Finite Group Databasebeta

← C2×#10590578 #11866706

Subgroups — C2×#10590578 #11866706

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×#895C211yesmaximal, characteristic
2C2×#63857C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic, complemented
4C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
5C2×#63637C211yesmaximal, characteristic, complemented
6C2×C3×#808C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590578C218yesmaximal, direct product factor
9C2×#5041—31nomaximal
10C2×#4864—31nomaximal
11C22×#634C2211yescharacteristic
12C22×C3×D12—21no—
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3C2211yescharacteristic
15C2×C32×C4⋊C4C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C2×C3×(C2×D3)⋊C4—21no—
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C3×#895—22no—
21C3×#895C2214yes—
22C2×Dic3⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63857—22no—
25#63857C2214yescomplemented
26C2×#3716—24no—
27C2×#3716C2214yescomplemented
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63637C2214yescomplemented
31C3×#808C2214yescomplemented
32#63562C2214yescomplemented
33C2×C3×#121—31no—
34C22×#214—31no—
35C2×#924—31no—
36C23×C3⋊C8—31no—
37C22×#204—31no—
38C22×D3×C8—31no—
39C2×#897—31no—
40C2×#895D311yescharacteristic
41C2×C3×#106—31no—
42C2×#832—31no—
43#5041—38no—
44C2×#810—31no—
45C2×#810—31no—
46C2×#810—61no—
47C2×#809—31no—
48C2×#808D311yescharacteristic, complemented
49#4864—38no—
50C23×C3×D3—21no—
51C23×C3×D3D411yescharacteristic
52C22×C32×C4—21no—
53C22×C32×C4C2311yescharacteristic
54C22×C3⋊Dic3—21no—
55C2×#634—22no—
56C2×#634—22no—
57C2×#634—21no—
58C2×#634C2312yes—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—24no—
64C2×C3×D12—21no—
65C2×C3×D12—44no—
66C2×C3×D12C2312yes—
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C32×C4⋊C4—21no—
72C32×C4⋊C4C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8D414yescomplemented
79C2×C3×C3⋊C8C2312yes—
80Dic3⋊Dic3—24no—
81(C2×D3)⋊Dic3—24no—
82#3716—28no—
83D3×C3⋊C8—28no—
84C2×#465—91noSylow
85C22×C3×D4—31no—
86C22×C3×D4—61no—
87C23×C3×C4—31no—
88C22×D12—21no—
89C22×D12C2×D311yescharacteristic
90C22×C4×D3C2×D311yescharacteristic
91C22×Dic6—31no—
92C22×Dic6—31no—
93C22×Dic6—61no—
94C22×C3×C8—31no—
95C3×#121—34no—
96C3×#121—62no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4C2×D311yescharacteristic
100C2×C3×C4⋊C4C2×D311yescharacteristic
101C2×C3×C22⋊C4—61no—
102C2×#217—61no—
103C2×#214—34no—
104C2×#214—64no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3—61no—
108C2×C4⋊Dic3C2×D311yescharacteristic
109#924—34no—
110#924—62no—
111C2×Dic3⋊C4—61no—
112C22×C3⋊C8—31no—
113C22×C3⋊C8—31no—
114C22×C3⋊C8—34no—
115C22×C3⋊C8—61no—
116C22×C3⋊C8—64no—
117C22×C3⋊C8C2×D311yescharacteristic
118C2×#204—34no—
119C2×#204—64no—
120C2×D3×C8—34no—
121C2×D3×C8—64no—
122#897—34no—
123#897—62no—
124#895—22no—
125#895C2×D314yes—
126C3×#106—34no—
127#832—34no—
128#810—34no—
129#810—34no—
130#810—64no—
131#809—34no—
132#808C2×D314yescomplemented
133C23×C32C2×D411yescharacteristic
134C22×C3×D3—22no—
135C22×C3×D3—22no—
136C22×C3×D3—22no—
137C22×C3×D3—42no—
138C22×C3×D3—42no—
139C22×C3×D3—42no—
140C22×C3×D3SD1614yescomplemented
141C22×C3×D3C2×D412yes—
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×Dic3—42no—
156C2×C3×Dic3C2×D412yes—
157C3×D12—22no—
158C3×D12—22no—
159C3×D12—48no—
160C3×D12—42no—
161C3×C4×D3—24no—
162C3×C4×D3—22no—
163C3×C4×D3—22no—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8C2×D414yescomplemented
166C22×SD16—91no—
167C23×C8—91no—
168C2×C22⋊Q8—91no—
169C2×#121—31no—
170#465—98no—
171C2×#106—31no—
172C2×#103—91no—
173C2×#102—91no—
174C24×C3—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3#6711yescharacteristic
178C2×C3×D4—32no—
179C2×C3×D4—64no—
180C2×C3×D4—62no—
181C2×C3×D4—61no—
182C2×C3×D4—62no—
183C2×C3×D4—124no—
184C22×C3×C4—21no—
185C22×C3×C4—21no—
186C22×C3×C4—21no—
187C22×C3×C4—31no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—41no—
191C22×C3×C4—62no—
192C22×C3×C4—62no—
193C22×C3×C4—61no—
194C22×C3×C4C22×D311yescharacteristic
195C22×C3×C4C22×D311yescharacteristic
196C22×Dic3—21no—
197C22×Dic3—61no—
198C22×Dic3—61no—
199C22×Dic3—121no—
200C22×Dic3#6711yescharacteristic
201C2×D12—22no—
202C2×D12—22no—
203C2×D12—24no—
204C2×D12—21no—
205C2×D12—44no—
206C2×D12C22×D312yes—
207C2×C4×D3—22no—
208C2×C4×D3—22no—
209C2×C4×D3#6712yes—
210C2×C4×D3C22×D312yes—
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—34no—
224C2×C3×C8—32no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4—21no—
227C3×C4⋊C4—22no—
228C3×C4⋊C4—32no—
229C3×C4⋊C4—41no—
230C3×C4⋊C4—61no—
231C3×C4⋊C4C22×D312yes—
232C3×C4⋊C4C22×D312yes—
233C3×C22⋊C4—64no—
234#217—64no—
235#214—68no—
236(C2×D3)⋊C4—24no—
237(C2×D3)⋊C4—64no—
238C4⋊Dic3—21no—
239C4⋊Dic3—64no—
240C4⋊Dic3C22×D312yes—
241Dic3⋊C4—64no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—68no—
248C2×C3⋊C8—122no—
249C2×C3⋊C8D1214yescomplemented
250C2×C3⋊C8C22×D312yes—
251#204—68no—
252D3×C8—68no—
253C22×C32#12112yes—
254C22×C32C2×SD1612yes—
255C22×C32#13512yes—
256C22×C32C22×D411yescharacteristic
257C2×C3×D3—22no—
258C2×C3×D3—22no—
259C2×C3×D3—28no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—42no—
263C2×C3×D3—84no—
264C2×C3×D3C2×SD1614yescomplemented
265C32×C4—42no—
266C32×C4#12112yes—
267C32×C4C22×D411yescharacteristic
268C32×C4C2×#4111yescharacteristic
269C3⋊Dic3—42no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C22×Q8—91no—
273C22×D4—31no—
274C22×D4—61no—
275C23×C4—31no—
276C2×SD16—94no—
277C2×SD16—184no—
278C22×C8—31no—
279C22×C8—94no—
280C22×C8—91no—
281C22×C8—184no—
282C22⋊Q8—94no—
283C22⋊Q8—182no—
284#121—34no—
285#121—62no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—181no—
288C2×C4⋊C4D3211yescharacteristic
289C2×C22⋊C4—61no—
290C2×C22⋊C4—181no—
291#106—34no—
292#103—94no—
293#102—94no—
294C23×C3—21no—
295C23×C3—34no—
296C23×C3—32no—
297C23×C3—62no—
298C23×C3—62no—
299C23×C3—62no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3D3×D411yescharacteristic
304C23×C3C2×#6711yescharacteristic
305C22×D3—22no—
306C22×D3—22no—
307C22×D3—22no—
308C22×D3—42no—
309C22×D3—42no—
310C22×D3—42no—
311C22×D3#21414yescomplemented
312C22×D3C2×#6712yes—
313C3×D4—62no—
314C3×D4—62no—
315C3×D4—128no—
316C3×D4—122no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—21no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—32no—
324C2×C3×C4—42no—
325C2×C3×C4—42no—
326C2×C3×C4—42no—
327C2×C3×C4—62no—
328C2×C3×C4—64no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—82no—
333C2×C3×C4—122no—
334C2×C3×C4C2×D1212yes—
335C2×C3×C4D3×D412yes—
336C2×C3×C4D3×D411yescharacteristic
337C2×C3×C4#23712yes—
338C2×C3×C4#23912yes—
339C2×C3×C4C2×#6711yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×C3×C4C23×D311yescharacteristic
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—42no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3—124no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3C2×#6712yes—
352D12—22no—
353D12—22no—
354D12—48no—
355D12—42no—
356C4×D3—24no—
357C4×D3—22no—
358C4×D3—22no—
359Dic6—64no—
360Dic6—62no—
361Dic6—62no—
362Dic6—62no—
363Dic6—62no—
364Dic6—122no—
365Dic6—124no—
366Dic6—122no—
367Dic6—122no—
368C3×C8—34no—
369C3⋊C8—62no—
370C3⋊C8—62no—
371C3⋊C8—122no—
372C3⋊C8C2×D1214yescomplemented
373C2×C32#46514yescomplemented
374C2×C32C2×#12111yescharacteristic
375C2×C32C22×SD1611yescharacteristic
376C2×C32C2×#13511yescharacteristic
377C3×D3—24no—
378C3×D3—82no—
379C24—31no—
380C24—61no—
381C2×Q8—92no—
382C2×Q8—181no—
383C2×Q8—182no—
384C2×Q8—182no—
385C2×D4—32no—
386C2×D4—64no—
387C2×D4—62no—
388C2×D4—62no—
389C2×D4—61no—
390C2×D4—124no—
391C22×C4—21no—
392C22×C4—31no—
393C22×C4—32no—
394C22×C4—32no—
395C22×C4—62no—
396C22×C4—62no—
397C22×C4—61no—
398C22×C4—181no—
399C22×C4C2×D3211yescharacteristic
400SD16—188no—
401C2×C8—32no—
402C2×C8—34no—
403C2×C8—92no—
404C2×C8—188no—
405C2×C8—182no—
406C4⋊C4—21no—
407C4⋊C4—32no—
408C4⋊C4—61no—
409C4⋊C4—184no—
410C4⋊C4C2×D3212yes—
411C22⋊C4—64no—
412C22⋊C4—184no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—22no—
417C22×C3—34no—
418C22×C3—68no—
419C22×C3—62no—
420C22×C3—62no—
421C22×C3—122no—
422C22×C3—122no—
423C22×C3—122no—
424C22×C3—244no—
425C22×C3#89512yes—
426C22×C3D3×SD1612yes—
427C22×C3#91612yes—
428C22×C3C2×#21412yes—
429C22×C3#93912yes—
430C22×C3#95012yes—
431C22×C3C2×D3×D411yescharacteristic
432C22×C3C22×#6711yescharacteristic
433C2×D3—22no—
434C2×D3—28no—
435C2×D3—22no—
436C2×D3—42no—
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—84no—
440C2×D3C2×#21414yescomplemented
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—42no—
445C3×C4—42no—
446C3×C4—62no—
447C3×C4—82no—
448C3×C4—122no—
449C3×C4#89512yes—
450C3×C4#93912yes—
451C3×C4C22×D1211yescharacteristic
452C3×C4C2×D3×D411yescharacteristic
453C3×C4C2×#23711yescharacteristic
454C3×C4C2×#23911yescharacteristic
455Dic3—22no—
456Dic3—42no—
457Dic3—124no—
458Dic3—122no—
459Dic3—122no—
460C32C2×#46511yescharacteristic, complemented, Sylow
461C23—32no—
462C23—34no—
463C23—62no—
464C23—62no—
465C23—62no—
466C23—122no—
467C23—122no—
468C23—122no—
469C23D3×#6711yescharacteristic
470Q8—182no—
471Q8—182no—
472Q8—362no—
473D4—62no—
474D4—62no—
475D4—128no—
476D4—122no—
477C2×C4—22no—
478C2×C4—32no—
479C2×C4—42no—
480C2×C4—62no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—64no—
484C2×C4—62no—
485C2×C4—122no—
486C2×C4—182no—
487C2×C4—362no—
488C2×C4#379612yes—
489C2×C4D3×D1212yes—
490C2×C4D3×#6711yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—34no—
493C8—182no—
494C2×C3—21no—
495C2×C3—21no—
496C2×C3—21no—
497C2×C3—24no—
498C2×C3—64no—
499C2×C3—242no—
500C2×C3#486414yescomplemented
501C2×C3#504114yescomplemented
502C2×C3C2×#89511yescharacteristic
503C2×C3C2×D3×SD1611yescharacteristic
504C2×C3C2×#91611yescharacteristic
505C2×C3C22×#21411yescharacteristic
506C2×C3C2×#93911yescharacteristic
507C2×C3C2×#95011yescharacteristic
508D3—24no—
509D3—82no—
510C22—34no—
511C22—62no—
512C22—62no—
513C22—68no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—244no—
518C22#6388612yes—
519C22D3×#21412yes—
520C22#6394712yes—
521C22C2×D3×#6711yescharacteristic
522C4—42no—
523C4—62no—
524C4—122no—
525C4—362no—
526C4#6388612yes—
527C4C2×#379611yescharacteristic
528C4C2×D3×D1211yescharacteristic
529C3—21no—
530C3C2×#486411yescharacteristic, complemented
531C3C2×#504111yescharacteristic, complemented
532C2—64no—
533C2—242no—
534C2#1059057814yesdirect product factor
535C2C2×#6388611yescharacteristic
536C2C2×D3×#21411yescharacteristic
537C2C2×#6394711yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C2×D4
prime radicalC2×C3×#895C2
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#465
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
2. C2×#63857C2semidirect
3. C22×#3716C2semidirect
4. C22×D3×C3⋊C8C2semidirect
5. C2×#63637C2semidirect
6. C2×C3×#808C2semidirect
7. C2×#63562C2semidirect
8. #10590578C2direct (N × H)
25. #63857C22semidirect
27. C2×#3716C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63637C22semidirect
31. C3×#808C22semidirect
32. #63562C22semidirect
48. C2×#808D3semidirect
78. C2×C3×C3⋊C8D4semidirect
132. #808C2×D3semidirect
140. C22×C3×D3SD16semidirect
165. C3×C3⋊C8C2×D4semidirect
249. C2×C3⋊C8D12semidirect
264. C2×C3×D3C2×SD16semidirect
311. C22×D3#214semidirect
372. C3⋊C8C2×D12semidirect
373. C2×C32#465semidirect
440. C2×D3C2×#214semidirect
460. C32C2×#465semidirect
500. C2×C3#4864semidirect
501. C2×C3#5041semidirect
530. C3C2×#4864semidirect
531. C3C2×#5041semidirect
534. C2#10590578direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×#638572
C22×#37162
C22×D3×C3⋊C82
C2×#636372
C2×C3×#8082
C2×#635622
#105905782
C2×#50413
C2×#48643