Finite Group Databasebeta

← C2×#10590366 #11865545

Subgroups — C2×#10590366 #11865545

Order 1152.

1293 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64084C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic, complemented
3C22×#3716C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic
5C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6C2×#63567C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590366C218yesmaximal, direct product factor
9C2×#5016—31nomaximal
10C2×#4844—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×#634C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C22×C3×C4×D3—21no—
15C2×C32×C42C2211yescharacteristic
16C2×#3752—21no—
17C2×#3752—21no—
18#64084—22no—
19#64084C2214yescomplemented
20C2×C3×(C2×D3)⋊C4—21no—
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C22×C3×C3⋊C8C2211yescharacteristic
23C22×C3×C3⋊C8C2211yescharacteristic
24C3×C4×D12—22no—
25C3×C4×D12C2214yescomplemented
26C2×#3716—24no—
27C2×#3716C2214yescomplemented
28C2×#3714—24no—
29C2×#3714C2214yes—
30C3×C4⋊(C3⋊C8)C2214yescomplemented
31#63567C2214yescomplemented
32#63564C2214yescomplemented
33C2×C3×C4×D4—31no—
34C22×#214—31no—
35C22×#213—31no—
36C22×D24—31no—
37C22×#204—31no—
38C2×#875—31no—
39C2×#875—31no—
40C2×#875—61no—
41C2×C4×D12D311yescharacteristic, complemented
42C2×C3×C4⋊C8—31no—
43C2×#821—31no—
44C2×#816—31no—
45#5016—38no—
46C2×#810—31no—
47C2×#809—31no—
48C2×C4⋊(C3⋊C8)D311yescharacteristic, complemented
49#4844—38no—
50C23×C3⋊D3—21no—
51C23×C3×D3—21no—
52C22×C32×C4D411yescharacteristic
53C22×C32×C4D411yescharacteristic
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×C4⋊(C3⋊D3)—22no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)C2312yes—
60C2×#634—22no—
61C2×#634—22no—
62C2×#634—21no—
63C2×#634C2312yes—
64C22×C3×Dic3—21no—
65C2×C3×D12—21no—
66C2×C3×D12—22no—
67C2×C3×D12D414yes—
68C2×C3×D12C2312yes—
69C2×C3×C4×D3—24no—
70C2×C3×C4×D3—44no—
71C32×C42D412yes—
72C32×C42C2312yes—
73#3752—24no—
74#3752—24no—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3C2312yes—
78C2×C3×C3⋊C8—22no—
79C2×C3×C3⋊C8—22no—
80C2×C3×C3⋊C8C2312yes—
81C2×C3×C3⋊C8C2312yes—
82#3716—28no—
83#3714—28no—
84C2×#463—91noSylow
85C22×C3×D4—31no—
86C23×C3×C4—61no—
87C22×D12—31no—
88C22×D12—31no—
89C22×D12—61no—
90C22×D12C2×D311yescharacteristic
91C22×C4×D3—21no—
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C22×C3×C8—31no—
96C22×C3×C8—31no—
97C3×C4×D4—34no—
98C3×C4×D4—62no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C22⋊C4—61no—
101C2×C3×C42—21no—
102C2×C3×C42C2×D311yescharacteristic
103C2×C3×C42C2×D311yescharacteristic
104C2×#214—34no—
105C2×#214—64no—
106C2×#213—34no—
107C2×#213—64no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—62no—
110C2×(C2×D3)⋊C4—62no—
111C2×(C2×D3)⋊C4—61no—
112C2×(C2×D3)⋊C4—61no—
113C2×(C2×D3)⋊C4—61no—
114C2×(C2×D3)⋊C4—61no—
115C2×C4⋊Dic3C2×D311yescharacteristic
116C22×C3⋊C8C2×D311yescharacteristic
117C22×C3⋊C8C2×D311yescharacteristic
118C2×D24—34no—
119C2×D24—64no—
120C2×#204—34no—
121C2×#204—64no—
122#875—34no—
123#875—34no—
124#875—64no—
125#875—64no—
126#875—62no—
127#875—62no—
128C4×D12—22no—
129C4×D12C2×D314yescomplemented
130C3×C4⋊C8—34no—
131#821—34no—
132#816—34no—
133#810—34no—
134#809—34no—
135C4⋊(C3⋊C8)C2×D314yescomplemented
136C23×C32C2×D411yescharacteristic
137C22×C3⋊D3—22no—
138C22×C3⋊D3—42no—
139C22×C3⋊D3—42no—
140C22×C3⋊D3—42no—
141C22×C3×D3—24no—
142C22×C3×D3—22no—
143C22×C3×D3—42no—
144C22×C3×D3—42no—
145C2×C32×C4—22no—
146C2×C32×C4—22no—
147C2×C32×C4C2×D412yes—
148C2×C32×C4C2×D412yes—
149C2×C32×C4C2×D412yes—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4#4112yes—
152C2×C32×C4C2411yescharacteristic
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—42no—
155C4⋊(C3⋊D3)—22no—
156C4⋊(C3⋊D3)—22no—
157C4⋊(C3⋊D3)—42no—
158#634—22no—
159#634—22no—
160#634—42no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—42no—
163C3×D12—24no—
164C3×D12—22no—
165C3×D12C2×D414yes—
166C3×C4×D3—48no—
167C3×C3⋊C8—22no—
168C3×C3⋊C8—22no—
169C22×SD16—91no—
170C22×D8—91no—
171C2×#124—91no—
172C2×C4×D4—31no—
173#463—98no—
174C2×C4⋊C8—31no—
175C2×#103—91no—
176C2×#102—91no—
177C24×C3—61no—
178C23×D3—21no—
179C23×D3—62no—
180C23×D3—61no—
181C23×D3—61no—
182C2×C3×D4—34no—
183C2×C3×D4—32no—
184C2×C3×D4—61no—
185C2×C3×D4—62no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—21no—
189C22×C3×C4—61no—
190C22×C3×C4—64no—
191C22×C3×C4—124no—
192C22×C3×C4D1211yescharacteristic
193C22×C3×C4D1211yescharacteristic
194C22×C3×C4#6711yescharacteristic
195C22×C3×C4#6711yescharacteristic
196C22×C3×C4C22×D311yescharacteristic
197C22×C3×C4C22×D311yescharacteristic
198C22×Dic3—21no—
199C22×Dic3—62no—
200C22×Dic3—61no—
201C22×Dic3—61no—
202C2×D12—22no—
203C2×D12—21no—
204C2×D12—32no—
205C2×D12—32no—
206C2×D12—62no—
207C2×D12—62no—
208C2×D12—62no—
209C2×D12—62no—
210C2×D12—62no—
211C2×D12—62no—
212C2×D12—61no—
213C2×D12—61no—
214C2×D12—122no—
215C2×D12—122no—
216C2×D12D1214yes—
217C2×D12C22×D312yes—
218C2×C4×D3—24no—
219C2×C4×D3—44no—
220C2×Dic6—32no—
221C2×Dic6—32no—
222C2×Dic6—62no—
223C2×Dic6—62no—
224C2×Dic6—62no—
225C2×Dic6—62no—
226C2×Dic6—62no—
227C2×Dic6—62no—
228C2×Dic6—61no—
229C2×Dic6—61no—
230C2×Dic6—122no—
231C2×Dic6—122no—
232C2×C3×C8—32no—
233C2×C3×C8—32no—
234C2×C3×C8—62no—
235C2×C3×C8—62no—
236C3×C4⋊C4—32no—
237C3×C4⋊C4—61no—
238C3×C22⋊C4—64no—
239C3×C42—22no—
240C3×C42—22no—
241C3×C42D1212yes—
242C3×C42#6712yes—
243C3×C42C22×D312yes—
244C3×C42C22×D312yes—
245#214—68no—
246#213—68no—
247(C2×D3)⋊C4—24no—
248(C2×D3)⋊C4—68no—
249(C2×D3)⋊C4—68no—
250(C2×D3)⋊C4—64no—
251(C2×D3)⋊C4—64no—
252(C2×D3)⋊C4—64no—
253(C2×D3)⋊C4—64no—
254C4⋊Dic3—21no—
255C4⋊Dic3C22×D312yes—
256C2×C3⋊C8—22no—
257C2×C3⋊C8—22no—
258C2×C3⋊C8C22×D312yes—
259C2×C3⋊C8C22×D312yes—
260D24—68no—
261#204—68no—
262C22×C32#12112yes—
263C22×C32#13512yes—
264C22×C32AGL(1,ℤ/8)12yes—
265C22×C32C22×D411yescharacteristic
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—84no—
270C2×C3×D3—24no—
271C2×C3×D3—42no—
272C2×C3×D3—42no—
273C2×C3×D3—48no—
274C32×C4—22no—
275C32×C4—22no—
276C32×C4#12112yes—
277C32×C4C22×D411yescharacteristic
278C32×C4C2×#4111yescharacteristic
279C3⋊Dic3—42no—
280C3×Dic3—42no—
281C22×Q8—91no—
282C22×D4—31no—
283C22×D4—91no—
284C23×C4—61no—
285C2×SD16—94no—
286C2×SD16—184no—
287C2×D8—94no—
288C2×D8—184no—
289C22×C8—31no—
290C22×C8—31no—
291#124—94no—
292#124—182no—
293C4×D4—34no—
294C4×D4—62no—
295C2×C4⋊C4—31no—
296C2×C22⋊C4—61no—
297C2×C22⋊C4—181no—
298C2×C22⋊C4—181no—
299C2×C42D3211yescharacteristic
300C4⋊C8—34no—
301#103—94no—
302#102—94no—
303C23×C3—21no—
304C23×C3—64no—
305C23×C3—62no—
306C23×C3—122no—
307C23×C3—122no—
308C23×C3C2×D1211yescharacteristic
309C23×C3C2×#6711yescharacteristic
310C22×D3—24no—
311C22×D3—22no—
312C22×D3—42no—
313C22×D3—42no—
314C22×D3—64no—
315C22×D3—62no—
316C22×D3—62no—
317C22×D3—124no—
318C22×D3—124no—
319C22×D3—124no—
320C22×D3—122no—
321C22×D3—122no—
322C22×D3—122no—
323C22×D3—122no—
324C22×D3—122no—
325C22×D3—122no—
326C3×D4—34no—
327C3×D4—64no—
328C3×D4—62no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—21no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—21no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—42no—
340C2×C3×C4—42no—
341C2×C3×C4—62no—
342C2×C3×C4—128no—
343C2×C3×C4—122no—
344C2×C3×C4C2×D1212yes—
345C2×C3×C4C2×D1212yes—
346C2×C3×C4C2×D1212yes—
347C2×C3×C4C2×D1211yescharacteristic
348C2×C3×C4#23512yes—
349C2×C3×C4D3×D412yes—
350C2×C3×C4#23912yes—
351C2×C3×C4C2×#6712yes—
352C2×C3×C4C2×#6712yes—
353C2×C3×C4C2×#6711yescharacteristic
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D311yescharacteristic
356C2×Dic3—22no—
357C2×Dic3—42no—
358C2×Dic3—64no—
359C2×Dic3—62no—
360C2×Dic3—62no—
361C2×Dic3—124no—
362C2×Dic3—122no—
363C2×Dic3—122no—
364D12—24no—
365D12—22no—
366D12—62no—
367D12—62no—
368D12—62no—
369D12—62no—
370D12—122no—
371D12—122no—
372D12—124no—
373D12—122no—
374D12—122no—
375D12C2×D1214yes—
376C4×D3—48no—
377Dic6—62no—
378Dic6—62no—
379Dic6—62no—
380Dic6—62no—
381Dic6—122no—
382Dic6—122no—
383Dic6—124no—
384Dic6—122no—
385Dic6—122no—
386C3×C8—62no—
387C3×C8—62no—
388C3⋊C8—22no—
389C3⋊C8—22no—
390C2×C32#46314yescomplemented
391C2×C32C2×#12111yescharacteristic
392C2×C32C2×#13511yescharacteristic
393C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
394C3⋊D3—82no—
395C3×D3—44no—
396C24—61no—
397C24—181no—
398C2×Q8—92no—
399C2×Q8—181no—
400C2×Q8—182no—
401C2×Q8—182no—
402C2×D4—32no—
403C2×D4—34no—
404C2×D4—62no—
405C2×D4—61no—
406C2×D4—92no—
407C2×D4—182no—
408C2×D4—182no—
409C2×D4—181no—
410C22×C4—61no—
411C22×C4—64no—
412C22×C4—124no—
413C22×C4—181no—
414C22×C4#62611yescharacteristic
415C22×C4#62611yescharacteristic
416C22×C4C2×D3211yescharacteristic
417SD16—188no—
418D8—188no—
419C2×C8—32no—
420C2×C8—32no—
421C2×C8—62no—
422C2×C8—62no—
423C4⋊C4—32no—
424C4⋊C4—61no—
425C22⋊C4—64no—
426C22⋊C4—184no—
427C22⋊C4—184no—
428C42#62612yes—
429C42C2×D3212yes—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—64no—
435C22×C3—122no—
436C22×C3—122no—
437C22×C3—128no—
438C22×C3#89512yes—
439C22×C3#90412yes—
440C22×C3#90812yes—
441C22×C3#93012yes—
442C22×C3#93212yes—
443C22×C3#95012yes—
444C22×C3C22×D1211yescharacteristic
445C22×C3C22×#6711yescharacteristic
446C2×D3—24no—
447C2×D3—48no—
448C2×D3—42no—
449C2×D3—42no—
450C2×D3—124no—
451C2×D3—124no—
452C2×D3—124no—
453C2×D3—122no—
454C2×D3—122no—
455C2×D3—122no—
456C2×D3—122no—
457C2×D3—122no—
458C2×D3—122no—
459C2×D3—248no—
460C2×D3—244no—
461C2×D3—244no—
462C3×C4—22no—
463C3×C4—22no—
464C3×C4—22no—
465C3×C4—22no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—22no—
469C3×C4—42no—
470C3×C4—42no—
471C3×C4—122no—
472C3×C4#89512yes—
473C3×C4#93012yes—
474C3×C4C22×D1211yescharacteristic
475C3×C4C2×#23511yescharacteristic
476C3×C4C2×D3×D411yescharacteristic
477C3×C4C2×#23911yescharacteristic
478Dic3—42no—
479Dic3—124no—
480Dic3—122no—
481Dic3—122no—
482C32C2×#46311yescharacteristic, complemented, Sylow
483C23—62no—
484C23—64no—
485C23—122no—
486C23—122no—
487C23—182no—
488C23—362no—
489C23—362no—
490C23—362no—
491C23C2×#62611yescharacteristic
492Q8—182no—
493Q8—182no—
494Q8—362no—
495D4—34no—
496D4—62no—
497D4—64no—
498D4—182no—
499D4—182no—
500D4—362no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—62no—
504C2×C4—128no—
505C2×C4—122no—
506C2×C4—182no—
507C2×C4—362no—
508C2×C4#379912yes—
509C2×C4D3×D1212yes—
510C2×C4C2×#62612yes—
511C2×C4C2×#62612yes—
512C2×C4C2×#62611yescharacteristic
513C2×C4C22×D3211yescharacteristic
514C8—62no—
515C8—62no—
516C2×C3—24no—
517C2×C3—21no—
518C2×C3—21no—
519C2×C3—21no—
520C2×C3—124no—
521C2×C3#484414yescomplemented
522C2×C3#501614yescomplemented
523C2×C3C2×#89511yescharacteristic
524C2×C3C2×#90411yescharacteristic
525C2×C3C2×#90811yescharacteristic
526C2×C3C2×#93011yescharacteristic
527C2×C3C2×#93211yescharacteristic
528C2×C3C2×#95011yescharacteristic
529D3—44no—
530D3—244no—
531D3—242no—
532D3—242no—
533C22—64no—
534C22—128no—
535C22—122no—
536C22—122no—
537C22—362no—
538C22—362no—
539C22—362no—
540C22—724no—
541C22#6382912yes—
542C22#6383012yes—
543C22#6390912yes—
544C22C22×#62611yescharacteristic
545C4—22no—
546C4—22no—
547C4—122no—
548C4—362no—
549C4#6390912yes—
550C4C2×#379911yescharacteristic
551C4C2×D3×D1211yescharacteristic
552C3—21no—
553C3C2×#484411yescharacteristic, complemented
554C3C2×#501611yescharacteristic, complemented
555C2—124no—
556C2—722no—
557C2#1059036614yesdirect product factor
558C2C2×#6382911yescharacteristic
559C2C2×#6383011yescharacteristic
560C2C2×#6390911yescharacteristic
subgroupG/H
centerC23C2×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC23×C32C2×D4
prime radicalC22×#3714C2
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×#64084C2semidirect
2. C2×C3×C4×D12C2semidirect
3. C22×#3716C2semidirect
5. C2×C3×C4⋊(C3⋊C8)C2semidirect
6. C2×#63567C2semidirect
7. C2×#63564C2semidirect
8. #10590366C2direct (N × H)
19. #64084C22semidirect
25. C3×C4×D12C22semidirect
27. C2×#3716C22semidirect
30. C3×C4⋊(C3⋊C8)C22semidirect
31. #63567C22semidirect
32. #63564C22semidirect
41. C2×C4×D12D3semidirect
48. C2×C4⋊(C3⋊C8)D3semidirect
129. C4×D12C2×D3semidirect
135. C4⋊(C3⋊C8)C2×D3semidirect
390. C2×C32#463semidirect
482. C32C2×#463semidirect
521. C2×C3#4844semidirect
522. C2×C3#5016semidirect
553. C3C2×#4844semidirect
554. C3C2×#5016semidirect
557. C2#10590366direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640842
C2×C3×C4×D122
C22×#37162
C22×#37142
C2×C3×C4⋊(C3⋊C8)2
C2×#635672
C2×#635642
#105903662
C2×#50163
C2×#48443