426C2×D3—48no—
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—68no—
430C2×D3—64no—
431C2×D3—64no—
432C2×D3—124no—
433C2×D3—1216no—
434C2×D3—124no—
435C2×D3—128no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—128no—
439C2×D3—122no—
440C2×D3—122no—
441C3×C4—24no—
442C3×C4—22no—
443C3×C4—22no—
444C3×C4—22no—
445C3×C4—22no—
446C3×C4—21no—
447C3×C4—21no—
448C3×C4—22no—
449C3×C4—42no—
450C3×C4—122no—
451C3×C4C4×D1212yes—
452C3×C4C4×#6712yes—
453C3×C4C22×C4×D311yescharacteristic
454C3×C4C22×C4×D311yescharacteristic
455C3×C4C2×#23511yescharacteristic
456C3×C4C2×#23511yescharacteristic
457Dic3—42no—
458Dic3—124no—
459Dic3—122no—
460Dic3—122no—
461C32C2×#44211yescharacteristic, complemented, Sylow
462C23—62no—
463C23—64no—
464C23—122no—
465C23—122no—
466C23—182no—
467C23—184no—
468C23—362no—
469C23—362no—
470C23C2×#62611yescharacteristic
471D4—34no—
472D4—62no—
473D4—64no—
474D4—94no—
475D4—182no—
476D4—184no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—62no—
480C2×C4—128no—
481C2×C4—122no—
482C2×C4—182no—
483C2×C4—368no—
484C2×C4—362no—
485C2×C4#379812yes—
486C2×C4C4×D3212yes—
487C2×C4C2×#62612yes—
488C2×C4C2×#62612yes—
489C2×C4C2×#62611yescharacteristic
490C2×C4C22×D3211yescharacteristic
491C8—34no—
492C8—62no—
493C2×C3—24no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—124no—
498C2×C3#471114yescomplemented
499C2×C3#501414yescomplemented
500C2×C3C2×C4×D1211yescharacteristic
501C2×C3C2×#90811yescharacteristic
502C2×C3C2×#90811yescharacteristic
503C2×C3C2×C4×#6711yescharacteristic
504C2×C3C2×#93211yescharacteristic
505C2×C3C2×#94911yescharacteristic
506D3—44no—
507D3—128no—
508D3—124no—
509D3—124no—
510C22—64no—
511C22—128no—
512C22—122no—
513C22—122no—
514C22—184no—
515C22—368no—
516C22—362no—
517C22—362no—
518C22#6382512yes—
519C22#6383012yes—
520C22C4×#62612yes—
521C22C22×#62611yescharacteristic
522C4—22no—
523C4—22no—
524C4—122no—
525C4—362no—
526C4C4×#62612yes—
527C4C2×#379811yescharacteristic
528C4C2×C4×D3211yescharacteristic
529C3—21no—
530C3C2×#471111yescharacteristic, complemented
531C3C2×#501411yescharacteristic, complemented
532C2—124no—
533C2—364no—
534C2#1059034614yesdirect product factor
535C2C2×#6382511yescharacteristic
536C2C2×#6383011yescharacteristic
537C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC23C2×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32C2×#442
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C4⋊(C3⋊D3)C2semidirect
2. C2×C3×C4×D12C2semidirect
4. C2×C3×#803C2semidirect
5. C2×#63573C2semidirect
6. C2×#63564C2semidirect
7. C2×#63563C2semidirect
8. #10590346C2direct (N × H)
19. C4×C4⋊(C3⋊D3)C22semidirect
25. C3×C4×D12C22semidirect
26. C2×#3714C4semidirect
28. C3×#803C22semidirect
29. #63573C22semidirect
30. #63564C22semidirect
31. #63563C22semidirect
38. C2×C4×D12D3semidirect
47. C2×#803D3semidirect
57. C2×C4⋊(C3⋊D3)C2×C4semidirect
64. C2×C3×D12C2×C4semidirect
77. C2×C3×C3⋊C8C2×C4semidirect
80. #3714C2×C4semidirect
122. C4×D12C2×D3semidirect
130. #803C2×D3semidirect
152. C4⋊(C3⋊D3)C22×C4semidirect
158. C3×D12C22×C4semidirect
161. C3×C3⋊C8C22×C4semidirect
209. C2×D12C4×D3semidirect
246. C2×C3⋊C8C4×D3semidirect
362. D12C2×C4×D3semidirect
370. C3⋊C8C2×C4×D3semidirect
371. C2×C32#442semidirect
461. C32C2×#442semidirect
498. C2×C3#4711semidirect
499. C2×C3#5014semidirect
530. C3C2×#4711semidirect
531. C3C2×#5014semidirect
534. C2#10590346direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×C4⋊(C3⋊D3)2
C2×C3×C4×D122
C22×#37142
C2×C3×#8032
C2×#635732
C2×#635642
C2×#635632
#105903462
C2×#50143
C2×#47113