Finite Group Databasebeta

← C2×#10596501 #11918678

Subgroups — C2×#10596501 #11918678

Order 1152.

2846 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C211yesmaximal, characteristic, complemented
2C22×#3802C211yesmaximal, characteristic, complemented
3C2×#64283C211yesmaximal, characteristic, complemented
4C2×#64236C214yesmaximal, complemented
5C2×#64227C212yesmaximal, complemented
6#10596501C2116yesmaximal, direct product factor
7C2×#64225C212yesmaximal, complemented
8C2×#64224C214yesmaximal, complemented
9C23×D32—21no—
10C22×C4×C3⋊D3C2211yescharacteristic
11C2×C3×#235—21no—
12C22×C3×D12—21no—
13C2×#3811—21no—
14C22×#625C2212yescomplemented
15C2×#3805C2212yescomplemented
16#64306—24no—
17#64306C2218yescomplemented
18C2×#3802—21no—
19C2×#3802—24no—
20C2×#3802—21no—
21C2×#3802C2212yes—
22C2×#3802C2218yescomplemented
23C2×#3802C2212yescomplemented
24C2×#3802C2211yescharacteristic, complemented
25C2×C4×D32—21no—
26C2×#3798C2212yescomplemented
27C2×#3797C2211yescharacteristic, complemented
28C2×#3796—21no—
29C2×#3792C2212yescomplemented
30#64283C2218yescomplemented
31C2×#3788C2212yescomplemented
32C2×#3787C2212yescomplemented
33C2×#3775C2218yescomplemented
34#64236C22132yescomplemented
35C2×#3774C2218yescomplemented
36#64227C22116yescomplemented
37#64225C22116yescomplemented
38#64224C22132yescomplemented
39C2×D3×#41—61no—
40C22×D3×D4—61no—
41C23×C3⋊D3D411yescharacteristic
42C23×C3×D3—22no—
43C22×D32—21no—
44C22×D32—22no—
45C22×D32—28no—
46C22×D32—22no—
47C22×D32—48no—
48C22×C32×C4D411yescharacteristic
49C22×C3⋊Dic3C2311yescharacteristic
50C2×C4×C3⋊D3D411yescharacteristic
51C2×C4×C3⋊D3D411yescharacteristic
52C2×C4×C3⋊D3D414yes—
53C2×C4×C3⋊D3C2311yescharacteristic
54C2×C4×C3⋊D3C2311yescharacteristic
55C2×C4×C3⋊D3C2314yes—
56C2×C3×#67—22no—
57C3×#235—28no—
58C2×C3×D12—21no—
59C2×C3×D12—22no—
60C2×C3×D12—28no—
61C2×C3×D12—22no—
62C2×C3×C4×D3—22no—
63C2×C3×Dic6—21no—
64#3811—28no—
65C2×#627C2312yescomplemented
66C2×#626—22no—
67C2×#625—24no—
68C2×#625—22no—
69C2×#625C2314yes—
70C2×#625C2318yescomplemented
71C2×#625C2312yescomplemented
72C2×#624—21no—
73#3805—24no—
74#3805C2318yescomplemented
75C2×D3×Dic3—22no—
76#3802—24no—
77#3802—24no—
78#3802—28no—
79#3802—28no—
80#3802—22no—
81#3802C2318yes—
82#3802C2318yescomplemented
83#3802C2314yescomplemented
84C4×D32—28no—
85#3798—24no—
86#3798C2318yescomplemented
87#3797—22no—
88#3797C2314yescomplemented
89#3796—28no—
90#3792C2318yescomplemented
91C2×#622C2314yescomplemented
92#3788C2318yescomplemented
93#3787C2318yescomplemented
94#3775C23132yescomplemented
95#3774C23132yescomplemented
96C22×AGL(1,ℤ/8)—91nomaximal, Sylow
97C24×D3—62no—
98C2×C3×#41—61no—
99C22×C3×D4—61no—
100C22×#67—62no—
101D3×#41—68no—
102D3×#41—68no—
103C2×#239—61no—
104C2×D3×Q8—61no—
105C2×#237—62no—
106C2×#237—61no—
107C2×D3×D4—62no—
108C2×D3×D4—68no—
109C2×D3×D4—62no—
110C2×D3×D4—61no—
111C2×D3×D4—62no—
112C2×D3×D4—62no—
113C2×D3×D4—68no—
114C2×D3×D4—62no—
115C2×#235—21no—
116C2×#235—62no—
117C22×D12—21no—
118C22×C4×D3—61no—
119C22×C4×D3—61no—
120C22×C4×D3—62no—
121C23×C32C2×D411yescharacteristic
122C22×C3⋊D3—24no—
123C22×C3⋊D3C2×D411yescharacteristic
124C22×C3⋊D3C2×D414yes—
125C22×C3⋊D3C2×D411yescharacteristic
126C22×C3×D3—24no—
127C22×C3×D3—28no—
128C22×C3×D3—22no—
129C22×C3×D3—48no—
130C2×D32—28no—
131C2×D32—28no—
132C2×D32—24no—
133C2×D32—48no—
134C2×D32—432no—
135C2×D32—44no—
136C2×D32—48no—
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2×D411yescharacteristic
139C2×C32×C4C2×D414yes—
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2411yescharacteristic
143C2×C3⋊Dic3C2412yes—
144C4×C3⋊D3C2×D414yes—
145C4×C3⋊D3C2×D412yes—
146C4×C3⋊D3C2×D412yes—
147C4×C3⋊D3C2×D414yes—
148C4×C3⋊D3C2412yes—
149C4×C3⋊D3C2412yes—
150C3×#67—28no—
151C2×C3×Dic3—22no—
152C3×D12—24no—
153C3×D12—28no—
154C3×D12—28no—
155C3×C4×D3—28no—
156C3×Dic6—24no—
157#627—22no—
158#627C2414yescomplemented
159#626—28no—
160#625—22no—
161#625—24no—
162#625—28no—
163#625C2418yes—
164#625C2414yescomplemented
165#624—24no—
166D3×Dic3—28no—
167#622C2418yescomplemented
168C22×#41—91no—
169C23×D4—91no—
170C2×AGL(1,ℤ/8)—94no—
171C2×AGL(1,ℤ/8)—916no—
172C2×AGL(1,ℤ/8)—94no—
173C22×SD16—92no—
174C22×D8—92no—
175C22×M16—91no—
176C24×C3—62no—
177C23×D3—22no—
178C23×D3—61no—
179C23×D3—61no—
180C23×D3—62no—
181C23×D3—64no—
182C23×D3—616no—
183C23×D3—64no—
184C23×D3—1216no—
185C3×#41—68no—
186C2×C3×Q8—61no—
187C2×C3×D4—62no—
188C2×C3×D4—68no—
189C2×C3×D4—62no—
190C2×C3×D4—61no—
191C2×C3×D4—62no—
192C22×C3×C4—21no—
193C22×C3×C4—21no—
194C22×C3×C4—62no—
195C2×#67—22no—
196C2×#67—64no—
197C2×#67—62no—
198C2×#67—68no—
199C2×#67—62no—
200C2×#67—68no—
201C2×#67—64no—
202C22×Dic3—61no—
203C22×Dic3—61no—
204C22×Dic3—62no—
205#239—68no—
206D3×Q8—64no—
207D3×Q8—64no—
208#237—68no—
209#237—68no—
210#237—68no—
211D3×D4—68no—
212D3×D4—68no—
213D3×D4—64no—
214D3×D4—68no—
215D3×D4—616no—
216D3×D4—616no—
217D3×D4—68no—
218D3×D4—64no—
219D3×D4—616no—
220#235—28no—
221#235—68no—
222#235—68no—
223C2×D12—22no—
224C2×D12—28no—
225C2×D12—22no—
226C2×D12—21no—
227C2×D12—62no—
228C2×C4×D3—22no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—61no—
233C2×C4×D3—64no—
234C2×C4×D3—61no—
235C2×C4×D3—61no—
236C2×C4×D3—64no—
237C2×C4×D3—61no—
238C2×C4×D3—61no—
239C2×C4×D3—64no—
240C2×C4×D3—64no—
241C2×C4×D3—616no—
242C2×C4×D3—62no—
243C2×C4×D3—62no—
244C2×Dic6—21no—
245C2×Dic6—62no—
246C22×C32—22no—
247C22×C32C22×D412yes—
248C22×C32C22×D411yescharacteristic
249C2×C3⋊D3—22no—
250C2×C3⋊D3—28no—
251C2×C3⋊D3AGL(1,ℤ/8)14yescomplemented
252C2×C3⋊D3C22×D412yes—
253C2×C3⋊D3C22×D412yes—
254C2×C3×D3—24no—
255C2×C3×D3—28no—
256C2×C3×D3—416no—
257C2×C3×D3—48no—
258C2×C3×D3—44no—
259D32—416no—
260D32—48no—
261D32—416no—
262C32×C4C22×D412yes—
263C32×C4C22×D412yes—
264C3⋊Dic3C22×D412yes—
265C3⋊Dic3C22×D411yescharacteristic
266C3⋊Dic3C2511yescharacteristic
267C3×Dic3—24no—
268C25—181no—
269C2×#41—61no—
270C2×#41—92no—
271C2×#41—92no—
272C2×#41—98no—
273C2×#41—181no—
274C2×#41—184no—
275C22×Q8—91no—
276C22×D4—61no—
277C22×D4—91no—
278C22×D4—92no—
279C22×D4—98no—
280C22×D4—92no—
281C22×D4—92no—
282C22×D4—181no—
283C22×D4—184no—
284C22×D4—181no—
285C22×D4—181no—
286C23×C4—91no—
287C23×C4—181no—
288AGL(1,ℤ/8)—932no—
289AGL(1,ℤ/8)—932no—
290C2×SD16—916no—
291C2×SD16—98no—
292C2×D8—916no—
293C2×D8—98no—
294C2×M16—92no—
295C2×M16—98no—
296C2×M16—92no—
297C22×C8—92no—
298C23×C3—21no—
299C23×C3—21no—
300C23×C3—62no—
301C23×C3—68no—
302C23×C3—64no—
303C23×C3—128no—
304C22×D3—22no—
305C22×D3—28no—
306C22×D3—24no—
307C22×D3—48no—
308C22×D3—61no—
309C22×D3—61no—
310C22×D3—64no—
311C22×D3—61no—
312C22×D3—61no—
313C22×D3—64no—
314C22×D3—68no—
315C22×D3—616no—
316C22×D3—616no—
317C22×D3—68no—
318C22×D3—124no—
319C22×D3—128no—
320C22×D3—1216no—
321C22×D3—1264no—
322C22×D3—1216no—
323C3×Q8—64no—
324C3×D4—68no—
325C3×D4—68no—
326C3×D4—64no—
327C3×D4—68no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—24no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—24no—
334C2×C3×C4—68no—
335C2×C3×C4—62no—
336#67—28no—
337#67—68no—
338#67—64no—
339#67—68no—
340#67—64no—
341#67—68no—
342#67—616no—
343C2×Dic3—22no—
344C2×Dic3—61no—
345C2×Dic3—62no—
346C2×Dic3—62no—
347C2×Dic3—61no—
348C2×Dic3—61no—
349C2×Dic3—62no—
350C2×Dic3—62no—
351C2×Dic3—61no—
352C2×Dic3—68no—
353D12—28no—
354D12—28no—
355D12—24no—
356D12—68no—
357C4×D3—28no—
358C4×D3—64no—
359C4×D3—62no—
360C4×D3—64no—
361C4×D3—62no—
362C4×D3—64no—
363C4×D3—62no—
364C4×D3—62no—
365C4×D3—64no—
366C4×D3—62no—
367C4×D3—62no—
368C4×D3—62no—
369C4×D3—62no—
370C4×D3—68no—
371C4×D3—68no—
372Dic6—24no—
373Dic6—64no—
374Dic6—64no—
375C2×C32—22no—
376C2×C32C2×AGL(1,ℤ/8)12yescomplemented
377C2×C32C23×D411yescharacteristic
378C3⋊D3—22no—
379C3⋊D3C2×AGL(1,ℤ/8)14yescomplemented
380C3×D3—48no—
381C3×D3—44no—
382C24—62no—
383C24—91no—
384C24—181no—
385C24—188no—
386C24—182no—
387C24—182no—
388C24—368no—
389#41—68no—
390#41—98no—
391#41—98no—
392#41—184no—
393#41—184no—
394#41—188no—
395C2×Q8—61no—
396C2×Q8—92no—
397C2×Q8—94no—
398C2×Q8—182no—
399C2×D4—62no—
400C2×D4—68no—
401C2×D4—62no—
402C2×D4—62no—
403C2×D4—61no—
404C2×D4—94no—
405C2×D4—98no—
406C2×D4—98no—
407C2×D4—92no—
408C2×D4—94no—
409C2×D4—98no—
410C2×D4—182no—
411C2×D4—188no—
412C2×D4—184no—
413C2×D4—188no—
414C2×D4—184no—
415C2×D4—182no—
416C2×D4—184no—
417C2×D4—182no—
418C2×D4—188no—
419C22×C4—62no—
420C22×C4—91no—
421C22×C4—91no—
422C22×C4—94no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—94no—
426C22×C4—91no—
427C22×C4—188no—
428C22×C4—181no—
429C22×C4—182no—
430C22×C4GO+(4,𝔽2)11yescharacteristic
431SD16—932no—
432D8—932no—
433M16—98no—
434M16—98no—
435C2×C8—98no—
436C2×C8—94no—
437C22×C3—24no—
438C22×C3—22no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—42no—
443C22×C3—64no—
444C22×C3—68no—
445C22×C3—1216no—
446C22×C3—128no—
447C22×C3—124no—
448C2×D3—24no—
449C2×D3—28no—
450C2×D3—416no—
451C2×D3—48no—
452C2×D3—44no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—62no—
456C2×D3—64no—
457C2×D3—64no—
458C2×D3—62no—
459C2×D3—616no—
460C2×D3—64no—
461C2×D3—128no—
462C2×D3—122no—
463C2×D3—1232no—
464C2×D3—1232no—
465C2×D3—1216no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—22no—
469C3×C4—22no—
470C3×C4—64no—
471Dic3—24no—
472Dic3—61no—
473Dic3—61no—
474Dic3—62no—
475Dic3—62no—
476Dic3—61no—
477Dic3—61no—
478C32C22×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
479C23—68no—
480C23—62no—
481C23—64no—
482C23—91no—
483C23—94no—
484C23—91no—
485C23—128no—
486C23—184no—
487C23—184no—
488C23—188no—
489C23—188no—
490C23—368no—
491C23—364no—
492C23—3632no—
493C23—368no—
494C23C2×GO+(4,𝔽2)11yescharacteristic
495Q8—64no—
496Q8—94no—
497Q8—182no—
498D4—68no—
499D4—68no—
500D4—68no—
501D4—64no—
502D4—94no—
503D4—98no—
504D4—188no—
505D4—188no—
506D4—184no—
507D4—182no—
508C2×C4—62no—
509C2×C4—68no—
510C2×C4—92no—
511C2×C4—92no—
512C2×C4—91no—
513C2×C4—91no—
514C2×C4—92no—
515C2×C4—92no—
516C2×C4—94no—
517C2×C4—92no—
518C2×C4—94no—
519C2×C4—92no—
520C2×C4—184no—
521C2×C4—188no—
522C2×C4C2×GO+(4,𝔽2)14yes—
523C2×C4C2×GO+(4,𝔽2)11yescharacteristic
524C2×C4C2×GO+(4,𝔽2)11yescharacteristic
525C8—98no—
526C2×C3—24no—
527C2×C3—22no—
528C2×C3—22no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—42no—
532C2×C3—128no—
533C2×C3—124no—
534D3—48no—
535D3—44no—
536D3—64no—
537D3—64no—
538D3—64no—
539D3—122no—
540C22—22no—
541C22—64no—
542C22—68no—
543C22—94no—
544C22—92no—
545C22—92no—
546C22—1216no—
547C22—128no—
548C22—124no—
549C22—188no—
550C22—182no—
551C22—3616no—
552C22—368no—
553C22—3616no—
554C22C22×GO+(4,𝔽2)12yes—
555C22C22×GO+(4,𝔽2)11yescharacteristic
556C4—64no—
557C4—91no—
558C4—92no—
559C4—91no—
560C4C22×GO+(4,𝔽2)12yes—
561C4C22×GO+(4,𝔽2)12yes—
562C3—21no—
563C3—21no—
564C2—22no—
565C2—94no—
566C2—128no—
567C2—124no—
568C2—182no—
569C2#1059650112yesdirect product factor
570C2C23×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
centerC22C22×GO+(4,𝔽2)
commutator, cosocleC3⋊Dic3C25
FrattiniC2C23×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32C22×AGL(1,ℤ/8)
LCSG ▷ C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×#64306C2semidirect
2. C22×#3802C2semidirect
3. C2×#64283C2semidirect
4. C2×#64236C2semidirect
5. C2×#64227C2semidirect
6. #10596501C2direct (N × H)
7. C2×#64225C2semidirect
8. C2×#64224C2semidirect
14. C22×#625C22semidirect
15. C2×#3805C22semidirect
17. #64306C22semidirect
22. C2×#3802C22semidirect
23. C2×#3802C22semidirect
24. C2×#3802C22semidirect
26. C2×#3798C22semidirect
27. C2×#3797C22semidirect
29. C2×#3792C22semidirect
30. #64283C22semidirect
31. C2×#3788C22semidirect
32. C2×#3787C22semidirect
33. C2×#3775C22semidirect
34. #64236C22semidirect
35. C2×#3774C22semidirect
36. #64227C22semidirect
37. #64225C22semidirect
38. #64224C22semidirect
65. C2×#627C23semidirect
70. C2×#625C23semidirect
71. C2×#625C23semidirect
74. #3805C23semidirect
82. #3802C23semidirect
83. #3802C23semidirect
86. #3798C23semidirect
88. #3797C23semidirect
90. #3792C23semidirect
91. C2×#622C23semidirect
92. #3788C23semidirect
93. #3787C23semidirect
94. #3775C23semidirect
95. #3774C23semidirect
158. #627C24semidirect
164. #625C24semidirect
167. #622C24semidirect
251. C2×C3⋊D3AGL(1,ℤ/8)semidirect
376. C2×C32C2×AGL(1,ℤ/8)semidirect
379. C3⋊D3C2×AGL(1,ℤ/8)semidirect
478. C32C22×AGL(1,ℤ/8)semidirect
569. C2#10596501direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643062
C22×#38022
C2×#642832
C2×#642362
C2×#642272
#105965012
C2×#642252
C2×#642242
C22×AGL(1,ℤ/8)9