Finite Group Databasebeta

← C2×#10594691 #11918941

Subgroups — C2×#10594691 #11918941

Order 1152.

2949 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C212yesmaximal, complemented
2C2×#64113C211yesmaximal, characteristic, complemented
3C22×C3×Dic12C211yesmaximal, characteristic, complemented
4C2×C3×#901C211yesmaximal, characteristic, complemented
5C2×#63833C212yesmaximal, complemented
6C2×#63808C212yesmaximal, complemented
7#10594691C2116yesmaximal, direct product factor
8C2×#63801C214yesmaximal, complemented
9C2×D3×Dic12C212yesmaximal, complemented
10C2×#5766—31nomaximal
11C2×#5753—31nomaximal
12C2×#3828C2212yes—
13C2×C3×#235C2211yescharacteristic
14C22×C3×Dic6C2212yes—
15C2×#3804—24no—
16C2×#3799C2214yes—
17C2×#3797—22no—
18#64297—28no—
19#64297C22116yescomplemented
20C2×#3796—22no—
21C2×D3×Dic6C2214yes—
22C22×C32×C8C2211yescharacteristic
23C2×#3746C2211yescharacteristic
24#64113C2218yescomplemented
25C2×#3745C2211yescharacteristic
26C2×#3744C2212yes—
27C2×C3×#208C2211yescharacteristic
28C2×C3×Dic12C2212yes—
29C2×C3×Dic12C2212yes—
30C2×C3×Dic12C2218yescomplemented
31C3×#901C2218yescomplemented
32C2×C3×ΓL(1,𝔽25)C2212yes—
33C2×C3×D3×C8C2212yes—
34C2×#3719C2214yes—
35#63833C22116yescomplemented
36C2×#3717C2214yes—
37#63808C22116yescomplemented
38#63801C22132yescomplemented
39D3×Dic12C22116yescomplemented
40C2×#1010—32no—
41C2×#1007—32no—
42C22×C3×Q16—31no—
43C2×C3×#131—31no—
44C2×#942—32no—
45#5766—316no—
46C2×#919—32no—
47C2×#918—34no—
48C2×D3×Q16—32no—
49#5753—316no—
50C2×#909—32no—
51C2×#909—34no—
52C22×Dic12—32no—
53C22×Dic12D311yescharacteristic, complemented
54C2×#904—31no—
55C2×#904—31no—
56C2×#904—32no—
57C2×#904—61no—
58C2×#901D311yescharacteristic, complemented
59C22×C32×C4C2311yescharacteristic
60C2×#638—22no—
61#3828—24no—
62#3828C2318yes—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C4×C3⋊D3—22no—
65C2×#634C2312yes—
66C2×C3×#67D412yes—
67C22×C3×Dic3—22no—
68C3×#235D414yes—
69C3×#235C2314yes—
70C2×C3×D12D411yescharacteristic
71C2×C3×C4×D3C2312yes—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—24no—
74C2×C3×Dic6D411yescharacteristic
75C2×C3×Dic6C2314yes—
76C2×C3×Dic6C2318yes—
77C2×#627—24no—
78C2×#626—24no—
79C2×#624—24no—
80#3804—232no—
81C2×D3×Dic3—24no—
82#3799—28no—
83#3799C23116yes—
84#3797—216no—
85#3796—216no—
86D3×Dic6—28no—
87D3×Dic6C23116yes—
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2314yes—
91#3746C2314yes—
92#3745C2314yes—
93#3744C2318yes—
94C3×#208C2314yes—
95C2×C3×C3⋊C8C2312yes—
96C3×Dic12C2318yes—
97C3×Dic12C2318yes—
98C3×ΓL(1,𝔽25)C2318yes—
99C3×D3×C8C2318yes—
100#3719C23116yes—
101#3717C23116yes—
102C2×#578—91noSylow
103C2×C3×#41—31no—
104C22×C3×Q8—32no—
105#1010—316no—
106#1010—68no—
107#1007—316no—
108#1007—68no—
109C2×#239—34no—
110C2×#239—62no—
111C2×D3×Q8—34no—
112C2×D3×Q8—62no—
113C2×D3×Q8—62no—
114C2×#237—62no—
115C2×#237—64no—
116C2×#235—32no—
117C2×#235—32no—
118C2×#235—34no—
119C2×#235—62no—
120C2×#235—64no—
121C2×#235C2×D311yescharacteristic
122C22×Dic6—34no—
123C22×Dic6C2×D312yes—
124C2×C3×Q16—32no—
125C2×C3×Q16—32no—
126C2×C3×Q16—38no—
127C3×#131—38no—
128C2×C3×M16—31no—
129C2×C3×M16—32no—
130C22×C3×C8—21no—
131C22×C3×C8—32no—
132C22×C3×C8C2×D311yescharacteristic
133C22×C3×C8C2×D311yescharacteristic
134C2×#216—34no—
135#942—316no—
136C2×#215—34no—
137C2×#208C2×D311yescharacteristic
138#919—316no—
139#918—332no—
140D3×Q16—316no—
141#909—316no—
142#909—332no—
143C2×Dic12—34no—
144C2×Dic12—31no—
145C2×Dic12—31no—
146C2×Dic12—316no—
147C2×Dic12—61no—
148C2×Dic12C2×D312yes—
149C2×Dic12C2×D312yes—
150C2×Dic12C2×D318yescomplemented
151#904—38no—
152#904—38no—
153#904—316no—
154#904—68no—
155C2×D24—31no—
156C2×D24—31no—
157C2×D24—61no—
158C2×#204—34no—
159C2×#204—32no—
160C2×#204—32no—
161C2×#204—62no—
162#901C2×D318yescomplemented
163C2×ΓL(1,𝔽25)C2×D312yes—
164C2×D3×C8C2×D312yes—
165C23×C32C2×D411yescharacteristic
166C22×C3⋊D3—22no—
167C22×C3×D3C2×D412yes—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2411yescharacteristic
171C2×C32×C4C2412yes—
172#638—28no—
173C2×C3⋊Dic3—22no—
174C4⋊(C3⋊D3)—22no—
175C4⋊(C3⋊D3)C2414yes—
176C4×C3⋊D3—28no—
177#634—22no—
178#634C2414yes—
179C3×#67C2×D418yes—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—28no—
182C2×C3×Dic3C2×D412yes—
183C3×D12C2×D414yes—
184C3×C4×D3C2×D414yes—
185C3×C4×D3C2414yes—
186C3×Dic6—24no—
187C3×Dic6—28no—
188C3×Dic6C2×D414yes—
189C3×Dic6C2418yes—
190#627—216no—
191#626—216no—
192#624—216no—
193D3×Dic3—216no—
194C32×C8C2412yes—
195C32×C8C2412yes—
196C3×C3⋊C8C2414yes—
197C2×2−1+4—92no—
198#578—916no—
199C2×#137—94no—
200C2×#137—92no—
201C2×#135—92no—
202C2×#135—91no—
203C22×Q16—31no—
204C22×Q16—92no—
205C2×#131—31no—
206C3×#41—34no—
207C3×#41—34no—
208C2×C3×Q8—31no—
209C2×C3×Q8—34no—
210C2×C3×Q8—38no—
211C2×C3×Q8—62no—
212C2×C3×Q8—64no—
213C2×C3×D4—32no—
214C2×C3×D4—31no—
215C22×C3×C4—21no—
216C22×C3×C4—32no—
217C22×C3×C4—62no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—64no—
221C2×#67—62no—
222C2×#67—62no—
223C2×#67—122no—
224C2×#67D1212yes—
225C22×Dic3—22no—
226C22×Dic3—64no—
227#239—316no—
228#239—616no—
229#239—68no—
230D3×Q8—316no—
231D3×Q8—616no—
232D3×Q8—68no—
233D3×Q8—616no—
234#237—616no—
235#237—632no—
236#235—38no—
237#235—38no—
238#235—316no—
239#235—68no—
240#235—68no—
241#235—64no—
242#235—64no—
243#235—632no—
244#235—124no—
245#235D1214yes—
246#235C22×D314yes—
247C2×D12—32no—
248C2×D12—32no—
249C2×D12—62no—
250C2×D12—64no—
251C2×D12D1211yescharacteristic
252C2×C4×D3—64no—
253C2×C4×D3—64no—
254C2×C4×D3—62no—
255C2×C4×D3—62no—
256C2×C4×D3—64no—
257C2×C4×D3—122no—
258C2×C4×D3C22×D312yes—
259C2×Dic6—22no—
260C2×Dic6—24no—
261C2×Dic6—32no—
262C2×Dic6—32no—
263C2×Dic6—316no—
264C2×Dic6—62no—
265C2×Dic6—68no—
266C2×Dic6—64no—
267C2×Dic6—64no—
268C2×Dic6D1211yescharacteristic
269C2×Dic6C22×D314yes—
270C2×Dic6C22×D318yes—
271C3×Q16—38no—
272C3×Q16—38no—
273C3×M16—34no—
274C3×M16—38no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—24no—
278C2×C3×C8—32no—
279C2×C3×C8—38no—
280C2×C3×C8C22×D311yescharacteristic
281C2×C3×C8C22×D311yescharacteristic
282C2×C3×C8C22×D314yes—
283C2×C3×C8C22×D311yescharacteristic
284C2×C3×C8C22×D311yescharacteristic
285C2×C3×C8C22×D314yes—
286#216—316no—
287#215—316no—
288#208C22×D314yes—
289C2×C3⋊C8C22×D312yes—
290Dic12—316no—
291Dic12—34no—
292Dic12—34no—
293Dic12—64no—
294Dic12C22×D318yes—
295Dic12C22×D318yes—
296D24—34no—
297D24—34no—
298D24—64no—
299#204—316no—
300#204—38no—
301#204—38no—
302#204—68no—
303ΓL(1,𝔽25)C22×D318yes—
304D3×C8C22×D318yes—
305C22×C32—22no—
306C22×C32C22×D412yes—
307C22×C32C22×D411yescharacteristic
308C2×C3⋊D3—24no—
309C2×C3⋊D3—44no—
310C2×C3×D3—24no—
311C2×C3×D3C22×D414yes—
312C32×C4C22×D412yes—
313C32×C4C22×D411yescharacteristic
314C32×C4C2511yescharacteristic
315C3⋊Dic3—24no—
316C3×Dic3—28no—
317C3×Dic3C22×D414yes—
3182−1+4—916no—
3192−1+4—188no—
320C2×#41—31no—
321C2×#41—94no—
322C2×#41—92no—
323C2×#41—184no—
324C2×#41—182no—
325C22×Q8—32no—
326C22×Q8—94no—
327C22×Q8—182no—
328#137—932no—
329#137—916no—
330#135—916no—
331#135—98no—
332C2×Q16—32no—
333C2×Q16—32no—
334C2×Q16—38no—
335C2×Q16—916no—
336C2×Q16—94no—
337C2×Q16—91no—
338C2×SD16—94no—
339C2×SD16—92no—
340C2×D8—91no—
341#131—38no—
342C2×M16—31no—
343C2×M16—32no—
344C22×C8—32no—
345C22×C8D3211yescharacteristic
346C23×C3—21no—
347C23×C3—32no—
348C23×C3C2×D1211yescharacteristic
349C23×C3D3×D411yescharacteristic
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—122no—
353C22×D3C2×D1212yes—
354C3×Q8—34no—
355C3×Q8—38no—
356C3×Q8—64no—
357C3×Q8—68no—
358C3×D4—38no—
359C3×D4—34no—
360C2×C3×C4—21no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—22no—
364C2×C3×C4—32no—
365C2×C3×C4—34no—
366C2×C3×C4—34no—
367C2×C3×C4—64no—
368C2×C3×C4—68no—
369C2×C3×C4C2×D1211yescharacteristic
370C2×C3×C4C2×D1212yes—
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D412yes—
373C2×C3×C4C23×D311yescharacteristic
374C2×C3×C4C23×D312yes—
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D312yes—
377#67—616no—
378#67—68no—
379#67—68no—
380#67—128no—
381#67C2×D1218yes—
382C2×Dic3—24no—
383C2×Dic3—28no—
384C2×Dic3—616no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—122no—
388C2×Dic3C2×D1212yes—
389D12—34no—
390D12—34no—
391D12—64no—
392D12—616no—
393D12—62no—
394D12—62no—
395D12—122no—
396D12C2×D1214yes—
397C4×D3—616no—
398C4×D3—616no—
399C4×D3—68no—
400C4×D3—68no—
401C4×D3—616no—
402C4×D3—128no—
403C4×D3C2×D1214yes—
404C4×D3C23×D314yes—
405Dic6—24no—
406Dic6—28no—
407Dic6—34no—
408Dic6—34no—
409Dic6—64no—
410Dic6—616no—
411Dic6—62no—
412Dic6—62no—
413Dic6—616no—
414Dic6—122no—
415Dic6C2×D1214yes—
416Dic6C23×D318yes—
417C3×C8—22no—
418C3×C8—22no—
419C3×C8—34no—
420C3×C8C23×D312yes—
421C3×C8C23×D312yes—
422C3×C8C23×D312yes—
423C3×C8C23×D312yes—
424C3⋊C8C23×D314yes—
425C2×C32—22no—
426C2×C32#57812yescomplemented
427C2×C32C23×D411yescharacteristic
428C3⋊D3—44no—
429C3×D3—24no—
430#41—34no—
431#41—34no—
432#41—916no—
433#41—98no—
434#41—188no—
435#41—1832no—
436#41—1816no—
437#41—184no—
438C2×Q8—31no—
439C2×Q8—34no—
440C2×Q8—38no—
441C2×Q8—62no—
442C2×Q8—64no—
443C2×Q8—916no—
444C2×Q8—92no—
445C2×Q8—184no—
446C2×Q8—188no—
447C2×Q8—1816no—
448C2×D4—32no—
449C2×D4—31no—
450C2×D4—92no—
451C2×D4—184no—
452C2×D4—182no—
453C22×C4—32no—
454C22×C4—62no—
455C22×C4—184no—
456C22×C4—184no—
457C22×C4—182no—
458C22×C4C2×D3211yescharacteristic
459Q16—38no—
460Q16—38no—
461Q16—916no—
462Q16—94no—
463SD16—916no—
464SD16—98no—
465D8—94no—
466M16—34no—
467M16—38no—
468C2×C8—32no—
469C2×C8—38no—
470C2×C8C2×D3211yescharacteristic
471C2×C8C2×D3211yescharacteristic
472C2×C8C2×D3214yes—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—21no—
477C22×C3—34no—
478C22×C3—42no—
479C22×C3—64no—
480C22×C3C22×D1212yes—
481C22×C3C22×D1211yescharacteristic
482C22×C3C2×D3×D412yes—
483C22×C3C2×D3×D411yescharacteristic
484C2×D3—24no—
485C2×D3—64no—
486C2×D3—64no—
487C2×D3—124no—
488C2×D3—124no—
489C2×D3—124no—
490C2×D3—244no—
491C2×D3C22×D1214yes—
492C3×C4—21no—
493C3×C4—22no—
494C3×C4—21no—
495C3×C4—34no—
496C3×C4—68no—
497C3×C4C22×D1211yescharacteristic
498C3×C4C22×D1212yes—
499C3×C4C2×D3×D411yescharacteristic
500C3×C4C2×D3×D412yes—
501C3×C4C24×D311yescharacteristic
502C3×C4C24×D311yescharacteristic
503Dic3—28no—
504Dic3—64no—
505Dic3—64no—
506Dic3—124no—
507Dic3C22×D1214yes—
508C32C2×#57811yescharacteristic, complemented, Sylow
509C23—32no—
510C23—182no—
511C23D3×D1211yescharacteristic
512Q8—34no—
513Q8—38no—
514Q8—64no—
515Q8—68no—
516Q8—94no—
517Q8—1816no—
518Q8—182no—
519D4—38no—
520D4—34no—
521D4—94no—
522D4—1816no—
523D4—188no—
524D4—182no—
525C2×C4—32no—
526C2×C4—34no—
527C2×C4—34no—
528C2×C4—68no—
529C2×C4—64no—
530C2×C4—1816no—
531C2×C4—1816no—
532C2×C4—182no—
533C2×C4—188no—
534C2×C4D3×D1212yes—
535C2×C4D3×D1211yescharacteristic
536C2×C4C22×D3212yes—
537C2×C4C22×D3211yescharacteristic
538C8—34no—
539C8C22×D3212yes—
540C8C22×D3212yes—
541C2×C3—22no—
542C2×C3—22no—
543C2×C3—21no—
544C2×C3—22no—
545C2×C3—42no—
546C2×C3—64no—
547C2×C3#575312yescomplemented
548C2×C3#576612yescomplemented
549C2×C3C23×D1211yescharacteristic
550C2×C3C22×D3×D411yescharacteristic
551D3—24no—
552D3—124no—
553D3—124no—
554D3—244no—
555C22—22no—
556C22—34no—
557C22—64no—
558C22—184no—
559C22—364no—
560C22C2×D3×D1212yes—
561C22C2×D3×D1211yescharacteristic
562C4—34no—
563C4—68no—
564C4—184no—
565C4C2×D3×D1211yescharacteristic
566C4C2×D3×D1212yes—
567C4C23×D3211yescharacteristic
568C3—21no—
569C3C2×#575311yescharacteristic, complemented
570C3C2×#576611yescharacteristic, complemented
571C2—22no—
572C2—64no—
573C2—364no—
574C2#1059469112yesdirect product factor
575C2C22×D3×D1211yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×#64297C2semidirect
2. C2×#64113C2semidirect
3. C22×C3×Dic12C2semidirect
4. C2×C3×#901C2semidirect
5. C2×#63833C2semidirect
6. C2×#63808C2semidirect
7. #10594691C2direct (N × H)
8. C2×#63801C2semidirect
9. C2×D3×Dic12C2semidirect
19. #64297C22semidirect
24. #64113C22semidirect
30. C2×C3×Dic12C22semidirect
31. C3×#901C22semidirect
35. #63833C22semidirect
37. #63808C22semidirect
38. #63801C22semidirect
39. D3×Dic12C22semidirect
53. C22×Dic12D3semidirect
58. C2×#901D3semidirect
150. C2×Dic12C2×D3semidirect
162. #901C2×D3semidirect
426. C2×C32#578semidirect
508. C32C2×#578semidirect
547. C2×C3#5753semidirect
548. C2×C3#5766semidirect
569. C3C2×#5753semidirect
570. C3C2×#5766semidirect
574. C2#10594691direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#642972
C2×#641132
C22×C3×Dic122
C2×C3×#9012
C2×#638332
C2×#638082
#105946912
C2×#638012
C2×D3×Dic122
C2×#57663
C2×#57533