Finite Group Databasebeta

← C2×#10590530 #11865559

Subgroups — C2×#10590530 #11865559

Order 1152.

1209 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×C3×#893C211yesmaximal, characteristic, complemented
2C2×#63860C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic
5C2×#63637C211yesmaximal, characteristic, complemented
6C2×C3×#809C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590530C218yesmaximal, direct product factor
9C2×#5016—31nomaximal
10C2×#4787—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3—21no—
15C2×C32×C4⋊C4C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#893—22no—
21C3×#893C2214yescomplemented
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63860—22no—
25#63860C2214yescomplemented
26C2×#3716—24no—
27C2×#3716C2214yescomplemented
28C2×#3713—24no—
29C2×#3713C2214yes—
30#63637C2214yescomplemented
31C3×#809C2214yescomplemented
32Dic3⋊(C3⋊C8)C2214yescomplemented
33C2×C3×C4×D4—31no—
34C2×#936—31no—
35C22×#214—31no—
36C22×#213—31no—
37C22×#213—31no—
38C22×#204—31no—
39C2×#893D311yescharacteristic, complemented
40C2×#875—31no—
41C2×C3×#102—31no—
42C2×Dic3⋊C8—31no—
43#5016—38no—
44C2×#810—31no—
45C2×#810—31no—
46C2×#810—61no—
47C2×#809D311yescharacteristic, complemented
48C2×C4⋊(C3⋊C8)—31no—
49#4787—38no—
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×#634—22no—
56C2×#634—22no—
57C2×#634—21no—
58C2×#634C2312yes—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—21no—
62C2×C3×D12—22no—
63C2×C3×D12—22no—
64C2×C3×D12—22no—
65C2×C3×D12—21no—
66C2×C3×D12D414yes—
67C2×C3×D12C2312yes—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3—44no—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×(C2×D3)⋊C4—24no—
76C3×C4×Dic3D412yes—
77C3×C4×Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8C2312yes—
80(C2×D3)⋊Dic3—24no—
81(C2×D3)⋊Dic3—24no—
82#3716—28no—
83#3713—28no—
84C2×#463—91noSylow
85C22×C3×D4—31no—
86C22×C3×D4—31no—
87C23×C3×C4—61no—
88C22×D12C2×D311yescharacteristic
89C22×D12C2×D311yescharacteristic
90C22×C4×D3—21no—
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×C3×C8—31no—
95C3×C4×D4—34no—
96C3×C4×D4—62no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4C2×D311yescharacteristic
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—31no—
102C2×#217—61no—
103C2×#217—61no—
104#936—34no—
105#936—62no—
106C2×#214—34no—
107C2×#214—64no—
108C2×#213—34no—
109C2×#213—34no—
110C2×#213—64no—
111C2×#213—64no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4×Dic3C2×D311yescharacteristic
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—61no—
119C22×C3⋊C8C2×D311yescharacteristic
120C2×#204—34no—
121C2×#204—64no—
122#893—22no—
123#893C2×D314yescomplemented
124#875—34no—
125#875—62no—
126C3×#102—34no—
127Dic3⋊C8—34no—
128#810—34no—
129#810—34no—
130#810—64no—
131#809C2×D314yescomplemented
132C4⋊(C3⋊C8)—34no—
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—24no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C2×C32×C4—22no—
143C2×C32×C4—42no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4#4112yes—
147C2×C32×C4C2411yescharacteristic
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3—42no—
150#634—22no—
151#634—22no—
152#634—42no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3C2×D412yes—
156C2×C3×Dic3C2×D412yes—
157C3×D12—24no—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—22no—
161C3×D12—42no—
162C3×D12C2×D414yes—
163C3×C4×D3—48no—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8—22no—
166C22×SD16—91no—
167C22×D8—91no—
168C2×#124—91no—
169C2×C4×D4—31no—
170#463—98no—
171C2×C4⋊C8—91no—
172C2×#103—91no—
173C2×#102—31no—
174C24×C3—61no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—21no—
178C2×C3×D4—34no—
179C2×C3×D4—32no—
180C2×C3×D4—32no—
181C2×C3×D4—62no—
182C2×C3×D4—62no—
183C2×C3×D4—62no—
184C2×C3×D4—61no—
185C2×C3×D4—61no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—31no—
190C22×C3×C4—31no—
191C22×C3×C4—41no—
192C22×C3×C4—64no—
193C22×C3×C4—124no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×Dic3—61no—
197C22×Dic3—61no—
198C22×Dic3—121no—
199C22×Dic3#6711yescharacteristic
200C22×Dic3#6711yescharacteristic
201C2×D12—22no—
202C2×D12—21no—
203C2×D12—22no—
204C2×D12—22no—
205C2×D12—21no—
206C2×D12D1214yes—
207C2×D12C22×D312yes—
208C2×D12C22×D312yes—
209C2×C4×D3—24no—
210C2×C4×D3—44no—
211C2×Dic6—32no—
212C2×Dic6—32no—
213C2×Dic6—62no—
214C2×Dic6—64no—
215C2×Dic6—62no—
216C2×Dic6—62no—
217C2×Dic6—62no—
218C2×Dic6—62no—
219C2×Dic6—61no—
220C2×Dic6—61no—
221C2×Dic6—121no—
222C2×Dic6—122no—
223C2×C3×C8—32no—
224C2×C3×C8—62no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—41no—
229C3×C4⋊C4C22×D312yes—
230C3×C4⋊C4C22×D312yes—
231C3×C22⋊C4—64no—
232C3×C42—32no—
233C3×C42—32no—
234#217—64no—
235#217—64no—
236#214—68no—
237#213—68no—
238#213—68no—
239(C2×D3)⋊C4—24no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242C4×Dic3#6712yes—
243C4×Dic3C22×D312yes—
244C2×C3⋊C8—22no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—32no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—62no—
250C2×C3⋊C8—122no—
251C2×C3⋊C8C22×D312yes—
252#204—68no—
253C22×C32#12112yes—
254C22×C32#13512yes—
255C22×C32AGL(1,ℤ/8)12yes—
256C22×C32C22×D411yescharacteristic
257C2×C3×D3—24no—
258C2×C3×D3—42no—
259C2×C3×D3—42no—
260C2×C3×D3—48no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—84no—
265C32×C4—42no—
266C32×C4#12112yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3⋊Dic3—42no—
270C3×Dic3—22no—
271C3×Dic3—22no—
272C22×Q8—91no—
273C22×D4—31no—
274C22×D4—31no—
275C23×C4—61no—
276C2×SD16—94no—
277C2×SD16—184no—
278C2×D8—94no—
279C2×D8—184no—
280C22×C8—31no—
281C22×C8—91no—
282#124—94no—
283#124—182no—
284C4×D4—34no—
285C4×D4—62no—
286C2×C4⋊C4D3211yescharacteristic
287C2×C22⋊C4—61no—
288C2×C22⋊C4—181no—
289C2×C22⋊C4—181no—
290C2×C42—31no—
291C4⋊C8—94no—
292#103—94no—
293#102—34no—
294C23×C3—21no—
295C23×C3—64no—
296C23×C3—62no—
297C23×C3—62no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—24no—
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—42no—
309C22×D3—42no—
310C22×D3—42no—
311C22×D3—42no—
312C22×D3—42no—
313C3×D4—34no—
314C3×D4—64no—
315C3×D4—62no—
316C3×D4—62no—
317C3×D4—62no—
318C3×D4—122no—
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—32no—
326C2×C3×C4—32no—
327C2×C3×C4—42no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—82no—
333C2×C3×C4—128no—
334C2×C3×C4C2×D1212yes—
335C2×C3×C4#23512yes—
336C2×C3×C4#23512yes—
337C2×C3×C4D3×D412yes—
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—122no—
347C2×Dic3—124no—
348C2×Dic3—122no—
349C2×Dic3—122no—
350C2×Dic3C2×#6712yes—
351C2×Dic3C2×#6712yes—
352D12—24no—
353D12—22no—
354D12—22no—
355D12—22no—
356D12—42no—
357D12C2×D1214yes—
358C4×D3—48no—
359Dic6—64no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—122no—
365Dic6—124no—
366Dic6—122no—
367Dic6—122no—
368C3×C8—62no—
369C3⋊C8—22no—
370C3⋊C8—62no—
371C3⋊C8—62no—
372C3⋊C8—122no—
373C2×C32#46314yescomplemented
374C2×C32C2×#12111yescharacteristic
375C2×C32C2×#13511yescharacteristic
376C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
377C3×D3—44no—
378C3×D3—82no—
379C24—61no—
380C24—61no—
381C2×Q8—92no—
382C2×Q8—181no—
383C2×Q8—182no—
384C2×Q8—182no—
385C2×D4—32no—
386C2×D4—32no—
387C2×D4—34no—
388C2×D4—62no—
389C2×D4—62no—
390C2×D4—62no—
391C2×D4—61no—
392C2×D4—61no—
393C22×C4—21no—
394C22×C4—31no—
395C22×C4—31no—
396C22×C4—64no—
397C22×C4—124no—
398C22×C4—181no—
399C22×C4C2×D3211yescharacteristic
400SD16—188no—
401D8—188no—
402C2×C8—32no—
403C2×C8—62no—
404C2×C8—92no—
405C2×C8—182no—
406C4⋊C4—21no—
407C4⋊C4C2×D3212yes—
408C22⋊C4—64no—
409C22⋊C4—184no—
410C22⋊C4—184no—
411C42—32no—
412C42—32no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—64no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—128no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—244no—
425C22×C3#88412yes—
426C22×C3#91112yes—
427C22×C3#91612yes—
428C22×C3#93012yes—
429C22×C3#93212yes—
430C22×C3#95012yes—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C22×#6711yescharacteristic
433C2×D3—24no—
434C2×D3—48no—
435C2×D3—42no—
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—84no—
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—62no—
447C3×C4—62no—
448C3×C4—82no—
449C3×C4#88412yes—
450C3×C4#93012yes—
451C3×C4C22×D1211yescharacteristic
452C3×C4C2×#23511yescharacteristic
453C3×C4C2×#23511yescharacteristic
454C3×C4C2×D3×D411yescharacteristic
455Dic3—22no—
456Dic3—22no—
457Dic3—124no—
458Dic3—122no—
459Dic3—122no—
460C32C2×#46311yescharacteristic, complemented, Sylow
461C23—62no—
462C23—64no—
463C23—62no—
464C23—122no—
465C23—122no—
466C23—122no—
467C23—122no—
468C23—122no—
469C23D3×#6711yescharacteristic
470Q8—182no—
471Q8—182no—
472Q8—362no—
473D4—34no—
474D4—62no—
475D4—62no—
476D4—62no—
477D4—64no—
478D4—122no—
479C2×C4—22no—
480C2×C4—32no—
481C2×C4—32no—
482C2×C4—42no—
483C2×C4—62no—
484C2×C4—62no—
485C2×C4—128no—
486C2×C4—182no—
487C2×C4—362no—
488C2×C4#379812yes—
489C2×C4D3×D1212yes—
490C2×C4D3×#6711yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—62no—
493C8—182no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—24no—
497C2×C3—21no—
498C2×C3—124no—
499C2×C3—242no—
500C2×C3#478714yescomplemented
501C2×C3#501614yescomplemented
502C2×C3C2×#88411yescharacteristic
503C2×C3C2×#91111yescharacteristic
504C2×C3C2×#91611yescharacteristic
505C2×C3C2×#93011yescharacteristic
506C2×C3C2×#93211yescharacteristic
507C2×C3C2×#95011yescharacteristic
508D3—44no—
509D3—82no—
510C22—64no—
511C22—122no—
512C22—122no—
513C22—128no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—244no—
518C22#6390612yes—
519C22#6393212yes—
520C22#6394712yes—
521C22C2×D3×#6711yescharacteristic
522C4—42no—
523C4—62no—
524C4—62no—
525C4—362no—
526C4#6390612yes—
527C4C2×#379811yescharacteristic
528C4C2×D3×D1211yescharacteristic
529C3—21no—
530C3C2×#478711yescharacteristic, complemented
531C3C2×#501611yescharacteristic, complemented
532C2—124no—
533C2—242no—
534C2#1059053014yesdirect product factor
535C2C2×#6390611yescharacteristic
536C2C2×#6393211yescharacteristic
537C2C2×#6394711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#463
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×#893C2semidirect
2. C2×#63860C2semidirect
3. C22×#3716C2semidirect
5. C2×#63637C2semidirect
6. C2×C3×#809C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590530C2direct (N × H)
21. C3×#893C22semidirect
25. #63860C22semidirect
27. C2×#3716C22semidirect
30. #63637C22semidirect
31. C3×#809C22semidirect
32. Dic3⋊(C3⋊C8)C22semidirect
39. C2×#893D3semidirect
47. C2×#809D3semidirect
123. #893C2×D3semidirect
131. #809C2×D3semidirect
373. C2×C32#463semidirect
460. C32C2×#463semidirect
500. C2×C3#4787semidirect
501. C2×C3#5016semidirect
530. C3C2×#4787semidirect
531. C3C2×#5016semidirect
534. C2#10590530direct (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×#638602
C22×#37162
C22×#37132
C2×#636372
C2×C3×#8092
C2×Dic3⋊(C3⋊C8)2
#105905302
C2×#50163
C2×#47873