Finite Group Databasebeta

← C2×#10594703 #11918940

Subgroups — C2×#10594703 #11918940

Order 1152.

2949 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C212yesmaximal, complemented
2C2×#64110C211yesmaximal, characteristic, complemented
3C22×C3×Dic12C211yesmaximal, characteristic, complemented
4C2×C3×#904C211yesmaximal, characteristic, complemented
5C2×#63827C212yesmaximal, complemented
6#10594703C2116yesmaximal, direct product factor
7C2×#63811C214yesmaximal, complemented
8C2×#63810C212yesmaximal, complemented
9C2×#63802C212yesmaximal, complemented
10C2×#5771—31nomaximal
11C2×#5766—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2212yes—
14C22×C3×Dic6C2212yes—
15C2×#3804—24no—
16C2×#3799—22no—
17C2×#3797C2214yes—
18#64297—28no—
19#64297C22116yescomplemented
20C2×#3796C2214yes—
21C2×D3×Dic6—22no—
22C22×C32×C8C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24#64110C2218yescomplemented
25C2×#3743C2212yes—
26C2×C8×C3⋊D3C2212yes—
27C2×C3×Dic12C2211yescharacteristic
28C2×C3×Dic12C2212yes—
29C2×C3×Dic12C2212yes—
30C2×C3×Dic12C2218yescomplemented
31C3×#904C2218yescomplemented
32C2×C3×D24C2211yescharacteristic
33C2×C3×#204C2212yes—
34C2×#3718C2214yes—
35#63827C22116yescomplemented
36C2×#3715C2214yes—
37#63811C22132yescomplemented
38#63810C22116yescomplemented
39#63802C22116yescomplemented
40C2×#1010—32no—
41C2×#1007—32no—
42C2×C3×#135—31no—
43C22×C3×Q16—31no—
44C2×#951—32no—
45C2×#942—32no—
46#5771—316no—
47#5766—316no—
48C2×#919—32no—
49C2×#918—34no—
50C2×D3×Q16—32no—
51C2×D3×Q16—32no—
52C2×#915—34no—
53C2×#912—32no—
54C22×Dic12D311yescharacteristic, complemented
55C2×#904D311yescharacteristic, complemented
56C2×#901—31no—
57C2×#901—31no—
58C2×#901—61no—
59C22×C32×C4C2311yescharacteristic
60C2×#638D412yes—
61#3828D414yes—
62#3828C2314yes—
63C2×C4⋊(C3⋊D3)D411yescharacteristic
64C2×C4×C3⋊D3C2312yes—
65C2×#634D411yescharacteristic
66C2×C3×#67—22no—
67C22×C3×Dic3—22no—
68C3×#235—24no—
69C3×#235C2318yes—
70C2×C3×D12C2312yes—
71C2×C3×C4×D3—22no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6—24no—
74C2×C3×Dic6C2312yes—
75C2×C3×Dic6C2314yes—
76C2×C3×Dic6C2318yes—
77C2×#627—24no—
78C2×#626—24no—
79C2×#624—24no—
80#3804—232no—
81C2×D3×Dic3—24no—
82#3799—216no—
83#3797—28no—
84#3797C23116yes—
85#3796—28no—
86#3796C23116yes—
87D3×Dic6—216no—
88C2×C32×C8C2311yescharacteristic
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2314yes—
91#3748C2314yes—
92C2×C3⋊(C3⋊C8)C2312yes—
93#3743C2318yes—
94C8×C3⋊D3C2318yes—
95C3×Dic12C2314yes—
96C3×Dic12C2318yes—
97C3×Dic12C2318yes—
98C3×D24C2314yes—
99C3×#204C2318yes—
100#3718C23116yes—
101#3715C23116yes—
102C2×#578—91noSylow
103C2×C3×#41—32no—
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—34no—
113C2×D3×Q8—62no—
114C2×#237—34no—
115C2×#237—64no—
116C2×#235—31no—
117C2×#235—31no—
118C2×#235—61no—
119C2×#235—62no—
120C2×#235—64no—
121C2×#235C2×D312yes—
122C22×Dic6—62no—
123C22×Dic6C2×D312yes—
124C3×#135—38no—
125C2×C3×Q16—32no—
126C2×C3×Q16—32no—
127C2×C3×Q16—38no—
128C2×C3×Q16—31no—
129C2×C3×SD16—32no—
130C2×C3×D8—31no—
131C22×C3×C8—21no—
132C22×C3×C8C2×D311yescharacteristic
133C22×C3×C8C2×D311yescharacteristic
134#951—316no—
135C2×#216—34no—
136C2×#216—34no—
137#942—316no—
138C2×#215—34no—
139C2×#214—34no—
140C2×#208—31no—
141C2×#208—31no—
142C2×#208—61no—
143#919—316no—
144#918—332no—
145D3×Q16—316no—
146D3×Q16—316no—
147#915—332no—
148#912—316no—
149C2×Dic12C2×D311yescharacteristic
150C2×Dic12C2×D312yes—
151C2×Dic12C2×D312yes—
152C2×Dic12C2×D318yescomplemented
153#904C2×D318yescomplemented
154C2×D24C2×D311yescharacteristic
155C2×#204C2×D312yes—
156#901—38no—
157#901—38no—
158#901—68no—
159C2×ΓL(1,𝔽25)—32no—
160C2×ΓL(1,𝔽25)—32no—
161C2×ΓL(1,𝔽25)—62no—
162C2×D3×C8—32no—
163C2×D3×C8—32no—
164C2×D3×C8—62no—
165C23×C32C2×D411yescharacteristic
166C22×C3⋊D3C2×D412yes—
167C22×C3×D3—22no—
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D412yes—
170C2×C32×C4C2411yescharacteristic
171C2×C32×C4C2412yes—
172#638C2×D418yes—
173C2×C3⋊Dic3C2×D412yes—
174C4⋊(C3⋊D3)C2×D414yes—
175C4×C3⋊D3C2×D414yes—
176C4×C3⋊D3C2414yes—
177#634C2×D414yes—
178C3×#67—28no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3—28no—
181C2×C3×Dic3—22no—
182C3×D12—22no—
183C3×D12C2414yes—
184C3×C4×D3—28no—
185C3×Dic6—28no—
186C3×Dic6—24no—
187C3×Dic6—22no—
188C3×Dic6C2418yes—
189C3×Dic6C2414yes—
190#627—216no—
191#626—216no—
192#624—216no—
193D3×Dic3—216no—
194C32×C8C2412yes—
195C32×C8C2412yes—
196C3⋊(C3⋊C8)C2414yes—
197C2×2−1+4—92no—
198#578—916no—
199C2×#137—94no—
200C2×#137—92no—
201C2×#135—31no—
202C2×#135—92no—
203C22×Q16—31no—
204C22×Q16—92no—
205C2×#131—91no—
206C3×#41—38no—
207C3×#41—64no—
208C2×C3×Q8—34no—
209C2×C3×Q8—38no—
210C2×C3×Q8—32no—
211C2×C3×Q8—62no—
212C2×C3×Q8—64no—
213C2×C3×D4—32no—
214C2×C3×D4—62no—
215C22×C3×C4—21no—
216C22×C3×C4—62no—
217C22×C3×C4—62no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C2×#67—22no—
221C2×#67—32no—
222C2×#67—32no—
223C2×#67—62no—
224C2×#67—64no—
225C22×Dic3—22no—
226C22×Dic3—64no—
227#239—316no—
228#239—616no—
229#239—68no—
230D3×Q8—316no—
231D3×Q8—316no—
232D3×Q8—68no—
233D3×Q8—68no—
234D3×Q8—616no—
235#237—316no—
236#237—68no—
237#237—632no—
238#235—24no—
239#235—34no—
240#235—34no—
241#235—34no—
242#235—34no—
243#235—64no—
244#235—64no—
245#235—616no—
246#235—632no—
247#235C22×D318yes—
248C2×D12—31no—
249C2×D12—31no—
250C2×D12—61no—
251C2×D12—64no—
252C2×D12C22×D312yes—
253C2×C4×D3—22no—
254C2×C4×D3—32no—
255C2×C4×D3—32no—
256C2×C4×D3—62no—
257C2×C4×D3—64no—
258C2×C4×D3—64no—
259C2×C4×D3—64no—
260C2×Dic6—22no—
261C2×Dic6—24no—
262C2×Dic6—31no—
263C2×Dic6—31no—
264C2×Dic6—61no—
265C2×Dic6—616no—
266C2×Dic6—64no—
267C2×Dic6—64no—
268C2×Dic6C22×D312yes—
269C2×Dic6C22×D314yes—
270C2×Dic6C22×D318yes—
271C3×Q16—34no—
272C3×Q16—38no—
273C3×Q16—38no—
274C3×SD16—38no—
275C3×D8—34no—
276C2×C3×C8—21no—
277C2×C3×C8—21no—
278C2×C3×C8—24no—
279C2×C3×C8C22×D311yescharacteristic
280C2×C3×C8C22×D311yescharacteristic
281C2×C3×C8C22×D311yescharacteristic
282C2×C3×C8C22×D311yescharacteristic
283C2×C3×C8C22×D314yes—
284C2×C3×C8C22×D314yes—
285#216—316no—
286#216—316no—
287#215—316no—
288#214—316no—
289#208—34no—
290#208—34no—
291#208—64no—
292C2×C3⋊C8—32no—
293C2×C3⋊C8—32no—
294C2×C3⋊C8—62no—
295Dic12C22×D314yes—
296Dic12C22×D318yes—
297Dic12C22×D318yes—
298D24C22×D314yes—
299#204C22×D318yes—
300ΓL(1,𝔽25)—38no—
301ΓL(1,𝔽25)—38no—
302ΓL(1,𝔽25)—68no—
303D3×C8—38no—
304D3×C8—38no—
305D3×C8—68no—
306C22×C32—22no—
307C22×C32C22×D412yes—
308C22×C32C22×D411yescharacteristic
309C2×C3⋊D3—24no—
310C2×C3⋊D3C22×D414yes—
311C2×C3×D3—24no—
312C2×C3×D3—44no—
313C32×C4C22×D411yescharacteristic
314C32×C4C22×D412yes—
315C32×C4C2511yescharacteristic
316C3⋊Dic3C22×D414yes—
317C3×Dic3—28no—
318C3×Dic3—24no—
3192−1+4—916no—
3202−1+4—188no—
321C2×#41—32no—
322C2×#41—91no—
323C2×#41—94no—
324C2×#41—184no—
325C2×#41—182no—
326C22×Q8—32no—
327C22×Q8—94no—
328C22×Q8—182no—
329#137—932no—
330#137—916no—
331#135—38no—
332#135—916no—
333C2×Q16—32no—
334C2×Q16—32no—
335C2×Q16—38no—
336C2×Q16—31no—
337C2×Q16—916no—
338C2×Q16—94no—
339C2×SD16—32no—
340C2×SD16—94no—
341C2×D8—31no—
342#131—98no—
343C2×M16—91no—
344C2×M16—92no—
345C22×C8—92no—
346C22×C8D3211yescharacteristic
347C23×C3—21no—
348C23×C3—62no—
349C23×C3D3×D411yescharacteristic
350C23×C3D3×D411yescharacteristic
351C22×D3—22no—
352C22×D3—32no—
353C22×D3—32no—
354C22×D3—62no—
355C3×Q8—38no—
356C3×Q8—34no—
357C3×Q8—62no—
358C3×Q8—64no—
359C3×Q8—68no—
360C3×D4—34no—
361C3×D4—68no—
362C3×D4—62no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—62no—
368C2×C3×C4—64no—
369C2×C3×C4—68no—
370C2×C3×C4—68no—
371C2×C3×C4D3×D411yescharacteristic
372C2×C3×C4D3×D412yes—
373C2×C3×C4D3×D411yescharacteristic
374C2×C3×C4D3×D412yes—
375C2×C3×C4C23×D311yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D312yes—
378C2×C3×C4C23×D312yes—
379#67—28no—
380#67—38no—
381#67—38no—
382#67—68no—
383#67—616no—
384C2×Dic3—24no—
385C2×Dic3—28no—
386C2×Dic3—22no—
387C2×Dic3—32no—
388C2×Dic3—32no—
389C2×Dic3—62no—
390C2×Dic3—616no—
391D12—22no—
392D12—34no—
393D12—34no—
394D12—64no—
395D12—616no—
396D12C23×D314yes—
397C4×D3—28no—
398C4×D3—34no—
399C4×D3—34no—
400C4×D3—34no—
401C4×D3—34no—
402C4×D3—64no—
403C4×D3—64no—
404C4×D3—616no—
405C4×D3—616no—
406C4×D3—616no—
407Dic6—28no—
408Dic6—24no—
409Dic6—22no—
410Dic6—34no—
411Dic6—34no—
412Dic6—64no—
413Dic6—616no—
414Dic6—616no—
415Dic6C23×D314yes—
416Dic6C23×D318yes—
417C3×C8—22no—
418C3×C8—22no—
419C3×C8C23×D312yes—
420C3×C8C23×D312yes—
421C3×C8C23×D312yes—
422C3×C8C23×D312yes—
423C3⋊C8—34no—
424C3⋊C8—34no—
425C3⋊C8—64no—
426C2×C32—22no—
427C2×C32#57812yescomplemented
428C2×C32C23×D411yescharacteristic
429C3⋊D3—24no—
430C3×D3—44no—
431#41—38no—
432#41—64no—
433#41—94no—
434#41—94no—
435#41—916no—
436#41—1832no—
437#41—1816no—
438#41—188no—
439C2×Q8—32no—
440C2×Q8—34no—
441C2×Q8—38no—
442C2×Q8—62no—
443C2×Q8—64no—
444C2×Q8—91no—
445C2×Q8—916no—
446C2×Q8—184no—
447C2×Q8—1816no—
448C2×Q8—188no—
449C2×D4—32no—
450C2×D4—62no—
451C2×D4—92no—
452C2×D4—91no—
453C2×D4—184no—
454C22×C4—62no—
455C22×C4—62no—
456C22×C4—92no—
457C22×C4—184no—
458C22×C4—184no—
459C22×C4C2×D3211yescharacteristic
460Q16—38no—
461Q16—38no—
462Q16—34no—
463Q16—916no—
464SD16—38no—
465SD16—916no—
466D8—34no—
467M16—94no—
468M16—98no—
469C2×C8—92no—
470C2×C8—98no—
471C2×C8C2×D3211yescharacteristic
472C2×C8C2×D3211yescharacteristic
473C2×C8C2×D3214yes—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—21no—
478C22×C3—42no—
479C22×C3—64no—
480C22×C3—124no—
481C22×C3C2×D3×D412yes—
482C22×C3C2×D3×D412yes—
483C22×C3C2×D3×D411yescharacteristic
484C22×C3C2×D3×D411yescharacteristic
485C2×D3—24no—
486C2×D3—34no—
487C2×D3—34no—
488C2×D3—44no—
489C2×D3—64no—
490C2×D3—64no—
491C2×D3—64no—
492C2×D3—124no—
493C3×C4—22no—
494C3×C4—21no—
495C3×C4—21no—
496C3×C4—64no—
497C3×C4—68no—
498C3×C4C2×D3×D412yes—
499C3×C4C2×D3×D411yescharacteristic
500C3×C4C2×D3×D411yescharacteristic
501C3×C4C2×D3×D412yes—
502C3×C4C24×D311yescharacteristic
503C3×C4C24×D311yescharacteristic
504Dic3—28no—
505Dic3—24no—
506Dic3—34no—
507Dic3—34no—
508Dic3—64no—
509C32C2×#57811yescharacteristic, complemented, Sylow
510C23—62no—
511C23—92no—
512C23#380211yescharacteristic
513Q8—34no—
514Q8—38no—
515Q8—68no—
516Q8—64no—
517Q8—62no—
518Q8—94no—
519Q8—1816no—
520D4—34no—
521D4—68no—
522D4—62no—
523D4—98no—
524D4—94no—
525D4—1816no—
526C2×C4—68no—
527C2×C4—62no—
528C2×C4—64no—
529C2×C4—68no—
530C2×C4—92no—
531C2×C4—94no—
532C2×C4—94no—
533C2×C4—1816no—
534C2×C4—1816no—
535C2×C4#380212yes—
536C2×C4#380211yescharacteristic
537C2×C4C22×D3212yes—
538C2×C4C22×D3211yescharacteristic
539C8—94no—
540C8C22×D3212yes—
541C8C22×D3212yes—
542C2×C3—22no—
543C2×C3—22no—
544C2×C3—21no—
545C2×C3—22no—
546C2×C3—42no—
547C2×C3—124no—
548C2×C3#576612yescomplemented
549C2×C3#577112yescomplemented
550C2×C3C22×D3×D411yescharacteristic
551C2×C3C22×D3×D411yescharacteristic
552D3—44no—
553D3—64no—
554D3—64no—
555D3—124no—
556C22—22no—
557C22—64no—
558C22—94no—
559C22—124no—
560C22—184no—
561C22C2×#380212yes—
562C22C2×#380211yescharacteristic
563C4—64no—
564C4—68no—
565C4—94no—
566C4C2×#380212yes—
567C4C2×#380211yescharacteristic
568C4C23×D3211yescharacteristic
569C3—21no—
570C3C2×#576611yescharacteristic, complemented
571C3C2×#577111yescharacteristic, complemented
572C2—22no—
573C2—124no—
574C2—184no—
575C2#1059470312yesdirect product factor
576C2C22×#380211yescharacteristic
subgroupG/H
centerC22C2×#3802
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×#64110C2semidirect
3. C22×C3×Dic12C2semidirect
4. C2×C3×#904C2semidirect
5. C2×#63827C2semidirect
6. #10594703C2direct (N × H)
7. C2×#63811C2semidirect
8. C2×#63810C2semidirect
9. C2×#63802C2semidirect
19. #64297C22semidirect
24. #64110C22semidirect
30. C2×C3×Dic12C22semidirect
31. C3×#904C22semidirect
35. #63827C22semidirect
37. #63811C22semidirect
38. #63810C22semidirect
39. #63802C22semidirect
54. C22×Dic12D3semidirect
55. C2×#904D3semidirect
152. C2×Dic12C2×D3semidirect
153. #904C2×D3semidirect
427. C2×C32#578semidirect
509. C32C2×#578semidirect
548. C2×C3#5766semidirect
549. C2×C3#5771semidirect
570. C3C2×#5766semidirect
571. C3C2×#5771semidirect
575. C2#10594703direct (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×#641102
C22×C3×Dic122
C2×C3×#9042
C2×#638272
#105947032
C2×#638112
C2×#638102
C2×#638022
C2×#57713
C2×#57663