Finite Group Databasebeta

← C2×#10596250 #11918915

Subgroups — C2×#10596250 #11918915

Order 1152.

4224 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×#64364C211yesmaximal, characteristic, complemented
3C2×C32×#137C211yesmaximal, characteristic, complemented
4C2×#64159C211yesmaximal, characteristic, complemented
5C22×#3756C211yesmaximal, characteristic, complemented
6#10596250C2116yesmaximal, direct product factor
7C2×#64127C212yesmaximal, complemented
8C2×Q16×C3⋊D3C212yesmaximal, complemented
9C2×#64125C212yesmaximal, complemented
10C2×#64124C212yesmaximal, complemented
11C2×#64118C211yesmaximal, characteristic, complemented
12C2×#64116C211yesmaximal, characteristic, complemented
13C2×#5779—34nomaximal
14C2×C32×#41C2211yescharacteristic
15C22×C32×Q8C2211yescharacteristic
16#64367—24no—
17#64367C2218yescomplemented
18#64364—24no—
19#64364C2218yescomplemented
20C2×#3832—21no—
21C2×#3832C2212yes—
22C2×Q8×C3⋊D3—21no—
23C2×Q8×C3⋊D3C2212yes—
24C2×Q8×C3⋊D3C2212yes—
25C2×#3830—22no—
26C2×#3830C2212yes—
27C2×#3828—22no—
28C2×#3828—21no—
29C2×#3828C2211yescharacteristic
30C2×#3828C2211yescharacteristic
31C22×#634—21no—
32C22×#634C2211yescharacteristic
33C32×#137C2218yescomplemented
34C2×C32×Q16C2212yes—
35C2×C32×SD16C2212yes—
36C2×C32×M16C2211yescharacteristic
37#64159C2218yescomplemented
38C2×#3756C2212yes—
39C2×#3756C2212yes—
40C2×#3756C2211yescharacteristic
41C2×#3756C2218yescomplemented
42C2×#3755C2211yescharacteristic
43C2×#3754C2211yescharacteristic
44C2×#3753C2211yescharacteristic
45C22×C3⋊(C3⋊C8)C2211yescharacteristic
46#64127C22116yescomplemented
47Q16×C3⋊D3C22116yescomplemented
48#64125C22116yescomplemented
49#64124C22116yescomplemented
50#64118C2218yescomplemented
51#64116C2218yescomplemented
52C2×#3746C2212yes—
53C2×#3744C2212yes—
54C2×#3743C2212yes—
55C2×C8×C3⋊D3C2212yes—
56C2×#1010—34no—
57C2×#1007—34no—
58C2×C3×#137D314yescomplemented
59C2×#950—34no—
60C22×#216—34no—
61#5779—364no—
62C2×#918—38no—
63C2×D3×Q16—38no—
64C2×#916—38no—
65C2×#915—38no—
66C2×#909—34no—
67C2×#907—34no—
68C32×#41—22no—
69C32×#41C2314yes—
70C2×C32×Q8—21no—
71C2×C32×Q8—22no—
72C2×C32×Q8C2311yescharacteristic
73C2×C32×Q8C2312yes—
74C2×C32×Q8C2314yes—
75C2×C32×D4—21no—
76C2×C32×D4C2311yescharacteristic
77C22×C32×C4—21no—
78C22×C32×C4—21no—
79C22×C32×C4C2311yescharacteristic
80C2×#638—21no—
81C2×#638—22no—
82C2×#638D412yes—
83C22×C3⋊Dic3—21no—
84C22×C3⋊Dic3—22no—
85#3832—28no—
86#3832—24no—
87#3832C2318yes—
88Q8×C3⋊D3—24no—
89Q8×C3⋊D3—24no—
90Q8×C3⋊D3—28no—
91Q8×C3⋊D3C2318yes—
92Q8×C3⋊D3C2318yes—
93#3830—216no—
94#3830—24no—
95#3830C2318yes—
96#3828—22no—
97#3828—216no—
98#3828—28no—
99#3828D414yes—
100#3828C2314yes—
101#3828C2314yes—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)D411yescharacteristic
104C2×C4⋊(C3⋊D3)C2311yescharacteristic
105C2×C4×C3⋊D3—22no—
106C2×C4×C3⋊D3—22no—
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3C2312yes—
110C2×#634—21no—
111C2×#634—22no—
112C2×#634—22no—
113C2×#634—22no—
114C2×#634—28no—
115C2×#634D411yescharacteristic
116C2×#634C2312yes—
117C2×#634C2314yes—
118C2×#634C2311yescharacteristic
119C32×Q16C2318yes—
120C32×SD16C2318yes—
121C32×M16C2314yes—
122C2×C32×C8C2312yes—
123#3756C2318yes—
124#3756C2318yes—
125#3756C2314yes—
126#3755C2314yes—
127#3754C2314yes—
128#3753C2314yes—
129C2×C3⋊(C3⋊C8)C2311yescharacteristic
130C2×C3⋊(C3⋊C8)C2311yescharacteristic
131C2×C3⋊(C3⋊C8)C2314yes—
132#3746C2318yes—
133#3744C2318yes—
134#3743C2318yes—
135C8×C3⋊D3C2318yes—
136C2×#578—91noSylow
137C2×C3×#41C2×D314yes—
138C22×C3×Q8C2×D314yes—
139#1010—332no—
140#1010—616no—
141#1007—332no—
142#1007—616no—
143C2×#239—38no—
144C2×#239—64no—
145C2×D3×Q8—38no—
146C2×D3×Q8—38no—
147C2×D3×Q8—64no—
148C2×#237—38no—
149C2×#237—68no—
150C2×#235—34no—
151C2×#235—34no—
152C2×#235—64no—
153C2×#235—68no—
154C22×Dic6—34no—
155C22×Dic6—64no—
156C3×#137C2×D3132yescomplemented
157C2×C3×Q16C2×D318yes—
158C2×C3×SD16C2×D318yes—
159C2×C3×M16C2×D314yes—
160#950—332no—
161C2×#216—38no—
162C2×#216—38no—
163C2×#216—34no—
164C2×#216—332no—
165C2×#215—34no—
166C2×#214—34no—
167C2×#213—34no—
168C22×C3⋊C8—34no—
169#918—364no—
170D3×Q16—364no—
171#916—364no—
172#915—364no—
173#909—332no—
174#907—332no—
175C2×Dic12—38no—
176C2×#204—38no—
177C2×ΓL(1,𝔽25)—38no—
178C2×D3×C8—38no—
179C23×C32—21no—
180C23×C32C2×D411yescharacteristic
181C22×C3⋊D3—21no—
182C22×C3⋊D3C2×D412yes—
183C32×Q8—21no—
184C32×Q8—22no—
185C32×Q8—24no—
186C32×Q8C2412yes—
187C32×Q8C2414yes—
188C32×D4—24no—
189C32×D4—21no—
190C32×D4C2412yes—
191C2×C32×C4—21no—
192C2×C32×C4—22no—
193C2×C32×C4—24no—
194C2×C32×C4—24no—
195C2×C32×C4C2×D411yescharacteristic
196C2×C32×C4C2×D412yes—
197C2×C32×C4C2411yescharacteristic
198C2×C32×C4C2412yes—
199#638—24no—
200#638—28no—
201#638C2×D418yes—
202C2×C3⋊Dic3—21no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—24no—
205C2×C3⋊Dic3—28no—
206C2×C3⋊Dic3C2×D412yes—
207C4⋊(C3⋊D3)—28no—
208C4⋊(C3⋊D3)—21no—
209C4⋊(C3⋊D3)C2×D414yes—
210C4⋊(C3⋊D3)C2412yes—
211C4×C3⋊D3—28no—
212C4×C3⋊D3—28no—
213C4×C3⋊D3—24no—
214C4×C3⋊D3—28no—
215C4×C3⋊D3C2×D414yes—
216C4×C3⋊D3C2414yes—
217#634—24no—
218#634—22no—
219#634—21no—
220#634—28no—
221#634—28no—
222#634C2×D414yes—
223#634C2414yes—
224#634C2412yes—
225C32×C8C2414yes—
226C3⋊(C3⋊C8)C2412yes—
227C3⋊(C3⋊C8)C2412yes—
228C2×2−1+4—91no—
229C2×2−1+4—91no—
230#578—916no—
231C2×#137—92no—
232C2×#137—92no—
233C2×#137—91no—
234C2×#137C3⋊D311yescharacteristic, complemented
235C2×#135—91no—
236C2×#135—92no—
237C22×Q16—91no—
238C22×Q16—92no—
239C2×#131—91no—
240C3×#41—28no—
241C3×#41C22×D3116yes—
242C2×C3×Q8—24no—
243C2×C3×Q8—28no—
244C2×C3×Q8C22×D314yes—
245C2×C3×Q8C22×D318yes—
246C2×C3×Q8C22×D3116yes—
247C2×C3×D4—24no—
248C2×C3×D4C22×D314yes—
249C22×C3×C4—24no—
250C22×C3×C4—24no—
251C22×C3×C4C22×D314yes—
252C2×#67—38no—
253C2×#67—68no—
254C2×#67—64no—
255C22×Dic3—68no—
256C22×Dic3—64no—
257#239—332no—
258#239—616no—
259#239—632no—
260D3×Q8—332no—
261D3×Q8—332no—
262D3×Q8—632no—
263D3×Q8—616no—
264D3×Q8—616no—
265#237—332no—
266#237—616no—
267#237—664no—
268#235—316no—
269#235—316no—
270#235—316no—
271#235—632no—
272#235—664no—
273#235—68no—
274C2×D12—34no—
275C2×D12—34no—
276C2×D12—68no—
277C2×C4×D3—38no—
278C2×C4×D3—68no—
279C2×C4×D3—68no—
280C2×C4×D3—68no—
281C2×C4×D3—64no—
282C2×Dic6—34no—
283C2×Dic6—38no—
284C2×Dic6—34no—
285C2×Dic6—316no—
286C2×Dic6—632no—
287C2×Dic6—68no—
288C2×Dic6—68no—
289C2×Dic6—64no—
290C2×Dic6—68no—
291C3×Q16C22×D3132yes—
292C3×SD16C22×D3132yes—
293C3×M16C22×D3116yes—
294C2×C3×C8C22×D318yes—
295#216—332no—
296#216—332no—
297#216—316no—
298#215—316no—
299#214—316no—
300#213—316no—
301C2×C3⋊C8—34no—
302C2×C3⋊C8—34no—
303C2×C3⋊C8—316no—
304Dic12—332no—
305#204—332no—
306ΓL(1,𝔽25)—332no—
307D3×C8—332no—
308C22×C32—22no—
309C22×C32—22no—
310C22×C32—42no—
311C22×C32C22×D412yes—
312C22×C32C22×D411yescharacteristic
313C2×C3⋊D3—24no—
314C2×C3⋊D3—22no—
315C2×C3⋊D3—42no—
316C2×C3⋊D3C22×D414yes—
317C32×C4—22no—
318C32×C4—24no—
319C32×C4C22×D411yescharacteristic
320C32×C4C22×D412yes—
321C32×C4C2511yescharacteristic
322C3⋊Dic3—22no—
323C3⋊Dic3—24no—
324C3⋊Dic3C22×D414yes—
3252−1+4—98no—
3262−1+4—98no—
3272−1+4—184no—
3282−1+4—184no—
329C2×#41—91no—
330C2×#41—92no—
331C2×#41—92no—
332C2×#41—91no—
333C2×#41—182no—
334C2×#41—181no—
335C2×#41—182no—
336C2×#41—181no—
337C2×#41C2×C3⋊D311yescharacteristic
338C22×Q8—92no—
339C22×Q8—92no—
340C22×Q8—91no—
341C22×Q8—181no—
342C22×Q8—181no—
343C22×Q8C2×C3⋊D311yescharacteristic
344#137—916no—
345#137—916no—
346#137—98no—
347#137C2×C3⋊D318yescomplemented
348#135—98no—
349#135—916no—
350C2×Q16—91no—
351C2×Q16—92no—
352C2×Q16—92no—
353C2×Q16—98no—
354C2×Q16—916no—
355C2×Q16—92no—
356C2×Q16C2×C3⋊D312yes—
357C2×SD16—91no—
358C2×SD16—91no—
359C2×SD16—92no—
360C2×SD16C2×C3⋊D312yes—
361C2×D8—91no—
362#131—98no—
363C2×M16—92no—
364C2×M16C2×C3⋊D311yescharacteristic
365C22×C8—91no—
366C22×C8—92no—
367C23×C3—24no—
368C23×C3D3×D414yes—
369C22×D3—38no—
370C22×D3—64no—
371C3×Q8—24no—
372C3×Q8—216no—
373C3×Q8—28no—
374C3×Q8C23×D318yes—
375C3×Q8C23×D3116yes—
376C3×D4—216no—
377C3×D4—24no—
378C3×D4C23×D318yes—
379C2×C3×C4—24no—
380C2×C3×C4—28no—
381C2×C3×C4—216no—
382C2×C3×C4—216no—
383C2×C3×C4D3×D414yes—
384C2×C3×C4D3×D418yes—
385C2×C3×C4C23×D314yes—
386C2×C3×C4C23×D318yes—
387#67—332no—
388#67—632no—
389#67—616no—
390C2×Dic3—38no—
391C2×Dic3—632no—
392C2×Dic3—64no—
393C2×Dic3—68no—
394C2×Dic3—616no—
395D12—316no—
396D12—38no—
397D12—632no—
398D12—64no—
399C4×D3—316no—
400C4×D3—316no—
401C4×D3—632no—
402C4×D3—632no—
403C4×D3—632no—
404C4×D3—616no—
405Dic6—316no—
406Dic6—316no—
407Dic6—38no—
408Dic6—632no—
409Dic6—632no—
410Dic6—616no—
411Dic6—68no—
412Dic6—64no—
413C3×C8C23×D3116yes—
414C3⋊C8—38no—
415C3⋊C8—38no—
416C2×C32—22no—
417C2×C32—42no—
418C2×C32#57812yescomplemented
419C2×C32C23×D411yescharacteristic
420C3⋊D3—24no—
421C3⋊D3—42no—
422#41—22no—
423#41—94no—
424#41—94no—
425#41—98no—
426#41—98no—
427#41—94no—
428#41—1816no—
429#41—188no—
430#41—184no—
431#41—184no—
432#41—1816no—
433#41—188no—
434#41—182no—
435#41C22×C3⋊D314yes—
436C2×Q8—21no—
437C2×Q8—22no—
438C2×Q8—91no—
439C2×Q8—98no—
440C2×Q8—98no—
441C2×Q8—91no—
442C2×Q8—92no—
443C2×Q8—94no—
444C2×Q8—182no—
445C2×Q8—182no—
446C2×Q8—188no—
447C2×Q8—184no—
448C2×Q8—184no—
449C2×Q8—188no—
450C2×Q8—181no—
451C2×Q8—182no—
452C2×Q8C22×C3⋊D311yescharacteristic
453C2×Q8C22×C3⋊D312yes—
454C2×Q8C22×C3⋊D314yes—
455C2×D4—21no—
456C2×D4—92no—
457C2×D4—91no—
458C2×D4—91no—
459C2×D4—182no—
460C2×D4—182no—
461C2×D4—181no—
462C2×D4C22×C3⋊D311yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—92no—
466C22×C4—182no—
467C22×C4—182no—
468C22×C4—182no—
469C22×C4—182no—
470C22×C4—181no—
471C22×C4—181no—
472C22×C4C22×C3⋊D311yescharacteristic
473Q16—94no—
474Q16—98no—
475Q16—98no—
476Q16—98no—
477Q16C22×C3⋊D318yes—
478SD16—94no—
479SD16—94no—
480SD16—98no—
481SD16C22×C3⋊D318yes—
482D8—94no—
483M16—98no—
484M16C22×C3⋊D314yes—
485C2×C8—91no—
486C2×C8—91no—
487C2×C8—94no—
488C2×C8—98no—
489C2×C8C22×C3⋊D312yes—
490C22×C3—28no—
491C22×C3—28no—
492C22×C3—48no—
493C22×C3C2×D3×D418yes—
494C22×C3C2×D3×D414yes—
495C2×D3—316no—
496C2×D3—616no—
497C2×D3—68no—
498C2×D3—128no—
499C3×C4—28no—
500C3×C4—216no—
501C3×C4C2×D3×D418yes—
502C3×C4C2×D3×D414yes—
503C3×C4C24×D314yes—
504Dic3—316no—
505Dic3—68no—
506Dic3—616no—
507C32C2×#57811yescharacteristic, complemented, Sylow
508C23—21no—
509C23—92no—
510C23—181no—
511C23D4×C3⋊D311yescharacteristic
512Q8—24no—
513Q8—22no—
514Q8—21no—
515Q8—94no—
516Q8—92no—
517Q8—94no—
518Q8—188no—
519Q8—188no—
520Q8—184no—
521Q8—181no—
522Q8—182no—
523Q8C23×C3⋊D312yes—
524Q8C23×C3⋊D314yes—
525D4—24no—
526D4—21no—
527D4—98no—
528D4—94no—
529D4—92no—
530D4—188no—
531D4—188no—
532D4—184no—
533D4—181no—
534D4C23×C3⋊D312yes—
535C2×C4—24no—
536C2×C4—21no—
537C2×C4—22no—
538C2×C4—24no—
539C2×C4—92no—
540C2×C4—94no—
541C2×C4—94no—
542C2×C4—188no—
543C2×C4—188no—
544C2×C4—188no—
545C2×C4—188no—
546C2×C4—184no—
547C2×C4—181no—
548C2×C4—182no—
549C2×C4—184no—
550C2×C4D4×C3⋊D312yes—
551C2×C4D4×C3⋊D311yescharacteristic
552C2×C4C23×C3⋊D312yes—
553C2×C4C23×C3⋊D311yescharacteristic
554C8—92no—
555C8—92no—
556C8C23×C3⋊D314yes—
557C2×C3—28no—
558C2×C3—48no—
559C2×C3#577918yescomplemented
560C2×C3C22×D3×D414yes—
561D3—616no—
562D3—128no—
563C22—22no—
564C22—22no—
565C22—42no—
566C22—94no—
567C22—184no—
568C22—182no—
569C22—362no—
570C22C2×D4×C3⋊D312yes—
571C22C2×D4×C3⋊D311yescharacteristic
572C4—22no—
573C4—24no—
574C4—94no—
575C4—182no—
576C4—184no—
577C4C2×D4×C3⋊D312yes—
578C4C2×D4×C3⋊D311yescharacteristic
579C4C24×C3⋊D311yescharacteristic
580C3C2×#577914yescomplemented
581C2—22no—
582C2—42no—
583C2—184no—
584C2—362no—
585C2#1059625012yesdirect product factor
586C2C22×D4×C3⋊D311yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC32×C4C25
FrattiniC4C24×C3⋊D3
FittingC2×C32×#137C2
socleC22×C32C22×D4
hypercenterC2×#137C3⋊D3
hypocenterC32C2×#578
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C2×#64364C2semidirect
3. C2×C32×#137C2semidirect
4. C2×#64159C2semidirect
5. C22×#3756C2semidirect
6. #10596250C2direct (N × H)
7. C2×#64127C2semidirect
8. C2×Q16×C3⋊D3C2semidirect
9. C2×#64125C2semidirect
10. C2×#64124C2semidirect
11. C2×#64118C2semidirect
12. C2×#64116C2semidirect
17. #64367C22semidirect
19. #64364C22semidirect
33. C32×#137C22semidirect
37. #64159C22semidirect
41. C2×#3756C22semidirect
46. #64127C22semidirect
47. Q16×C3⋊D3C22semidirect
48. #64125C22semidirect
49. #64124C22semidirect
50. #64118C22semidirect
51. #64116C22semidirect
58. C2×C3×#137D3semidirect
156. C3×#137C2×D3semidirect
234. C2×#137C3⋊D3semidirect
347. #137C2×C3⋊D3semidirect
418. C2×C32#578semidirect
507. C32C2×#578semidirect
559. C2×C3#5779semidirect
580. C3C2×#5779semidirect
585. C2#10596250direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643672
C2×#643642
C2×C32×#1372
C2×#641592
C22×#37562
#105962502
C2×#641272
C2×Q16×C3⋊D32
C2×#641252
C2×#641242
C2×#641182
C2×#641162
C2×#57793