Finite Group Databasebeta

← C2×#10590505 #11869451

Subgroups — C2×#10590505 #11869451

Order 1152.

1001 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic, complemented
2C2×#63908C211yesmaximal, characteristic
3C2×#63635C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63562C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590505C218yesmaximal, direct product factor
9C2×#5003—31nomaximal
10C2×#4784—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×#625—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#892—22no—
22C3×#892C2214yescomplemented
23C2×(C2×D3)⋊Dic3—21no—
24#63908—22no—
25#63908C2214yes—
26#63635C2214yescomplemented
27C3×#809C2214yescomplemented
28#63575C2214yescomplemented
29#63562C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yescomplemented
31C2×C3×#117—31no—
32C2×#938—31no—
33C2×#930—31no—
34C2×#892D311yescharacteristic, complemented
35C2×C3×#102—31no—
36C2×#832—31no—
37C2×#830—31no—
38C2×(C2×D3)⋊C8—31no—
39C2×#818—31no—
40#5003—38no—
41C2×#809—31no—
42C2×#809D311yescharacteristic, complemented
43C2×#808—31no—
44C2×#808—31no—
45C2×#808—61no—
46C2×#807—31no—
47#4784—38no—
48C23×C3×D3—21no—
49C23×C3×D3D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C22×C3⋊Dic3—21no—
53C22×C3×Dic3—21no—
54C22×C3×Dic3D411yescharacteristic
55C2×C3×D12—22no—
56C2×C3×D12—22no—
57C2×C3×D12—21no—
58C2×C3×D12C2312yes—
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3D412yes—
62C2×C3×C4×D3C2312yes—
63C2×#625—24no—
64C2×#625—44no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C4⋊(C3⋊Dic3)—21no—
68C4⋊(C3⋊Dic3)C2312yes—
69C2×C3⋊(C3⋊C8)—22no—
70C2×C3⋊(C3⋊C8)C2312yes—
71C3×(C2×D3)⋊C4—24no—
72C3×C4⋊Dic3—21no—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3—24no—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77(C2×D3)⋊Dic3—24no—
78C2×#482—91noSylow
79C22×C3×D4—31no—
80C23×C3×C4—31no—
81C22×#67—61no—
82C22×#67—61no—
83C22×D12C2×D311yescharacteristic
84C22×C4×D3C2×D311yescharacteristic
85C22×C3×C8—31no—
86C3×#117—34no—
87C3×#117—62no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—31no—
90C2×C3×C4⋊C4C2×D311yescharacteristic
91C2×C3×C4⋊C4C2×D311yescharacteristic
92C2×C3×C22⋊C4—61no—
93C2×C3×C42—61no—
94C2×#217—61no—
95#938—34no—
96#938—62no—
97#930—34no—
98#930—62no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3—31no—
102C2×C4⋊Dic3—31no—
103C2×C4⋊Dic3—61no—
104C2×C4⋊Dic3C2×D311yescharacteristic
105C2×C4×Dic3—21no—
106C22×C3⋊C8—31no—
107C22×C3⋊C8—31no—
108C22×C3⋊C8—61no—
109C22×C3⋊C8C2×D311yescharacteristic
110#892—22no—
111#892C2×D314yescomplemented
112C3×#102—34no—
113#832—34no—
114#830—34no—
115(C2×D3)⋊C8—34no—
116#818—34no—
117#809—34no—
118#809C2×D314yescomplemented
119#808—34no—
120#808—34no—
121#808—64no—
122#807—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3×D3—22no—
125C22×C3×D3—22no—
126C22×C3×D3—22no—
127C22×C3×D3—22no—
128C22×C3×D3—42no—
129C22×C3×D3—42no—
130C22×C3×D3—42no—
131C22×C3×D3C2×D412yes—
132C2×C32×C4—22no—
133C2×C32×C4—42no—
134C2×C32×C4C2×D411yescharacteristic
135C2×C32×C4#4112yes—
136C2×C32×C4#4112yes—
137C2×C32×C4C2411yescharacteristic
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—42no—
140C2×C3×Dic3—22no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—42no—
143C2×C3×Dic3C2×D412yes—
144C3×D12—22no—
145C3×D12—22no—
146C3×D12—42no—
147C3×C4×D3—24no—
148C3×C4×D3—22no—
149C3×C4×D3—22no—
150#625—48no—
151C3⋊(C3⋊C8)—22no—
152C3×C3⋊C8—22no—
153C2×#121—91no—
154C2×#117—31no—
155#482—98no—
156C2×#107—91no—
157C2×#106—91no—
158C2×#102—31no—
159C2×#102—91no—
160C2×C22⋊C8—91no—
161C24×C3—31no—
162C24×C3—61no—
163C23×D3—21no—
164C23×D3#6711yescharacteristic
165C2×C3×D4—32no—
166C2×C3×D4—62no—
167C2×C3×D4—62no—
168C2×C3×D4—61no—
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—21no—
172C22×C3×C4—31no—
173C22×C3×C4—32no—
174C22×C3×C4—32no—
175C22×C3×C4—41no—
176C22×C3×C4—62no—
177C22×C3×C4—62no—
178C22×C3×C4—61no—
179C22×C3×C4C22×D311yescharacteristic
180C22×C3×C4C22×D311yescharacteristic
181C2×#67—64no—
182C2×#67—64no—
183C2×#67—124no—
184C2×#67—124no—
185C22×Dic3—21no—
186C22×Dic3—61no—
187C22×Dic3—61no—
188C22×Dic3—121no—
189C22×Dic3#6711yescharacteristic
190C2×D12—22no—
191C2×D12—22no—
192C2×D12—21no—
193C2×D12C22×D312yes—
194C2×C4×D3—22no—
195C2×C4×D3—22no—
196C2×C4×D3#6712yes—
197C2×C4×D3C22×D312yes—
198C2×C3×C8—32no—
199C2×C3×C8—62no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—22no—
203C3×C4⋊C4—32no—
204C3×C4⋊C4—41no—
205C3×C4⋊C4—61no—
206C3×C4⋊C4C22×D312yes—
207C3×C4⋊C4C22×D312yes—
208C3×C22⋊C4—64no—
209C3×C42—64no—
210#217—64no—
211(C2×D3)⋊C4—24no—
212(C2×D3)⋊C4—64no—
213C4⋊Dic3—21no—
214C4⋊Dic3—32no—
215C4⋊Dic3—32no—
216C4⋊Dic3—62no—
217C4⋊Dic3—61no—
218C4⋊Dic3—61no—
219C4⋊Dic3—121no—
220C4⋊Dic3C22×D312yes—
221C4×Dic3—24no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—32no—
224C2×C3⋊C8—32no—
225C2×C3⋊C8—62no—
226C2×C3⋊C8—64no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8C22×D312yes—
230C22×C32#12312yes—
231C22×C32#13512yes—
232C22×C32AGL(1,ℤ/8)12yes—
233C22×C32C22×D411yescharacteristic
234C2×C3×D3—22no—
235C2×C3×D3—22no—
236C2×C3×D3—22no—
237C2×C3×D3—44no—
238C2×C3×D3—42no—
239C2×C3×D3—42no—
240C2×C3×D3—42no—
241C2×C3×D3—84no—
242C32×C4—42no—
243C32×C4#12312yes—
244C32×C4C2×#4111yescharacteristic
245C32×C4C2×#4111yescharacteristic
246C3⋊Dic3—42no—
247C3×Dic3—22no—
248C3×Dic3—42no—
249C22×D4—31no—
250C22×D4—181no—
251C23×C4—31no—
252C22×C8—31no—
253C22×C8—91no—
254#121—94no—
255#121—182no—
256#117—34no—
257#117—62no—
258C2×C4⋊C4—31no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4D3211yescharacteristic
261C2×C22⋊C4—61no—
262C2×C22⋊C4—181no—
263C2×C42—61no—
264#107—94no—
265#106—94no—
266#102—34no—
267#102—94no—
268C22⋊C8—94no—
269C23×C3—21no—
270C23×C3—32no—
271C23×C3—62no—
272C23×C3—62no—
273C23×C3—62no—
274C23×C3—62no—
275C23×C3—122no—
276C23×C3—122no—
277C23×C3—122no—
278C23×C3D3×D411yescharacteristic
279C23×C3C2×#6711yescharacteristic
280C22×D3—22no—
281C22×D3—22no—
282C22×D3—22no—
283C22×D3—22no—
284C22×D3—42no—
285C22×D3—42no—
286C22×D3—42no—
287C22×D3C2×#6712yes—
288C3×D4—62no—
289C3×D4—62no—
290C3×D4—122no—
291C2×C3×C4—22no—
292C2×C3×C4—22no—
293C2×C3×C4—21no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—32no—
298C2×C3×C4—42no—
299C2×C3×C4—42no—
300C2×C3×C4—42no—
301C2×C3×C4—62no—
302C2×C3×C4—64no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—62no—
306C2×C3×C4—82no—
307C2×C3×C4—122no—
308C2×C3×C4#23512yes—
309C2×C3×C4#23512yes—
310C2×C3×C4#23512yes—
311C2×C3×C4D3×D411yescharacteristic
312C2×C3×C4#23712yes—
313C2×C3×C4C2×#6711yescharacteristic
314C2×C3×C4C23×D311yescharacteristic
315C2×C3×C4C23×D311yescharacteristic
316#67—128no—
317#67—128no—
318C2×Dic3—22no—
319C2×Dic3—22no—
320C2×Dic3—42no—
321C2×Dic3—62no—
322C2×Dic3—62no—
323C2×Dic3—122no—
324C2×Dic3—122no—
325C2×Dic3—122no—
326C2×Dic3—242no—
327C2×Dic3C2×#6712yes—
328D12—22no—
329D12—22no—
330D12—42no—
331C4×D3—24no—
332C4×D3—22no—
333C4×D3—22no—
334C3×C8—62no—
335C3⋊C8—22no—
336C3⋊C8—64no—
337C3⋊C8—62no—
338C3⋊C8—62no—
339C2×C32#48214yescomplemented
340C2×C32C2×#12311yescharacteristic
341C2×C32C2×#13511yescharacteristic
342C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
343C3×D3—42no—
344C3×D3—82no—
345C24—31no—
346C24—61no—
347C2×D4—32no—
348C2×D4—62no—
349C2×D4—62no—
350C2×D4—61no—
351C2×D4—184no—
352C2×D4—364no—
353C22×C4—21no—
354C22×C4—31no—
355C22×C4—32no—
356C22×C4—32no—
357C22×C4—62no—
358C22×C4—62no—
359C22×C4—61no—
360C22×C4—181no—
361C22×C4C2×D3211yescharacteristic
362C2×C8—32no—
363C2×C8—62no—
364C2×C8—92no—
365C2×C8—182no—
366C4⋊C4—21no—
367C4⋊C4—32no—
368C4⋊C4—61no—
369C4⋊C4—92no—
370C4⋊C4—181no—
371C4⋊C4C2×D3212yes—
372C22⋊C4—64no—
373C22⋊C4—184no—
374C42—64no—
375C22×C3—21no—
376C22×C3—22no—
377C22×C3—22no—
378C22×C3—22no—
379C22×C3—62no—
380C22×C3—62no—
381C22×C3—62no—
382C22×C3—124no—
383C22×C3—122no—
384C22×C3—122no—
385C22×C3—122no—
386C22×C3—244no—
387C22×C3#88312yes—
388C22×C3#91212yes—
389C22×C3#91412yes—
390C22×C3#92912yes—
391C22×C3#94912yes—
392C22×C3#95012yes—
393C22×C3C2×D3×D411yescharacteristic
394C22×C3C22×#6711yescharacteristic
395C2×D3—22no—
396C2×D3—22no—
397C2×D3—22no—
398C2×D3—44no—
399C2×D3—42no—
400C2×D3—42no—
401C2×D3—42no—
402C2×D3—84no—
403C3×C4—21no—
404C3×C4—21no—
405C3×C4—22no—
406C3×C4—42no—
407C3×C4—42no—
408C3×C4—62no—
409C3×C4—82no—
410C3×C4—122no—
411C3×C4#88312yes—
412C3×C4#92912yes—
413C3×C4C2×#23511yescharacteristic
414C3×C4C2×#23511yescharacteristic
415C3×C4C2×#23511yescharacteristic
416C3×C4C2×#23711yescharacteristic
417Dic3—22no—
418Dic3—42no—
419Dic3—122no—
420Dic3—122no—
421Dic3—242no—
422C32C2×#48211yescharacteristic, complemented, Sylow
423C23—32no—
424C23—62no—
425C23—62no—
426C23—62no—
427C23—62no—
428C23—122no—
429C23—122no—
430C23—122no—
431C23D3×#6711yescharacteristic
432D4—62no—
433D4—62no—
434D4—122no—
435D4—368no—
436C2×C4—22no—
437C2×C4—32no—
438C2×C4—42no—
439C2×C4—62no—
440C2×C4—62no—
441C2×C4—62no—
442C2×C4—64no—
443C2×C4—62no—
444C2×C4—122no—
445C2×C4—182no—
446C2×C4—362no—
447C2×C4#379512yes—
448C2×C4#379812yes—
449C2×C4D3×#6711yescharacteristic
450C2×C4C22×D3211yescharacteristic
451C8—62no—
452C8—182no—
453C2×C3—21no—
454C2×C3—24no—
455C2×C3—21no—
456C2×C3—21no—
457C2×C3—122no—
458C2×C3—242no—
459C2×C3#478414yescomplemented
460C2×C3#500314yescomplemented
461C2×C3C2×#88311yescharacteristic
462C2×C3C2×#91211yescharacteristic
463C2×C3C2×#91411yescharacteristic
464C2×C3C2×#92911yescharacteristic
465C2×C3C2×#94911yescharacteristic
466C2×C3C2×#95011yescharacteristic
467D3—42no—
468D3—82no—
469C22—62no—
470C22—62no—
471C22—62no—
472C22—124no—
473C22—122no—
474C22—122no—
475C22—122no—
476C22—244no—
477C22#6390512yes—
478C22#6393312yes—
479C22#6393912yes—
480C22C2×D3×#6711yescharacteristic
481C4—42no—
482C4—62no—
483C4—122no—
484C4—362no—
485C4#6390512yes—
486C4C2×#379511yescharacteristic
487C4C2×#379811yescharacteristic
488C3—21no—
489C3C2×#478411yescharacteristic, complemented
490C3C2×#500311yescharacteristic, complemented
491C2—122no—
492C2—242no—
493C2#1059050514yesdirect product factor
494C2C2×#6390511yescharacteristic
495C2C2×#6393311yescharacteristic
496C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63908C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#482
LCSG ▷ C2×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×#892C2semidirect
3. C2×#63635C2semidirect
4. C2×C3×#809C2semidirect
5. C2×#63575C2semidirect
6. C2×#63562C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590505C2direct (N × H)
22. C3×#892C22semidirect
26. #63635C22semidirect
27. C3×#809C22semidirect
28. #63575C22semidirect
29. #63562C22semidirect
30. (C2×D3)⋊(C3⋊C8)C22semidirect
34. C2×#892D3semidirect
42. C2×#809D3semidirect
111. #892C2×D3semidirect
118. #809C2×D3semidirect
339. C2×C32#482semidirect
422. C32C2×#482semidirect
459. C2×C3#4784semidirect
460. C2×C3#5003semidirect
489. C3C2×#4784semidirect
490. C3C2×#5003semidirect
493. C2#10590505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8922
C2×#639082
C2×#636352
C2×C3×#8092
C2×#635752
C2×#635622
C2×(C2×D3)⋊(C3⋊C8)2
#105905052
C2×#50033
C2×#47843