Finite Group Databasebeta

← C2×#10590455 #11860165

Subgroups — C2×#10590455 #11860165

Order 1152.

1281 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#893C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C22×#3713C211yesmaximal, characteristic
4C2×#63635C211yesmaximal, characteristic, complemented
5C2×C3×#809C211yesmaximal, characteristic, complemented
6C2×#63563C211yesmaximal, characteristic, complemented
7C2×#63554C211yesmaximal, characteristic, complemented
8#10590455C218yesmaximal, direct product factor
9C2×#5014—31nomaximal
10C2×#4785—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C22×D3×Dic3—21no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×C4×Dic3C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893—22no—
22C3×#893C2214yescomplemented
23C2×(C2×D3)⋊Dic3—21no—
24Dic3×D12—22no—
25Dic3×D12C2214yescomplemented
26C2×#3713C418yescomplemented
27C2×#3713C2214yes—
28#63635C2214yescomplemented
29C3×#809C2214yescomplemented
30#63563C2214yescomplemented
31#63554C2214yescomplemented
32C2×C3×C4×D4—31no—
33C2×D4×Dic3—31no—
34C22×#213—31no—
35C22×#213—31no—
36C2×#893D311yescharacteristic, complemented
37C2×C4×D12—31no—
38C2×C3×#102—31no—
39C2×#832—31no—
40C2×#821—31no—
41C2×#815—31no—
42#5014—38no—
43C2×#809D311yescharacteristic, complemented
44C2×#808—31no—
45C2×#808—31no—
46C2×#808—61no—
47C2×#803—31no—
48#4785—38no—
49C23×C3×D3—21no—
50C23×C3×D3—21no—
51C22×C32×C4—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C22×C3×Dic3D411yescharacteristic
56C2×C3×D12—21no—
57C2×C3×D12—21no—
58C2×C3×D12—22no—
59C2×C3×D12—22no—
60C2×C3×D12C2×C414yescomplemented
61C2×C3×D12C2×C414yescomplemented
62C2×C3×D12C2312yes—
63C2×C3×D12C2312yes—
64C2×C3×C4×D3—24no—
65C2×C3×C4×D3—44no—
66C2×D3×Dic3—24no—
67C2×D3×Dic3—44no—
68C32×C4⋊C4—21no—
69C32×C4⋊C4C2312yes—
70C4⋊(C3⋊Dic3)—21no—
71C4⋊(C3⋊Dic3)C2312yes—
72C2×C3⋊(C3⋊C8)C2×C414yescomplemented
73C2×C3⋊(C3⋊C8)C2312yes—
74C3×(C2×D3)⋊C4—24no—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79(C2×D3)⋊Dic3—24no—
80#3713C2×C4116yescomplemented
81C2×#442—91noSylow
82C22×C3×D4—31no—
83C22×C3×D4—31no—
84C23×C3×C4—61no—
85C23×Dic3—61no—
86C22×D12C2×D311yescharacteristic
87C22×D12C2×D311yescharacteristic
88C22×C4×D3—21no—
89C22×C4×D3—61no—
90C22×C3×C8—31no—
91C3×C4×D4—34no—
92C3×C4×D4—62no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2×D311yescharacteristic
95C2×C3×C4⋊C4C2×D311yescharacteristic
96C2×C3×C22⋊C4—61no—
97C2×C3×C42—31no—
98C2×#217—61no—
99D4×Dic3—34no—
100D4×Dic3—62no—
101C2×#213—38no—
102C2×#213—38no—
103C2×#213—34no—
104C2×#213—34no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3—31no—
108C2×C4⋊Dic3—31no—
109C2×C4⋊Dic3—61no—
110C2×C4×Dic3C2×D311yescharacteristic
111C22×C3⋊C8—31no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—61no—
114C22×C3⋊C8C2×D311yescharacteristic
115#893—22no—
116#893C2×D314yescomplemented
117C4×D12—34no—
118C4×D12—62no—
119C3×#102—34no—
120#832—34no—
121#821—34no—
122#815—34no—
123#809C2×D314yescomplemented
124#808—34no—
125#808—34no—
126#808—64no—
127#803—34no—
128C23×C32C2×D411yescharacteristic
129C22×C3×D3—24no—
130C22×C3×D3—24no—
131C22×C3×D3—22no—
132C22×C3×D3—22no—
133C22×C3×D3—42no—
134C22×C3×D3—42no—
135C22×C3×D3—42no—
136C22×C3×D3—42no—
137C2×C32×C4—22no—
138C2×C32×C4—42no—
139C2×C32×C4C22×C412yes—
140C2×C32×C4C2×D411yescharacteristic
141C2×C32×C4#4112yes—
142C2×C32×C4C2411yescharacteristic
143C2×C3⋊Dic3—22no—
144C2×C3⋊Dic3—42no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3C2×D412yes—
148C2×C3×Dic3C2×D412yes—
149C3×D12—24no—
150C3×D12—24no—
151C3×D12—22no—
152C3×D12—22no—
153C3×D12C22×C414yescomplemented
154C3×D12C22×C414yescomplemented
155C3×C4×D3—48no—
156D3×Dic3—48no—
157C3⋊(C3⋊C8)C22×C414yescomplemented
158C3×C3⋊C8—22no—
159C22×D8—91no—
160C2×C4×D4—31no—
161C2×C4×D4—91no—
162#442—98no—
163C2×#106—91no—
164C2×#102—31no—
165C2×#102—91no—
166C2×#97—91no—
167C24×C3—61no—
168C24×C3—61no—
169C23×D3—21no—
170C23×D3—21no—
171C2×C3×D4—34no—
172C2×C3×D4—34no—
173C2×C3×D4—32no—
174C2×C3×D4—32no—
175C2×C3×D4—62no—
176C2×C3×D4—61no—
177C2×C3×D4—62no—
178C2×C3×D4—61no—
179C22×C3×C4—21no—
180C22×C3×C4—21no—
181C22×C3×C4—21no—
182C22×C3×C4—31no—
183C22×C3×C4—31no—
184C22×C3×C4—41no—
185C22×C3×C4—64no—
186C22×C3×C4—124no—
187C22×C3×C4C22×D311yescharacteristic
188C22×C3×C4C22×D311yescharacteristic
189C22×Dic3—61no—
190C22×Dic3—61no—
191C22×Dic3—64no—
192C22×Dic3—121no—
193C22×Dic3—124no—
194C22×Dic3#6711yescharacteristic
195C22×Dic3#6711yescharacteristic
196C2×D12—22no—
197C2×D12—21no—
198C2×D12—22no—
199C2×D12—21no—
200C2×D12C4×D314yescomplemented
201C2×D12C4×D314yescomplemented
202C2×D12C22×D312yes—
203C2×D12C22×D312yes—
204C2×C4×D3—24no—
205C2×C4×D3—44no—
206C2×C4×D3—64no—
207C2×C4×D3—124no—
208C2×C3×C8—32no—
209C2×C3×C8—62no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4—21no—
212C3×C4⋊C4—22no—
213C3×C4⋊C4—41no—
214C3×C4⋊C4C22×D312yes—
215C3×C4⋊C4C22×D312yes—
216C3×C22⋊C4—64no—
217C3×C42—32no—
218C3×C42—32no—
219#217—64no—
220#213—316no—
221#213—316no—
222(C2×D3)⋊C4—24no—
223(C2×D3)⋊C4—64no—
224C4⋊Dic3—32no—
225C4⋊Dic3—32no—
226C4⋊Dic3—62no—
227C4⋊Dic3—61no—
228C4⋊Dic3—61no—
229C4⋊Dic3—121no—
230C4×Dic3#6712yes—
231C4×Dic3C22×D312yes—
232C2×C3⋊C8—22no—
233C2×C3⋊C8—34no—
234C2×C3⋊C8—34no—
235C2×C3⋊C8—32no—
236C2×C3⋊C8—32no—
237C2×C3⋊C8—62no—
238C2×C3⋊C8—64no—
239C2×C3⋊C8C22×D312yes—
240C22×C32C4×D412yes—
241C22×C32AGL(1,ℤ/8)12yes—
242C22×C32AGL(1,ℤ/8)12yes—
243C22×C32C22×D411yescharacteristic
244C2×C3×D3—24no—
245C2×C3×D3—24no—
246C2×C3×D3—42no—
247C2×C3×D3—42no—
248C2×C3×D3—42no—
249C2×C3×D3—42no—
250C2×C3×D3—48no—
251C2×C3×D3—48no—
252C32×C4—42no—
253C32×C4C4×D412yes—
254C32×C4C23×C411yescharacteristic
255C32×C4C2×#4111yescharacteristic
256C3⋊Dic3—42no—
257C3×Dic3—22no—
258C3×Dic3—22no—
259C22×D4—31no—
260C22×D4—31no—
261C23×C4—61no—
262C23×C4—181no—
263C2×D8—98no—
264C2×D8—94no—
265C22×C8—31no—
266C22×C8—91no—
267C4×D4—34no—
268C4×D4—62no—
269C4×D4—94no—
270C4×D4—182no—
271C2×C4⋊C4—91no—
272C2×C4⋊C4D3211yescharacteristic
273C2×C22⋊C4—61no—
274C2×C22⋊C4—181no—
275C2×C42—31no—
276#106—94no—
277#102—34no—
278#102—94no—
279#97—94no—
280C23×C3—21no—
281C23×C3—64no—
282C23×C3—64no—
283C23×C3—62no—
284C23×C3—62no—
285C23×C3—122no—
286C23×C3—122no—
287C23×C3—122no—
288C23×C3—122no—
289C23×C3D3×D411yescharacteristic
290C23×C3C2×#6711yescharacteristic
291C22×D3—24no—
292C22×D3—24no—
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—42no—
296C22×D3—42no—
297C22×D3—42no—
298C22×D3—42no—
299C3×D4—34no—
300C3×D4—34no—
301C3×D4—64no—
302C3×D4—64no—
303C3×D4—62no—
304C3×D4—62no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—21no—
308C2×C3×C4—22no—
309C2×C3×C4—22no—
310C2×C3×C4—21no—
311C2×C3×C4—32no—
312C2×C3×C4—32no—
313C2×C3×C4—42no—
314C2×C3×C4—42no—
315C2×C3×C4—42no—
316C2×C3×C4—62no—
317C2×C3×C4—62no—
318C2×C3×C4—82no—
319C2×C3×C4—128no—
320C2×C3×C4C2×C4×D312yes—
321C2×C3×C4C2×C4×D312yes—
322C2×C3×C4#23512yes—
323C2×C3×C4D3×D411yescharacteristic
324C2×C3×C4#23712yes—
325C2×C3×C4C2×#6711yescharacteristic
326C2×C3×C4C23×D311yescharacteristic
327C2×C3×C4C23×D311yescharacteristic
328C2×Dic3—22no—
329C2×Dic3—22no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—122no—
333C2×Dic3—128no—
334C2×Dic3—122no—
335C2×Dic3—122no—
336C2×Dic3—242no—
337C2×Dic3C2×#6712yes—
338C2×Dic3C2×#6712yes—
339D12—24no—
340D12—24no—
341D12—22no—
342D12—22no—
343D12C2×C4×D314yescomplemented
344D12C2×C4×D314yescomplemented
345C4×D3—48no—
346C4×D3—128no—
347C3×C8—62no—
348C3⋊C8—22no—
349C3⋊C8—34no—
350C3⋊C8—34no—
351C3⋊C8—64no—
352C2×C32#44214yescomplemented
353C2×C32C2×C4×D411yescharacteristic
354C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
355C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
356C3×D3—44no—
357C3×D3—44no—
358C24—61no—
359C24—61no—
360C2×D4—32no—
361C2×D4—32no—
362C2×D4—34no—
363C2×D4—34no—
364C2×D4—62no—
365C2×D4—62no—
366C2×D4—61no—
367C2×D4—61no—
368C22×C4—21no—
369C22×C4—31no—
370C22×C4—31no—
371C22×C4—64no—
372C22×C4—124no—
373C22×C4—184no—
374C22×C4—181no—
375C22×C4—364no—
376C22×C4C2×D3211yescharacteristic
377D8—916no—
378C2×C8—32no—
379C2×C8—62no—
380C2×C8—92no—
381C2×C8—94no—
382C4⋊C4—21no—
383C4⋊C4—92no—
384C4⋊C4—181no—
385C4⋊C4C2×D3212yes—
386C22⋊C4—64no—
387C22⋊C4—184no—
388C42—32no—
389C42—32no—
390C22×C3—21no—
391C22×C3—22no—
392C22×C3—22no—
393C22×C3—22no—
394C22×C3—64no—
395C22×C3—64no—
396C22×C3—122no—
397C22×C3—122no—
398C22×C3—128no—
399C22×C3—122no—
400C22×C3—128no—
401C22×C3—122no—
402C22×C3#67⋊C412yes—
403C22×C3#91112yes—
404C22×C3#91412yes—
405C22×C3C4×#6712yes—
406C22×C3#93212yes—
407C22×C3#94912yes—
408C22×C3C2×D3×D411yescharacteristic
409C22×C3C22×#6711yescharacteristic
410C2×D3—24no—
411C2×D3—24no—
412C2×D3—42no—
413C2×D3—42no—
414C2×D3—48no—
415C2×D3—42no—
416C2×D3—48no—
417C2×D3—42no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—22no—
421C3×C4—42no—
422C3×C4—42no—
423C3×C4—62no—
424C3×C4—62no—
425C3×C4—82no—
426C3×C4#67⋊C412yes—
427C3×C4C4×#6712yes—
428C3×C4C22×C4×D311yescharacteristic
429C3×C4C22×C4×D311yescharacteristic
430C3×C4C2×#23511yescharacteristic
431C3×C4C2×#23711yescharacteristic
432Dic3—22no—
433Dic3—22no—
434Dic3—122no—
435Dic3—122no—
436Dic3—242no—
437C32C2×#44211yescharacteristic, complemented, Sylow
438C23—62no—
439C23—62no—
440C23—64no—
441C23—64no—
442C23—122no—
443C23—122no—
444C23—122no—
445C23—122no—
446C23D3×#6711yescharacteristic
447D4—34no—
448D4—34no—
449D4—62no—
450D4—62no—
451D4—64no—
452D4—64no—
453C2×C4—22no—
454C2×C4—32no—
455C2×C4—32no—
456C2×C4—42no—
457C2×C4—62no—
458C2×C4—62no—
459C2×C4—128no—
460C2×C4—182no—
461C2×C4—368no—
462C2×C4—362no—
463C2×C4#379512yes—
464C2×C4C4×D3212yes—
465C2×C4D3×#6711yescharacteristic
466C2×C4C22×D3211yescharacteristic
467C8—62no—
468C8—94no—
469C2×C3—21no—
470C2×C3—21no—
471C2×C3—21no—
472C2×C3—24no—
473C2×C3—124no—
474C2×C3—124no—
475C2×C3#478514yescomplemented
476C2×C3#501414yescomplemented
477C2×C3C2×#67⋊C411yescharacteristic
478C2×C3C2×#91111yescharacteristic
479C2×C3C2×#91411yescharacteristic
480C2×C3C2×C4×#6711yescharacteristic
481C2×C3C2×#93211yescharacteristic
482C2×C3C2×#94911yescharacteristic
483D3—44no—
484D3—44no—
485C22—64no—
486C22—64no—
487C22—122no—
488C22—122no—
489C22—122no—
490C22—122no—
491C22—128no—
492C22—128no—
493C22#6387912yes—
494C22#6393212yes—
495C22#6393912yes—
496C22C2×D3×#6711yescharacteristic
497C4—42no—
498C4—62no—
499C4—62no—
500C4—362no—
501C4#6387912yes—
502C4C2×#379511yescharacteristic
503C4C2×C4×D3211yescharacteristic
504C3—21no—
505C3C2×#478511yescharacteristic, complemented
506C3C2×#501411yescharacteristic, complemented
507C2—124no—
508C2—124no—
509C2#1059045514yesdirect product factor
510C2C2×#6387911yescharacteristic
511C2C2×#6393211yescharacteristic
512C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#442
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
1. C2×C3×#893C2semidirect
2. C2×Dic3×D12C2semidirect
4. C2×#63635C2semidirect
5. C2×C3×#809C2semidirect
6. C2×#63563C2semidirect
7. C2×#63554C2semidirect
8. #10590455C2direct (N × H)
22. C3×#893C22semidirect
25. Dic3×D12C22semidirect
26. C2×#3713C4semidirect
28. #63635C22semidirect
29. C3×#809C22semidirect
30. #63563C22semidirect
31. #63554C22semidirect
36. C2×#893D3semidirect
43. C2×#809D3semidirect
60. C2×C3×D12C2×C4semidirect
61. C2×C3×D12C2×C4semidirect
72. C2×C3⋊(C3⋊C8)C2×C4semidirect
80. #3713C2×C4semidirect
116. #893C2×D3semidirect
123. #809C2×D3semidirect
153. C3×D12C22×C4semidirect
154. C3×D12C22×C4semidirect
157. C3⋊(C3⋊C8)C22×C4semidirect
200. C2×D12C4×D3semidirect
201. C2×D12C4×D3semidirect
343. D12C2×C4×D3semidirect
344. D12C2×C4×D3semidirect
352. C2×C32#442semidirect
437. C32C2×#442semidirect
475. C2×C3#4785semidirect
476. C2×C3#5014semidirect
505. C3C2×#4785semidirect
506. C3C2×#5014semidirect
509. C2#10590455direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8932
C2×Dic3×D122
C22×#37132
C2×#636352
C2×C3×#8092
C2×#635632
C2×#635542
#105904552
C2×#50143
C2×#47853