Finite Group Databasebeta

← C2×#10590754 #11865562

Subgroups — C2×#10590754 #11865562

Order 1152.

1229 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2C2×Dic3×D12C211yesmaximal, characteristic, complemented
3C2×#63864C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic
5C2×#63648C211yesmaximal, characteristic, complemented
6C2×C3×Dic3⋊C8C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590754C218yesmaximal, direct product factor
9C2×#5165—31nomaximal
10C2×#4844—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×D3×Dic3—21no—
15C22×C32×C8C2211yescharacteristic
16C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C22×C3×C3⋊C8C2211yescharacteristic
19C2×C3×#204—24no—
20C2×C3×#204C2214yescomplemented
21C2×#3722—21no—
22C2×#3722—21no—
23C2×(C2×D3)⋊Dic3—21no—
24Dic3×D12—22no—
25Dic3×D12C2214yescomplemented
26#63864—22no—
27#63864C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yes—
30#63648C2214yescomplemented
31C3×Dic3⋊C8C2214yescomplemented
32#63566C2214yescomplemented
33C22×C3×SD16—31no—
34C2×#947—31no—
35C2×D4×Dic3—31no—
36C22×#213—31no—
37C22×D24—31no—
38C22×#204D311yescharacteristic, complemented
39C2×#875—31no—
40C2×C4×D12—31no—
41C2×C3×C4⋊C8—31no—
42C2×#835—31no—
43#5165—38no—
44C2×#821—31no—
45C2×#821—31no—
46C2×#821—61no—
47C2×#816—31no—
48C2×Dic3⋊C8D311yescharacteristic, complemented
49#4844—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—21no—
62C2×C3×D12—22no—
63C2×C3×D12D414yes—
64C2×C3×D12C2312yes—
65C2×C3×Dic6—22no—
66C2×C3×Dic6—22no—
67C2×C3×Dic6—21no—
68C2×C3×Dic6C2312yes—
69C2×D3×Dic3—24no—
70C2×D3×Dic3—44no—
71C2×C32×C8—22no—
72C2×C32×C8C2312yes—
73C4⋊(C3⋊Dic3)—21no—
74C4⋊(C3⋊Dic3)C2312yes—
75C3×C4×Dic3D412yes—
76C3×C4×Dic3C2312yes—
77C2×C3×C3⋊C8—22no—
78C2×C3×C3⋊C8C2312yes—
79C3×#204—28no—
80#3722—24no—
81#3722—24no—
82(C2×D3)⋊Dic3—24no—
83#3714—28no—
84C2×#463—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C23×Dic3—61no—
88C22×D12—31no—
89C22×D12—31no—
90C22×D12—61no—
91C22×D12C2×D311yescharacteristic
92C22×C4×D3—61no—
93C22×Dic6C2×D311yescharacteristic
94C2×C3×SD16—34no—
95C2×C3×SD16—64no—
96C22×C3×C8—21no—
97C22×C3×C8—31no—
98C22×C3×C8C2×D311yescharacteristic
99C22×C3×C8C2×D311yescharacteristic
100C2×C3×C42—31no—
101C2×#217—61no—
102#947—34no—
103#947—62no—
104D4×Dic3—34no—
105D4×Dic3—62no—
106C2×#213—34no—
107C2×#213—64no—
108C2×(C2×D3)⋊C4—61no—
109C2×(C2×D3)⋊C4—61no—
110C2×(C2×D3)⋊C4—61no—
111C2×(C2×D3)⋊C4—61no—
112C2×(C2×D3)⋊C4—61no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—61no—
116C2×C4×Dic3C2×D311yescharacteristic
117C22×C3⋊C8C2×D311yescharacteristic
118C2×D24—34no—
119C2×D24—64no—
120C2×#204—24no—
121C2×#204C2×D314yescomplemented
122#875—34no—
123#875—62no—
124C4×D12—34no—
125C4×D12—62no—
126C3×C4⋊C8—34no—
127#835—34no—
128#821—34no—
129#821—34no—
130#821—64no—
131#816—34no—
132Dic3⋊C8C2×D314yescomplemented
133C23×C32C2×D411yescharacteristic
134C22×C3⋊D3—22no—
135C22×C3⋊D3—42no—
136C22×C3⋊D3—42no—
137C22×C3⋊D3—42no—
138C22×C3×D3—24no—
139C22×C3×D3—22no—
140C22×C3×D3—42no—
141C22×C3×D3—42no—
142C2×C32×C4C2×D411yescharacteristic
143C2×C32×C4C2×D412yes—
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—42no—
148C4⋊(C3⋊D3)—22no—
149C4⋊(C3⋊D3)—22no—
150C4⋊(C3⋊D3)—42no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—42no—
155C2×C3×Dic3C2×D412yes—
156C2×C3×Dic3C2×D412yes—
157C3×D12—24no—
158C3×D12—22no—
159C3×D12C2×D414yes—
160C3×Dic6—22no—
161C3×Dic6—22no—
162C3×Dic6—42no—
163D3×Dic3—48no—
164C32×C8—22no—
165C3×C3⋊C8—22no—
166C22×SD16—31no—
167C22×D8—91no—
168C2×#124—91no—
169C2×C4×D4—91no—
170#463—98no—
171C2×C4⋊C8—31no—
172C2×#103—91no—
173C2×#102—91no—
174C24×C3—61no—
175C23×D3—21no—
176C23×D3—61no—
177C23×D3—61no—
178C23×D3—121no—
179C2×C3×Q8—32no—
180C2×C3×Q8—61no—
181C2×C3×Q8—62no—
182C2×C3×Q8—62no—
183C2×C3×D4—34no—
184C2×C3×D4—32no—
185C2×C3×D4—61no—
186C2×C3×D4—62no—
187C22×C3×C4—21no—
188C22×C3×C4—31no—
189C22×C3×C4—31no—
190C22×C3×C4—61no—
191C22×C3×C4C22×D311yescharacteristic
192C22×C3×C4C22×D311yescharacteristic
193C22×Dic3—21no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3—64no—
197C22×Dic3—121no—
198C22×Dic3—124no—
199C22×Dic3D1211yescharacteristic
200C22×Dic3D1211yescharacteristic
201C2×D12—21no—
202C2×D12—22no—
203C2×D12—32no—
204C2×D12—32no—
205C2×D12—62no—
206C2×D12—64no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—62no—
211C2×D12—61no—
212C2×D12—61no—
213C2×D12—121no—
214C2×D12—122no—
215C2×D12#6714yes—
216C2×D12C22×D312yes—
217C2×C4×D3—64no—
218C2×C4×D3—124no—
219C2×Dic6—22no—
220C2×Dic6—22no—
221C2×Dic6—21no—
222C2×Dic6C22×D312yes—
223C3×SD16—68no—
224C2×C3×C8—22no—
225C2×C3×C8—22no—
226C2×C3×C8—22no—
227C2×C3×C8—32no—
228C2×C3×C8—42no—
229C2×C3×C8—62no—
230C2×C3×C8C22×D312yes—
231C2×C3×C8C22×D312yes—
232C3×C42—32no—
233C3×C42—32no—
234#217—64no—
235#213—68no—
236(C2×D3)⋊C4—64no—
237(C2×D3)⋊C4—64no—
238(C2×D3)⋊C4—64no—
239(C2×D3)⋊C4—64no—
240(C2×D3)⋊C4—64no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243C4⋊Dic3—62no—
244C4⋊Dic3—61no—
245C4⋊Dic3—61no—
246C4⋊Dic3—121no—
247C4×Dic3D1212yes—
248C4×Dic3C22×D312yes—
249C2×C3⋊C8—22no—
250C2×C3⋊C8C22×D312yes—
251D24—68no—
252#204—28no—
253C22×C32#12112yes—
254C22×C32#13512yes—
255C22×C32AGL(1,ℤ/8)12yes—
256C22×C32C22×D411yescharacteristic
257C2×C3⋊D3—42no—
258C2×C3⋊D3—42no—
259C2×C3⋊D3—42no—
260C2×C3⋊D3—84no—
261C2×C3×D3—24no—
262C2×C3×D3—42no—
263C2×C3×D3—42no—
264C2×C3×D3—48no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3⋊Dic3—42no—
269C3×Dic3—22no—
270C3×Dic3—22no—
271C3×Dic3—42no—
272C22×Q8—31no—
273C22×D4—31no—
274C22×D4—91no—
275C23×C4—181no—
276C2×SD16—34no—
277C2×SD16—64no—
278C2×D8—94no—
279C2×D8—184no—
280C22×C8—31no—
281C22×C8D3211yescharacteristic
282#124—94no—
283#124—182no—
284C4×D4—94no—
285C4×D4—182no—
286C2×C4⋊C4—91no—
287C2×C22⋊C4—181no—
288C2×C22⋊C4—181no—
289C2×C22⋊C4—181no—
290C2×C42—31no—
291C4⋊C8—34no—
292#103—94no—
293#102—94no—
294C23×C3—21no—
295C23×C3—64no—
296C23×C3—62no—
297C23×C3—122no—
298C23×C3—122no—
299C23×C3C2×D1211yescharacteristic
300C23×C3D3×D411yescharacteristic
301C22×D3—24no—
302C22×D3—22no—
303C22×D3—42no—
304C22×D3—42no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—122no—
308C22×D3—124no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3—122no—
315C22×D3—242no—
316C22×D3—242no—
317C3×Q8—62no—
318C3×Q8—62no—
319C3×Q8—122no—
320C3×D4—34no—
321C3×D4—64no—
322C3×D4—62no—
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—32no—
328C2×C3×C4—32no—
329C2×C3×C4—62no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—122no—
333C2×C3×C4C2×D1211yescharacteristic
334C2×C3×C4D3×D411yescharacteristic
335C2×C3×C4D3×D412yes—
336C2×C3×C4#23712yes—
337C2×C3×C4#23912yes—
338C2×C3×C4C2×#6712yes—
339C2×C3×C4C23×D311yescharacteristic
340C2×C3×C4C23×D311yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—42no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—122no—
348C2×Dic3—128no—
349C2×Dic3—122no—
350C2×Dic3—122no—
351C2×Dic3—242no—
352C2×Dic3C2×D1212yes—
353C2×Dic3C2×D1212yes—
354D12—24no—
355D12—22no—
356D12—64no—
357D12—62no—
358D12—62no—
359D12—62no—
360D12—62no—
361D12—122no—
362D12—124no—
363D12—122no—
364D12—122no—
365D12C2×#6714yes—
366C4×D3—128no—
367Dic6—22no—
368Dic6—22no—
369Dic6—42no—
370C3×C8—22no—
371C3×C8—22no—
372C3×C8—42no—
373C3×C8—62no—
374C3⋊C8—22no—
375C2×C32#46314yescomplemented
376C2×C32C2×#12111yescharacteristic
377C2×C32C2×#13511yescharacteristic
378C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
379C3⋊D3—82no—
380C3×D3—44no—
381C24—61no—
382C24—181no—
383C2×Q8—32no—
384C2×Q8—61no—
385C2×Q8—62no—
386C2×Q8—62no—
387C2×D4—32no—
388C2×D4—34no—
389C2×D4—62no—
390C2×D4—61no—
391C2×D4—92no—
392C2×D4—182no—
393C2×D4—181no—
394C2×D4—182no—
395C22×C4—31no—
396C22×C4—31no—
397C22×C4—61no—
398C22×C4—184no—
399C22×C4—181no—
400C22×C4—364no—
401C22×C4C2×D3211yescharacteristic
402SD16—68no—
403D8—188no—
404C2×C8—22no—
405C2×C8—32no—
406C2×C8—62no—
407C2×C8C2×D3212yes—
408C4⋊C4—92no—
409C4⋊C4—181no—
410C22⋊C4—184no—
411C22⋊C4—184no—
412C22⋊C4—184no—
413C42—32no—
414C42—32no—
415C22×C3—21no—
416C22×C3—22no—
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—64no—
420C22×C3—122no—
421C22×C3—122no—
422C22×C3—128no—
423C22×C3#89512yes—
424C22×C3#90412yes—
425C22×C3#90812yes—
426C22×C3#91412yes—
427C22×C3#91612yes—
428C22×C3#93912yes—
429C22×C3C22×D1211yescharacteristic
430C22×C3C2×D3×D411yescharacteristic
431C2×D3—24no—
432C2×D3—48no—
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—124no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—242no—
443C2×D3—242no—
444C2×D3—248no—
445C2×D3—244no—
446C2×D3—244no—
447C3×C4—21no—
448C3×C4—21no—
449C3×C4—22no—
450C3×C4—62no—
451C3×C4—62no—
452C3×C4—122no—
453C3×C4#89512yes—
454C3×C4#93912yes—
455C3×C4C2×D3×D411yescharacteristic
456C3×C4C2×#23711yescharacteristic
457C3×C4C2×#23911yescharacteristic
458C3×C4C22×#6711yescharacteristic
459Dic3—22no—
460Dic3—22no—
461Dic3—42no—
462Dic3—122no—
463Dic3—122no—
464Dic3—242no—
465C32C2×#46311yescharacteristic, complemented, Sylow
466C23—62no—
467C23—64no—
468C23—122no—
469C23—122no—
470C23—182no—
471C23—362no—
472C23—362no—
473C23—362no—
474C23D3×D1211yescharacteristic
475Q8—62no—
476Q8—62no—
477Q8—122no—
478D4—34no—
479D4—62no—
480D4—64no—
481D4—182no—
482D4—182no—
483D4—362no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—122no—
490C2×C4—182no—
491C2×C4—368no—
492C2×C4—362no—
493C2×C4#379612yes—
494C2×C4D3×D1211yescharacteristic
495C2×C4D3×#6712yes—
496C2×C4C22×D3211yescharacteristic
497C8—22no—
498C8—62no—
499C2×C3—24no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—124no—
504C2×C3#484414yescomplemented
505C2×C3#516514yescomplemented
506C2×C3C2×#89511yescharacteristic
507C2×C3C2×#90411yescharacteristic
508C2×C3C2×#90811yescharacteristic
509C2×C3C2×#91411yescharacteristic
510C2×C3C2×#91611yescharacteristic
511C2×C3C2×#93911yescharacteristic
512D3—44no—
513D3—244no—
514D3—242no—
515D3—242no—
516C22—64no—
517C22—128no—
518C22—122no—
519C22—122no—
520C22—362no—
521C22—362no—
522C22—362no—
523C22—724no—
524C22#6379412yes—
525C22#6380612yes—
526C22#6388612yes—
527C22C2×D3×D1211yescharacteristic
528C4—62no—
529C4—62no—
530C4—122no—
531C4—362no—
532C4#6388612yes—
533C4C2×#379611yescharacteristic
534C4C2×D3×#6711yescharacteristic
535C3—21no—
536C3C2×#484411yescharacteristic, complemented
537C3C2×#516511yescharacteristic, complemented
538C2—124no—
539C2—722no—
540C2#1059075414yesdirect product factor
541C2C2×#6379411yescharacteristic
542C2C2×#6380611yescharacteristic
543C2C2×#6388611yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
hypercenterC22×C8D32
hypocenterC32C2×#463
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
2. C2×Dic3×D12C2semidirect
3. C2×#63864C2semidirect
5. C2×#63648C2semidirect
6. C2×C3×Dic3⋊C8C2semidirect
7. C2×#63566C2semidirect
8. #10590754C2direct (N × H)
20. C2×C3×#204C22semidirect
25. Dic3×D12C22semidirect
27. #63864C22semidirect
30. #63648C22semidirect
31. C3×Dic3⋊C8C22semidirect
32. #63566C22semidirect
38. C22×#204D3semidirect
48. C2×Dic3⋊C8D3semidirect
121. C2×#204C2×D3semidirect
132. Dic3⋊C8C2×D3semidirect
375. C2×C32#463semidirect
465. C32C2×#463semidirect
504. C2×C3#4844semidirect
505. C2×C3#5165semidirect
536. C3C2×#4844semidirect
537. C3C2×#5165semidirect
540. C2#10590754direct (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×Dic3×D122
C2×#638642
C22×#37142
C2×#636482
C2×C3×Dic3⋊C82
C2×#635662
#105907542
C2×#51653
C2×#48443