Finite Group Databasebeta

← C2×#10590750 #11865560

Subgroups — C2×#10590750 #11865560

Order 1152.

1197 conjugacy classes of subgroups.

The subgroup lattice has 535 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#204C211yesmaximal, characteristic, complemented
2C2×#63898C211yesmaximal, characteristic, complemented
3C2×#63863C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic
5C2×#63641C211yesmaximal, characteristic, complemented
6C2×C3×#821C211yesmaximal, characteristic, complemented
7C2×#63565C211yesmaximal, characteristic, complemented
8#10590750C218yesmaximal, direct product factor
9C2×#5165—31nomaximal
10C2×#4787—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×Dic6C2211yescharacteristic
14C22×D3×Dic3—21no—
15C22×C32×C8C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4⋊Dic3C2211yescharacteristic
19C2×C3×#204—24no—
20C2×C3×#204C2214yescomplemented
21C2×(C2×D3)⋊Dic3—21no—
22C2×(C2×D3)⋊Dic3—21no—
23C2×(C2×D3)⋊Dic3—21no—
24#63898—22no—
25#63898C2214yescomplemented
26#63863—22no—
27#63863C2214yescomplemented
28C2×#3713—24no—
29C2×#3713C2214yes—
30#63641C2214yescomplemented
31C3×#821C2214yescomplemented
32#63565C2214yescomplemented
33C22×C3×SD16—31no—
34C2×#947—31no—
35C2×#936—31no—
36C2×D4×Dic3—31no—
37C22×#213—31no—
38C22×#213—31no—
39C22×#204D311yescharacteristic, complemented
40C2×#893—31no—
41C2×C3×#102—31no—
42C2×#835—31no—
43#5165—38no—
44C2×#821D311yescharacteristic, complemented
45C2×Dic3⋊C8—31no—
46C2×Dic3⋊C8—31no—
47C2×Dic3⋊C8—61no—
48C2×#810—31no—
49#4787—38no—
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3D411yescharacteristic
54C22×C3⋊Dic3D411yescharacteristic
55C22×C3×Dic3—21no—
56C22×C3×Dic3—21no—
57C2×C3×D12—21no—
58C2×C3×D12—22no—
59C2×C3×D12—22no—
60C2×C3×D12—22no—
61C2×C3×D12—21no—
62C2×C3×D12D414yes—
63C2×C3×D12C2312yes—
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⋊Dic3D412yes—
74C4×C3⋊Dic3C2312yes—
75C2×C3⋊(C3⋊C8)—22no—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3C2312yes—
79C3×#204—28no—
80(C2×D3)⋊Dic3—24no—
81(C2×D3)⋊Dic3—24no—
82(C2×D3)⋊Dic3—24no—
83#3713—28no—
84C2×#463—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×C3×D4—31no—
88C23×Dic3—61no—
89C22×D12C2×D311yescharacteristic
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—61no—
92C22×Dic6C2×D311yescharacteristic
93C2×C3×SD16—34no—
94C2×C3×SD16—64no—
95C22×C3×C8—21no—
96C22×C3×C8C2×D311yescharacteristic
97C22×C3×C8C2×D311yescharacteristic
98C2×C3×C4⋊C4—31no—
99C2×#217—61no—
100C2×#217—61no—
101C2×#217—61no—
102#947—34no—
103#947—62no—
104#936—34no—
105#936—62no—
106D4×Dic3—34no—
107D4×Dic3—62no—
108C2×#213—34no—
109C2×#213—34no—
110C2×#213—64no—
111C2×#213—64no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C2×C4×Dic3—31no—
117C2×C4×Dic3—31no—
118C2×C4×Dic3—61no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—31no—
121C22×C3⋊C8—61no—
122C2×#204—24no—
123C2×#204C2×D314yescomplemented
124#893—34no—
125#893—62no—
126C3×#102—34no—
127#835—34no—
128#821C2×D314yescomplemented
129Dic3⋊C8—34no—
130Dic3⋊C8—34no—
131Dic3⋊C8—64no—
132#810—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×C4C2×D411yescharacteristic
143C2×C32×C4C2×D412yes—
144C2×C32×C4#4112yes—
145C2×C32×C4C2411yescharacteristic
146C2×C3⋊Dic3—22no—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3C2×D412yes—
149C2×C3⋊Dic3C2×D412yes—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—42no—
153C2×C3×Dic3—42no—
154C3×D12—24no—
155C3×D12—22no—
156C3×D12—22no—
157C3×D12—22no—
158C3×D12—42no—
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—91no—
172C2×#103—91no—
173C2×#102—31no—
174C24×C3—61no—
175C24×C3—61no—
176C23×D3—21no—
177C23×D3—21no—
178C2×C3×Q8—32no—
179C2×C3×Q8—61no—
180C2×C3×Q8—62no—
181C2×C3×Q8—62no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—32no—
185C2×C3×D4—62no—
186C2×C3×D4—61no—
187C2×C3×D4—61no—
188C2×C3×D4—62no—
189C2×C3×D4—62no—
190C22×C3×C4—21no—
191C22×C3×C4—61no—
192C22×C3×C4—61no—
193C22×C3×C4C22×D311yescharacteristic
194C22×C3×C4C22×D311yescharacteristic
195C22×Dic3—21no—
196C22×Dic3—21no—
197C22×Dic3—31no—
198C22×Dic3—31no—
199C22×Dic3—31no—
200C22×Dic3—31no—
201C22×Dic3—61no—
202C22×Dic3—61no—
203C22×Dic3—64no—
204C22×Dic3—124no—
205C2×D12—21no—
206C2×D12—22no—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—21no—
210C2×D12#6714yes—
211C2×D12C22×D312yes—
212C2×D12C22×D312yes—
213C2×C4×D3—64no—
214C2×C4×D3—124no—
215C2×Dic6—22no—
216C2×Dic6—22no—
217C2×Dic6—21no—
218C2×Dic6C22×D312yes—
219C3×SD16—68no—
220C2×C3×C8—22no—
221C2×C3×C8—22no—
222C2×C3×C8—22no—
223C2×C3×C8—42no—
224C2×C3×C8C22×D312yes—
225C2×C3×C8C22×D312yes—
226C3×C4⋊C4—32no—
227C3×C4⋊C4—61no—
228#217—64no—
229#217—64no—
230#217—64no—
231#213—68no—
232#213—68no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—64no—
235(C2×D3)⋊C4—64no—
236C4⋊Dic3—21no—
237C4⋊Dic3C22×D312yes—
238C4×Dic3—32no—
239C4×Dic3—32no—
240C4×Dic3—32no—
241C4×Dic3—32no—
242C4×Dic3—62no—
243C4×Dic3—62no—
244C2×C3⋊C8—32no—
245C2×C3⋊C8—32no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—122no—
250#204—28no—
251C22×C32#12112yes—
252C22×C32#13512yes—
253C22×C32AGL(1,ℤ/8)12yes—
254C22×C32C22×D411yescharacteristic
255C2×C3×D3—24no—
256C2×C3×D3—42no—
257C2×C3×D3—42no—
258C2×C3×D3—48no—
259C2×C3×D3—42no—
260C2×C3×D3—42no—
261C2×C3×D3—42no—
262C2×C3×D3—84no—
263C32×C4#12112yes—
264C32×C4C22×D411yescharacteristic
265C32×C4C2×#4111yescharacteristic
266C3⋊Dic3—22no—
267C3⋊Dic3—22no—
268C3×Dic3—42no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×D4—31no—
272C22×D4—31no—
273C23×C4—181no—
274C2×SD16—34no—
275C2×SD16—64no—
276C2×D8—94no—
277C2×D8—184no—
278C22×C8—91no—
279C22×C8D3211yescharacteristic
280#124—94no—
281#124—182no—
282C4×D4—94no—
283C4×D4—182no—
284C2×C4⋊C4—31no—
285C2×C22⋊C4—181no—
286C2×C22⋊C4—181no—
287C2×C22⋊C4—181no—
288C2×C42—91no—
289C4⋊C8—94no—
290#103—94no—
291#102—34no—
292C23×C3—21no—
293C23×C3—64no—
294C23×C3—62no—
295C23×C3—62no—
296C23×C3—122no—
297C23×C3—122no—
298C23×C3—122no—
299C23×C3—122no—
300C23×C3—122no—
301C23×C3D3×D411yescharacteristic
302C23×C3D3×D411yescharacteristic
303C22×D3—24no—
304C22×D3—22no—
305C22×D3—22no—
306C22×D3—42no—
307C22×D3—42no—
308C22×D3—42no—
309C22×D3—42no—
310C22×D3—42no—
311C3×Q8—62no—
312C3×Q8—62no—
313C3×Q8—122no—
314C3×D4—34no—
315C3×D4—64no—
316C3×D4—62no—
317C3×D4—62no—
318C3×D4—62no—
319C3×D4—122no—
320C2×C3×C4—21no—
321C2×C3×C4—22no—
322C2×C3×C4—21no—
323C2×C3×C4—22no—
324C2×C3×C4—62no—
325C2×C3×C4—62no—
326C2×C3×C4—122no—
327C2×C3×C4—122no—
328C2×C3×C4#23512yes—
329C2×C3×C4D3×D411yescharacteristic
330C2×C3×C4D3×D411yescharacteristic
331C2×C3×C4D3×D412yes—
332C2×C3×C4#23712yes—
333C2×C3×C4C2×#6712yes—
334C2×C3×C4C23×D311yescharacteristic
335C2×C3×C4C23×D311yescharacteristic
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—32no—
339C2×Dic3—32no—
340C2×Dic3—32no—
341C2×Dic3—32no—
342C2×Dic3—42no—
343C2×Dic3—42no—
344C2×Dic3—62no—
345C2×Dic3—62no—
346C2×Dic3—64no—
347C2×Dic3—62no—
348C2×Dic3—62no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—122no—
352C2×Dic3—128no—
353D12—24no—
354D12—22no—
355D12—22no—
356D12—22no—
357D12—42no—
358D12C2×#6714yes—
359C4×D3—128no—
360Dic6—22no—
361Dic6—22no—
362Dic6—42no—
363C3×C8—22no—
364C3×C8—22no—
365C3×C8—42no—
366C3⋊C8—62no—
367C3⋊C8—62no—
368C3⋊C8—122no—
369C2×C32#46314yescomplemented
370C2×C32C2×#12111yescharacteristic
371C2×C32C2×#13511yescharacteristic
372C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
373C3×D3—44no—
374C3×D3—82no—
375C24—61no—
376C24—61no—
377C2×Q8—32no—
378C2×Q8—61no—
379C2×Q8—62no—
380C2×Q8—62no—
381C2×D4—32no—
382C2×D4—32no—
383C2×D4—34no—
384C2×D4—62no—
385C2×D4—62no—
386C2×D4—61no—
387C2×D4—61no—
388C2×D4—62no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—91no—
392C22×C4—91no—
393C22×C4—184no—
394C22×C4—364no—
395C22×C4C2×D3211yescharacteristic
396SD16—68no—
397D8—188no—
398C2×C8—22no—
399C2×C8—92no—
400C2×C8—182no—
401C2×C8C2×D3212yes—
402C4⋊C4—32no—
403C4⋊C4—61no—
404C22⋊C4—184no—
405C22⋊C4—184no—
406C22⋊C4—184no—
407C42—92no—
408C42—92no—
409C22×C3—21no—
410C22×C3—22no—
411C22×C3—22no—
412C22×C3—22no—
413C22×C3—64no—
414C22×C3—122no—
415C22×C3—122no—
416C22×C3—128no—
417C22×C3—122no—
418C22×C3—122no—
419C22×C3—122no—
420C22×C3—244no—
421C22×C3#88412yes—
422C22×C3#91112yes—
423C22×C3#91412yes—
424C22×C3#91612yes—
425C22×C3#91612yes—
426C22×C3#93912yes—
427C22×C3C2×D3×D411yescharacteristic
428C22×C3C2×D3×D411yescharacteristic
429C2×D3—24no—
430C2×D3—48no—
431C2×D3—42no—
432C2×D3—42no—
433C2×D3—42no—
434C2×D3—42no—
435C2×D3—42no—
436C2×D3—84no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—22no—
440C3×C4—122no—
441C3×C4—122no—
442C3×C4#88412yes—
443C3×C4#93912yes—
444C3×C4C2×#23511yescharacteristic
445C3×C4C2×D3×D411yescharacteristic
446C3×C4C2×#23711yescharacteristic
447C3×C4C22×#6711yescharacteristic
448Dic3—42no—
449Dic3—42no—
450Dic3—64no—
451Dic3—62no—
452Dic3—62no—
453Dic3—62no—
454Dic3—62no—
455Dic3—122no—
456C32C2×#46311yescharacteristic, complemented, Sylow
457C23—62no—
458C23—64no—
459C23—62no—
460C23—122no—
461C23—122no—
462C23—122no—
463C23—122no—
464C23—122no—
465C23#380211yescharacteristic
466Q8—62no—
467Q8—62no—
468Q8—122no—
469D4—34no—
470D4—62no—
471D4—62no—
472D4—62no—
473D4—64no—
474D4—122no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—92no—
478C2×C4—92no—
479C2×C4—122no—
480C2×C4—122no—
481C2×C4—182no—
482C2×C4—182no—
483C2×C4—368no—
484C2×C4#379512yes—
485C2×C4#380211yescharacteristic
486C2×C4D3×#6712yes—
487C2×C4C22×D3211yescharacteristic
488C8—22no—
489C8—182no—
490C2×C3—24no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—124no—
495C2×C3—242no—
496C2×C3#478714yescomplemented
497C2×C3#516514yescomplemented
498C2×C3C2×#88411yescharacteristic
499C2×C3C2×#91111yescharacteristic
500C2×C3C2×#91411yescharacteristic
501C2×C3C2×#91611yescharacteristic
502C2×C3C2×#91611yescharacteristic
503C2×C3C2×#93911yescharacteristic
504D3—44no—
505D3—82no—
506C22—64no—
507C22—128no—
508C22—122no—
509C22—122no—
510C22—122no—
511C22—122no—
512C22—122no—
513C22—244no—
514C22#6379812yes—
515C22#6380912yes—
516C22#6388512yes—
517C22C2×#380211yescharacteristic
518C4—122no—
519C4—122no—
520C4—182no—
521C4—182no—
522C4#6388512yes—
523C4C2×#379511yescharacteristic
524C4C2×D3×#6711yescharacteristic
525C3—21no—
526C3C2×#478711yescharacteristic, complemented
527C3C2×#516511yescharacteristic, complemented
528C2—124no—
529C2—242no—
530C2#1059075014yesdirect product factor
531C2C2×#6379811yescharacteristic
532C2C2×#6380911yescharacteristic
533C2C2×#6388511yescharacteristic
subgroupG/H
centerC23#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
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×#63898C2semidirect
3. C2×#63863C2semidirect
5. C2×#63641C2semidirect
6. C2×C3×#821C2semidirect
7. C2×#63565C2semidirect
8. #10590750C2direct (N × H)
20. C2×C3×#204C22semidirect
25. #63898C22semidirect
27. #63863C22semidirect
30. #63641C22semidirect
31. C3×#821C22semidirect
32. #63565C22semidirect
39. C22×#204D3semidirect
44. C2×#821D3semidirect
123. C2×#204C2×D3semidirect
128. #821C2×D3semidirect
369. C2×C32#463semidirect
456. C32C2×#463semidirect
496. C2×C3#4787semidirect
497. C2×C3#5165semidirect
526. C3C2×#4787semidirect
527. C3C2×#5165semidirect
530. C2#10590750direct (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×#638982
C2×#638632
C22×#37132
C2×#636412
C2×C3×#8212
C2×#635652
#105907502
C2×#51653
C2×#47873