Finite Group Databasebeta

← C2×#10591634 #11866703

Subgroups — C2×#10591634 #11866703

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×#946C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic
4C22×D3×C3⋊C8C211yesmaximal, characteristic, complemented
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591634C218yesmaximal, direct product factor
7C2×#63573C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5171—31nomaximal
10C2×#5048—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×#625—21no—
15C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#946—22no—
18C3×#946C2214yescomplemented
19C2×C3×#215—24no—
20C2×C3×#215C2214yescomplemented
21C2×C3×(C2×D3)⋊C4—21no—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4—21no—
24C22×C3×C3⋊C8C2211yescharacteristic
25C2×(C2×D3)⋊Dic3—21no—
26#63908—22no—
27#63908C2214yes—
28C2×D3×C3⋊C8—24no—
29C2×D3×C3⋊C8C2214yescomplemented
30#63662C2214yescomplemented
31#63573C2214yescomplemented
32#63562C2214yescomplemented
33C22×C3×SD16—31no—
34C2×C3×C22⋊Q8—31no—
35C2×#946D311yescharacteristic, complemented
36C22×#215D311yescharacteristic, complemented
37C2×#938—31no—
38C2×#930—31no—
39C23×C3⋊C8—31no—
40C22×D3×C8—31no—
41C2×#835—31no—
42C2×#835—31no—
43C2×#835—61no—
44C2×#832—31no—
45#5171—38no—
46C2×#817—31no—
47#5048—38no—
48C2×#809—31no—
49C2×#808—31no—
50C23×C3×D3—21no—
51C23×C3×D3D411yescharacteristic
52C2×C32×Q8—21no—
53C2×C32×Q8—22no—
54C2×C32×Q8—22no—
55C2×C32×Q8C2312yes—
56C22×C32×C4—21no—
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3—21no—
59C22×C3×Dic3—21no—
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×C4×D3—22no—
66C2×C3×C4×D3—22no—
67C2×C3×C4×D3D412yes—
68C2×C3×C4×D3C2312yes—
69C2×#625—24no—
70C2×#625—44no—
71C4⋊(C3⋊Dic3)—21no—
72C4⋊(C3⋊Dic3)C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)C2312yes—
75C3×#215—28no—
76C3×(C2×D3)⋊C4—24no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×Dic3⋊C4—24no—
80C2×C3×C3⋊C8D414yescomplemented
81C2×C3×C3⋊C8C2312yes—
82(C2×D3)⋊Dic3—24no—
83D3×C3⋊C8—28no—
84C2×#465—91noSylow
85C22×C3×Q8—21no—
86C22×C3×Q8C2×D311yescharacteristic
87C22×C3×Q8C2×D311yescharacteristic
88C22×C3×D4—31no—
89C23×C3×C4—31no—
90C22×#67—61no—
91C22×#67—61no—
92C22×D12C2×D311yescharacteristic
93C22×C4×D3C2×D311yescharacteristic
94C2×C3×SD16—34no—
95C2×C3×SD16—64no—
96C22×C3×C8—31no—
97C3×C22⋊Q8—34no—
98C3×C22⋊Q8—62no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C22⋊C4—61no—
102C2×#217—61no—
103#946—22no—
104#946C2×D314yescomplemented
105C2×#215—24no—
106C2×#215C2×D314yescomplemented
107#938—34no—
108#938—62no—
109#930—34no—
110#930—62no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—61no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—61no—
116C2×C4⋊Dic3C2×D311yescharacteristic
117C2×Dic3⋊C4—21no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—34no—
121C22×C3⋊C8—61no—
122C22×C3⋊C8—64no—
123C22×C3⋊C8C2×D311yescharacteristic
124C2×D3×C8—34no—
125C2×D3×C8—64no—
126#835—34no—
127#835—34no—
128#835—64no—
129#832—34no—
130#817—34no—
131#809—34no—
132#808—34no—
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—
142C32×Q8—22no—
143C32×Q8—22no—
144C32×Q8—42no—
145C2×C32×C4—22no—
146C2×C32×C4—42no—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4C2×D412yes—
149C2×C32×C4#4112yes—
150C2×C32×C4C2411yescharacteristic
151C2×C3⋊Dic3—22no—
152C2×C3⋊Dic3—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—42no—
160C3×C4×D3—24no—
161C3×C4×D3—22no—
162C3×C4×D3—22no—
163#625—48no—
164C3⋊(C3⋊C8)—22no—
165C3×C3⋊C8C2×D414yescomplemented
166C22×SD16—31no—
167C23×C8—91no—
168C2×C22⋊Q8—31no—
169C2×#121—91no—
170#465—98no—
171C2×#106—91no—
172C2×#103—91no—
173C2×#102—91no—
174C24×C3—31no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3#6711yescharacteristic
178C2×C3×Q8—21no—
179C2×C3×Q8—21no—
180C2×C3×Q8—24no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—22no—
185C2×C3×Q8—22no—
186C2×C3×Q8—41no—
187C2×C3×Q8—42no—
188C2×C3×Q8C22×D312yes—
189C2×C3×Q8C22×D312yes—
190C2×C3×D4—32no—
191C2×C3×D4—62no—
192C2×C3×D4—62no—
193C2×C3×D4—61no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—31no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4—41no—
201C22×C3×C4—62no—
202C22×C3×C4—62no—
203C22×C3×C4—61no—
204C22×C3×C4C22×D311yescharacteristic
205C22×C3×C4C22×D311yescharacteristic
206C2×#67—64no—
207C2×#67—64no—
208C2×#67—124no—
209C2×#67—124no—
210C22×Dic3—21no—
211C22×Dic3—61no—
212C22×Dic3—61no—
213C22×Dic3—121no—
214C22×Dic3#6711yescharacteristic
215C2×D12—22no—
216C2×D12—22no—
217C2×D12—21no—
218C2×D12C22×D312yes—
219C2×C4×D3—22no—
220C2×C4×D3—22no—
221C2×C4×D3#6712yes—
222C2×C4×D3C22×D312yes—
223C3×SD16—68no—
224C2×C3×C8—34no—
225C2×C3×C8—32no—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—64no—
228C3×C4⋊C4—61no—
229C3×C22⋊C4—64no—
230#217—64no—
231#215—28no—
232(C2×D3)⋊C4—24no—
233(C2×D3)⋊C4—64no—
234C4⋊Dic3—21no—
235C4⋊Dic3—32no—
236C4⋊Dic3—32no—
237C4⋊Dic3—62no—
238C4⋊Dic3—61no—
239C4⋊Dic3—61no—
240C4⋊Dic3—121no—
241C4⋊Dic3C22×D312yes—
242Dic3⋊C4—24no—
243C2×C3⋊C8—32no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—68no—
249C2×C3⋊C8—122no—
250C2×C3⋊C8#6714yescomplemented
251C2×C3⋊C8C22×D312yes—
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×Q8D3211yescharacteristic
273C22×D4—31no—
274C22×D4—181no—
275C23×C4—31no—
276C2×SD16—34no—
277C2×SD16—64no—
278C22×C8—31no—
279C22×C8—94no—
280C22×C8—91no—
281C22×C8—184no—
282C22⋊Q8—34no—
283C22⋊Q8—62no—
284#121—94no—
285#121—182no—
286C2×C4⋊C4—31no—
287C2×C4⋊C4—61no—
288C2×C4⋊C4—91no—
289C2×C22⋊C4—61no—
290C2×C22⋊C4—181no—
291#106—94no—
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#21514yescomplemented
312C22×D3C2×#6712yes—
313C3×Q8—24no—
314C3×Q8—22no—
315C3×Q8—22no—
316C3×Q8—22no—
317C3×Q8—22no—
318C3×Q8—42no—
319C3×Q8—44no—
320C3×Q8—42no—
321C3×Q8—42no—
322C3×D4—62no—
323C3×D4—62no—
324C3×D4—122no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—22no—
330C2×C3×C4—21no—
331C2×C3×C4—32no—
332C2×C3×C4—42no—
333C2×C3×C4—44no—
334C2×C3×C4—42no—
335C2×C3×C4—42no—
336C2×C3×C4—62no—
337C2×C3×C4—64no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4—122no—
342C2×C3×C4D3×D411yescharacteristic
343C2×C3×C4D3×D412yes—
344C2×C3×C4#23712yes—
345C2×C3×C4#23712yes—
346C2×C3×C4C2×#6712yes—
347C2×C3×C4C2×#6711yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350#67—128no—
351#67—128no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—42no—
355C2×Dic3—62no—
356C2×Dic3—62no—
357C2×Dic3—122no—
358C2×Dic3—122no—
359C2×Dic3—122no—
360C2×Dic3—242no—
361C2×Dic3C2×#6712yes—
362D12—22no—
363D12—22no—
364D12—42no—
365C4×D3—24no—
366C4×D3—22no—
367C4×D3—22no—
368C3×C8—34no—
369C3⋊C8—62no—
370C3⋊C8—62no—
371C3⋊C8—122no—
372C3⋊C8C2×#6714yescomplemented
373C2×C32#46514yescomplemented
374C2×C32C2×#12111yescharacteristic
375C2×C32C22×SD1611yescharacteristic
376C2×C32C2×#13511yescharacteristic
377C3×D3—24no—
378C3×D3—82no—
379C24—31no—
380C24—61no—
381C2×Q8—21no—
382C2×Q8—22no—
383C2×Q8—22no—
384C2×Q8C2×D3212yes—
385C2×D4—32no—
386C2×D4—62no—
387C2×D4—62no—
388C2×D4—61no—
389C2×D4—184no—
390C2×D4—364no—
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—68no—
401C2×C8—32no—
402C2×C8—34no—
403C2×C8—92no—
404C2×C8—188no—
405C2×C8—182no—
406C4⋊C4—32no—
407C4⋊C4—64no—
408C4⋊C4—61no—
409C4⋊C4—92no—
410C4⋊C4—181no—
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×C3D3×SD1612yes—
426C22×C3#91612yes—
427C22×C3#93812yes—
428C22×C3#93912yes—
429C22×C3C2×#21512yes—
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×#21514yescomplemented
441C3×C4—21no—
442C3×C4—21no—
443C3×C4—22no—
444C3×C4—44no—
445C3×C4—42no—
446C3×C4—42no—
447C3×C4—62no—
448C3×C4—122no—
449C3×C4#93812yes—
450C3×C4#93912yes—
451C3×C4C2×D3×D411yescharacteristic
452C3×C4C2×#23711yescharacteristic
453C3×C4C2×#23711yescharacteristic
454C3×C4C22×#6711yescharacteristic
455Dic3—22no—
456Dic3—42no—
457Dic3—122no—
458Dic3—122no—
459Dic3—242no—
460C32C2×#46511yescharacteristic, complemented, Sylow
461C23—32no—
462C23—34no—
463C23—62no—
464C23—62no—
465C23—62no—
466C23—122no—
467C23—122no—
468C23—122no—
469C23D3×#6711yescharacteristic
470Q8—22no—
471Q8—22no—
472Q8—42no—
473D4—62no—
474D4—62no—
475D4—122no—
476D4—368no—
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#380512yes—
489C2×C4D3×#6712yes—
490C2×C4D3×#6711yescharacteristic
491C2×C4C22×D3211yescharacteristic
492C8—34no—
493C8—182no—
494C2×C3—21no—
495C2×C3—24no—
496C2×C3—21no—
497C2×C3—21no—
498C2×C3—64no—
499C2×C3—242no—
500C2×C3#504814yescomplemented
501C2×C3#517114yescomplemented
502C2×C3C2×D3×SD1611yescharacteristic
503C2×C3C2×#91611yescharacteristic
504C2×C3C2×#93811yescharacteristic
505C2×C3C2×#93911yescharacteristic
506C2×C3C22×#21511yescharacteristic
507C2×C3C2×#95011yescharacteristic
508D3—24no—
509D3—82no—
510C22—34no—
511C22—62no—
512C22—68no—
513C22—62no—
514C22—122no—
515C22—122no—
516C22—122no—
517C22—244no—
518C22D3×#21512yes—
519C22#6394712yes—
520C22#6397012yes—
521C22C2×D3×#6711yescharacteristic
522C4—42no—
523C4—62no—
524C4—122no—
525C4—362no—
526C4#6397012yes—
527C4C2×#380511yescharacteristic
528C4C2×D3×#6711yescharacteristic
529C3—21no—
530C3C2×#504811yescharacteristic, complemented
531C3C2×#517111yescharacteristic, complemented
532C2—64no—
533C2—242no—
534C2#1059163414yesdirect product factor
535C2C2×D3×#21511yescharacteristic
536C2C2×#6394711yescharacteristic
537C2C2×#6397011yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC2×#63908C2
hypercenterC22×Q8D32
hypocenterC32C2×#465
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3×#946C2semidirect
2. C22×C3×#215C2semidirect
4. C22×D3×C3⋊C8C2semidirect
5. C2×#63662C2semidirect
6. #10591634C2direct (N × H)
7. C2×#63573C2semidirect
8. C2×#63562C2semidirect
18. C3×#946C22semidirect
20. C2×C3×#215C22semidirect
29. C2×D3×C3⋊C8C22semidirect
30. #63662C22semidirect
31. #63573C22semidirect
32. #63562C22semidirect
35. C2×#946D3semidirect
36. C22×#215D3semidirect
80. C2×C3×C3⋊C8D4semidirect
104. #946C2×D3semidirect
106. C2×#215C2×D3semidirect
140. C22×C3×D3SD16semidirect
165. C3×C3⋊C8C2×D4semidirect
250. C2×C3⋊C8#67semidirect
264. C2×C3×D3C2×SD16semidirect
311. C22×D3#215semidirect
372. C3⋊C8C2×#67semidirect
373. C2×C32#465semidirect
440. C2×D3C2×#215semidirect
460. C32C2×#465semidirect
500. C2×C3#5048semidirect
501. C2×C3#5171semidirect
530. C3C2×#5048semidirect
531. C3C2×#5171semidirect
534. C2#10591634direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9462
C22×C3×#2152
C2×#639082
C22×D3×C3⋊C82
C2×#636622
#105916342
C2×#635732
C2×#635622
C2×#51713
C2×#50483