Finite Group Databasebeta

← C2×#10590799 #11865607

Subgroups — C2×#10590799 #11865607

Order 1152.

1269 conjugacy classes of subgroups.

The subgroup lattice has 553 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2C2×#63911C211yesmaximal, characteristic
3C2×Dic3×Dic6C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×#63648C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#63563C211yesmaximal, characteristic, complemented
8#10590799C218yesmaximal, direct product factor
9C2×#5163—31nomaximal
10C2×#4848—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×#626—21no—
15C22×#626—21no—
16C22×C32×C8C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C22×C3×C3⋊C8C2211yescharacteristic
20C2×C3×#204—24no—
21C2×C3×#204C2214yescomplemented
22C2×Dic3⋊Dic3—21no—
23C2×Dic32—21no—
24#63911—22no—
25#63911C2214yes—
26Dic3×Dic6—22no—
27Dic3×Dic6C2214yescomplemented
28C2×#3717—24no—
29C2×#3717C2214yescomplemented
30#63648C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32#63563C2214yescomplemented
33C22×C3×SD16—31no—
34C2×Q8×Dic3—31no—
35C22×#215—31no—
36C2×#940—31no—
37C22×#204—31no—
38C22×#204D311yescharacteristic, complemented
39C2×#874—31no—
40C2×C4×Dic6—31no—
41C2×C3×C4⋊C8—31no—
42C2×#832—31no—
43#5163—38no—
44C2×#821—31no—
45C2×#821—31no—
46C2×#821—31no—
47C2×#821—61no—
48C2×Dic3⋊C8D311yescharacteristic, complemented
49#4848—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3—21no—
54C2×C4⋊(C3⋊D3)—22no—
55C2×C4⋊(C3⋊D3)—22no—
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)C2312yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3D411yescharacteristic
60C22×C3×Dic3D411yescharacteristic
61C2×C3×D12—22no—
62C2×C3×D12—22no—
63C2×C3×D12—21no—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—21no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6D414yescomplemented
68C2×C3×Dic6C2312yes—
69C2×#626—24no—
70C2×#626—24no—
71C2×#626—44no—
72C2×#626—44no—
73C2×C32×C8—22no—
74C2×C32×C8C2312yes—
75C4⋊(C3⋊Dic3)—21no—
76C4⋊(C3⋊Dic3)C2312yes—
77C3×C4×Dic3D412yes—
78C3×C4×Dic3C2312yes—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81C3×#204—28no—
82Dic3⋊Dic3—24no—
83Dic32—24no—
84#3717—28no—
85C2×#460—91noSylow
86C22×C3×Q8—31no—
87C22×C3×D4—31no—
88C22×#67—61no—
89C22×#67—61no—
90C22×D12—31no—
91C22×D12—31no—
92C22×D12—61no—
93C22×D12—61no—
94C22×D12—61no—
95C22×D12C2×D311yescharacteristic
96C22×Dic6C2×D311yescharacteristic
97C2×C3×SD16—34no—
98C2×C3×SD16—64no—
99C22×C3×C8—21no—
100C22×C3×C8—31no—
101C22×C3×C8C2×D311yescharacteristic
102C22×C3×C8C2×D311yescharacteristic
103C2×C3×C42—31no—
104Q8×Dic3—34no—
105Q8×Dic3—62no—
106C2×#215—34no—
107C2×#215—64no—
108#940—34no—
109#940—62no—
110C2×C4⋊Dic3—31no—
111C2×C4⋊Dic3—31no—
112C2×C4⋊Dic3—61no—
113C2×C4⋊Dic3—61no—
114C2×Dic3⋊C4—61no—
115C2×C4×Dic3—61no—
116C2×C4×Dic3—61no—
117C2×C4×Dic3C2×D311yescharacteristic
118C22×C3⋊C8C2×D311yescharacteristic
119C2×#204—24no—
120C2×#204—34no—
121C2×#204—64no—
122C2×#204C2×D314yescomplemented
123#874—34no—
124#874—62no—
125C4×Dic6—34no—
126C4×Dic6—62no—
127C3×C4⋊C8—34no—
128#832—34no—
129#821—34no—
130#821—34no—
131#821—34no—
132#821—64no—
133Dic3⋊C8C2×D314yescomplemented
134C23×C32C2×D411yescharacteristic
135C22×C3⋊D3—22no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C22×C3⋊D3—42no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C22×C3×D3—42no—
143C2×C32×C4C2×D411yescharacteristic
144C2×C32×C4C2×D412yes—
145C2×C32×C4#4112yes—
146C2×C32×C4C2411yescharacteristic
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—42no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—22no—
151C4⋊(C3⋊D3)—42no—
152C2×C3×Dic3—24no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3SD1614yescomplemented
156C2×C3×Dic3C2×D412yes—
157C2×C3×Dic3C2×D412yes—
158C3×D12—22no—
159C3×D12—22no—
160C3×D12—42no—
161C3×Dic6—24no—
162C3×Dic6—22no—
163C3×Dic6C2×D414yescomplemented
164#626—48no—
165#626—48no—
166C32×C8—22no—
167C3×C3⋊C8—22no—
168C22×SD16—31no—
169C22×SD16—91no—
170C2×#127—91no—
171C2×C4×Q8—91no—
172#460—98no—
173C2×C4⋊C8—31no—
174C2×#102—91no—
175C2×#102—91no—
176C24×C3—61no—
177C23×D3—21no—
178C23×D3—61no—
179C23×D3—61no—
180C23×D3—121no—
181C2×C3×Q8—34no—
182C2×C3×Q8—32no—
183C2×C3×Q8—61no—
184C2×C3×Q8—62no—
185C2×C3×D4—32no—
186C2×C3×D4—61no—
187C2×C3×D4—62no—
188C2×C3×D4—62no—
189C22×C3×C4—21no—
190C22×C3×C4—31no—
191C22×C3×C4—31no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C2×#67—64no—
196C2×#67—64no—
197C2×#67—124no—
198C2×#67—124no—
199C22×Dic3—21no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C22×Dic3—121no—
203C22×Dic3D1211yescharacteristic
204C22×Dic3D1211yescharacteristic
205C2×D12—22no—
206C2×D12—22no—
207C2×D12—21no—
208C2×D12—32no—
209C2×D12—32no—
210C2×D12—62no—
211C2×D12—64no—
212C2×D12—62no—
213C2×D12—62no—
214C2×D12—62no—
215C2×D12—62no—
216C2×D12—64no—
217C2×D12—64no—
218C2×D12—61no—
219C2×D12—61no—
220C2×D12—121no—
221C2×D12—122no—
222C2×D12—124no—
223C2×D12—124no—
224C2×D12C22×D312yes—
225C2×Dic6—21no—
226C2×Dic6—22no—
227C2×Dic6#6714yescomplemented
228C2×Dic6C22×D312yes—
229C3×SD16—68no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C2×C3×C8—32no—
234C2×C3×C8—42no—
235C2×C3×C8—62no—
236C2×C3×C8C22×D312yes—
237C2×C3×C8C22×D312yes—
238C3×C42—32no—
239C3×C42—32no—
240#215—68no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—64no—
247C4⋊Dic3—121no—
248Dic3⋊C4—64no—
249C4×Dic3—64no—
250C4×Dic3—64no—
251C4×Dic3D1212yes—
252C4×Dic3C22×D312yes—
253C2×C3⋊C8—22no—
254C2×C3⋊C8C22×D312yes—
255#204—28no—
256#204—68no—
257C22×C32#12112yes—
258C22×C32C2×SD1612yes—
259C22×C32AGL(1,ℤ/8)12yes—
260C22×C32C22×D411yescharacteristic
261C2×C3⋊D3—42no—
262C2×C3⋊D3—42no—
263C2×C3⋊D3—42no—
264C2×C3⋊D3—84no—
265C2×C3×D3—42no—
266C2×C3×D3—42no—
267C2×C3×D3—42no—
268C2×C3×D3—84no—
269C32×C4#12112yes—
270C32×C4C22×D411yescharacteristic
271C32×C4C2×#4111yescharacteristic
272C3⋊Dic3—42no—
273C3×Dic3—24no—
274C3×Dic3—22no—
275C3×Dic3C2×SD1614yescomplemented
276C22×Q8—31no—
277C22×D4—31no—
278C22×D4—91no—
279C22×D4—181no—
280C22×D4—181no—
281C2×SD16—34no—
282C2×SD16—64no—
283C2×SD16—94no—
284C2×SD16—184no—
285C22×C8—31no—
286C22×C8D3211yescharacteristic
287#127—94no—
288#127—182no—
289C4×Q8—94no—
290C4×Q8—182no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—181no—
293C2×C42—31no—
294C2×C42—181no—
295C4⋊C8—34no—
296#102—94no—
297#102—94no—
298C23×C3—21no—
299C23×C3—62no—
300C23×C3—122no—
301C23×C3—122no—
302C23×C3—122no—
303C23×C3C2×D1211yescharacteristic
304C23×C3D3×D411yescharacteristic
305C22×D3—22no—
306C22×D3—42no—
307C22×D3—42no—
308C22×D3—42no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—122no—
312C22×D3—124no—
313C22×D3—122no—
314C22×D3—122no—
315C22×D3—122no—
316C22×D3—122no—
317C22×D3—122no—
318C22×D3—122no—
319C22×D3—242no—
320C22×D3—242no—
321C3×Q8—34no—
322C3×Q8—64no—
323C3×Q8—62no—
324C3×D4—62no—
325C3×D4—62no—
326C3×D4—122no—
327C2×C3×C4—21no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—34no—
332C2×C3×C4—32no—
333C2×C3×C4—32no—
334C2×C3×C4—64no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4C2×D1211yescharacteristic
338C2×C3×C4D3×D411yescharacteristic
339C2×C3×C4D3×D412yes—
340C2×C3×C4#23712yes—
341C2×C3×C4#23912yes—
342C2×C3×C4C2×#6712yes—
343C2×C3×C4C23×D311yescharacteristic
344C2×C3×C4C23×D311yescharacteristic
345#67—128no—
346#67—128no—
347C2×Dic3—22no—
348C2×Dic3—24no—
349C2×Dic3—22no—
350C2×Dic3—62no—
351C2×Dic3—62no—
352C2×Dic3—122no—
353C2×Dic3—122no—
354C2×Dic3—122no—
355C2×Dic3—242no—
356C2×Dic3#20414yescomplemented
357C2×Dic3C2×D1212yes—
358C2×Dic3C2×D1212yes—
359D12—22no—
360D12—22no—
361D12—42no—
362D12—64no—
363D12—62no—
364D12—62no—
365D12—62no—
366D12—62no—
367D12—122no—
368D12—124no—
369D12—128no—
370D12—128no—
371D12—122no—
372D12—122no—
373Dic6—24no—
374Dic6—22no—
375Dic6C2×#6714yescomplemented
376C3×C8—22no—
377C3×C8—22no—
378C3×C8—42no—
379C3×C8—62no—
380C3⋊C8—22no—
381C2×C32#46014yescomplemented
382C2×C32C2×#12111yescharacteristic
383C2×C32C22×SD1611yescharacteristic
384C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
385C3⋊D3—82no—
386C3×D3—82no—
387C24—61no—
388C24—181no—
389C2×Q8—32no—
390C2×Q8—34no—
391C2×Q8—62no—
392C2×Q8—61no—
393C2×D4—32no—
394C2×D4—62no—
395C2×D4—61no—
396C2×D4—62no—
397C2×D4—92no—
398C2×D4—184no—
399C2×D4—184no—
400C2×D4—182no—
401C2×D4—181no—
402C2×D4—182no—
403C2×D4—364no—
404C2×D4—364no—
405C22×C4—31no—
406C22×C4—31no—
407C22×C4—61no—
408C22×C4—181no—
409C22×C4C2×D3211yescharacteristic
410SD16—68no—
411SD16—188no—
412C2×C8—22no—
413C2×C8—32no—
414C2×C8—62no—
415C2×C8C2×D3212yes—
416C4⋊C4—92no—
417C4⋊C4—184no—
418C4⋊C4—181no—
419C42—32no—
420C42—32no—
421C42—184no—
422C22×C3—21no—
423C22×C3—22no—
424C22×C3—22no—
425C22×C3—22no—
426C22×C3—122no—
427C22×C3—122no—
428C22×C3—122no—
429C22×C3—244no—
430C22×C3#89512yes—
431C22×C3C2×#20412yes—
432C22×C3#90812yes—
433C22×C3D3×SD1612yes—
434C22×C3#91412yes—
435C22×C3#93912yes—
436C22×C3C22×D1211yescharacteristic
437C22×C3C2×D3×D411yescharacteristic
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—42no—
441C2×D3—84no—
442C2×D3—124no—
443C2×D3—122no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3—242no—
450C2×D3—242no—
451C2×D3—248no—
452C2×D3—244no—
453C2×D3—244no—
454C3×C4—21no—
455C3×C4—21no—
456C3×C4—22no—
457C3×C4—34no—
458C3×C4—62no—
459C3×C4—64no—
460C3×C4#89512yes—
461C3×C4#93912yes—
462C3×C4C2×D3×D411yescharacteristic
463C3×C4C2×#23711yescharacteristic
464C3×C4C2×#23911yescharacteristic
465C3×C4C22×#6711yescharacteristic
466Dic3—22no—
467Dic3—24no—
468Dic3—122no—
469Dic3—122no—
470Dic3—242no—
471Dic3C2×#20414yescomplemented
472C32C2×#46011yescharacteristic, complemented, Sylow
473C23—62no—
474C23—122no—
475C23—122no—
476C23—122no—
477C23—182no—
478C23—362no—
479C23—362no—
480C23—362no—
481C23D3×D1211yescharacteristic
482Q8—34no—
483Q8—62no—
484Q8—64no—
485D4—62no—
486D4—62no—
487D4—122no—
488D4—182no—
489D4—182no—
490D4—368no—
491D4—368no—
492D4—362no—
493C2×C4—32no—
494C2×C4—34no—
495C2×C4—32no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—64no—
499C2×C4—182no—
500C2×C4—362no—
501C2×C4#379612yes—
502C2×C4D3×D1211yescharacteristic
503C2×C4D3×#6712yes—
504C2×C4C22×D3211yescharacteristic
505C8—22no—
506C8—62no—
507C2×C3—21no—
508C2×C3—24no—
509C2×C3—21no—
510C2×C3—21no—
511C2×C3—242no—
512C2×C3#484814yescomplemented
513C2×C3#516314yescomplemented
514C2×C3C2×#89511yescharacteristic
515C2×C3C22×#20411yescharacteristic
516C2×C3C2×#90811yescharacteristic
517C2×C3C2×D3×SD1611yescharacteristic
518C2×C3C2×#91411yescharacteristic
519C2×C3C2×#93911yescharacteristic
520D3—82no—
521D3—244no—
522D3—242no—
523D3—242no—
524C22—122no—
525C22—122no—
526C22—122no—
527C22—244no—
528C22—362no—
529C22—362no—
530C22—362no—
531C22—724no—
532C22D3×#20412yes—
533C22#6379412yes—
534C22#6388612yes—
535C22C2×D3×D1211yescharacteristic
536C4—34no—
537C4—64no—
538C4—62no—
539C4—362no—
540C4#6388612yes—
541C4C2×#379611yescharacteristic
542C4C2×D3×#6711yescharacteristic
543C3—21no—
544C3C2×#484811yescharacteristic, complemented
545C3C2×#516311yescharacteristic, complemented
546C2—242no—
547C2—722no—
548C2#1059079914yesdirect product factor
549C2C2×D3×#20411yescharacteristic
550C2C2×#6379411yescharacteristic
551C2C2×#6388611yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC2×#63911C2
hypercenterC22×C8D32
hypocenterC32C2×#460
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#204C2semidirect
3. C2×Dic3×Dic6C2semidirect
4. C22×#3717C2semidirect
5. C2×#63648C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×#63563C2semidirect
8. #10590799C2direct (N × H)
21. C2×C3×#204C22semidirect
27. Dic3×Dic6C22semidirect
29. C2×#3717C22semidirect
30. #63648C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. #63563C22semidirect
38. C22×#204D3semidirect
48. C2×Dic3⋊C8D3semidirect
67. C2×C3×Dic6D4semidirect
122. C2×#204C2×D3semidirect
133. Dic3⋊C8C2×D3semidirect
155. C2×C3×Dic3SD16semidirect
163. C3×Dic6C2×D4semidirect
227. C2×Dic6#67semidirect
275. C3×Dic3C2×SD16semidirect
356. C2×Dic3#204semidirect
375. Dic6C2×#67semidirect
381. C2×C32#460semidirect
471. Dic3C2×#204semidirect
472. C32C2×#460semidirect
512. C2×C3#4848semidirect
513. C2×C3#5163semidirect
544. C3C2×#4848semidirect
545. C3C2×#5163semidirect
548. C2#10590799direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2042
C2×#639112
C2×Dic3×Dic62
C22×#37172
C2×#636482
C2×C3×Dic3⋊C82
C2×#635632
#105907992
C2×#51633
C2×#48483