Finite Group Databasebeta

← C2×#10590425 #11869449

Subgroups — C2×#10590425 #11869449

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 509 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#892C211yesmaximal, characteristic, complemented
2C2×#63909C211yesmaximal, characteristic
3C2×#63636C211yesmaximal, characteristic, complemented
4C2×C3×#808C211yesmaximal, characteristic, complemented
5C2×#63576C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic, complemented
7C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590425C218yesmaximal, direct product factor
9C2×#5003—31nomaximal
10C2×#4866—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C22×#626—21no—
14C2×C32×C4⋊C4C2211yescharacteristic
15C22×C3⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×(C2×D3)⋊C4—21no—
17C2×C3×C4⋊Dic3C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×C4×Dic3—21no—
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#892—22no—
22C3×#892C2214yescomplemented
23C2×#3722—21no—
24#63909—22no—
25#63909C2214yes—
26#63636C2214yescomplemented
27C3×#808C2214yescomplemented
28#63576C2214yescomplemented
29#63564C2214yescomplemented
30(C2×D3)⋊(C3⋊C8)C2214yescomplemented
31C2×C3×#117—31no—
32C2×#930—31no—
33C2×#895—31no—
34C2×#892D311yescharacteristic, complemented
35C2×C3×#106—31no—
36C2×#830—31no—
37C2×#821—31no—
38C2×(C2×D3)⋊C8—31no—
39#5003—38no—
40C2×#809—31no—
41C2×#809—31no—
42C2×#809—31no—
43C2×#809—61no—
44C2×#808D311yescharacteristic, complemented
45C2×#807—31no—
46C2×#807—31no—
47#4866—38no—
48C23×C3⋊D3—21no—
49C23×C3×D3D411yescharacteristic
50C22×C32×C4—21no—
51C22×C32×C4C2311yescharacteristic
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)—21no—
55C2×C4⋊(C3⋊D3)C2312yes—
56C22×C3×Dic3—21no—
57C22×C3×Dic3—21no—
58C22×C3×Dic3D411yescharacteristic
59C2×C3×C4×D3—22no—
60C2×C3×C4×D3—22no—
61C2×C3×C4×D3D412yes—
62C2×C3×C4×D3C2312yes—
63C2×#626—24no—
64C2×#626—44no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4C2312yes—
67C2×C3⋊(C3⋊C8)—22no—
68C2×C3⋊(C3⋊C8)C2312yes—
69C3×(C2×D3)⋊C4—24no—
70C3×C4⋊Dic3—21no—
71C3×C4⋊Dic3—21no—
72C3×C4⋊Dic3C2312yes—
73C3×C4⋊Dic3C2312yes—
74C3×C4×Dic3—24no—
75C2×C3×C3⋊C8—22no—
76C2×C3×C3⋊C8C2312yes—
77#3722—24no—
78C2×#482—91noSylow
79C23×C3×C4—31no—
80C22×#67—61no—
81C22×D12—31no—
82C22×D12—31no—
83C22×D12—61no—
84C22×D12—61no—
85C22×C4×D3C2×D311yescharacteristic
86C22×C3×C8—31no—
87C3×#117—34no—
88C3×#117—62no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—31no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C4⋊C4C2×D311yescharacteristic
93C2×C3×C4⋊C4C2×D311yescharacteristic
94C2×C3×C22⋊C4—61no—
95C2×C3×C42—61no—
96#930—34no—
97#930—62no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—61no—
100C2×(C2×D3)⋊C4—61no—
101C2×C4⋊Dic3C2×D311yescharacteristic
102C2×C4⋊Dic3C2×D311yescharacteristic
103C2×C4×Dic3—21no—
104C22×C3⋊C8—31no—
105C22×C3⋊C8—31no—
106C22×C3⋊C8—61no—
107C22×C3⋊C8C2×D311yescharacteristic
108#895—34no—
109#895—62no—
110#892—22no—
111#892C2×D314yescomplemented
112C3×#106—34no—
113#830—34no—
114#821—34no—
115(C2×D3)⋊C8—34no—
116#809—34no—
117#809—34no—
118#809—34no—
119#809—64no—
120#808C2×D314yescomplemented
121#807—34no—
122#807—34no—
123C23×C32C2×D411yescharacteristic
124C22×C3⋊D3—22no—
125C22×C3⋊D3—42no—
126C22×C3⋊D3—42no—
127C22×C3⋊D3—42no—
128C22×C3×D3—22no—
129C22×C3×D3—22no—
130C22×C3×D3—22no—
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
138C4⋊(C3⋊D3)—22no—
139C4⋊(C3⋊D3)—22no—
140C4⋊(C3⋊D3)—42no—
141C2×C3×Dic3—22no—
142C2×C3×Dic3—22no—
143C2×C3×Dic3—22no—
144C2×C3×Dic3—42no—
145C2×C3×Dic3—42no—
146C2×C3×Dic3C2×D412yes—
147C3×C4×D3—24no—
148C3×C4×D3—22no—
149C3×C4×D3—22no—
150#626—48no—
151C3⋊(C3⋊C8)—22no—
152C3×C3⋊C8—22no—
153C2×#121—91no—
154C2×#117—31no—
155#482—98no—
156C2×#107—91no—
157C2×#106—31no—
158C2×#102—91no—
159C2×#102—91no—
160C2×C22⋊C8—91no—
161C24×C3—31no—
162C23×D3—61no—
163C23×D3—61no—
164C23×D3—121no—
165C23×D3#6711yescharacteristic
166C22×C3×C4—21no—
167C22×C3×C4—21no—
168C22×C3×C4—21no—
169C22×C3×C4—31no—
170C22×C3×C4—32no—
171C22×C3×C4—32no—
172C22×C3×C4—41no—
173C22×C3×C4—62no—
174C22×C3×C4—62no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—64no—
180C2×#67—124no—
181C22×Dic3—21no—
182C22×Dic3—21no—
183C22×Dic3#6711yescharacteristic
184C2×D12—32no—
185C2×D12—32no—
186C2×D12—62no—
187C2×D12—64no—
188C2×D12—62no—
189C2×D12—62no—
190C2×D12—62no—
191C2×D12—62no—
192C2×D12—64no—
193C2×D12—61no—
194C2×D12—61no—
195C2×D12—122no—
196C2×D12—121no—
197C2×D12—124no—
198C2×C4×D3—22no—
199C2×C4×D3—22no—
200C2×C4×D3#6712yes—
201C2×C4×D3C22×D312yes—
202C2×C3×C8—32no—
203C2×C3×C8—62no—
204C3×C4⋊C4—21no—
205C3×C4⋊C4—21no—
206C3×C4⋊C4—22no—
207C3×C4⋊C4—32no—
208C3×C4⋊C4—32no—
209C3×C4⋊C4—41no—
210C3×C4⋊C4—61no—
211C3×C4⋊C4—61no—
212C3×C4⋊C4C22×D312yes—
213C3×C4⋊C4C22×D312yes—
214C3×C22⋊C4—64no—
215C3×C42—64no—
216(C2×D3)⋊C4—24no—
217(C2×D3)⋊C4—64no—
218(C2×D3)⋊C4—64no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3C22×D312yes—
222C4⋊Dic3C22×D312yes—
223C4×Dic3—24no—
224C2×C3⋊C8—22no—
225C2×C3⋊C8—32no—
226C2×C3⋊C8—32no—
227C2×C3⋊C8—62no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—62no—
230C2×C3⋊C8—122no—
231C2×C3⋊C8C22×D312yes—
232C22×C32#12312yes—
233C22×C32#13512yes—
234C22×C32AGL(1,ℤ/8)12yes—
235C22×C32C22×D411yescharacteristic
236C2×C3⋊D3—42no—
237C2×C3⋊D3—42no—
238C2×C3⋊D3—42no—
239C2×C3⋊D3—84no—
240C2×C3×D3—22no—
241C2×C3×D3—22no—
242C2×C3×D3—22no—
243C2×C3×D3—44no—
244C32×C4—42no—
245C32×C4#12312yes—
246C32×C4C2×#4111yescharacteristic
247C32×C4C2×#4111yescharacteristic
248C3×Dic3—22no—
249C3×Dic3—42no—
250C3×Dic3—42no—
251C22×D4—91no—
252C22×D4—181no—
253C23×C4—31no—
254C22×C8—31no—
255C22×C8—91no—
256#121—94no—
257#121—182no—
258#117—34no—
259#117—62no—
260C2×C4⋊C4—31no—
261C2×C4⋊C4—31no—
262C2×C4⋊C4D3211yescharacteristic
263C2×C22⋊C4—61no—
264C2×C22⋊C4—181no—
265C2×C42—61no—
266#107—94no—
267#106—34no—
268#102—94no—
269#102—94no—
270C22⋊C8—94no—
271C23×C3—21no—
272C23×C3—32no—
273C23×C3—62no—
274C23×C3—62no—
275C23×C3—62no—
276C23×C3D3×D411yescharacteristic
277C23×C3C2×#6711yescharacteristic
278C22×D3—22no—
279C22×D3—22no—
280C22×D3—22no—
281C22×D3—62no—
282C22×D3—62no—
283C22×D3—122no—
284C22×D3—124no—
285C22×D3—122no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—122no—
289C22×D3—122no—
290C22×D3—122no—
291C22×D3—242no—
292C22×D3—242no—
293C22×D3C2×#6712yes—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—21no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—21no—
300C2×C3×C4—32no—
301C2×C3×C4—42no—
302C2×C3×C4—42no—
303C2×C3×C4—42no—
304C2×C3×C4—62no—
305C2×C3×C4—64no—
306C2×C3×C4—62no—
307C2×C3×C4—62no—
308C2×C3×C4—62no—
309C2×C3×C4—62no—
310C2×C3×C4—82no—
311C2×C3×C4—122no—
312C2×C3×C4—122no—
313C2×C3×C4#23512yes—
314C2×C3×C4#23512yes—
315C2×C3×C4#23512yes—
316C2×C3×C4D3×D411yescharacteristic
317C2×C3×C4#23912yes—
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C23×D311yescharacteristic
320C2×C3×C4C23×D311yescharacteristic
321#67—128no—
322C2×Dic3—22no—
323C2×Dic3—22no—
324C2×Dic3—22no—
325C2×Dic3—42no—
326C2×Dic3—42no—
327C2×Dic3C2×#6712yes—
328D12—64no—
329D12—62no—
330D12—62no—
331D12—62no—
332D12—62no—
333D12—122no—
334D12—124no—
335D12—128no—
336D12—122no—
337D12—122no—
338C4×D3—24no—
339C4×D3—22no—
340C4×D3—22no—
341C3×C8—62no—
342C3⋊C8—22no—
343C3⋊C8—62no—
344C3⋊C8—62no—
345C3⋊C8—122no—
346C2×C32#48214yescomplemented
347C2×C32C2×#12311yescharacteristic
348C2×C32C2×#13511yescharacteristic
349C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
350C3⋊D3—82no—
351C3×D3—42no—
352C24—31no—
353C24—181no—
354C2×D4—92no—
355C2×D4—184no—
356C2×D4—182no—
357C2×D4—182no—
358C2×D4—181no—
359C2×D4—364no—
360C22×C4—21no—
361C22×C4—31no—
362C22×C4—32no—
363C22×C4—32no—
364C22×C4—62no—
365C22×C4—62no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4C2×D3211yescharacteristic
369C2×C8—32no—
370C2×C8—62no—
371C2×C8—92no—
372C2×C8—182no—
373C4⋊C4—21no—
374C4⋊C4—32no—
375C4⋊C4—32no—
376C4⋊C4—61no—
377C4⋊C4—61no—
378C4⋊C4C2×D3212yes—
379C22⋊C4—64no—
380C22⋊C4—184no—
381C42—64no—
382C22×C3—21no—
383C22×C3—22no—
384C22×C3—22no—
385C22×C3—22no—
386C22×C3—62no—
387C22×C3—62no—
388C22×C3—62no—
389C22×C3—124no—
390C22×C3#89412yes—
391C22×C3#91412yes—
392C22×C3#91612yes—
393C22×C3#92912yes—
394C22×C3#94912yes—
395C22×C3#95012yes—
396C22×C3C2×D3×D411yescharacteristic
397C22×C3C22×#6711yescharacteristic
398C2×D3—22no—
399C2×D3—22no—
400C2×D3—22no—
401C2×D3—44no—
402C2×D3—124no—
403C2×D3—122no—
404C2×D3—122no—
405C2×D3—122no—
406C2×D3—122no—
407C2×D3—122no—
408C2×D3—122no—
409C2×D3—242no—
410C2×D3—242no—
411C2×D3—248no—
412C2×D3—244no—
413C2×D3—244no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—22no—
417C3×C4—42no—
418C3×C4—42no—
419C3×C4—62no—
420C3×C4—82no—
421C3×C4—122no—
422C3×C4—122no—
423C3×C4#89412yes—
424C3×C4#92912yes—
425C3×C4C2×#23511yescharacteristic
426C3×C4C2×#23511yescharacteristic
427C3×C4C2×#23511yescharacteristic
428C3×C4C2×#23911yescharacteristic
429Dic3—22no—
430Dic3—42no—
431Dic3—42no—
432C32C2×#48211yescharacteristic, complemented, Sylow
433C23—32no—
434C23—62no—
435C23—62no—
436C23—62no—
437C23—182no—
438C23—362no—
439C23—362no—
440C23—362no—
441C23D3×#6711yescharacteristic
442D4—182no—
443D4—182no—
444D4—368no—
445D4—362no—
446C2×C4—22no—
447C2×C4—32no—
448C2×C4—42no—
449C2×C4—62no—
450C2×C4—62no—
451C2×C4—62no—
452C2×C4—64no—
453C2×C4—62no—
454C2×C4—62no—
455C2×C4—122no—
456C2×C4—122no—
457C2×C4#379812yes—
458C2×C4#379912yes—
459C2×C4D3×#6711yescharacteristic
460C2×C4C22×D3211yescharacteristic
461C8—62no—
462C8—182no—
463C2×C3—21no—
464C2×C3—21no—
465C2×C3—24no—
466C2×C3—21no—
467C2×C3—122no—
468C2×C3#486614yescomplemented
469C2×C3#500314yescomplemented
470C2×C3C2×#89411yescharacteristic
471C2×C3C2×#91411yescharacteristic
472C2×C3C2×#91611yescharacteristic
473C2×C3C2×#92911yescharacteristic
474C2×C3C2×#94911yescharacteristic
475C2×C3C2×#95011yescharacteristic
476D3—42no—
477D3—244no—
478D3—242no—
479D3—242no—
480C22—62no—
481C22—62no—
482C22—62no—
483C22—124no—
484C22—362no—
485C22—362no—
486C22—362no—
487C22—724no—
488C22#6385012yes—
489C22#6393512yes—
490C22#6393912yes—
491C22C2×D3×#6711yescharacteristic
492C4—42no—
493C4—62no—
494C4—122no—
495C4—122no—
496C4#6385012yes—
497C4C2×#379811yescharacteristic
498C4C2×#379911yescharacteristic
499C3—21no—
500C3C2×#486611yescharacteristic, complemented
501C3C2×#500311yescharacteristic, complemented
502C2—122no—
503C2—722no—
504C2#1059042514yesdirect product factor
505C2C2×#6385011yescharacteristic
506C2C2×#6393511yescharacteristic
507C2C2×#6393911yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×#63909C2
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×#63636C2semidirect
4. C2×C3×#808C2semidirect
5. C2×#63576C2semidirect
6. C2×#63564C2semidirect
7. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
8. #10590425C2direct (N × H)
22. C3×#892C22semidirect
26. #63636C22semidirect
27. C3×#808C22semidirect
28. #63576C22semidirect
29. #63564C22semidirect
30. (C2×D3)⋊(C3⋊C8)C22semidirect
34. C2×#892D3semidirect
44. C2×#808D3semidirect
111. #892C2×D3semidirect
120. #808C2×D3semidirect
346. C2×C32#482semidirect
432. C32C2×#482semidirect
468. C2×C3#4866semidirect
469. C2×C3#5003semidirect
500. C3C2×#4866semidirect
501. C3C2×#5003semidirect
504. C2#10590425direct (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×#639092
C2×#636362
C2×C3×#8082
C2×#635762
C2×#635642
C2×(C2×D3)⋊(C3⋊C8)2
#105904252
C2×#50033
C2×#48663