Finite Group Databasebeta

← C2×#10590348 #11865547

Subgroups — C2×#10590348 #11865547

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
1C2×C3×#875C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic
5C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63562C211yesmaximal, characteristic, complemented
8#10590348C218yesmaximal, direct product factor
9C2×#5057—31nomaximal
10C2×#5016—31nomaximal
11C22×C3×D12C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C22×C3×C4×D3—21no—
14C22×C3×Dic6C2211yescharacteristic
15C2×C32×C42C2211yescharacteristic
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×(C2×D3)⋊C4—21no—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C3×#875—22no—
23C3×#875C2214yescomplemented
24C3×C4×D12—22no—
25C3×C4×D12C2214yescomplemented
26C2×#3715—24no—
27C2×#3715C2214yescomplemented
28C2×#3713—24no—
29C2×#3713C2214yes—
30C4⋊(C3⋊(C3⋊C8))C2214yescomplemented
31#63565C2214yescomplemented
32#63562C2214yescomplemented
33C2×C3×#124—31no—
34C2×C3×C4×D4—31no—
35C22×#215—31no—
36C22×#214—31no—
37C22×#213—31no—
38C22×#213—31no—
39C2×#875D311yescharacteristic, complemented
40C2×C4×D12D311yescharacteristic, complemented
41C2×#835—31no—
42C2×#832—31no—
43#5057—38no—
44#5016—38no—
45C2×#810—31no—
46C2×#809—31no—
47C2×C4⋊(C3⋊C8)—31no—
48C2×C4⋊(C3⋊C8)—31no—
49C2×C4⋊(C3⋊C8)—61no—
50C23×C3×D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
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×C4×D3—24no—
66C2×C3×C4×D3—44no—
67C2×C3×Dic6—22no—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—21no—
70C2×C3×Dic6C2312yes—
71C32×C42D412yes—
72C32×C42C2312yes—
73C2×C3⋊(C3⋊C8)—22no—
74C2×C3⋊(C3⋊C8)—22no—
75C2×C3⋊(C3⋊C8)C2312yes—
76C2×C3⋊(C3⋊C8)C2312yes—
77C3×(C2×D3)⋊C4—24no—
78C3×(C2×D3)⋊C4—24no—
79C3×(C2×D3)⋊C4—24no—
80C3×C4⋊Dic3—21no—
81C3×C4⋊Dic3C2312yes—
82#3715—28no—
83#3713—28no—
84C2×#463—91noSylow
85C22×C3×Q8—31no—
86C22×C3×D4—31no—
87C22×C3×D4—31no—
88C23×C3×C4—61no—
89C22×D12C2×D311yescharacteristic
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—21no—
92C22×Dic6C2×D311yescharacteristic
93C3×#124—34no—
94C3×#124—62no—
95C3×C4×D4—34no—
96C3×C4×D4—62no—
97C2×C3×C4⋊C4—31no—
98C2×C3×C22⋊C4—61no—
99C2×C3×C22⋊C4—61no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—21no—
102C2×C3×C42C2×D311yescharacteristic
103C2×C3×C42C2×D311yescharacteristic
104C2×#215—34no—
105C2×#215—64no—
106C2×#214—34no—
107C2×#214—64no—
108C2×#213—34no—
109C2×#213—34no—
110C2×#213—64no—
111C2×#213—64no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—31no—
119C22×C3⋊C8—31no—
120C22×C3⋊C8—61no—
121C22×C3⋊C8—61no—
122#875—22no—
123#875C2×D314yescomplemented
124C4×D12—22no—
125C4×D12C2×D314yescomplemented
126#835—34no—
127#832—34no—
128#810—34no—
129#809—34no—
130C4⋊(C3⋊C8)—34no—
131C4⋊(C3⋊C8)—34no—
132C4⋊(C3⋊C8)—64no—
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×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C2×D412yes—
145C2×C32×C4C2×D412yes—
146C2×C32×C4C2×D412yes—
147C2×C32×C4C2×D411yescharacteristic
148C2×C32×C4#4112yes—
149C2×C32×C4C2411yescharacteristic
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×C4×D3—48no—
161C3×Dic6—22no—
162C3×Dic6—22no—
163C3×Dic6—42no—
164C3⋊(C3⋊C8)—22no—
165C3⋊(C3⋊C8)—22no—
166C22×SD16—91no—
167C22×D8—91no—
168C2×#124—31no—
169C2×C4×D4—31no—
170#463—98no—
171C2×C4⋊C8—91no—
172C2×#103—91no—
173C2×#102—91no—
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—62no—
187C2×C3×D4—62no—
188C2×C3×D4—61no—
189C2×C3×D4—61no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—21no—
193C22×C3×C4—61no—
194C22×C3×C4—61no—
195C22×C3×C4—64no—
196C22×C3×C4—124no—
197C22×C3×C4#6711yescharacteristic
198C22×C3×C4#6711yescharacteristic
199C22×C3×C4#6711yescharacteristic
200C22×C3×C4#6711yescharacteristic
201C22×C3×C4C22×D311yescharacteristic
202C22×C3×C4C22×D311yescharacteristic
203C22×Dic3—21no—
204C22×Dic3—21no—
205C2×D12—22no—
206C2×D12—21no—
207C2×D12—22no—
208C2×D12—22no—
209C2×D12—21no—
210C2×D12D1214yes—
211C2×D12C22×D312yes—
212C2×D12C22×D312yes—
213C2×C4×D3—24no—
214C2×C4×D3—44no—
215C2×Dic6—22no—
216C2×Dic6—22no—
217C2×Dic6—21no—
218C2×Dic6C22×D312yes—
219C3×C4⋊C4—32no—
220C3×C4⋊C4—61no—
221C3×C22⋊C4—64no—
222C3×C22⋊C4—64no—
223C3×C22⋊C4—64no—
224C3×C42—22no—
225C3×C42—22no—
226C3×C42#6712yes—
227C3×C42#6712yes—
228C3×C42C22×D312yes—
229C3×C42C22×D312yes—
230#215—68no—
231#214—68no—
232#213—68no—
233#213—68no—
234(C2×D3)⋊C4—24no—
235(C2×D3)⋊C4—24no—
236(C2×D3)⋊C4—24no—
237C4⋊Dic3—21no—
238C4⋊Dic3C22×D312yes—
239C2×C3⋊C8—32no—
240C2×C3⋊C8—32no—
241C2×C3⋊C8—32no—
242C2×C3⋊C8—32no—
243C2×C3⋊C8—62no—
244C2×C3⋊C8—62no—
245C2×C3⋊C8—62no—
246C2×C3⋊C8—62no—
247C2×C3⋊C8—62no—
248C2×C3⋊C8—62no—
249C2×C3⋊C8—122no—
250C2×C3⋊C8—122no—
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—22no—
264C32×C4—22no—
265C32×C4#12112yes—
266C32×C4C22×D411yescharacteristic
267C32×C4C2×#4111yescharacteristic
268C3×Dic3—42no—
269C3×Dic3—42no—
270C22×Q8—31no—
271C22×D4—31no—
272C22×D4—31no—
273C23×C4—61no—
274C2×SD16—94no—
275C2×SD16—184no—
276C2×D8—94no—
277C2×D8—184no—
278C22×C8—91no—
279C22×C8—91no—
280#124—34no—
281#124—62no—
282C4×D4—34no—
283C4×D4—62no—
284C2×C4⋊C4—31no—
285C2×C22⋊C4—61no—
286C2×C22⋊C4—61no—
287C2×C22⋊C4—61no—
288C2×C42D3211yescharacteristic
289C4⋊C8—94no—
290#103—94no—
291#102—94no—
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×C3C2×#6711yescharacteristic
302C23×C3C2×#6711yescharacteristic
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—24no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—21no—
326C2×C3×C4—22no—
327C2×C3×C4—22no—
328C2×C3×C4—22no—
329C2×C3×C4—21no—
330C2×C3×C4—22no—
331C2×C3×C4—42no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—128no—
335C2×C3×C4—122no—
336C2×C3×C4—122no—
337C2×C3×C4C2×D1212yes—
338C2×C3×C4#23512yes—
339C2×C3×C4D3×D412yes—
340C2×C3×C4#23712yes—
341C2×C3×C4C2×#6712yes—
342C2×C3×C4C2×#6712yes—
343C2×C3×C4C2×#6712yes—
344C2×C3×C4C2×#6712yes—
345C2×C3×C4C2×#6711yescharacteristic
346C2×C3×C4C2×#6711yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—42no—
352C2×Dic3—42no—
353D12—24no—
354D12—22no—
355D12—22no—
356D12—22no—
357D12—42no—
358D12C2×D1214yes—
359C4×D3—48no—
360Dic6—22no—
361Dic6—22no—
362Dic6—42no—
363C3⋊C8—62no—
364C3⋊C8—62no—
365C3⋊C8—62no—
366C3⋊C8—62no—
367C3⋊C8—122no—
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—62no—
387C2×D4—61no—
388C2×D4—61no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—64no—
392C22×C4—124no—
393C22×C4#62511yescharacteristic
394C22×C4#62511yescharacteristic
395C22×C4C2×D3211yescharacteristic
396SD16—188no—
397D8—188no—
398C2×C8—92no—
399C2×C8—92no—
400C2×C8—182no—
401C2×C8—182no—
402C4⋊C4—32no—
403C4⋊C4—61no—
404C22⋊C4—64no—
405C22⋊C4—64no—
406C22⋊C4—64no—
407C42#62512yes—
408C42C2×D3212yes—
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#93012yes—
422C22×C3#93212yes—
423C22×C3#93812yes—
424C22×C3#94912yes—
425C22×C3#95012yes—
426C22×C3#95012yes—
427C22×C3C22×#6711yescharacteristic
428C22×C3C22×#6711yescharacteristic
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—24no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—22no—
441C3×C4—22no—
442C3×C4—21no—
443C3×C4—21no—
444C3×C4—22no—
445C3×C4—42no—
446C3×C4—122no—
447C3×C4—122no—
448C3×C4#93012yes—
449C3×C4#93812yes—
450C3×C4C22×D1211yescharacteristic
451C3×C4C2×#23511yescharacteristic
452C3×C4C2×D3×D411yescharacteristic
453C3×C4C2×#23711yescharacteristic
454Dic3—42no—
455Dic3—42no—
456C32C2×#46311yescharacteristic, complemented, Sylow
457C23—62no—
458C23—64no—
459C23—62no—
460C23—122no—
461C23—122no—
462C23—122no—
463C23—122no—
464C23—122no—
465C23C2×#62511yescharacteristic
466Q8—62no—
467Q8—62no—
468Q8—122no—
469D4—34no—
470D4—62no—
471D4—62no—
472D4—62no—
473D4—64no—
474D4—122no—
475C2×C4—22no—
476C2×C4—22no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—128no—
480C2×C4—122no—
481C2×C4—122no—
482C2×C4#379512yes—
483C2×C4D3×D1212yes—
484C2×C4C2×#62512yes—
485C2×C4C2×#62512yes—
486C2×C4C2×#62511yescharacteristic
487C2×C4C22×D3211yescharacteristic
488C8—182no—
489C8—182no—
490C2×C3—24no—
491C2×C3—21no—
492C2×C3—21no—
493C2×C3—21no—
494C2×C3—124no—
495C2×C3—242no—
496C2×C3#501614yescomplemented
497C2×C3#505714yescomplemented
498C2×C3C2×#93011yescharacteristic
499C2×C3C2×#93211yescharacteristic
500C2×C3C2×#93811yescharacteristic
501C2×C3C2×#94911yescharacteristic
502C2×C3C2×#95011yescharacteristic
503C2×C3C2×#95011yescharacteristic
504D3—44no—
505D3—82no—
506C22—64no—
507C22—128no—
508C22—122no—
509C22—122no—
510C22—122no—
511C22—122no—
512C22—122no—
513C22—244no—
514C22#6382212yes—
515C22#6382312yes—
516C22#6390812yes—
517C22C22×#62511yescharacteristic
518C4—22no—
519C4—22no—
520C4—122no—
521C4—122no—
522C4#6390812yes—
523C4C2×#379511yescharacteristic
524C4C2×D3×D1211yescharacteristic
525C3—21no—
526C3C2×#501611yescharacteristic, complemented
527C3C2×#505711yescharacteristic, complemented
528C2—124no—
529C2—242no—
530C2#1059034814yesdirect product factor
531C2C2×#6382211yescharacteristic
532C2C2×#6382311yescharacteristic
533C2C2×#6390811yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3713C2
hypercenterC2×C42D32
hypocenterC32C2×#463
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C3×#875C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C22×#3715C2semidirect
5. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
6. C2×#63565C2semidirect
7. C2×#63562C2semidirect
8. #10590348C2direct (N × H)
23. C3×#875C22semidirect
25. C3×C4×D12C22semidirect
27. C2×#3715C22semidirect
30. C4⋊(C3⋊(C3⋊C8))C22semidirect
31. #63565C22semidirect
32. #63562C22semidirect
39. C2×#875D3semidirect
40. C2×C4×D12D3semidirect
123. #875C2×D3semidirect
125. C4×D12C2×D3semidirect
369. C2×C32#463semidirect
456. C32C2×#463semidirect
496. C2×C3#5016semidirect
497. C2×C3#5057semidirect
526. C3C2×#5016semidirect
527. C3C2×#5057semidirect
530. C2#10590348direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#8752
C2×C3×C4×D122
C22×#37152
C22×#37132
C2×C4⋊(C3⋊(C3⋊C8))2
C2×#635652
C2×#635622
#105903482
C2×#50573
C2×#50163